# --- T2-COPYRIGHT-NOTE-BEGIN --- # This copyright note is auto-generated by ./scripts/Create-CopyPatch. # # T2 SDE: package/.../dietlibc/0-libm.patch # Copyright (C) 2018 The T2 SDE Project # # More information can be found in the files COPYING and README. # # This patch file is dual-licensed. It is available under the license the # patched project is licensed under, as long as it is an OpenSource license # as defined at http://www.opensource.org/ (e.g. BSD, X11) or under the terms # of the GNU General Public License as published by the Free Software # Foundation; either version 2 of the License, or (at your option) any later # version. # --- T2-COPYRIGHT-NOTE-END --- diff -urN dietlibc-0.30/include/math.h dietlibc-0.30-libm/include/math.h --- dietlibc-0.30/include/math.h 2004-08-03 22:28:46.000000000 +0000 +++ dietlibc-0.30-libm/include/math.h 2006-06-25 11:25:32.000000000 +0000 @@ -5,6 +5,75 @@ __BEGIN_DECLS +/* All floating-point numbers can be put in one of these categories. */ +enum + { + FP_NAN, +# define FP_NAN FP_NAN + FP_INFINITE, +# define FP_INFINITE FP_INFINITE + FP_ZERO, +# define FP_ZERO FP_ZERO + FP_SUBNORMAL, +# define FP_SUBNORMAL FP_SUBNORMAL + FP_NORMAL +# define FP_NORMAL FP_NORMAL + }; + +# if __BYTE_ORDER == __BIG_ENDIAN +# define __nan_bytes { 0x7f, 0xc0, 0, 0 } +# endif +# if __BYTE_ORDER == __LITTLE_ENDIAN +# define __nan_bytes { 0, 0, 0xc0, 0x7f } +# endif + +static union { unsigned char __c[4]; float __d; } __nan_union = { __nan_bytes }; +# define NAN (__nan_union.__d) + +# define X_TLOSS 1.41484755040568800000e+16 + +/* Types of exceptions in the `type' field. */ +# define DOMAIN 1 +# define SING 2 +# define OVERFLOW 3 +# define UNDERFLOW 4 +# define TLOSS 5 +# define PLOSS 6 + +/* SVID mode specifies returning this large value instead of infinity. */ +# define HUGE 3.40282347e+38F + +# ifdef __cplusplus +struct __exception +# else +struct exception +# endif + { + int type; + char *name; + double arg1; + double arg2; + double retval; + }; + +/* Support for various different standard error handling behaviors. */ +typedef enum +{ + _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ + _SVID_, /* According to System V, release 4. */ + _XOPEN_, /* Nowadays also Unix98. */ + _POSIX_, + _ISOC_ /* Actually this is ISO C99. */ +} _LIB_VERSION_TYPE; + +#define _LIB_VERSION _POSIX_ + +# ifdef __cplusplus +extern int matherr (struct __exception *__exc) throw (); +# else +extern int matherr (struct exception *__exc); +# endif + #define M_E 2.7182818284590452354 /* e */ #define M_LOG2E 1.4426950408889634074 /* log_2 e */ #define M_LOG10E 0.43429448190325182765 /* log_10 e */ --- dietlibc-0.30/libm/README 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/README 2006-06-25 11:20:06.000000000 +0000 @@ -0,0 +1,16 @@ +The routines included in this math library are derived from the +math library for Apple's MacOS X/Darwin math library, which was +itself swiped from FreeBSD. The original copyright information +is as follows: + + Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + + Developed at SunPro, a Sun Microsystems, Inc. business. + Permission to use, copy, modify, and distribute this + software is freely granted, provided that this notice + is preserved. + +It has been ported to work with uClibc and generally behave +by Erik Andersen + 22 May, 2001 +Adapted for dietlibc by Rene Rebe , 2006 diff -urN dietlibc-0.30/libm/acosh.c dietlibc-0.30-libm/libm/acosh.c --- dietlibc-0.30/libm/acosh.c 2001-07-27 20:30:34.000000000 +0000 +++ dietlibc-0.30-libm/libm/acosh.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,6 +0,0 @@ -#include - -double acosh ( double x ) -{ - return log ( x + sqrt (x*x - 1.) ); -} diff -urN dietlibc-0.30/libm/asinh.c dietlibc-0.30-libm/libm/asinh.c --- dietlibc-0.30/libm/asinh.c 2001-07-27 20:30:34.000000000 +0000 +++ dietlibc-0.30-libm/libm/asinh.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,6 +0,0 @@ -#include - -double asinh ( double x ) -{ - return log ( x + sqrt (x*x + 1.) ); -} diff -urN dietlibc-0.30/libm/atanh.c dietlibc-0.30-libm/libm/atanh.c --- dietlibc-0.30/libm/atanh.c 2001-07-27 20:30:34.000000000 +0000 +++ dietlibc-0.30-libm/libm/atanh.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,8 +0,0 @@ -#include - -extern const float __half; - -double atanh ( double x ) -{ - return __half * log ( (1.+x) / (1.-x) ); -} diff -urN dietlibc-0.30/libm/bessel.c dietlibc-0.30-libm/libm/bessel.c --- dietlibc-0.30/libm/bessel.c 2005-03-15 08:51:23.000000000 +0000 +++ dietlibc-0.30-libm/libm/bessel.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,171 +0,0 @@ -/*--------------------------------------------------------------------------* - -Name j0, j1, jn - Bessel functions - y0, y1, yn - Weber functions - -Usage double j0 (double x); - double j1 (double x); - double jn (int n, double x); - double y0 (double x); - double y1 (double x); - double yn (int n, double x); - -Prototype in math.h - -Description j0, j1 and jn calculate the Bessel function. - y0, y1 and yn calcualte the Weber function. - -Return value return their return values as doubles. - -*---------------------------------------------------------------------------*/ - -#include - -#define M_C 0.5772156649015328 -#if 0 -#define M_1_PI 0.318309886183790671538 -#define M_2_PI 0.636619772367581343076 -#define M_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148 -#endif - - -#define EXPL(x) ((((short *)(void *)&x)[4] & 0x7FFF) >> 0) -#define EXPD(x) ((((short *)(void *)&x)[3] & 0x7FF0) >> 4) -#define EXPF(x) ((((short *)(void *)&x)[1] & 0x7F80) >> 7) - -#define SQUARE(x) (long) (My - (x) * (x) ) - - -static long double P ( int My, double* x ) -{ - long double Sum = 0.; - long double Fact = 1.; - long double z182 = -0.015625 / (x[0] * x[0]); - register int i; - - for ( i = 1; ; i += 2 ) { - Fact *= SQUARE(i+i-1) * SQUARE(i+i+1) * z182 / (i*(i+1)); - if ( EXPL (Fact) < 0x3FFF-53 ) - break; - Sum += Fact; - } - return 1. + Sum; -} - -static long double Q ( int My, double* x ) -{ - long double Fact = (My-1) / x[0] * 0.125; - long double Sum = Fact; - long double z182 = -0.015625 / (x[0]*x[0]); - register int i; - - for ( i = 2; ; i += 2 ) { - Fact *= SQUARE(i+i-1) * SQUARE(i+i+1) * z182 / (i*(i+1)); - if ( EXPL (Fact) < 0x3FFF-53 ) - break; - Sum += Fact; - } - return Sum; -} - - -static long double ___jn ( int n, double* x ) -{ - long double Sum; - long double Fact; - long double y; - register int i; - double xx; - long double Xi; - int My; - - if ( n < 0 ) - return n & 1 ? ___jn (-n, x) : -___jn (-n, x); - - if ((x[0] >= 17.7+0.0144*(n*n))) { - Xi = x[0] - M_PI * (n*0.5 + 0.25); - My = n*n << 2; - - return sqrt ( M_2_PI/x[0] ) * ( P(My,x) * cos(Xi) - Q(My,x) * sin(Xi) ); - } - xx = x[0] * 0.5; - Sum = 0.; - Fact = 1.; - y = -xx * xx; - - for ( i = 1; i <= n; i++ ) - Fact *= xx/i; - for ( i = 1; ; i++ ) { - Sum += Fact; - Fact *= y / (i*(n+i)); - if ( EXPL (Sum) - EXPL(Fact) > 53 || !EXPL(Fact) ) - break; - } - return Sum; -} - - -static long double ___yn ( int n, double* x ) -{ - long double Sum1; - long double Sum2; - long double Fact1; - long double Fact2; - long double F1; - long double F2; - long double y; - register int i; - double xx; - long double Xi; - unsigned int My; - - if ( EXPD (x[0]) == 0 ) - return -1./0.; /* ignore the gcc warning, this is intentional */ - - if ( (x[0] >= (n>=32 ? 25.8 : (n<8 ? 17.4+0.1*n : 16.2+0.3*n))) ) { - Xi = x[0] - M_PI * (n*0.5+0.25); - My = n*n << 2; - - return sqrt ( M_2_PI / x[0] ) * ( P(My,x) * sin(Xi) + Q(My,x) * cos(Xi) ); - } - - Sum1 = Sum2 = F1 = F2 = 0; - Fact1 = 1. / (xx = x[0] * 0.5 ); - Fact2 = 1.; - y = xx*xx; - - for ( i = 1; i < n; i++ ) - Fact1 *= (n-i) / xx; - - for ( i = 1; i <= n; i++ ) { - Sum1 += Fact1; - if ( i == n ) - break; - Fact1 *= y/(i*(n-i)); - } - - for (i=1; i<=n; i++) { - Fact2 *= xx / i; - F1 += 1. / i; - } - - for ( i = 1; ; i++ ) { - Sum2 += Fact2 * (F1+F2); - Fact2 *= -y / (i*(n+i)); - if ( EXPL (Sum2) - EXPL (Fact2) > 53 || !EXPL (Fact2) ) - break; - F1 += 1. / (n+i); - F2 += 1. / i; - } - - return M_1_PI * (2. * (M_C + log(xx)) * ___jn (n, x) - Sum1 - Sum2); -} - - -double j0 ( double x ) { return ___jn ( 0,&x ); } -double j1 ( double x ) { return ___jn ( 1,&x ); } -double jn ( int n, double x ) { return ___jn ( n,&x ); } -double y0 ( double x ) { return ___yn ( 0,&x ); } -double y1 ( double x ) { return ___yn ( 1,&x ); } -double yn ( int n, double x ) { return ___yn ( n,&x ); } - diff -urN dietlibc-0.30/libm/cosh.c dietlibc-0.30-libm/libm/cosh.c --- dietlibc-0.30/libm/cosh.c 2001-07-27 20:30:34.000000000 +0000 +++ dietlibc-0.30-libm/libm/cosh.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,9 +0,0 @@ -#include - -extern const float __half; - -double cosh ( double x ) -{ - long double y = exp (x); - return (y + 1./y) * __half; -} diff -urN dietlibc-0.30/libm/e_acos.c dietlibc-0.30-libm/libm/e_acos.c --- dietlibc-0.30/libm/e_acos.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_acos.c 2006-06-25 11:20:05.000000000 +0000 @@ -0,0 +1,111 @@ +/* @(#)e_acos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $"; +#endif + +/* __ieee754_acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 + * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) + * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) + * = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term + * for f so that f+c ~ sqrt(z). + * For x<-0.5 + * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) + * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: __ieee754_sqrt + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +#ifdef __STDC__ + double __ieee754_acos(double x) +#else + double __ieee754_acos(x) + double x; +#endif +{ + double z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3ff00000) { /* |x| >= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3fe00000) { /* |x| < 0.5 */ + if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = __ieee754_sqrt(z); + r = p/q; + w = r*s-pio2_lo; + return pi - 2.0*(s+w); + } else { /* x > 0.5 */ + z = (one-x)*0.5; + s = __ieee754_sqrt(z); + df = s; + SET_LOW_WORD(df,0); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return 2.0*(df+w); + } +} diff -urN dietlibc-0.30/libm/e_acosh.c dietlibc-0.30-libm/libm/e_acosh.c --- dietlibc-0.30/libm/e_acosh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_acosh.c 2006-06-25 11:20:21.000000000 +0000 @@ -0,0 +1,69 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $"; +#endif + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +#ifdef __STDC__ + double __ieee754_acosh(double x) +#else + double __ieee754_acosh(x) + double x; +#endif +{ + double t; + int32_t hx; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + if(hx<0x3ff00000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x41b00000) { /* x > 2**28 */ + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one))); + } else { /* 10.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +huge = 1.000e+300, +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ + /* coefficient for R(x^2) */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +#ifdef __STDC__ + double __ieee754_asin(double x) +#else + double __ieee754_asin(x) + double x; +#endif +{ + double t=0.0,w,p,q,c,r,s; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>= 0x3ff00000) { /* |x|>= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3fe00000) { /* |x|<0.5 */ + if(ix<0x3e400000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else { + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + } + /* 1> |x|>= 0.5 */ + w = one-fabs(x); + t = w*0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = __ieee754_sqrt(t); + if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + w = s; + SET_LOW_WORD(w,0); + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff -urN dietlibc-0.30/libm/e_atan2.c dietlibc-0.30-libm/libm/e_atan2.c --- dietlibc-0.30/libm/e_atan2.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_atan2.c 2006-06-25 11:20:24.000000000 +0000 @@ -0,0 +1,130 @@ +/* @(#)e_atan2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $"; +#endif + +/* __ieee754_atan2(y,x) + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +tiny = 1.0e-300, +zero = 0.0, +pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ +pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ +pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ +pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ + +#ifdef __STDC__ + double __ieee754_atan2(double y, double x) +#else + double __ieee754_atan2(y,x) + double y,x; +#endif +{ + double z; + int32_t k,m,hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + EXTRACT_WORDS(hy,ly,y); + iy = hy&0x7fffffff; + if(((ix|((lx|-lx)>>31))>0x7ff00000)|| + ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ + return x+y; + if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7ff00000) { + if(iy==0x7ff00000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>20; + if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=atan(fabs(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int32_t zh; + GET_HIGH_WORD(zh,z); + SET_HIGH_WORD(z,zh ^ 0x80000000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff -urN dietlibc-0.30/libm/e_atanh.c dietlibc-0.30-libm/libm/e_atanh.c --- dietlibc-0.30/libm/e_atanh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_atanh.c 2006-06-25 11:20:24.000000000 +0000 @@ -0,0 +1,74 @@ +/* @(#)e_atanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $"; +#endif + +/* __ieee754_atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, huge = 1e300; +#else +static double one = 1.0, huge = 1e300; +#endif + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_atanh(double x) +#else + double __ieee754_atanh(x) + double x; +#endif +{ + double t; + int32_t hx,ix; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3ff00000) + return x/zero; + if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_HIGH_WORD(x,ix); + if(ix<0x3fe00000) { /* x < 0.5 */ + t = x+x; + t = 0.5*log1p(t+t*x/(one-x)); + } else + t = 0.5*log1p((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff -urN dietlibc-0.30/libm/e_cosh.c dietlibc-0.30-libm/libm/e_cosh.c --- dietlibc-0.30/libm/e_cosh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_cosh.c 2006-06-25 11:20:06.000000000 +0000 @@ -0,0 +1,93 @@ +/* @(#)e_cosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $"; +#endif + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, half=0.5, huge = 1.0e300; +#else +static double one = 1.0, half=0.5, huge = 1.0e300; +#endif + +#ifdef __STDC__ + double __ieee754_cosh(double x) +#else + double __ieee754_cosh(x) + double x; +#endif +{ + double t,w; + int32_t ix; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e43) { + t = expm1(fabs(x)); + w = one+t; + if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x40360000) { + t = __ieee754_exp(fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633CE || + ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { + w = __ieee754_exp(half*fabs(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff -urN dietlibc-0.30/libm/e_exp.c dietlibc-0.30-libm/libm/e_exp.c --- dietlibc-0.30/libm/e_exp.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_exp.c 2006-06-25 11:20:01.000000000 +0000 @@ -0,0 +1,172 @@ +/* @(#)e_exp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_exp.c,v 1.8 1995/05/10 20:45:03 jtc Exp $"; +#endif + +/* __ieee754_exp(x) + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better + * accuracy. + * + * 2. Approximation of exp(r) by a special rational function on + * the interval [0,0.34658]: + * Write + * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... + * We use a special Reme algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error + * of this polynomial approximation is bounded by 2**-59. In + * other words, + * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 + * (where z=r*r, and the values of P1 to P5 are listed below) + * and + * | 5 | -59 + * | 2.0+P1*z+...+P5*z - R(z) | <= 2 + * | | + * The computation of exp(r) thus becomes + * 2*r + * exp(r) = 1 + ------- + * R - r + * r*R1(r) + * = 1 + r + ----------- (for better accuracy) + * 2 - R1(r) + * where + * 2 4 10 + * R1(r) = r - (P1*r + P2*r + ... + P5*r ). + * + * 3. Scale back to obtain exp(x): + * From step 1, we have + * exp(x) = 2^k * exp(r) + * + * Special cases: + * exp(INF) is INF, exp(NaN) is NaN; + * exp(-INF) is 0, and + * for finite argument, only exp(0)=1 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then exp(x) overflow + * if x < -7.45133219101941108420e+02 then exp(x) underflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.0, +halF[2] = {0.5,-0.5,}, +huge = 1.0e+300, +twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ +ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ + -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ +ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ + + +#ifdef __STDC__ + double __ieee754_exp(double x) /* default IEEE double exp */ +#else + double __ieee754_exp(x) /* default IEEE double exp */ + double x; +#endif +{ + double y; + double hi = 0.0; + double lo = 0.0; + double c; + double t; + int32_t k=0; + int32_t xsb; + u_int32_t hx; + + GET_HIGH_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((hx&0xfffff)|lx)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom1000*twom1000; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = invln2*x+halF[xsb]; + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + x = hi - lo; + } + else if(hx < 0x3e300000) { /* when |x|<2**-28 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-2.0)-x); + else y = one-((lo-(x*c)/(2.0-c))-hi); + if(k >= -1021) { + u_int32_t hy; + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */ + return y; + } else { + u_int32_t hy; + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */ + return y*twom1000; + } +} diff -urN dietlibc-0.30/libm/e_fmod.c dietlibc-0.30-libm/libm/e_fmod.c --- dietlibc-0.30/libm/e_fmod.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_fmod.c 2006-06-25 11:20:07.000000000 +0000 @@ -0,0 +1,140 @@ +/* @(#)e_fmod.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_fmod.c,v 1.8 1995/05/10 20:45:07 jtc Exp $"; +#endif + +/* + * __ieee754_fmod(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, Zero[] = {0.0, -0.0,}; +#else +static double one = 1.0, Zero[] = {0.0, -0.0,}; +#endif + +#ifdef __STDC__ + double __ieee754_fmod(double x, double y) +#else + double __ieee754_fmod(x,y) + double x,y ; +#endif +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + u_int32_t lx,ly,lz; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ + ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<=hy) { + if((hx>31]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(hx<0x00100000) { /* subnormal x */ + if(hx==0) { + for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; + } else { + for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; + } + } else ix = (hx>>20)-1023; + + /* determine iy = ilogb(y) */ + if(hy<0x00100000) { /* subnormal y */ + if(hy==0) { + for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; + } else { + for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; + } + } else iy = (hy>>20)-1023; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -1022) + hx = 0x00100000|(0x000fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -1022-ix; + if(n<=31) { + hx = (hx<>(32-n)); + lx <<= n; + } else { + hx = lx<<(n-32); + lx = 0; + } + } + if(iy >= -1022) + hy = 0x00100000|(0x000fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -1022-iy; + if(n<=31) { + hy = (hy<>(32-n)); + ly <<= n; + } else { + hy = ly<<(n-32); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx>31); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + hx = hz+hz+(lz>>31); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00100000) { /* normalize x */ + hx = hx+hx+(lx>>31); lx = lx+lx; + iy -= 1; + } + if(iy>= -1022) { /* normalize output */ + hx = ((hx-0x00100000)|((iy+1023)<<20)); + INSERT_WORDS(x,hx|sx,lx); + } else { /* subnormal output */ + n = -1022 - iy; + if(n<=20) { + lx = (lx>>n)|((u_int32_t)hx<<(32-n)); + hx >>= n; + } else if (n<=31) { + lx = (hx<<(32-n))|(lx>>n); hx = sx; + } else { + lx = hx>>(n-32); hx = sx; + } + INSERT_WORDS(x,hx|sx,lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff -urN dietlibc-0.30/libm/e_gamma.c dietlibc-0.30-libm/libm/e_gamma.c --- dietlibc-0.30/libm/e_gamma.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_gamma.c 2006-06-25 11:20:16.000000000 +0000 @@ -0,0 +1,34 @@ + +/* @(#)e_gamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* __ieee754_gamma(x) + * Return the logarithm of the Gamma function of x. + * + * Method: call __ieee754_gamma_r + */ + +#include "math_private.h" + +extern int signgam; + +#ifdef __STDC__ + //__private_extern__ + double __ieee754_gamma(double x) +#else + double __ieee754_gamma(x) + double x; +#endif +{ + return __ieee754_gamma_r(x,&signgam); +} diff -urN dietlibc-0.30/libm/e_gamma_r.c dietlibc-0.30-libm/libm/e_gamma_r.c --- dietlibc-0.30/libm/e_gamma_r.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_gamma_r.c 2006-06-25 11:20:20.000000000 +0000 @@ -0,0 +1,33 @@ + +/* @(#)e_gamma_r.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* __ieee754_gamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: See __ieee754_lgamma_r + */ + +#include "math_private.h" + +#ifdef __STDC__ + //__private_extern__ + double __ieee754_gamma_r(double x, int *signgamp) +#else + double __ieee754_gamma_r(x,signgamp) + double x; int *signgamp; +#endif +{ + return __ieee754_lgamma_r(x,signgamp); +} diff -urN dietlibc-0.30/libm/e_hypot.c dietlibc-0.30-libm/libm/e_hypot.c --- dietlibc-0.30/libm/e_hypot.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_hypot.c 2006-06-25 11:20:00.000000000 +0000 @@ -0,0 +1,128 @@ +/* @(#)e_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $"; +#endif + +/* __ieee754_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double __ieee754_hypot(double x, double y) +#else + double __ieee754_hypot(x,y) + double x, y; +#endif +{ + double a=x,b=y,t1,t2,y1,y2,w; + int32_t j,k,ha,hb; + + GET_HIGH_WORD(ha,x); + ha &= 0x7fffffff; + GET_HIGH_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_HIGH_WORD(a,ha); /* a <- |a| */ + SET_HIGH_WORD(b,hb); /* b <- |b| */ + if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ + k=0; + if(ha > 0x5f300000) { /* a>2**500 */ + if(ha >= 0x7ff00000) { /* Inf or NaN */ + u_int32_t low; + w = a+b; /* for sNaN */ + GET_LOW_WORD(low,a); + if(((ha&0xfffff)|low)==0) w = a; + GET_LOW_WORD(low,b); + if(((hb^0x7ff00000)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + if(hb < 0x20b00000) { /* b < 2**-500 */ + if(hb <= 0x000fffff) { /* subnormal b or 0 */ + u_int32_t low; + GET_LOW_WORD(low,b); + if((hb|low)==0) return a; + t1=0; + SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + } else { /* scale a and b by 2^600 */ + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_HIGH_WORD(t1,ha); + t2 = a-t1; + w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1 = 0; + SET_HIGH_WORD(y1,hb); + y2 = b - y1; + t1 = 0; + SET_HIGH_WORD(t1,ha+0x00100000); + t2 = a - t1; + w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int32_t high; + t1 = 1.0; + GET_HIGH_WORD(high,t1); + SET_HIGH_WORD(t1,high+(k<<20)); + return t1*w; + } else return w; +} diff -urN dietlibc-0.30/libm/e_j0.c dietlibc-0.30-libm/libm/e_j0.c --- dietlibc-0.30/libm/e_j0.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_j0.c 2006-06-25 11:20:13.000000000 +0000 @@ -0,0 +1,487 @@ +/* @(#)e_j0.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $"; +#endif + +/* __ieee754_j0(x), __ieee754_y0(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; + * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * where + * U(z) = u00 + u01*z + ... + u06*z^6 + * V(z) = 1 + v01*z + ... + v04*z^4 + * with absolute approximation error bounded by 2**-72. + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static double pzero(double), qzero(double); +#else +static double pzero(), qzero(); +#endif + +#ifdef __STDC__ +static const double +#else +static double +#endif +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ +R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ +R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ +R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ +S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ +S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ +S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ +S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_j0(double x) +#else + double __ieee754_j0(x) + double x; +#endif +{ + double z, s,c,ss,cc,r,u,v; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/(x*x); + x = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c)0x48000000) z = (invsqrtpi*cc)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*cc-v*ss)/sqrt(x); + } + return z; + } + if(ix<0x3f200000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x3e400000) return one; /* |x|<2**-27 */ + else return one - 0.25*x*x; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3FF00000) { /* |x| < 1.00 */ + return one + z*(-0.25+(r/s)); + } else { + u = 0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +#ifdef __STDC__ +static const double +#else +static double +#endif +u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ +u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ +u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ +u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ +u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ +u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ +u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ +v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ +v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ +v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ +v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ + +#ifdef __STDC__ + double __ieee754_y0(double x) +#else + double __ieee754_y0(x) + double x; +#endif +{ + double z, s,c,ss,cc,u,v; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c)0x48000000) z = (invsqrtpi*ss)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if(ix<=0x3e400000) { /* x < 2**-27 */ + return(u00 + tpi*__ieee754_log(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +#ifdef __STDC__ +static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ + -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ + -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ + -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ + -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ +}; +#ifdef __STDC__ +static const double pS8[5] = { +#else +static double pS8[5] = { +#endif + 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ + 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ + 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ + 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ + 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ +}; + +#ifdef __STDC__ +static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ + -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ + -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ + -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ + -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ + -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ +}; +#ifdef __STDC__ +static const double pS5[5] = { +#else +static double pS5[5] = { +#endif + 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ + 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ + 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ + 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ + 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ +}; + +#ifdef __STDC__ +static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ + -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ + -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ + -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ + -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ + -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ +}; +#ifdef __STDC__ +static const double pS3[5] = { +#else +static double pS3[5] = { +#endif + 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ + 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ + 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ + 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ + 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ +}; + +#ifdef __STDC__ +static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ + -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ + -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ + -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ + -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ + -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ +}; +#ifdef __STDC__ +static const double pS2[5] = { +#else +static double pS2[5] = { +#endif + 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ + 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ + 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ + 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ + 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ +}; + +#ifdef __STDC__ + static double pzero(double x) +#else + static double pzero(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p = 0,*q = 0; +#else + double *p,*q; +#endif + double z,r,s; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = pR8; q= pS8;} + else if(ix>=0x40122E8B){p = pR5; q= pS5;} + else if(ix>=0x4006DB6D){p = pR3; q= pS3;} + else if(ix>=0x40000000){p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +#ifdef __STDC__ +static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ + 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ + 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ + 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ + 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ +}; +#ifdef __STDC__ +static const double qS8[6] = { +#else +static double qS8[6] = { +#endif + 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ + 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ + 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ + 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ + 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ + -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ +}; + +#ifdef __STDC__ +static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ + 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ + 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ + 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ + 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ + 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ +}; +#ifdef __STDC__ +static const double qS5[6] = { +#else +static double qS5[6] = { +#endif + 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ + 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ + 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ + 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ + 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ + -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ +}; + +#ifdef __STDC__ +static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ + 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ + 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ + 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ + 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ + 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ +}; +#ifdef __STDC__ +static const double qS3[6] = { +#else +static double qS3[6] = { +#endif + 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ + 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ + 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ + 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ + 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ + -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ +}; + +#ifdef __STDC__ +static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ + 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ + 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ + 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ + 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ + 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ +}; +#ifdef __STDC__ +static const double qS2[6] = { +#else +static double qS2[6] = { +#endif + 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ + 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ + 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ + 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ + 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ + -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ +}; + +#ifdef __STDC__ + static double qzero(double x) +#else + static double qzero(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p=0,*q=0; +#else + double *p,*q; +#endif + double s,r,z; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qR8; q= qS8;} + else if(ix>=0x40122E8B){p = qR5; q= qS5;} + else if(ix>=0x4006DB6D){p = qR3; q= qS3;} + else if(ix>=0x40000000){p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-.125 + r/s)/x; +} diff -urN dietlibc-0.30/libm/e_j1.c dietlibc-0.30-libm/libm/e_j1.c --- dietlibc-0.30/libm/e_j1.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_j1.c 2006-06-25 11:20:13.000000000 +0000 @@ -0,0 +1,486 @@ +/* @(#)e_j1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $"; +#endif + +/* __ieee754_j1(x), __ieee754_y1(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j1(x): + * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... + * 2. Reduce x to |x| since j1(x)=-j1(-x), and + * for x in (0,2) + * j1(x) = x/2 + x*z*R0/S0, where z = x*x; + * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) + * for x in (2,inf) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * as follow: + * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (sin(x) + cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j1(nan)= nan + * j1(0) = 0 + * j1(inf) = 0 + * + * Method -- y1(x): + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 2. For x<2. + * Since + * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) + * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. + * We use the following function to approximate y1, + * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 + * where for x in [0,2] (abs err less than 2**-65.89) + * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 + * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 + * Note: For tiny x, 1/x dominate y1 and hence + * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) + * 3. For x>=2. + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * by method mentioned above. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static double pone(double), qone(double); +#else +static double pone(), qone(); +#endif + +#ifdef __STDC__ +static const double +#else +static double +#endif +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0,2] */ +r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ +r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ +r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ +r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ +s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ +s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ +s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ +s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ +s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_j1(double x) +#else + double __ieee754_j1(x) + double x; +#endif +{ + double z, s,c,ss,cc,r,u,v,y; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/x; + y = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(y); + c = cos(y); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure y+y not overflow */ + z = cos(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); + else { + u = pone(y); v = qone(y); + z = invsqrtpi*(u*cc-v*ss)/sqrt(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x3e400000) { /* |x|<2**-27 */ + if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*0.5+r/s); +} + +#ifdef __STDC__ +static const double U0[5] = { +#else +static double U0[5] = { +#endif + -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ + 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ + -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ + 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ + -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ +}; +#ifdef __STDC__ +static const double V0[5] = { +#else +static double V0[5] = { +#endif + 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ + 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ + 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ + 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ + 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ +}; + +#ifdef __STDC__ + double __ieee754_y1(double x) +#else + double __ieee754_y1(x) + double x; +#endif +{ + double z, s,c,ss,cc,u,v; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = cos(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); + else { + u = pone(x); v = qone(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if(ix<=0x3c900000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +#ifdef __STDC__ +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ + 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ + 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ + 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ + 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ +}; +#ifdef __STDC__ +static const double ps8[5] = { +#else +static double ps8[5] = { +#endif + 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ + 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ + 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ + 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ + 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ +}; + +#ifdef __STDC__ +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ + 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ + 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ + 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ + 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ + 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ +}; +#ifdef __STDC__ +static const double ps5[5] = { +#else +static double ps5[5] = { +#endif + 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ + 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ + 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ + 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ + 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ +}; + +#ifdef __STDC__ +static const double pr3[6] = { +#else +static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ + 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ + 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ + 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ + 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ + 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ +}; +#ifdef __STDC__ +static const double ps3[5] = { +#else +static double ps3[5] = { +#endif + 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ + 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ + 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ + 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ + 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ +}; + +#ifdef __STDC__ +static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ + 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ + 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ + 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ + 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ + 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ +}; +#ifdef __STDC__ +static const double ps2[5] = { +#else +static double ps2[5] = { +#endif + 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ + 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ + 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ + 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ + 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ +}; + +#ifdef __STDC__ + static double pone(double x) +#else + static double pone(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p=0,*q=0; +#else + double *p,*q; +#endif + double z,r,s; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = pr8; q= ps8;} + else if(ix>=0x40122E8B){p = pr5; q= ps5;} + else if(ix>=0x4006DB6D){p = pr3; q= ps3;} + else if(ix>=0x40000000){p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +#ifdef __STDC__ +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ + -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ + -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ + -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ + -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ +}; +#ifdef __STDC__ +static const double qs8[6] = { +#else +static double qs8[6] = { +#endif + 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ + 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ + 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ + 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ + 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ + -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ +}; + +#ifdef __STDC__ +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ + -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ + -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ + -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ + -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ + -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ +}; +#ifdef __STDC__ +static const double qs5[6] = { +#else +static double qs5[6] = { +#endif + 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ + 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ + 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ + 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ + 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ + -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ +}; + +#ifdef __STDC__ +static const double qr3[6] = { +#else +static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ + -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ + -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ + -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ + -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ + -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ +}; +#ifdef __STDC__ +static const double qs3[6] = { +#else +static double qs3[6] = { +#endif + 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ + 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ + 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ + 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ + 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ + -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ +}; + +#ifdef __STDC__ +static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ + -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ + -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ + -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ + -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ + -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ +}; +#ifdef __STDC__ +static const double qs2[6] = { +#else +static double qs2[6] = { +#endif + 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ + 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ + 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ + 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ + 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ + -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ +}; + +#ifdef __STDC__ + static double qone(double x) +#else + static double qone(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p=0,*q=0; +#else + double *p,*q; +#endif + double s,r,z; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qr8; q= qs8;} + else if(ix>=0x40122E8B){p = qr5; q= qs5;} + else if(ix>=0x4006DB6D){p = qr3; q= qs3;} + else if(ix>=0x40000000){p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (.375 + r/s)/x; +} diff -urN dietlibc-0.30/libm/e_jn.c dietlibc-0.30-libm/libm/e_jn.c --- dietlibc-0.30/libm/e_jn.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_jn.c 2006-06-25 11:20:14.000000000 +0000 @@ -0,0 +1,281 @@ +/* @(#)e_jn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $"; +#endif + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for nx, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ +one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ + +#ifdef __STDC__ +static const double zero = 0.00000000000000000000e+00; +#else +static double zero = 0.00000000000000000000e+00; +#endif + +#ifdef __STDC__ + double __ieee754_jn(int n, double x) +#else + double __ieee754_jn(n,x) + int n; double x; +#endif +{ + int32_t i,hx,ix,lx, sgn; + double a, b, temp=0, di; + double z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0(x)); + if(n==1) return(__ieee754_j1(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabs(x); + if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ + b = zero; + else if((double)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = cos(x)+sin(x); break; + case 1: temp = -cos(x)+sin(x); break; + case 2: temp = -cos(x)-sin(x); break; + case 3: temp = cos(x)-sin(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + a = __ieee754_j0(x); + b = __ieee754_j1(x); + for(i=1;i33) /* underflow */ + b = zero; + else { + temp = x*0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (double)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + double t,v; + double q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(double)x; h = 2.0/(double)x; + q0 = w; z = w+h; q1 = w*z - 1.0; k=1; + while(q1<1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_log(fabs(v*tmp)); + if(tmp<7.09782712893383973096e+02) { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>1e100) { + a /= b; + t /= b; + b = one; + } + } + } + b = (t*__ieee754_j0(x)/b); + } + } + if(sgn==1) return -b; else return b; +} + +#ifdef __STDC__ + double __ieee754_yn(int n, double x) +#else + double __ieee754_yn(n,x) + int n; double x; +#endif +{ + int32_t i,hx,ix,lx; + int32_t sign; + double a, b, temp=0; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0(x)); + if(n==1) return(sign*__ieee754_y1(x)); + if(ix==0x7ff00000) return zero; + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = sin(x)-cos(x); break; + case 1: temp = -sin(x)-cos(x); break; + case 2: temp = -sin(x)+cos(x); break; + case 3: temp = sin(x)+cos(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + u_int32_t high; + a = __ieee754_y0(x); + b = __ieee754_y1(x); + /* quit if b is -inf */ + GET_HIGH_WORD(high,b); + for(i=1;i0) return b; else return -b; +} diff -urN dietlibc-0.30/libm/e_lgamma.c dietlibc-0.30-libm/libm/e_lgamma.c --- dietlibc-0.30/libm/e_lgamma.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_lgamma.c 2006-06-25 11:20:15.000000000 +0000 @@ -0,0 +1,34 @@ + +/* @(#)e_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* __ieee754_lgamma(x) + * Return the logarithm of the Gamma function of x. + * + * Method: call __ieee754_lgamma_r + */ + +#include "math_private.h" + +extern int signgam; + +#ifdef __STDC__ + //__private_extern__ + double __ieee754_lgamma(double x) +#else + double __ieee754_lgamma(x) + double x; +#endif +{ + return __ieee754_lgamma_r(x,&signgam); +} diff -urN dietlibc-0.30/libm/e_lgamma_r.c dietlibc-0.30-libm/libm/e_lgamma_r.c --- dietlibc-0.30/libm/e_lgamma_r.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_lgamma_r.c 2006-06-25 11:20:23.000000000 +0000 @@ -0,0 +1,316 @@ +/* @(#)er_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_lgamma_r.c,v 1.7 1995/05/10 20:45:42 jtc Exp $"; +#endif + +/* __ieee754_lgamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * where + * poly(z) is a 14 degree polynomial. + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * with accuracy + * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * where + * |w - f(z)| < 2**-58.74 + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ +a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ +a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ +a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ +a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ +a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ +a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ +a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ +a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ +a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ +a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ +a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ +tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ +tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ +/* tt = -(tail of tf) */ +tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ +t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ +t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ +t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ +t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ +t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ +t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ +t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ +t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ +t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ +t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ +t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ +t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ +t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ +t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ +t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ +u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ +u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ +u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ +u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ +u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ +v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ +v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ +v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ +v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ +v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ +s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ +s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ +s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ +s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ +s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ +s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ +r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ +r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ +r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ +r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ +r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ +r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ +w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ +w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ +w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ +w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ +w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ +w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ +w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ + +#ifdef __STDC__ +static const double zero= 0.00000000000000000000e+00; +#else +static double zero= 0.00000000000000000000e+00; +#endif + +static +#ifdef __GNUC__ +__inline__ +#endif +#ifdef __STDC__ + double sin_pi(double x) +#else + double sin_pi(x) + double x; +#endif +{ + double y,z; + int n,ix; + + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floor(y); + if(z!=y) { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */ + n = (int) (y*4.0); + } else { + if(ix>=0x43400000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x43300000) z = y+two52; /* exact */ + GET_LOW_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sin(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cos(pi*(0.5-y),zero); break; + case 3: + case 4: y = __kernel_sin(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; + default: y = __kernel_sin(pi*(y-2.0),zero,0); break; + } + return -y; +} + + +#ifdef __STDC__ + double __ieee754_lgamma_r(double x, int *signgamp) +#else + double __ieee754_lgamma_r(x,signgamp) + double x; int *signgamp; +#endif +{ + double t,y,z,nadj=0,p,p1,p2,p3,q,r,w; + int i,hx,lx,ix; + + EXTRACT_WORDS(hx,lx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x*x; + if((ix|lx)==0) return one/zero; + if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_log(-x); + } else return -__ieee754_log(x); + } + if(hx<0) { + if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ + return one/zero; + t = sin_pi(x); + if(t==zero) return one/zero; /* -integer */ + nadj = __ieee754_log(pi/fabs(t*x)); + if(t=0x3FE76944) {y = one-x; i= 0;} + else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-0.5*y + p1/p2); + } + } + else if(ix<0x40200000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(double)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6.0); /* FALLTHRU */ + case 6: z *= (y+5.0); /* FALLTHRU */ + case 5: z *= (y+4.0); /* FALLTHRU */ + case 4: z *= (y+3.0); /* FALLTHRU */ + case 3: z *= (y+2.0); /* FALLTHRU */ + r += __ieee754_log(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x43900000) { + t = __ieee754_log(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(__ieee754_log(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff -urN dietlibc-0.30/libm/e_log.c dietlibc-0.30-libm/libm/e_log.c --- dietlibc-0.30/libm/e_log.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_log.c 2006-06-25 11:20:02.000000000 +0000 @@ -0,0 +1,147 @@ +/* @(#)e_log.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; +#endif + +/* __ieee754_log(x) + * Return the logrithm of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_log(double x) +#else + double __ieee754_log(x) + double x; +#endif +{ + double hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,hx,i,j; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if(f==zero) {if(k==0) return zero; else {dk=(double)k; + return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*(0.5-0.33333333333333333*f); + if(k==0) return f-R; else {dk=(double)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/(2.0+f); + dk = (double)k; + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff -urN dietlibc-0.30/libm/e_log10.c dietlibc-0.30-libm/libm/e_log10.c --- dietlibc-0.30/libm/e_log10.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_log10.c 2006-06-25 11:20:14.000000000 +0000 @@ -0,0 +1,98 @@ +/* @(#)e_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc Exp $"; +#endif + +/* __ieee754_log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ +log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ +log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_log10(double x) +#else + double __ieee754_log10(x) + double x; +#endif +{ + double y,z; + int32_t i,k,hx; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + i = ((u_int32_t)k&0x80000000)>>31; + hx = (hx&0x000fffff)|((0x3ff-i)<<20); + y = (double)(k+i); + SET_HIGH_WORD(x,hx); + z = y*log10_2lo + ivln10*__ieee754_log(x); + return z+y*log10_2hi; +} diff -urN dietlibc-0.30/libm/e_pow.c dietlibc-0.30-libm/libm/e_pow.c --- dietlibc-0.30/libm/e_pow.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_pow.c 2006-06-25 11:20:02.000000000 +0000 @@ -0,0 +1,308 @@ +/* @(#)e_pow.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; +#endif + +/* __ieee754_pow(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 53-24 = 29 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular + * pow(integer,integer) + * always returns the correct integer provided it is + * representable. + * + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ +dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ +zero = 0.0, +one = 1.0, +two = 2.0, +two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ +huge = 1.0e300, +tiny = 1.0e-300, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ +L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ +L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ +L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ +L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ +L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ +lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ +lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ +ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ +cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ +cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ +cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ +ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ +ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ +ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ + +#ifdef __STDC__ + double __ieee754_pow(double x, double y) +#else + double __ieee754_pow(x,y) + double x, y; +#endif +{ + double z,ax,z_h,z_l,p_h,p_l; + double y1,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if((iy|ly)==0) return one; + + /* +-NaN return x+y */ + if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || + iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) + return x+y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x43400000) yisint = 2; /* even integer y */ + else if(iy>=0x3ff00000) { + k = (iy>>20)-0x3ff; /* exponent */ + if(k>20) { + j = ly>>(52-k); + if((j<<(52-k))==ly) yisint = 2-(j&1); + } else if(ly==0) { + j = iy>>(20-k); + if((j<<(20-k))==iy) yisint = 2-(j&1); + } + } + } + + /* special value of y */ + if(ly==0) { + if (iy==0x7ff00000) { /* y is +-inf */ + if(((ix-0x3ff00000)|lx)==0) + return y - y; /* inf**+-1 is NaN */ + else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3ff00000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3fe00000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return __ieee754_sqrt(x); + } + } + + ax = fabs(x); + /* special value of x */ + if(lx==0) { + if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3ff00000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + /* (x<0)**(non-int) is NaN */ + if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); + + /* |y| is huge */ + if(iy>0x41e00000) { /* if |y| > 2**31 */ + if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ + if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; + if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; + } + /* over/underflow if x is not close to one */ + if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; + if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = x-1; /* t has 20 trailing zeros */ + w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); + u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + SET_LOW_WORD(t1,0); + t2 = v-(t1-u); + } else { + double s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00100000) + {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } + n += ((ix)>>20)-0x3ff; + j = ix&0x000fffff; + /* determine interval */ + ix = j|0x3ff00000; /* normalize ix */ + if(j<=0x3988E) k=0; /* |x|>1)|0x20000000)+0x00080000+(k<<18)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = s*s; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = 3.0+s2+r; + SET_LOW_WORD(t_h,0); + t_l = r-((t_h-3.0)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + p_h = u+v; + SET_LOW_WORD(p_h,0); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (double)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + SET_LOW_WORD(t1,0); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) + s = -one;/* (-ve)**(odd int) */ + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + y1 = y; + SET_LOW_WORD(y1,0); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + EXTRACT_WORDS(j,i,z); + if (j>=0x40900000) { /* z >= 1024 */ + if(((j-0x40900000)|i)!=0) /* if z > 1024 */ + return s*huge*huge; /* overflow */ + else { + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ + if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ + return s*tiny*tiny; /* underflow */ + else { + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>20)-0x3ff; + n = 0; + if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00100000>>(k+1)); + k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ + t = zero; + SET_HIGH_WORD(t,n&~(0x000fffff>>k)); + n = ((n&0x000fffff)|0x00100000)>>(20-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + SET_LOW_WORD(t,0); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_HIGH_WORD(j,z); + j += (n<<20); + if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ + else SET_HIGH_WORD(z,j); + return s*z; +} diff -urN dietlibc-0.30/libm/e_rem_pio2.c dietlibc-0.30-libm/libm/e_rem_pio2.c --- dietlibc-0.30/libm/e_rem_pio2.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_rem_pio2.c 2006-06-25 11:20:15.000000000 +0000 @@ -0,0 +1,183 @@ +/* @(#)e_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $"; +#endif + +/* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include "math.h" +#include "math_private.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +#ifdef __STDC__ +static const int32_t two_over_pi[] = { +#else +static int32_t two_over_pi[] = { +#endif +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, +}; + +#ifdef __STDC__ +static const int32_t npio2_hw[] = { +#else +static int32_t npio2_hw[] = { +#endif +0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, +0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, +0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, +0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, +0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, +0x404858EB, 0x404921FB, +}; + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +#ifdef __STDC__ +static const double +#else +static double +#endif +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ +pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ +pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ +pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ +pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ +pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + +#ifdef __STDC__ + int32_t __ieee754_rem_pio2(double x, double *y) +#else + int32_t __ieee754_rem_pio2(x,y) + double x,y[]; +#endif +{ + double z=0.0,w,t,r,fn; + double tx[3]; + int32_t e0,i,j,nx,n,ix,hx; + u_int32_t low; + + GET_HIGH_WORD(hx,x); /* high word of x */ + ix = hx&0x7fffffff; + if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ + t = fabs(x); + n = (int32_t) (t*invpio2+half); + fn = (double)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 85 bit */ + if(n<32&&ix!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + u_int32_t high; + j = ix>>20; + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>16) { /* 2nd iteration needed, good to 118 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>49) { /* 3rd iteration need, 151 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + else return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7ff00000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + GET_LOW_WORD(low,x); + SET_LOW_WORD(z,low); + e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ + SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); + for(i=0;i<2;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff -urN dietlibc-0.30/libm/e_remainder.c dietlibc-0.30-libm/libm/e_remainder.c --- dietlibc-0.30/libm/e_remainder.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_remainder.c 2006-06-25 11:20:04.000000000 +0000 @@ -0,0 +1,80 @@ +/* @(#)e_remainder.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_remainder.c,v 1.8 1995/05/10 20:46:05 jtc Exp $"; +#endif + +/* __ieee754_remainder(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmod() return x-[x/p]chopped*p exactlp. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + + +#ifdef __STDC__ + double __ieee754_remainder(double x, double p) +#else + double __ieee754_remainder(x,p) + double x,p; +#endif +{ + int32_t hx,hp; + u_int32_t sx,lx,lp; + double p_half; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hp,lp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7ff00000)|| /* x not finite */ + ((hp>=0x7ff00000)&& /* p is NaN */ + (((hp-0x7ff00000)|lp)!=0))) + return (x*p)/(x*p); + + + if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabs(x); + p = fabs(p); + if (hp<0x00200000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_HIGH_WORD(hx,x); + SET_HIGH_WORD(x,hx^sx); + return x; +} diff -urN dietlibc-0.30/libm/e_scalb.c dietlibc-0.30-libm/libm/e_scalb.c --- dietlibc-0.30/libm/e_scalb.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_scalb.c 2006-06-25 11:20:10.000000000 +0000 @@ -0,0 +1,55 @@ +/* @(#)e_scalb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_scalb.c,v 1.6 1995/05/10 20:46:09 jtc Exp $"; +#endif + +/* + * __ieee754_scalb(x, fn) is provide for + * passing various standard test suite. One + * should use scalbn() instead. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef _SCALB_INT +#ifdef __STDC__ + double __ieee754_scalb(double x, int fn) +#else + double __ieee754_scalb(x,fn) + double x; int fn; +#endif +#else +#ifdef __STDC__ + double __ieee754_scalb(double x, double fn) +#else + double __ieee754_scalb(x,fn) + double x, fn; +#endif +#endif +{ +#ifdef _SCALB_INT + return scalbn(x,fn); +#else + if (isnan(x)||isnan(fn)) return x*fn; + if (!finite(fn)) { + if(fn>0.0) return x*fn; + else return x/(-fn); + } + if (rint(fn)!=fn) return (fn-fn)/(fn-fn); + if ( fn > 65000.0) return scalbn(x, 65000); + if (-fn > 65000.0) return scalbn(x,-65000); + return scalbn(x,(int)fn); +#endif +} diff -urN dietlibc-0.30/libm/e_sinh.c dietlibc-0.30-libm/libm/e_sinh.c --- dietlibc-0.30/libm/e_sinh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_sinh.c 2006-06-25 11:20:10.000000000 +0000 @@ -0,0 +1,86 @@ +/* @(#)e_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $"; +#endif + +/* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, shuge = 1.0e307; +#else +static double one = 1.0, shuge = 1.0e307; +#endif + +#ifdef __STDC__ + double __ieee754_sinh(double x) +#else + double __ieee754_sinh(x) + double x; +#endif +{ + double t,w,h; + int32_t ix,jx; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3e300000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1(fabs(x)); + if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { + w = __ieee754_exp(0.5*fabs(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff -urN dietlibc-0.30/libm/e_sqrt.c dietlibc-0.30-libm/libm/e_sqrt.c --- dietlibc-0.30/libm/e_sqrt.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/e_sqrt.c 2006-06-25 11:20:12.000000000 +0000 @@ -0,0 +1,453 @@ +/* @(#)e_sqrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; +#endif + +/* __ieee754_sqrt(x) + * Return correctly rounded sqrt. + * ------------------------------------------ + * | Use the hardware sqrt if you have one | + * ------------------------------------------ + * Method: + * Bit by bit method using integer arithmetic. (Slow, but portable) + * 1. Normalization + * Scale x to y in [1,4) with even powers of 2: + * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then + * sqrt(x) = 2^k * sqrt(y) + * 2. Bit by bit computation + * Let q = sqrt(y) truncated to i bit after binary point (q = 1), + * i 0 + * i+1 2 + * s = 2*q , and y = 2 * ( y - q ). (1) + * i i i i + * + * To compute q from q , one checks whether + * i+1 i + * + * -(i+1) 2 + * (q + 2 ) <= y. (2) + * i + * -(i+1) + * If (2) is false, then q = q ; otherwise q = q + 2 . + * i+1 i i+1 i + * + * With some algebric manipulation, it is not difficult to see + * that (2) is equivalent to + * -(i+1) + * s + 2 <= y (3) + * i i + * + * The advantage of (3) is that s and y can be computed by + * i i + * the following recurrence formula: + * if (3) is false + * + * s = s , y = y ; (4) + * i+1 i i+1 i + * + * otherwise, + * -i -(i+1) + * s = s + 2 , y = y - s - 2 (5) + * i+1 i i+1 i i + * + * One may easily use induction to prove (4) and (5). + * Note. Since the left hand side of (3) contain only i+2 bits, + * it does not necessary to do a full (53-bit) comparison + * in (3). + * 3. Final rounding + * After generating the 53 bits result, we compute one more bit. + * Together with the remainder, we can decide whether the + * result is exact, bigger than 1/2ulp, or less than 1/2ulp + * (it will never equal to 1/2ulp). + * The rounding mode can be detected by checking whether + * huge + tiny is equal to huge, and whether huge - tiny is + * equal to huge for some floating point number "huge" and "tiny". + * + * Special cases: + * sqrt(+-0) = +-0 ... exact + * sqrt(inf) = inf + * sqrt(-ve) = NaN ... with invalid signal + * sqrt(NaN) = NaN ... with invalid signal for signaling NaN + * + * Other methods : see the appended file at the end of the program below. + *--------------- + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0, tiny=1.0e-300; +#else +static double one = 1.0, tiny=1.0e-300; +#endif + +#ifdef __STDC__ + double __ieee754_sqrt(double x) +#else + double __ieee754_sqrt(x) + double x; +#endif +{ + double z; + int32_t sign = (int)0x80000000; + int32_t ix0,s0,q,m,t,i; + u_int32_t r,t1,s1,ix1,q1; + + EXTRACT_WORDS(ix0,ix1,x); + + /* take care of Inf and NaN */ + if((ix0&0x7ff00000)==0x7ff00000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix0<=0) { + if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix0<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix0>>20); + if(m==0) { /* subnormal x */ + while(ix0==0) { + m -= 21; + ix0 |= (ix1>>11); ix1 <<= 21; + } + for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1; + m -= i-1; + ix0 |= (ix1>>(32-i)); + ix1 <<= i; + } + m -= 1023; /* unbias exponent */ + ix0 = (ix0&0x000fffff)|0x00100000; + if(m&1){ /* odd m, double x to make it even */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + } + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ + r = 0x00200000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s0+r; + if(t<=ix0) { + s0 = t+r; + ix0 -= t; + q += r; + } + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + r>>=1; + } + + r = sign; + while(r!=0) { + t1 = s1+r; + t = s0; + if((t>31); + ix1 += ix1; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if((ix0|ix1)!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;} + else if (z>one) { + if (q1==(u_int32_t)0xfffffffe) q+=1; + q1+=2; + } else + q1 += (q1&1); + } + } + ix0 = (q>>1)+0x3fe00000; + ix1 = q1>>1; + if ((q&1)==1) ix1 |= sign; + ix0 += (m <<20); + INSERT_WORDS(z,ix0,ix1); + return z; +} + +/* +Other methods (use floating-point arithmetic) +------------- +(This is a copy of a drafted paper by Prof W. Kahan +and K.C. Ng, written in May, 1986) + + Two algorithms are given here to implement sqrt(x) + (IEEE double precision arithmetic) in software. + Both supply sqrt(x) correctly rounded. The first algorithm (in + Section A) uses newton iterations and involves four divisions. + The second one uses reciproot iterations to avoid division, but + requires more multiplications. Both algorithms need the ability + to chop results of arithmetic operations instead of round them, + and the INEXACT flag to indicate when an arithmetic operation + is executed exactly with no roundoff error, all part of the + standard (IEEE 754-1985). The ability to perform shift, add, + subtract and logical AND operations upon 32-bit words is needed + too, though not part of the standard. + +A. sqrt(x) by Newton Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + + 1 11 52 ...widths + ------------------------------------------------------ + x: |s| e | f | + ------------------------------------------------------ + msb lsb msb lsb ...order + + + ------------------------ ------------------------ + x0: |s| e | f1 | x1: | f2 | + ------------------------ ------------------------ + + By performing shifts and subtracts on x0 and x1 (both regarded + as integers), we obtain an 8-bit approximation of sqrt(x) as + follows. + + k := (x0>>1) + 0x1ff80000; + y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits + Here k is a 32-bit integer and T1[] is an integer array containing + correction terms. Now magically the floating value of y (y's + leading 32-bit word is y0, the value of its trailing word is 0) + approximates sqrt(x) to almost 8-bit. + + Value of T1: + static int T1[32]= { + 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592, + 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, + 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, + 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,}; + + (2) Iterative refinement + + Apply Heron's rule three times to y, we have y approximates + sqrt(x) to within 1 ulp (Unit in the Last Place): + + y := (y+x/y)/2 ... almost 17 sig. bits + y := (y+x/y)/2 ... almost 35 sig. bits + y := y-(y-x/y)/2 ... within 1 ulp + + + Remark 1. + Another way to improve y to within 1 ulp is: + + y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x) + y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x) + + 2 + (x-y )*y + y := y + 2* ---------- ...within 1 ulp + 2 + 3y + x + + + This formula has one division fewer than the one above; however, + it requires more multiplications and additions. Also x must be + scaled in advance to avoid spurious overflow in evaluating the + expression 3y*y+x. Hence it is not recommended uless division + is slow. If division is very slow, then one should use the + reciproot algorithm given in section B. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + I := FALSE; ... reset INEXACT flag I + R := RZ; ... set rounding mode to round-toward-zero + z := x/y; ... chopped quotient, possibly inexact + If(not I) then { ... if the quotient is exact + if(z=y) { + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + } else { + z := z - ulp; ... special rounding + } + } + i := TRUE; ... sqrt(x) is inexact + If (r=RN) then z=z+ulp ... rounded-to-nearest + If (r=RP) then { ... round-toward-+inf + y = y+ulp; z=z+ulp; + } + y := y+z; ... chopped sum + y0:=y0-0x00100000; ... y := y/2 is correctly rounded. + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + + (4) Special cases + + Square root of +inf, +-0, or NaN is itself; + Square root of a negative number is NaN with invalid signal. + + +B. sqrt(x) by Reciproot Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + (see section A). By performing shifs and subtracts on x0 and y0, + we obtain a 7.8-bit approximation of 1/sqrt(x) as follows. + + k := 0x5fe80000 - (x0>>1); + y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits + + Here k is a 32-bit integer and T2[] is an integer array + containing correction terms. Now magically the floating + value of y (y's leading 32-bit word is y0, the value of + its trailing word y1 is set to zero) approximates 1/sqrt(x) + to almost 7.8-bit. + + Value of T2: + static int T2[64]= { + 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, + 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, + 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, + 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, + 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, + 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, + 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, + 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,}; + + (2) Iterative refinement + + Apply Reciproot iteration three times to y and multiply the + result by x to get an approximation z that matches sqrt(x) + to about 1 ulp. To be exact, we will have + -1ulp < sqrt(x)-z<1.0625ulp. + + ... set rounding mode to Round-to-nearest + y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x) + y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x) + ... special arrangement for better accuracy + z := x*y ... 29 bits to sqrt(x), with z*y<1 + z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x) + + Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that + (a) the term z*y in the final iteration is always less than 1; + (b) the error in the final result is biased upward so that + -1 ulp < sqrt(x) - z < 1.0625 ulp + instead of |sqrt(x)-z|<1.03125ulp. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + R := RZ; ... set rounding mode to round-toward-zero + switch(r) { + case RN: ... round-to-nearest + if(x<= z*(z-ulp)...chopped) z = z - ulp; else + if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp; + break; + case RZ:case RM: ... round-to-zero or round-to--inf + R:=RP; ... reset rounding mod to round-to-+inf + if(x=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp; + break; + case RP: ... round-to-+inf + if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else + if(x>z*z ...chopped) z = z+ulp; + break; + } + + Remark 3. The above comparisons can be done in fixed point. For + example, to compare x and w=z*z chopped, it suffices to compare + x1 and w1 (the trailing parts of x and w), regarding them as + two's complement integers. + + ...Is z an exact square root? + To determine whether z is an exact square root of x, let z1 be the + trailing part of z, and also let x0 and x1 be the leading and + trailing parts of x. + + If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0 + I := 1; ... Raise Inexact flag: z is not exact + else { + j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2 + k := z1 >> 26; ... get z's 25-th and 26-th + fraction bits + I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); + } + R:= r ... restore rounded mode + return sqrt(x):=z. + + If multiplication is cheaper then the foregoing red tape, the + Inexact flag can be evaluated by + + I := i; + I := (z*z!=x) or I. + + Note that z*z can overwrite I; this value must be sensed if it is + True. + + Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be + zero. + + -------------------- + z1: | f2 | + -------------------- + bit 31 bit 0 + + Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd + or even of logb(x) have the following relations: + + ------------------------------------------------- + bit 27,26 of z1 bit 1,0 of x1 logb(x) + ------------------------------------------------- + 00 00 odd and even + 01 01 even + 10 10 odd + 10 00 even + 11 01 even + ------------------------------------------------- + + (4) Special cases (see (4) of Section A). + + */ + diff -urN dietlibc-0.30/libm/erf.c dietlibc-0.30-libm/libm/erf.c --- dietlibc-0.30/libm/erf.c 2002-11-18 01:16:51.000000000 +0000 +++ dietlibc-0.30-libm/libm/erf.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,95 +0,0 @@ -#include "dietlibm.h" - -/*--------------------------------------------------------------------------* - z - 1 | -x²/2 -Name erf(z) = --------- | e dx - sqrt(2pi) | - 0 - - oo - 1 | -x²/2 - erfc(z) = -------- | e dx - sqrt(2pi) | - z - -Usage double erf (double x); - double erfc(double x); - -Prototype in math.h - -Description erf(x) is the probability a normal distributed event occures - within the range [0,x]. erfc(x) is the probability a normal - distributed event occures within the range [x,oo]. - -Return value return their respective function value. - -*---------------------------------------------------------------------------*/ - - -/* even function in (0): Coefficients for gamma(0) */ - -static const double tab1 [9 + 1] = { - 0.398942280401432677926, -0.066490380066905446321, 9.97355701003581694794E-3, -1.18732821548045439878E-3, 1.15434687616155288764E-4, -9.44465625950361453450E-6, 6.65969351631665127484E-7, -4.12266741486268888409E-8, 2.27352982437280636972E-9, -1.13011716416192129505E-10 -}; - -/* non even or odd function in (x), x>0: Coefficients for gamma(x), x>0 */ - -static const double tab2 [] [31 + 1] = { - { -0.158655253931457051468, +0.241970724519143349823, -0.120985362259571674911, 0, +0.0201642270432619458197, -4.03284540865238916394E-3, -2.01642270432619458197E-3, +7.68161030219502697887E-4, +1.20025160971797296538E-4, -8.80184513793180174807E-5, -1.86705805956129127862E-6, +7.37124220917704609315E-6, -4.72826391707080259142E-7, -4.83395817951682973566E-7, +6.57036391970156141055E-8, +2.5544260402922190768E-8, -5.4292285616752144141E-9, -1.08932444506260820153E-9, +3.44399256708718202774E-10, +3.6021429664641554881E-11, -1.81147204852239925966E-11, -7.66935128389784976374E-13, +8.19047721646461768154E-13, -3.78144699611990981391E-15, -3.24856460059989147863E-14, +1.44438130842455313227E-15, +1.14391687912824634892E-15, -9.38053726039148625184E-17, -3.59908648108845288945E-17, +4.36020846676166022246E-18, +1.01298640134330880603E-18, -1.68640470512244526894E-19 }, - { -0.0227501319481792072104, +0.0539909665131880519553, -0.0539909665131880519553, +0.0269954832565940259776, -4.49924720943233766301E-3, -2.24962360471616883129E-3, +1.34977416282970129877E-3, -1.17837426913704081544E-4, -1.15159303574756261652E-4, +3.70473728554448438507E-5, +2.82690796888936559912E-6, -3.54513195524355369855E-6, +3.76695631261094890352E-7, +1.92024079214184701051E-7, -5.22690859049557191018E-8, -4.91799344974114749666E-9, +3.66377919234006038965E-9, -1.5981997209104676352E-10, -1.73812379171063320997E-10, +2.62403075313043113473E-11, +5.60918720760414713346E-12, -1.72126983666416144614E-12, -8.63428809787622525331E-14, +7.89441765474563834480E-14, -3.13747960081562321348E-15, -2.77519506625391157547E-15, +3.29321944203493138076E-16, +7.44375150395529134369E-17, -1.66428523299294690222E-17, -1.32735612757620496568E-18, +6.24122437514304644794E-19, +1.12471123532438919306E-21 }, - { -1.3498980316300945272E-3, +4.43184841193800717687E-3, -6.64777261790701076574E-3, +5.90913121591734290293E-3, -3.32388630895350538287E-3, +1.10796210298450179421E-3, -1.10796210298450179595E-4, -8.44161602273906129349E-5, +4.35270826172482847927E-5, -6.30190085030867423515E-6, -1.9785037553294674925E-6, +1.05520200284238266374E-6, -1.13913852579575399458E-7, -4.81174572974454799623E-8, +1.78216871733806513653E-8, -5.85637697215219690327E-10, -9.29791350219350980904E-10, +1.96377023046901260016E-10, +1.58870373467897094393E-11, -1.22699105512396660364E-11, +1.08794270836433192571E-12, +3.99646995170699427940E-13, -1.01594404465456044793E-13, -3.33469605506835759271E-15, +4.46588935876766499879E-15, -4.08076707607833277747E-16, -1.17808602368979218862E-16, +2.76224909899945482352E-17, +1.09206599392049874162E-18, -1.03145418746203977253E-18, +6.79984672177279963209E-20, +2.55831283729070534712E-20 }, - { -3.16712418331199212695E-5, +1.33830225764885351832E-4, -2.67660451529770703664E-4, +3.34575564412213379613E-4, -2.89965489157251595673E-4, +1.8178605666396926958E-4, -8.25286392216793003064E-5, +2.55180251904870680833E-5, -3.91665839292075186649E-6, -7.40182052221464123606E-7, +6.44220233592652481453E-7, -1.73701553397390201613E-7, +9.09595464817154590424E-9, +9.44943118114780783705E-9, -3.29957075383376125942E-9, +2.94920746951281580686E-10, +1.18744773902482360274E-10, -4.42039585809856402486E-11, +3.61422484008923382324E-12, +1.43638335494248833511E-12, -4.58476794992724591068E-13, +2.23496663226445199624E-14, +1.57839046076890756440E-14, -3.67258220998453293248E-15, -1.69716269032291432153E-17, +1.43497778353923791279E-16, -2.14499365995613073838E-17, -1.93255135682867953692E-18, +1.01377499752128183701E-18, -7.55713215369572830154E-20, -2.25510650946079103289E-20, +5.26633993110171917109E-21 }, - { -2.86651571879193912033E-7, +1.48671951473429770924E-6, -3.7167987868357442731E-6, +5.9468780589371908374E-6, -6.81413110919886450076E-6, +5.92209940035828587496E-6, -4.02653201907205629582E-6, +2.17108246596119665457E-6, -9.25512396325170449452E-7, +3.03096091545533908077E-7, -6.92802772105295808398E-8, +6.69226396924248971087E-9, +2.46006252876483997508E-9, -1.41806830376639605249E-9, +3.44251040657349801884E-10, -2.6965166176434937652E-11, -1.16546962748761528049E-11, +4.91490145086991326748E-12, -7.55854519365765424197E-13, -4.53988828124843593484E-14, +4.71533558309731405623E-14, -9.17323049919073092370E-15, +4.35542982587998484108E-17, +3.71238868922011013332E-16, -7.90772907386322623053E-17, +1.58463483904927528072E-18, +2.61503941976309571331E-18, -5.40699423853895351239E-19, +6.61825040533797444037E-21, +1.68378440730394776550E-20, -3.01930850797704474581E-21, -3.80658085177617928332E-23 }, - { -9.8658764503769814198E-10, +6.07588284982328549581E-9, -1.82276485494698564874E-8, +3.54426499573024987263E-8, -5.01260335110421053478E-8, +5.48348427196551516061E-8, -4.81513715848495375522E-8, +3.47446467489597046263E-8, -2.08994095347716137282E-8, +1.0554987922587771203E-8, -4.4752674615729637229E-9, +1.57746505810079893253E-9, -4.49697115294871911476E-10, +9.63210042443717269402E-11, -1.16300711402336909847E-11, -1.31070037808191623761E-12, +1.16993345829435057496E-12, -3.40636420312606285351E-13, +5.23724821541706939045E-14, +3.93541148139975862961E-16, -2.59886413069218394637E-15, +7.24729556829529838503E-16, -8.51485747763574768020E-17, -7.86503719948806184368E-18, +5.35986191777031053618E-18, -9.84873767617830925356E-19, +2.93759678710573738811E-20, +2.85458592629073152182E-20, -7.12725445137377009753E-21, +5.25419393758902871947E-22, +1.24299023131490990316E-22, -4.04419210566489645405E-23 }, - { -1.27981254388583500631E-12, +9.1347204083645933588E-12, -3.19715214292760767584E-11, +7.30777632669167468738E-11, -1.22557498812224960902E-10, +1.60618833847077433236E-10, -1.71047639646627010648E-10, +1.51926349902927316213E-10, -1.14609023345779936276E-10, +7.43697341394886835864E-11, -4.18713451557949730558E-11, +2.05606050331840905587E-11, -8.82161466664564577599E-12, +3.30031395277698236679E-12, -1.06851205331295409813E-12, +2.94333808755089195146E-13, -6.64411715537625335642E-14, +1.11264855981436243262E-14, -8.52918435682649455145E-16, -2.38837813662069487819E-16, +1.23994634366691956599E-16, -3.05269770279941723219E-17, +4.34539596489459676621E-18, -5.55819387468189608390E-20, -1.56974672263484202926E-19, +4.60835492190702561464E-20, -6.61112150617493330405E-21, +7.28424268476803924831E-23, +2.09156005934313228089E-22, -5.29080328670107625978E-23, +5.61375000671507211726E-24, +3.82199410465700894394E-25 }, - { -6.22096057427178413283E-16, +5.05227108353689229741E-15, -2.02090843341475691883E-14, +5.30488463771373691202E-14, -1.02729512031916810045E-13, +1.56409892294496290711E-13, -1.94849254788406146283E-13, +2.04064637342166989709E-13, -1.83187931471980616892E-13, +1.42994099344605424348E-13, -9.8111907789286062426E-14, +5.96545975367403288587E-14, -3.23370114040930933005E-14, +1.56932853967230342257E-14, -6.83548101324218922896E-15, +2.67410077774155118457E-15, -9.38313996431647887562E-16, +2.94090734842381109313E-16, -8.16448235152204729921E-17, +1.9758222496699617607E-17, -4.03590262164308783690E-18, +6.43662361965717426956E-19, -5.93446415094778572090E-20, -6.07164564350191039536E-21, +4.38906686886388095825E-21, -1.17175498170220204828E-21, +1.98482140750318604418E-22, -1.70803571702439545981E-23, -1.94600332107885234554E-24, +1.10477141319981582738E-24, -2.31975718243847439962E-25, +2.54148402104633283670E-26 }, - { -1.12858840595384064928E-19, +1.02797735716689148111E-18, -4.62589810725101166456E-18, +1.37063647622252197466E-17, -3.0068337697131575822E-17, +5.2067053140503053517E-17, -7.40914680178037035E-17, +8.9062000172830588611E-17, -9.22563786210983011008E-17, +8.35975730487397716492E-17, -6.70372487553237232779E-17, +4.80088566412770650047E-17, -3.09280630297969106245E-17, +1.8026496052333452774E-17, -9.54924880090907168481E-18, +4.61362333444861021959E-18, -2.03812361224098073479E-18, +8.24578860830779678155E-19, -3.0572087552697254564E-19, +1.03827313453936543577E-19, -3.22407758977306397999E-20, +9.12052549039695437376E-21, -2.33541947993595580264E-21, +5.35339963891271164659E-22, -1.07674173853083520575E-22, +1.82413373046113374293E-23, -2.33864726317468746329E-24, +1.29928813344150027051E-25, +3.86668349205203745336E-26, -1.63203452712600670685E-26, +3.65165372186699607411E-27, -5.51243539825332137371E-28 }, - { -7.61985302416052609616E-24, +7.69459862670641937159E-23, -3.84729931335320968601E-22, +1.26960877340655919637E-21, -3.10990027829384449637E-21, +6.02935924057670511377E-21, -9.6342786971886625897E-21, +1.30454744197246721374E-20, -1.52745988785284834672E-20, +1.57034665186695273938E-20, -1.43457243961336621961E-20, +1.17567385540485497556E-20, -8.7104848256363928121E-21, +5.87137214731944288587E-21, -3.61951956727412561213E-21, +2.04954715001535632502E-21, -1.06982832733527370879E-21, +5.1628428354196120786E-22, -2.30885865897937993512E-22, +9.58556229281154921137E-23, -3.69911125531027884646E-23, +1.32784897023484841369E-23, -4.43433027366044567275E-24, +1.37688611947822111040E-24, -3.96971995397574368025E-25, +1.06008163579031271153E-25, -2.61149430849477426613E-26, +5.89698164189548613154E-27, -1.20793190886658723050E-27, +2.20446342551066852143E-28, -3.46061447029252398335E-29, +4.28913922246949096952E-30 } -}; - -static const double tab3 [8] = { +1, -1, +3, -15, +105, -945, +10395, -135135.0 }; - - -/* - Calculated: oo - 1 | -x²/2 - gauss(z) = --------- | e dx - sqrt(2pi) | - z - - gauss ( 0) = 0.5 - gauss ( 1) ~ 0.1586 - gauss ( 2) ~ 0.02275 - gauss ( 4) ~ 3.17e-5 - gauss (10) ~ 7.62e-24 - gauss (oo) = 0 - - Note: only for z>0 -*/ -#include -#include - -#define M_1_SQRT2PI 0.398942280401432686 - -static long double gauss ( double x ) -{ - unsigned int i = (unsigned int)(x + 0.5); - double y = x * x; - - if ( i > 150 ) return 0.; - if ( i > 10 ) return M_1_SQRT2PI * exp (-0.5*y) / x * __poly (1./y, 7, tab3); - if ( i > 0 ) return -__poly ((x-i), 31, tab2 [i-1]); - return 0.5 - x * __poly (y, 9, tab1); - } - -double erf ( double x ) -{ - return x < 0. ? -0.5 + gauss(-x) : 0.5 - gauss(x); -} - -double erfc ( double x ) -{ - return x < 0. ? 1.0 - gauss(-x) : gauss(x); -} - diff -urN dietlibc-0.30/libm/float_wrappers.c dietlibc-0.30-libm/libm/float_wrappers.c --- dietlibc-0.30/libm/float_wrappers.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/float_wrappers.c 2006-06-25 11:20:09.000000000 +0000 @@ -0,0 +1,563 @@ +/* vi: set sw=4 ts=4: */ +/* + * Wrapper functions implementing all the float math functions + * defined by SuSv3 by actually calling the double version of + * each function and then casting the result back to a float + * to return to the user. + * + * Copyright (C) 2005 by Erik Andersen + * + * This program is free software; you can redistribute it and/or modify it + * under the terms of the GNU Library General Public License as published by + * the Free Software Foundation; either version 2 of the License, or (at your + * option) any later version. + * + * This program is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public License + * for more details. + * + * You should have received a copy of the GNU Library General Public License + * along with this program; if not, write to the Free Software Foundation, + * Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + */ + +#include "math.h" + +/* For the time being, do _NOT_ implement these functions + * that are defined by SuSv3 */ +#if 0 +float exp2f(float); +float fmaf(float, float, float); +float fmaxf(float, float); +float fminf(float, float); +float fdimf(float, float); +long long llrintf(float); +long long llroundf(float); +long lroundf(float); +float log2f(float); +long lrintf(float); +float nexttowardf(float, long double); +float remquof(float, float, int *); +float roundf(float); +float scalblnf(float, long); +float truncf(float); +float tgammaf(float); +#endif + +/* Implement the following, as defined by SuSv3 */ +#if 0 +float acosf(float); +float acoshf(float); +float asinf(float); +float asinhf(float); +float atan2f(float, float); +float atanf(float); +float atanhf(float); +float cbrtf(float); +float ceilf(float); +float copysignf(float, float); +float cosf(float); +float coshf(float); +float erfcf(float); +float erff(float); +float expf(float); +float expm1f(float); +float fabsf(float); +float floorf(float); +float fmodf(float, float); +float frexpf(float value, int *); +float hypotf(float, float); +int ilogbf(float); +float ldexpf(float, int); +float lgammaf(float); +float log10f(float); +float log1pf(float); +float logbf(float); +float logf(float); +float modff(float, float *); +float nearbyintf(float); +float nextafterf(float, float); +float powf(float, float); +float remainderf(float, float); +float rintf(float); +float scalbnf(float, int); +float sinf(float); +float sinhf(float); +float sqrtf(float); +float tanf(float); +float tanhf(float); +#endif + +#ifdef L_acosf +float acosf (float x) +{ + return (float) acos( (double)x ); +} +#endif + + +#ifdef L_acoshf +float acoshf (float x) +{ + return (float) acosh( (double)x ); +} +#endif + + +#ifdef L_asinf +float asinf (float x) +{ + return (float) asin( (double)x ); +} +#endif + + +#ifdef L_asinhf +float asinhf (float x) +{ + return (float) asinh( (double)x ); +} +#endif + + +#ifdef L_atan2f +float atan2f (float x, float y) +{ + return (float) atan2( (double)x, (double)y ); +} +#endif + + +#ifdef L_atanf +float atanf (float x) +{ + return (float) atan( (double)x ); +} +#endif + + +#ifdef L_atanhf +float atanhf (float x) +{ + return (float) atanh( (double)x ); +} +#endif + + +#ifdef L_cbrtf +float cbrtf (float x) +{ + return (float) cbrt( (double)x ); +} +#endif + + +#ifdef L_ceilf +float ceilf (float x) +{ + return (float) ceil( (double)x ); +} +#endif + + +#ifdef L_copysignf +float copysignf (float x, float y) +{ + return (float) copysign( (double)x, (double)y ); +} +#endif + + +#ifdef L_cosf +float cosf (float x) +{ + return (float) cos( (double)x ); +} +#endif + + +#ifdef L_coshf +float coshf (float x) +{ + return (float) cosh( (double)x ); +} +#endif + + +#ifdef L_erfcf +float erfcf (float x) +{ + return (float) erfc( (double)x ); +} +#endif + + +#ifdef L_erff +float erff (float x) +{ + return (float) erf( (double)x ); +} +#endif + + +#if 0 +#ifdef L_exp2f +float exp2f (float x) +{ + return (float) exp2( (double)x ); +} +#endif +#endif + + +#ifdef L_expf +float expf (float x) +{ + return (float) exp( (double)x ); +} +#endif + + +#ifdef L_expm1f +float expm1f (float x) +{ + return (float) expm1( (double)x ); +} +#endif + + +#ifdef L_fabsf +float fabsf (float x) +{ + return (float) fabs( (double)x ); +} +#endif + + +#if 0 +#ifdef L_fdimf +float fdimf (float x, float y) +{ + return (float) fdim( (double)x, (double)y ); +} +#endif +#endif + + +#ifdef L_floorf +float floorf (float x) +{ + return (float) floor( (double)x ); +} +#endif + + +#if 0 +#ifdef L_fmaf +float fmaf (float x, float y, float z) +{ + return (float) fma( (double)x, (double)y, (double)z ); +} +#endif + + +#ifdef L_fmaxf +float fmaxf (float x, float y) +{ + return (float) fmax( (double)x, (double)y ); +} +#endif + + +#ifdef L_fminf +float fminf (float x, float y) +{ + return (float) fmin( (double)x, (double)y ); +} +#endif +#endif + + +#ifdef L_fmodf +float fmodf (float x, float y) +{ + return (float) fmod( (double)x, (double)y ); +} +#endif + + +#ifdef L_frexpf +float frexpf (float x, int *exp) +{ + return (float) frexp( (double)x, exp ); +} +#endif + + +#ifdef L_hypotf +float hypotf (float x, float y) +{ + return (float) hypot( (double)x, (double)y ); +} +#endif + + +#ifdef L_ilogbf +int ilogbf (float x) +{ + return (float) ilogb( (double)x ); +} +#endif + + +#ifdef L_ldexpf +float ldexpf (float x, int exp) +{ + return (float) ldexp( (double)x, exp ); +} +#endif + + +#ifdef L_lgammaf +float lgammaf (float x) +{ + return (float) lgamma( (double)x ); +} +#endif + + +#if 0 +#ifdef L_llrintf +long long llrintf (float x) +{ + return (float) llrint( (double)x ); +} +#endif + + +#ifdef L_llroundf +long long llroundf (float x) +{ + return (float) llround( (double)x ); +} +#endif +#endif + +#ifdef L_log10f +float log10f (float x) +{ + return (float) log10( (double)x ); +} +#endif + + +#ifdef L_log1pf +float log1pf (float x) +{ + return (float) log1p( (double)x ); +} +#endif + + +#if 0 +#ifdef L_log2f +float log2f (float x) +{ + return (float) log2( (double)x ); +} +#endif +#endif + + +#ifdef L_logbf +float logbf (float x) +{ + return (float) logb( (double)x ); +} +#endif + + +#ifdef L_logf +float logf (float x) +{ + return (float) log( (double)x ); +} +#endif + + +#if 0 +#ifdef L_lrintf +long lrintf (float x) +{ + return (float) lrint( (double)x ); +} +#endif + + +#ifdef L_lroundf +long lroundf (float x) +{ + return (float) lround( (double)x ); +} +#endif +#endif + + +#ifdef L_modff +float modff (float x, float *iptr) +{ + double y, result; + result = modf ( x, &y ); + *iptr = (float)y; + return (float) result; + +} +#endif + + +#if 0 +#ifdef L_nearbyintf +float nearbyintf (float x) +{ + return (float) nearbyint( (double)x ); +} +#endif +#endif + + +#ifdef L_nextafterf +float nextafterf (float x, float y) +{ + return (float) nextafter( (double)x, (double)y ); +} +#endif + + +#if 0 +#ifdef L_nexttowardf +float nexttowardf (float x, long double y) +{ + return (float) nexttoward( (double)x, (double)y ); +} +#endif +#endif + +#ifdef L_powf +float powf (float x, float y) +{ + return (float) pow( (double)x, (double)y ); +} +#endif + + +#ifdef L_remainderf +float remainderf (float x, float y) +{ + return (float) remainder( (double)x, (double)y ); +} +#endif + + +#if 0 +#ifdef L_remquof +float remquof (float x, float y, int *quo) +{ + return (float) remquo( (double)x, (double)y, quo ); +} +#endif +#endif + + +#ifdef L_rintf +float rintf (float x) +{ + return (float) rint( (double)x ); +} +#endif + + +#if 0 +#ifdef L_roundf +float roundf (float x) +{ + return (float) round( (double)x ); +} +#endif + + +#ifdef L_scalblnf +float scalblnf (float x, long exp) +{ + return (float) scalbln( (double)x, exp ); +} +#endif +#endif + + +#ifdef L_scalbnf +float scalbnf (float x, int exp) +{ + return (float) scalbn( (double)x, exp ); +} +#endif + + +#ifdef L_sinf +float sinf (float x) +{ + return (float) sin( (double)x ); +} +#endif + + +#ifdef L_sinhf +float sinhf (float x) +{ + return (float) sinh( (double)x ); +} +#endif + + +#ifdef L_sqrtf +float sqrtf (float x) +{ + return (float) sqrt( (double)x ); +} +#endif + + +#ifdef L_tanf +float tanf (float x) +{ + return (float) tan( (double)x ); +} +#endif + + +#ifdef L_tanhf +float tanhf (float x) +{ + return (float) tanh( (double)x ); +} +#endif + + +#if 0 +#ifdef L_tgammaf +float tgammaf (float x) +{ + return (float) tgamma( (double)x ); +} +#endif + + +#ifdef L_truncf +float truncf (float x) +{ + return (float) trunc( (double)x ); +} +#endif +#endif + + diff -urN dietlibc-0.30/libm/fp_private.h dietlibc-0.30-libm/libm/fp_private.h --- dietlibc-0.30/libm/fp_private.h 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/fp_private.h 2006-06-25 11:20:24.000000000 +0000 @@ -0,0 +1,89 @@ +/******************************************************************************* +* * +* File fp_private.h, * +* All pack 4 dependencies for the MathLib elems plus some defines used * +* throughout MathLib. * +* * +* Copyright © 1991 Apple Computer, Inc. All rights reserved. * +* * +* Written by Ali Sazegari, started on October 1991, * +* * +* W A R N I N G: This routine expects a 64 bit double model. * +* * +*******************************************************************************/ + +#define NoException 0 + +/******************************************************************************* +* Values of constants. * +*******************************************************************************/ + +//#define SgnMask 0x8000 +#define dSgnMask 0x80000000 +#define sSgnMask 0x7FFFFFFF + +//#define ExpMask 0x7FFF +#define dExpMask 0x7FF00000 +#define sExpMask 0xFF000000 + + /* according to rounding BIG & SMALL are: */ +#define BIG 1.1e+300 /* used to deliver ±° or largest number, */ +#define SMALL 1.1e-300 /* used to deliver ±0 or smallest number. */ +#define InfExp 0x7FF +#define dMaxExp 0x7FF00000 + +#define MaxExpP1 1024 +#define MaxExp 1023 + +#define DenormLimit -52 + +//#define ManMask 0x80000000 +#define dManMask 0x00080000 + +//#define IsItDenorm 0x80000000 +#define dIsItDenorm 0x00080000 + +//#define xIsItSNaN 0x40000000 +#define dIsItSNaN 0x00080000 + +#define dHighMan 0x000FFFFF +#define dFirstBitSet 0x00080000 +#define BIAS 0x3FF + +//#define GetSign 0x8000 +#define dGetSign 0x80000000 +#define sGetSign 0x80000000 + +//#define Infinity(x) ( x.hex.exponent & ExpMask ) == ExpMask +#define dInfinity(x) ( x.hex.high & dExpMask ) == dExpMask +#define sInfinity(x) ( ( x.hexsgl << 1 ) & sExpMask ) == sExpMask + +//#define Exponent(x) x.hex.exponent & ExpMask +#define dExponent(x) x.hex.high & dExpMask +#define sExponent(x) ( ( x.hexsgl << 1 ) & sExpMask ) + +#define sZero(x) ( x.hexsgl & sSgnMask ) == 0 +//#define Sign(x) ( x.hex.exponent & SgnMask ) == SgnMask + +/******************************************************************************* +* Types used in the auxiliary functions. * +*******************************************************************************/ + +#include + +typedef struct /* Hex representation of a double. */ + { +#if defined(__BIG_ENDIAN__) + uint32_t high; + uint32_t low; +#else + uint32_t low; + uint32_t high; +#endif + } dHexParts; + +typedef union + { + unsigned char byties[8]; + double dbl; + } DblInHex; diff -urN dietlibc-0.30/libm/fpmacros.c dietlibc-0.30-libm/libm/fpmacros.c --- dietlibc-0.30/libm/fpmacros.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/fpmacros.c 2006-06-25 11:20:12.000000000 +0000 @@ -0,0 +1,291 @@ +/*********************************************************************** +** File: fpmacros.c +** +** Contains: C source code for implementations of floating-point +** functions which involve float format numbers, as +** defined in header . In particular, this file +** contains implementations of functions +** __fpclassify(d,f), __isnormal(d,f), __isfinite(d,f), +** __isnan(d,f), and __signbit(d,f). This file targets +** PowerPC platforms. +** +** Written by: Robert A. Murley, Ali Sazegari +** +** Copyright: c 2001 by Apple Computer, Inc., all rights reserved +** +** Change History (most recent first): +** +** 07 Jul 01 ram First created from fpfloatfunc.c, fp.c, +** classify.c and sign.c in MathLib v3 Mac OS9. +** +***********************************************************************/ + +#include +#define _GNU_SOURCE +#include +#include +#include "math_private.h" +#include "fp_private.h" + +#define SIGN_MASK 0x80000000 +#define NSIGN_MASK 0x7fffffff +#define FEXP_MASK 0x7f800000 +#define FFRAC_MASK 0x007fffff + +/*********************************************************************** + int __fpclassifyf(float x) returns the classification code of the + argument x, as defined in . + + Exceptions: INVALID signaled if x is a signaling NaN; in this case, + the FP_QNAN code is returned. + + Calls: none +***********************************************************************/ + +int __fpclassifyf ( float x ) +{ + unsigned int iexp; + + union { + u_int32_t lval; + float fval; + } z; + + z.fval = x; + iexp = z.lval & FEXP_MASK; /* isolate float exponent */ + + if (iexp == FEXP_MASK) { /* NaN or INF case */ + if ((z.lval & 0x007fffff) == 0) + return FP_INFINITE; + return FP_NAN; + } + + if (iexp != 0) /* normal float */ + return FP_NORMAL; + + if (x == 0.0) + return FP_ZERO; /* zero */ + else + return FP_SUBNORMAL; /* must be subnormal */ +} + + +/*********************************************************************** + Function __fpclassify, + Implementation of classify of a double number for the PowerPC. + + Exceptions: INVALID signaled if x is a signaling NaN; in this case, + the FP_QNAN code is returned. + + Calls: none +***********************************************************************/ + +int __fpclassify ( double arg ) +{ + register unsigned int exponent; + union + { + dHexParts hex; + double dbl; + } x; + + x.dbl = arg; + + exponent = x.hex.high & dExpMask; + if ( exponent == dExpMask ) + { + if ( ( ( x.hex.high & dHighMan ) | x.hex.low ) == 0 ) + return FP_INFINITE; + else + return FP_NAN; + } + else if ( exponent != 0) + return FP_NORMAL; + else { + if ( arg == 0.0 ) + return FP_ZERO; + else + return FP_SUBNORMAL; + } +} + + +/*********************************************************************** + int __isnormalf(float x) returns nonzero if and only if x is a + normalized float number and zero otherwise. + + Exceptions: INVALID is raised if x is a signaling NaN; in this case, + zero is returned. + + Calls: none +***********************************************************************/ + +int __isnormalf ( float x ) +{ + unsigned int iexp; + union { + u_int32_t lval; + float fval; + } z; + + z.fval = x; + iexp = z.lval & FEXP_MASK; /* isolate float exponent */ + return ((iexp != FEXP_MASK) && (iexp != 0)); +} + + +int __isnormal ( double x ) +{ + return ( __fpclassify ( x ) == FP_NORMAL ); +} + + +/*********************************************************************** + int __isfinitef(float x) returns nonzero if and only if x is a + finite (normal, subnormal, or zero) float number and zero otherwise. + + Exceptions: INVALID is raised if x is a signaling NaN; in this case, + zero is returned. + + Calls: none +***********************************************************************/ + +int __finitef ( float x ) +{ + union { + u_int32_t lval; + float fval; + } z; + + z.fval = x; + return ((z.lval & FEXP_MASK) != FEXP_MASK); +} +weak_alias (__finitef, finitef) + +int __finite ( double x ) +{ + return ( __fpclassify ( x ) >= FP_ZERO ); +} +weak_alias (__finite, finite) + + +/*********************************************************************** + int __signbitf(float x) returns nonzero if and only if the sign + bit of x is set and zero otherwise. + + Exceptions: INVALID is raised if x is a signaling NaN. + + Calls: none +***********************************************************************/ + +int __signbitf ( float x ) +{ + union { + u_int32_t lval; + float fval; + } z; + + z.fval = x; + return ((z.lval & SIGN_MASK) != 0); +} + + +/*********************************************************************** + Function sign of a double. + Implementation of sign bit for the PowerPC. + + Calls: none +***********************************************************************/ + +int __signbit ( double arg ) +{ + union + { + dHexParts hex; + double dbl; + } x; + int sign; + + x.dbl = arg; + sign = ( ( x.hex.high & dSgnMask ) == dSgnMask ) ? 1 : 0; + return sign; +} + + +/*********************************************************************** +* int __isinff(float x) returns -1 if value represents negative +* infinity, 1 if value represents positive infinity, +* and 0 otherwise. +* +* Calls: __signbit +* +***********************************************************************/ +int __isinff ( float x ) +{ + int class = __fpclassifyf(x); + if ( class == FP_INFINITE ) { + return ( (__signbitf(x)) ? -1 : 1); + } + return 0; +} +weak_alias (__isinff, isinff) + +int __isinf ( double x ) +{ + int class = __fpclassify(x); + if ( class == FP_INFINITE ) { + return ( (__signbit(x)) ? -1 : 1); + } + return 0; +} +weak_alias (__isinf, isinf) + +#if 0 +int __isinfl ( long double x ) +{ + int class = __fpclassify(x); + if ( class == FP_INFINITE ) { + return ( (__signbit(x)) ? -1 : 1); + } + return 0; +} +weak_alias (__isinfl, isinfl); +#endif + +/*********************************************************************** + int __isnanf(float x) returns nonzero if and only if x is a + NaN and zero otherwise. + + Exceptions: INVALID is raised if x is a signaling NaN; in this case, + nonzero is returned. + + Calls: none +***********************************************************************/ + +int __isnanf ( float x ) +{ + union { + u_int32_t lval; + float fval; + } z; + + z.fval = x; + return (((z.lval&FEXP_MASK) == FEXP_MASK) && ((z.lval&FFRAC_MASK) != 0)); +} +weak_alias (__isnanf, isnanf); + +int __isnan ( double x ) +{ + int class = __fpclassify(x); + return ( class == FP_NAN ); +} +weak_alias (__isnan, isnan); + +#if 0 +int __isnanl ( long double x ) +{ + int class = __fpclassify(x); + return ( class == FP_NAN ); +} +weak_alias (__isnanl, isnanl); +#endif + diff -urN dietlibc-0.30/libm/gamma.c dietlibc-0.30-libm/libm/gamma.c --- dietlibc-0.30/libm/gamma.c 2005-03-15 08:51:23.000000000 +0000 +++ dietlibc-0.30-libm/libm/gamma.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,115 +0,0 @@ -#include "dietlibm.h" - -/*--------------------------------------------------------------------------* - -Name gamma, lgamma - gamma function - -Usage double gamma (double x); - double lgamma(double x); - extern int signgam; - -Prototype in math.h - -Description gamma returns the logarithm of the absolute value of the - gamma function. So it is possible â(x) for very large x. - The sign is stored in signgam, a extern variable - overwritten during every call to gamma(). lgamma() is - a synonym for gamma(). - You can calculate â(x) by the following sequence: - - double gammafunction(double x) - { double y=exp(gamma(x)); - - return signgam ? -y : +y; - } - -Return value gamma returns a value in range (-0.1208, +oo). For a input - value of zero, it returns +oo and errno is set to: - - ERANGE Result out of range - -*---------------------------------------------------------------------------*/ - -#include -#include - -#if defined(__powerpc__) -/* workaround http://gcc.gnu.org/bugzilla/show_bug.cgi?id=26374 */ -#define B0 + 1.0/ 6/ 1/ 2 -#define B1 - 1.0/ 30/ 3/ 4 -#define B2 + 1.0/ 42/ 5/ 6 -#define B3 - 1.0/ 30/ 7/ 8 -#define B4 + 5.0/ 66/ 9/10 -#define B5 - 691.0/2730/11/12 -#define B6 + 7.0/ 6/13/14 -#define B7 - 3617.0/ 510/15/16 -#define B8 + 43867.0/ 798/17/18 -#define B9 - 174611.0/ 330/19/20 -#define B10 + 854513.0/ 138/21/22 -#define B11 - 236364091.0/2730/23/24 -#define B12 + 8553103.0/ 6/25/26 -#else -#define B0 + 1.0l/ 6/ 1/ 2 -#define B1 - 1.0l/ 30/ 3/ 4 -#define B2 + 1.0l/ 42/ 5/ 6 -#define B3 - 1.0l/ 30/ 7/ 8 -#define B4 + 5.0l/ 66/ 9/10 -#define B5 - 691.0l/2730/11/12 -#define B6 + 7.0l/ 6/13/14 -#define B7 - 3617.0l/ 510/15/16 -#define B8 + 43867.0l/ 798/17/18 -#define B9 - 174611.0l/ 330/19/20 -#define B10 + 854513.0l/ 138/21/22 -#define B11 - 236364091.0l/2730/23/24 -#define B12 + 8553103.0l/ 6/25/26 -#endif - -static const double coeff[] = { B0, B1, B2, B3, B4, B5, B6, B7, B8, B9, B10 }; -int signgam; - -#define EXPL(x) (((short *)(void *)&x)[4] & 0x7FFF) - -static double logfact ( long double x ) -{ - long double z = 2. * M_PI * x; - register int e = EXPL (x); - - static unsigned char list [] = { 6, 4, 3, 3, 2, 2 }; - - return (log(x) - 1) * x + 0.5*log(z) + __poly (1./(x*x), e<0x4003 ? 10 : (e>0x4008 ? 1 : list [e-0x4003] ), coeff) / x; -} - - -double lgamma ( double x ) -{ - register int k = floor (x); - long double w; - long double y; - long double z; - - signgam = 0; - - if ( k >= 7 ) - return logfact (x-1); - - if ( k == x ) - switch (k) { - case 1 : - case 2 : return 0.000000000000000000000000000l; - case 3 : return 0.693147180559945309432805516l; - case 4 : return 1.791759469228055000858148560l; - case 5 : return 3.178053830347945619723759592l; - case 6 : return 4.787491742782045994244981560l; - default: return 1./0.; /* ignore the gcc warning, this is intentional */ - } - - z = logfact (y = x - k + 7.0 - 1); - w = 1; - for ( k = 7 - k; k--; ) - w *= y, y -= 1.; - - signgam = k >= 0 ? 0 : k & 1; - return z - log (w); -} - -double gamma ( double val ) __attribute__ ((weak,alias("lgamma"))); diff -urN dietlibc-0.30/libm/ipow.c dietlibc-0.30-libm/libm/ipow.c --- dietlibc-0.30/libm/ipow.c 2002-03-04 18:25:54.000000000 +0000 +++ dietlibc-0.30-libm/libm/ipow.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,29 +0,0 @@ -#define _GNU_SOURCE -#include -/* - * This is not standard, but often you only need such this function - * which is much shorter than the generic pow() function. - * - * double ipow ( double mant, int expo ); - */ - -double ipow ( double mant, int expo ) -{ - double ret = 1.; - unsigned int e = expo; /* Some attention is necessary for expo = 2^31 */ - - if ( (int)e < 0 ) { - e = -e; - mant = 1./mant; - } - - while (1) { - if ( e & 1 ) - ret *= mant; - if ( (e >>= 1) == 0 ) - break; - mant *= mant; - } - - return ret; -} diff -urN dietlibc-0.30/libm/k_cos.c dietlibc-0.30-libm/libm/k_cos.c --- dietlibc-0.30/libm/k_cos.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/k_cos.c 2006-06-25 11:20:24.000000000 +0000 @@ -0,0 +1,96 @@ +/* @(#)k_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; +#endif + +/* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm + * 1. Since cos(-x) = cos(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. + * 3. cos(x) is approximated by a polynomial of degree 14 on + * [0,pi/4] + * 4 14 + * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x + * where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 + * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 + * | | + * + * 4 6 8 10 12 14 + * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then + * cos(x) = 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y + * ~ cos(x) - x*y, + * a correction term is necessary in cos(x) and hence + * cos(x+y) = 1 - (x*x/2 - (r - x*y)) + * For better accuracy when x > 0.3, let qx = |x|/4 with + * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. + * Then + * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). + * Note that 1-qx and (x*x/2-qx) is EXACT here, and the + * magnitude of the latter is at least a quarter of x*x/2, + * thus, reducing the rounding error in the subtraction. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ +C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ +C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ +C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ +C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ + +#ifdef __STDC__ + double __kernel_cos(double x, double y) +#else + double __kernel_cos(x, y) + double x,y; +#endif +{ + double a,hz,z,r,qx; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x3e400000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3FD33333) /* if |x| < 0.3 */ + return one - (0.5*z - (z*r - x*y)); + else { + if(ix > 0x3fe90000) { /* x > 0.78125 */ + qx = 0.28125; + } else { + INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ + } + hz = 0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff -urN dietlibc-0.30/libm/k_rem_pio2.c dietlibc-0.30-libm/libm/k_rem_pio2.c --- dietlibc-0.30/libm/k_rem_pio2.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/k_rem_pio2.c 2006-06-25 11:20:07.000000000 +0000 @@ -0,0 +1,320 @@ +/* @(#)k_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $"; +#endif + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + * double x[],y[]; int e0,nx,prec; int ipio2[]; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] ouput result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precison, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0] + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * ipio2[] + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The recommended value is 2,3,4, + * 6 for single, double, extended,and quad. + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ +#else +static int init_jk[] = {2,3,4,6}; +#endif + +#ifdef __STDC__ +static const double PIo2[] = { +#else +static double PIo2[] = { +#endif + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ +}; + +#ifdef __STDC__ +static const double +#else +static double +#endif +zero = 0.0, +one = 1.0, +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ + +#ifdef __STDC__ + int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2) +#else + int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + double x[], y[]; int e0,nx,prec; int32_t ipio2[]; +#endif +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + double z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/24; if(jv<0) jv=0; + q0 = e0-24*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (double)((int32_t)(twon24* z)); + iq[i] = (int32_t)(z-two24*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbn(z,q0); /* actual value of z */ + z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (double)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(24-q0)); n += i; + iq[jz-1] -= i<<(24-q0); + ih = iq[jz-1]>>(23-q0); + } + else if(q0==0) ih = iq[jz-1]>>23; + else if(z>=0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7fffff; break; + case 2: + iq[jz-1] &= 0x3fffff; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbn(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (double) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==0.0) { + jz -= 1; q0 -= 24; + while(iq[jz]==0) { jz--; q0-=24;} + } else { /* break z into 24-bit if necessary */ + z = scalbn(z,-q0); + if(z>=two24) { + fw = (double)((int32_t)(twon24*z)); + iq[jz] = (int32_t)(z-two24*fw); + jz += 1; q0 += 24; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbn(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(double)iq[i]; fw*=twon24; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff -urN dietlibc-0.30/libm/k_sin.c dietlibc-0.30-libm/libm/k_sin.c --- dietlibc-0.30/libm/k_sin.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/k_sin.c 2006-06-25 11:20:25.000000000 +0000 @@ -0,0 +1,79 @@ +/* @(#)k_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $"; +#endif + +/* __kernel_sin( x, y, iy) + * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ +S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ +S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ +S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ +S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ +S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ + +#ifdef __STDC__ + double __kernel_sin(double x, double y, int iy) +#else + double __kernel_sin(x, y, iy) + double x,y; int iy; /* iy=0 if y is zero */ +#endif +{ + double z,r,v; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x3e400000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff -urN dietlibc-0.30/libm/k_standard.c dietlibc-0.30-libm/libm/k_standard.c --- dietlibc-0.30/libm/k_standard.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/k_standard.c 2006-06-25 11:20:23.000000000 +0000 @@ -0,0 +1,782 @@ +/* @(#)k_standard.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_standard.c,v 1.6 1995/05/10 20:46:35 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" +#include + +#ifndef _USE_WRITE +#include /* fputs(), stderr */ +#define WRITE2(u,v) fputs(u, stderr) +#else /* !defined(_USE_WRITE) */ +#include /* write */ +#define WRITE2(u,v) write(2, u, v) +#undef fflush +#endif /* !defined(_USE_WRITE) */ + +#ifdef __STDC__ +static const double zero = 0.0; /* used as const */ +#else +static double zero = 0.0; /* used as const */ +#endif + +/* + * Standard conformance (non-IEEE) on exception cases. + * Mapping: + * 1 -- acos(|x|>1) + * 2 -- asin(|x|>1) + * 3 -- atan2(+-0,+-0) + * 4 -- hypot overflow + * 5 -- cosh overflow + * 6 -- exp overflow + * 7 -- exp underflow + * 8 -- y0(0) + * 9 -- y0(-ve) + * 10-- y1(0) + * 11-- y1(-ve) + * 12-- yn(0) + * 13-- yn(-ve) + * 14-- lgamma(finite) overflow + * 15-- lgamma(-integer) + * 16-- log(0) + * 17-- log(x<0) + * 18-- log10(0) + * 19-- log10(x<0) + * 20-- pow(0.0,0.0) + * 21-- pow(x,y) overflow + * 22-- pow(x,y) underflow + * 23-- pow(0,negative) + * 24-- pow(neg,non-integral) + * 25-- sinh(finite) overflow + * 26-- sqrt(negative) + * 27-- fmod(x,0) + * 28-- remainder(x,0) + * 29-- acosh(x<1) + * 30-- atanh(|x|>1) + * 31-- atanh(|x|=1) + * 32-- scalb overflow + * 33-- scalb underflow + * 34-- j0(|x|>X_TLOSS) + * 35-- y0(x>X_TLOSS) + * 36-- j1(|x|>X_TLOSS) + * 37-- y1(x>X_TLOSS) + * 38-- jn(|x|>X_TLOSS, n) + * 39-- yn(x>X_TLOSS, n) + * 40-- gamma(finite) overflow + * 41-- gamma(-integer) + * 42-- pow(NaN,0.0) + */ + + +#ifdef __STDC__ + double __kernel_standard(double x, double y, int type) +#else + double __kernel_standard(x,y,type) + double x,y; int type; +#endif +{ + struct exception exc; +#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + +#ifdef _USE_WRITE + (void) fflush(stdout); +#endif + exc.arg1 = x; + exc.arg2 = y; + switch(type) { + case 1: + case 101: + /* acos(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "acos" : "acosf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("acos: DOMAIN error\n", 19); + } + errno = EDOM; + } + break; + case 2: + case 102: + /* asin(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "asin" : "asinf"; + exc.retval = zero; + if(_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("asin: DOMAIN error\n", 19); + } + errno = EDOM; + } + break; + case 3: + case 103: + /* atan2(+-0,+-0) */ + exc.arg1 = y; + exc.arg2 = x; + exc.type = DOMAIN; + exc.name = type < 100 ? "atan2" : "atan2f"; + exc.retval = zero; + if(_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("atan2: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 4: + case 104: + /* hypot(finite,finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "hypot" : "hypotf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 5: + case 105: + /* cosh(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "cosh" : "coshf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 6: + case 106: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "exp" : "expf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 7: + case 107: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "exp" : "expf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 8: + case 108: + /* y0(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "y0" : "y0f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 9: + case 109: + /* y0(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "y0" : "y0f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 10: + case 110: + /* y1(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "y1" : "y1f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 11: + case 111: + /* y1(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "y1" : "y1f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 12: + case 112: + /* yn(n,0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "yn" : "ynf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 13: + case 113: + /* yn(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "yn" : "ynf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 14: + case 114: + /* lgamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "lgamma" : "lgammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 15: + case 115: + /* lgamma(-integer) or lgamma(0) */ + exc.type = SING; + exc.name = type < 100 ? "lgamma" : "lgammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("lgamma: SING error\n", 19); + } + errno = EDOM; + } + break; + case 16: + case 116: + /* log(0) */ + exc.type = SING; + exc.name = type < 100 ? "log" : "logf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: SING error\n", 16); + } + errno = EDOM; + } + break; + case 17: + case 117: + /* log(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "log" : "logf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: DOMAIN error\n", 18); + } + errno = EDOM; + } + break; + case 18: + case 118: + /* log10(0) */ + exc.type = SING; + exc.name = type < 100 ? "log10" : "log10f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: SING error\n", 18); + } + errno = EDOM; + } + break; + case 19: + case 119: + /* log10(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "log10" : "log10f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 20: + case 120: + /* pow(0.0,0.0) */ + /* error only if _LIB_VERSION == _SVID_ */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : "powf"; + exc.retval = zero; + if (_LIB_VERSION != _SVID_) exc.retval = 1.0; + else if (!matherr(&exc)) { + (void) WRITE2("pow(0,0): DOMAIN error\n", 23); + errno = EDOM; + } + break; + case 21: + case 121: + /* pow(x,y) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "pow" : "powf"; + if (_LIB_VERSION == _SVID_) { + exc.retval = HUGE; + y *= 0.5; + if(xzero) ? HUGE : -HUGE); + else + exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 26: + case 126: + /* sqrt(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "sqrt" : "sqrtf"; + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("sqrt: DOMAIN error\n", 19); + } + errno = EDOM; + } + break; + case 27: + case 127: + /* fmod(x,0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "fmod" : "fmodf"; + if (_LIB_VERSION == _SVID_) + exc.retval = x; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("fmod: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 28: + case 128: + /* remainder(x,0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "remainder" : "remainderf"; + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("remainder: DOMAIN error\n", 24); + } + errno = EDOM; + } + break; + case 29: + case 129: + /* acosh(x<1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "acosh" : "acoshf"; + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("acosh: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 30: + case 130: + /* atanh(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "atanh" : "atanhf"; + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 31: + case 131: + /* atanh(|x|=1) */ + exc.type = SING; + exc.name = type < 100 ? "atanh" : "atanhf"; + exc.retval = x/zero; /* sign(x)*inf */ + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: SING error\n", 18); + } + errno = EDOM; + } + break; + case 32: + case 132: + /* scalb overflow; SVID also returns +-HUGE_VAL */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "scalb" : "scalbf"; + exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 33: + case 133: + /* scalb underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "scalb" : "scalbf"; + exc.retval = copysign(zero,x); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 34: + case 134: + /* j0(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "j0" : "j0f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 35: + case 135: + /* y0(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "y0" : "y0f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 36: + case 136: + /* j1(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "j1" : "j1f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 37: + case 137: + /* y1(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "y1" : "y1f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 38: + case 138: + /* jn(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "jn" : "jnf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 39: + case 139: + /* yn(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "yn" : "ynf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 40: + case 140: + /* gamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "gamma" : "gammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 41: + case 141: + /* gamma(-integer) or gamma(0) */ + exc.type = SING; + exc.name = type < 100 ? "gamma" : "gammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("gamma: SING error\n", 18); + } + errno = EDOM; + } + break; + case 42: + case 142: + /* pow(NaN,0.0) */ + /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : "powf"; + exc.retval = x; + if (_LIB_VERSION == _IEEE_ || + _LIB_VERSION == _POSIX_) exc.retval = 1.0; + else if (!matherr(&exc)) { + errno = EDOM; + } + break; + } + return exc.retval; +} diff -urN dietlibc-0.30/libm/k_tan.c dietlibc-0.30-libm/libm/k_tan.c --- dietlibc-0.30/libm/k_tan.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/k_tan.c 2006-06-25 11:20:25.000000000 +0000 @@ -0,0 +1,131 @@ +/* @(#)k_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: k_tan.c,v 1.8 1995/05/10 20:46:37 jtc Exp $"; +#endif + +/* __kernel_tan( x, y, k ) + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k=1) or + * -1/tan (if k= -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. + * 3. tan(x) is approximated by a odd polynomial of degree 27 on + * [0,0.67434] + * 3 27 + * tan(x) ~ x + T1*x + ... + T13*x + * where + * + * |tan(x) 2 4 26 | -59.2 + * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 + * | x | + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * 3 2 2 2 2 + * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) + * then + * 3 2 + * tan(x+y) = x + (T1*x + (x *(r+y)+y)) + * + * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include "math.h" +#include "math_private.h" +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ +pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */ +T[] = { + 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */ + 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */ + 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */ + 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */ + 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */ + 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */ + 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */ + 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */ + 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */ + 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */ + 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */ + -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */ + 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */ +}; + +#ifdef __STDC__ + double __kernel_tan(double x, double y, int iy) +#else + double __kernel_tan(x, y, iy) + double x,y; int iy; +#endif +{ + double z,r,v,w,s; + int32_t ix,hx; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; /* high word of |x| */ + if(ix<0x3e300000) /* x < 2**-28 */ + {if((int)x==0) { /* generate inexact */ + u_int32_t low; + GET_LOW_WORD(low,x); + if(((ix|low)|(iy+1))==0) return one/fabs(x); + else return (iy==1)? x: -one/x; + } + } + if(ix>=0x3FE59428) { /* |x|>=0.6744 */ + if(hx<0) {x = -x; y = -y;} + z = pio4-x; + w = pio4lo-y; + x = z+w; y = 0.0; + } + z = x*x; + w = z*z; + /* Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); + v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); + s = z*x; + r = y + z*(s*(r+v)+y); + r += T[0]*s; + w = x+r; + if(ix>=0x3FE59428) { + v = (double)iy; + return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); + } + if(iy==1) return w; + else { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + double a,t; + z = w; + SET_LOW_WORD(z,0); + v = r-(z - x); /* z+v = r+x */ + t = a = -1.0/w; /* a = -1.0/w */ + SET_LOW_WORD(t,0); + s = 1.0+t*z; + return t+a*(s+t*v); + } +} diff -urN dietlibc-0.30/libm/math_private.h dietlibc-0.30-libm/libm/math_private.h --- dietlibc-0.30/libm/math_private.h 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/math_private.h 2006-06-25 11:26:34.000000000 +0000 @@ -0,0 +1,236 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $Id: math_private.h,v 1.3 2004/02/09 07:10:38 andersen Exp $ + */ + +#ifndef _MATH_PRIVATE_H_ +#define _MATH_PRIVATE_H_ + +# define weak_alias(name, aliasname) _weak_alias (name, aliasname) +# define _weak_alias(name, aliasname) \ + extern __typeof (name) aliasname __attribute__ ((weak, alias (#name))); + +#include +#include +#define u_int32_t uint32_t + +/* The original fdlibm code used statements like: + n0 = ((*(int*)&one)>>29)^1; * index of high word * + ix0 = *(n0+(int*)&x); * high word of x * + ix1 = *((1-n0)+(int*)&x); * low word of x * + to dig two 32 bit words out of the 64 bit IEEE floating point + value. That is non-ANSI, and, moreover, the gcc instruction + scheduler gets it wrong. We instead use the following macros. + Unlike the original code, we determine the endianness at compile + time, not at run time; I don't see much benefit to selecting + endianness at run time. */ + +/* A union which permits us to convert between a double and two 32 bit + ints. */ + +/* + * Math on arm is special: + * For FPA, float words are always big-endian. + * For VFP, floats words follow the memory system mode. + */ + +#if (__BYTE_ORDER == __BIG_ENDIAN) || \ + (!defined(__VFP_FP__) && (defined(__arm__) || defined(__thumb__))) + +typedef union +{ + double value; + struct + { + u_int32_t msw; + u_int32_t lsw; + } parts; +} ieee_double_shape_type; + +#else + +typedef union +{ + double value; + struct + { + u_int32_t lsw; + u_int32_t msw; + } parts; +} ieee_double_shape_type; + +#endif + +/* Get two 32 bit ints from a double. */ + +#define EXTRACT_WORDS(ix0,ix1,d) \ +do { \ + ieee_double_shape_type ew_u; \ + ew_u.value = (d); \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (0) + +/* Get the more significant 32 bit int from a double. */ + +#define GET_HIGH_WORD(i,d) \ +do { \ + ieee_double_shape_type gh_u; \ + gh_u.value = (d); \ + (i) = gh_u.parts.msw; \ +} while (0) + +/* Get the less significant 32 bit int from a double. */ + +#define GET_LOW_WORD(i,d) \ +do { \ + ieee_double_shape_type gl_u; \ + gl_u.value = (d); \ + (i) = gl_u.parts.lsw; \ +} while (0) + +/* Set a double from two 32 bit ints. */ + +#define INSERT_WORDS(d,ix0,ix1) \ +do { \ + ieee_double_shape_type iw_u; \ + iw_u.parts.msw = (ix0); \ + iw_u.parts.lsw = (ix1); \ + (d) = iw_u.value; \ +} while (0) + +/* Set the more significant 32 bits of a double from an int. */ + +#define SET_HIGH_WORD(d,v) \ +do { \ + ieee_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Set the less significant 32 bits of a double from an int. */ + +#define SET_LOW_WORD(d,v) \ +do { \ + ieee_double_shape_type sl_u; \ + sl_u.value = (d); \ + sl_u.parts.lsw = (v); \ + (d) = sl_u.value; \ +} while (0) + +/* A union which permits us to convert between a float and a 32 bit + int. */ + +typedef union +{ + float value; + u_int32_t word; +} ieee_float_shape_type; + +/* Get a 32 bit int from a float. */ + +#define GET_FLOAT_WORD(i,d) \ +do { \ + ieee_float_shape_type gf_u; \ + gf_u.value = (d); \ + (i) = gf_u.word; \ +} while (0) + +/* Set a float from a 32 bit int. */ + +#define SET_FLOAT_WORD(d,i) \ +do { \ + ieee_float_shape_type sf_u; \ + sf_u.word = (i); \ + (d) = sf_u.value; \ +} while (0) + +/* ieee style elementary functions */ +extern double __ieee754_sqrt __P((double)); +extern double __ieee754_acos __P((double)); +extern double __ieee754_acosh __P((double)); +extern double __ieee754_log __P((double)); +extern double __ieee754_atanh __P((double)); +extern double __ieee754_asin __P((double)); +extern double __ieee754_atan2 __P((double,double)); +extern double __ieee754_exp __P((double)); +extern double __ieee754_cosh __P((double)); +extern double __ieee754_fmod __P((double,double)); +extern double __ieee754_pow __P((double,double)); +extern double __ieee754_lgamma_r __P((double,int *)); +extern double __ieee754_gamma_r __P((double,int *)); +extern double __ieee754_lgamma __P((double)); +extern double __ieee754_gamma __P((double)); +extern double __ieee754_log10 __P((double)); +extern double __ieee754_sinh __P((double)); +extern double __ieee754_hypot __P((double,double)); +extern double __ieee754_j0 __P((double)); +extern double __ieee754_j1 __P((double)); +extern double __ieee754_y0 __P((double)); +extern double __ieee754_y1 __P((double)); +extern double __ieee754_jn __P((int,double)); +extern double __ieee754_yn __P((int,double)); +extern double __ieee754_remainder __P((double,double)); +extern int __ieee754_rem_pio2 __P((double,double*)); +#if defined(_SCALB_INT) +extern double __ieee754_scalb __P((double,int)); +#else +extern double __ieee754_scalb __P((double,double)); +#endif + +/* fdlibm kernel function */ +extern double __kernel_standard __P((double,double,int)); +extern double __kernel_sin __P((double,double,int)); +extern double __kernel_cos __P((double,double)); +extern double __kernel_tan __P((double,double,int)); +extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*)); + + +/* ieee style elementary float functions */ +extern float __ieee754_sqrtf __P((float)); +extern float __ieee754_acosf __P((float)); +extern float __ieee754_acoshf __P((float)); +extern float __ieee754_logf __P((float)); +extern float __ieee754_atanhf __P((float)); +extern float __ieee754_asinf __P((float)); +extern float __ieee754_atan2f __P((float,float)); +extern float __ieee754_expf __P((float)); +extern float __ieee754_coshf __P((float)); +extern float __ieee754_fmodf __P((float,float)); +extern float __ieee754_powf __P((float,float)); +extern float __ieee754_lgammaf_r __P((float,int *)); +extern float __ieee754_gammaf_r __P((float,int *)); +extern float __ieee754_lgammaf __P((float)); +extern float __ieee754_gammaf __P((float)); +extern float __ieee754_log10f __P((float)); +extern float __ieee754_sinhf __P((float)); +extern float __ieee754_hypotf __P((float,float)); +extern float __ieee754_j0f __P((float)); +extern float __ieee754_j1f __P((float)); +extern float __ieee754_y0f __P((float)); +extern float __ieee754_y1f __P((float)); +extern float __ieee754_jnf __P((int,float)); +extern float __ieee754_ynf __P((int,float)); +extern float __ieee754_remainderf __P((float,float)); +extern int __ieee754_rem_pio2f __P((float,float*)); +extern float __ieee754_scalbf __P((float,float)); + +/* float versions of fdlibm kernel functions */ +extern float __kernel_sinf __P((float,float,int)); +extern float __kernel_cosf __P((float,float)); +extern float __kernel_tanf __P((float,float,int)); +extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const int*)); + +#endif /* _MATH_PRIVATE_H_ */ diff -urN dietlibc-0.30/libm/modf.c dietlibc-0.30-libm/libm/modf.c --- dietlibc-0.30/libm/modf.c 2003-03-30 19:19:53.000000000 +0000 +++ dietlibc-0.30-libm/libm/modf.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,7 +0,0 @@ -#include - -double modf(double x, double *iptr) { - double fmod_result = fmod(x,1.0); - *iptr = x - fmod_result; - return fmod_result; -} diff -urN dietlibc-0.30/libm/nan.c dietlibc-0.30-libm/libm/nan.c --- dietlibc-0.30/libm/nan.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/nan.c 2006-06-25 11:20:03.000000000 +0000 @@ -0,0 +1,48 @@ +/*********************************************************************** + nan, nanf, nanl - return quiet NaN + + These functions shall return a quiet NaN, if available, with content + indicated through tagp. + + If the implementation does not support quiet NaNs, these functions + shall return zero. + + Calls: strlen(), sprintf(), strtod() + +***********************************************************************/ +#include +#include +#include +#include + +double nan (const char *tagp) +{ + if (tagp[0] != '\0') { + char buf[6 + strlen (tagp)]; + sprintf (buf, "NAN(%s)", tagp); + return strtod (buf, NULL); + } + return NAN; +} + +float nanf (const char *tagp) +{ + if (tagp[0] != '\0') { + char buf[6 + strlen (tagp)]; + sprintf (buf, "NAN(%s)", tagp); + return strtof (buf, NULL); + } + return NAN; +} + +#if 0 +long double nanl (const char *tagp) +{ + if (tagp[0] != '\0') { + char buf[6 + strlen (tagp)]; + sprintf (buf, "NAN(%s)", tagp); + return strtold (buf, NULL); + } + return NAN; +} +#endif diff -urN dietlibc-0.30/libm/poly.c dietlibc-0.30-libm/libm/poly.c --- dietlibc-0.30/libm/poly.c 2002-11-18 01:16:51.000000000 +0000 +++ dietlibc-0.30-libm/libm/poly.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,41 +0,0 @@ -/*--------------------------------------------------------------------------* - -Name __poly - generates a polynomial from arguments - -Usage double __poly ( double x, int n, const double* c ); - -Prototype in math.h - -Description __poly generates a polynomial in x, of degree n, with - coefficients c[0], c[1], ..., c[n]. For example, if n=4, - the generated polynomial is - - c[4]*x^4 + c[3]*x^3 + c[2]*x^2 + c[1]*x + c[0] - - The polynomial is calculated using Horner's method: - - polynom = (..((x*c[n] + c[n-1])*x + c[n-2])..)*x + c[0] - -Return value __poly returns the value of the polynomial as evaluated for - the given x. - A range error occurs if the result exceeds double range. - -*---------------------------------------------------------------------------*/ - -#include -#include "dietlibm.h" - -double __poly ( double x, size_t n, const double* c) -{ - long double ret; - size_t i; - - i = n; - c += n; - ret = 0; - do - ret = ret * x + *c--; - while ( i-- ); - - return ret; -} diff -urN dietlibc-0.30/libm/pow.c dietlibc-0.30-libm/libm/pow.c --- dietlibc-0.30/libm/pow.c 2003-10-10 13:37:34.000000000 +0000 +++ dietlibc-0.30-libm/libm/pow.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,42 +0,0 @@ - -#include -#include "dietlibm.h" - -double pow ( double mant, double expo ) -{ - unsigned int e; - long double ret; - - /* special cases 0^x */ - if ( mant == 0. ) { - if ( expo > 0. ) - return 0.; - else if ( expo == 0. ) - return 1.; - else - return 1./mant; - } - - /* special cases x^n with n is integer */ - if ( expo == (int) (e = (int) expo) ) { - - if ( (int)e < 0 ) { - e = -e; - mant = 1./mant; - } - - ret = 1.; - - while (1) { - if ( e & 1 ) - ret *= mant; - if ( (e >>= 1) == 0 ) - break; - mant *= mant; - } - return ret; - } - - /* normal case */ - return exp ( log (mant) * expo ); -} diff -urN dietlibc-0.30/libm/rint.c dietlibc-0.30-libm/libm/rint.c --- dietlibc-0.30/libm/rint.c 2001-07-30 13:45:43.000000000 +0000 +++ dietlibc-0.30-libm/libm/rint.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,5 +0,0 @@ -#include - -double rint(double x) { - return floor(x+0.5); -} diff -urN dietlibc-0.30/libm/s_asinh.c dietlibc-0.30-libm/libm/s_asinh.c --- dietlibc-0.30/libm/s_asinh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_asinh.c 2006-06-25 11:19:59.000000000 +0000 @@ -0,0 +1,65 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $"; +#endif + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +huge= 1.00000000000000000000e+300; + +#ifdef __STDC__ + double asinh(double x) +#else + double asinh(x) + double x; +#endif +{ + double t,w; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = __ieee754_log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); + w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); + } + if(hx>0) return w; else return -w; +} diff -urN dietlibc-0.30/libm/s_atan.c dietlibc-0.30-libm/libm/s_atan.c --- dietlibc-0.30/libm/s_atan.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_atan.c 2006-06-25 11:20:16.000000000 +0000 @@ -0,0 +1,139 @@ +/* @(#)s_atan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_atan.c,v 1.8 1995/05/10 20:46:45 jtc Exp $"; +#endif + +/* atan(x) + * Method + * 1. Reduce x to positive by atan(x) = -atan(-x). + * 2. According to the integer k=4t+0.25 chopped, t=x, the argument + * is further reduced to one of the following intervals and the + * arctangent of t is evaluated by the corresponding formula: + * + * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) + * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) + * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) + * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) + * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double atanhi[] = { +#else +static double atanhi[] = { +#endif + 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ + 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ + 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ + 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ +}; + +#ifdef __STDC__ +static const double atanlo[] = { +#else +static double atanlo[] = { +#endif + 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ + 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ + 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ + 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ +}; + +#ifdef __STDC__ +static const double aT[] = { +#else +static double aT[] = { +#endif + 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ + -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ + 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ + -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ + 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ + -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ + 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ + -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ + 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ + -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ + 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ +}; + +#ifdef __STDC__ + static const double +#else + static double +#endif +one = 1.0, +huge = 1.0e300; + +#ifdef __STDC__ + double atan(double x) +#else + double atan(x) + double x; +#endif +{ + double w,s1,s2,z; + int32_t ix,hx,id; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x44100000) { /* if |x| >= 2^66 */ + u_int32_t low; + GET_LOW_WORD(low,x); + if(ix>0x7ff00000|| + (ix==0x7ff00000&&(low!=0))) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ + if (ix < 0x3e200000) { /* |x| < 2^-29 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabs(x); + if (ix < 0x3ff30000) { /* |x| < 1.1875 */ + if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = (2.0*x-one)/(2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x40038000) { /* |x| < 2.4375 */ + id = 2; x = (x-1.5)/(one+1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} diff -urN dietlibc-0.30/libm/s_cbrt.c dietlibc-0.30-libm/libm/s_cbrt.c --- dietlibc-0.30/libm/s_cbrt.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_cbrt.c 2006-06-25 11:20:16.000000000 +0000 @@ -0,0 +1,93 @@ +/* @(#)s_cbrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_cbrt.c,v 1.8 1995/05/10 20:46:49 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +/* cbrt(x) + * Return cube root of x + */ +#ifdef __STDC__ +static const u_int32_t +#else +static u_int32_t +#endif + B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ + B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ + +#ifdef __STDC__ +static const double +#else +static double +#endif +C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ +D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ +E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ +F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ +G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ + +#ifdef __STDC__ + double cbrt(double x) +#else + double cbrt(x) + double x; +#endif +{ + int32_t hx; + double r,s,t=0.0,w; + u_int32_t sign; + u_int32_t high,low; + + GET_HIGH_WORD(hx,x); + sign=hx&0x80000000; /* sign= sign(x) */ + hx ^=sign; + if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ + GET_LOW_WORD(low,x); + if((hx|low)==0) + return(x); /* cbrt(0) is itself */ + + SET_HIGH_WORD(x,hx); /* x <- |x| */ + /* rough cbrt to 5 bits */ + if(hx<0x00100000) /* subnormal number */ + {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ + t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); + } + else + SET_HIGH_WORD(t,hx/3+B1); + + + /* new cbrt to 23 bits, may be implemented in single precision */ + r=t*t/x; + s=C+r*t; + t*=G+F/(s+E+D/s); + + /* chopped to 20 bits and make it larger than cbrt(x) */ + GET_HIGH_WORD(high,t); + INSERT_WORDS(t,high+0x00000001,0); + + + /* one step newton iteration to 53 bits with error less than 0.667 ulps */ + s=t*t; /* t*t is exact */ + r=x/s; + w=t+t; + r=(r-t)/(w+r); /* r-s is exact */ + t=t+t*r; + + /* retore the sign bit */ + GET_HIGH_WORD(high,t); + SET_HIGH_WORD(t,high|sign); + return(t); +} diff -urN dietlibc-0.30/libm/s_ceil.c dietlibc-0.30-libm/libm/s_ceil.c --- dietlibc-0.30/libm/s_ceil.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_ceil.c 2006-06-25 11:29:20.000000000 +0000 @@ -0,0 +1,81 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ceil.c,v 1.8 1995/05/10 20:46:53 jtc Exp $"; +#endif + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double huge = 1.0e300; +#else +static double huge = 1.0e300; +#endif + +#ifdef __STDC__ + double __ceil(double x) +#else + double __ceil(x) + double x; +#endif +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;i1=0;} + else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) { + if(j0==20) i0+=1; + else { + j = i1 + (1<<(52-j0)); + if(j>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;} + else if(i0!=0) { i0=0x3f800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} +weak_alias (__ceilf, ceilf) diff -urN dietlibc-0.30/libm/s_copysign.c dietlibc-0.30-libm/libm/s_copysign.c --- dietlibc-0.30/libm/s_copysign.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_copysign.c 2006-06-25 11:20:05.000000000 +0000 @@ -0,0 +1,39 @@ +/* @(#)s_copysign.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_copysign.c,v 1.8 1995/05/10 20:46:57 jtc Exp $"; +#endif + +/* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double copysign(double x, double y) +#else + double copysign(x,y) + double x,y; +#endif +{ + u_int32_t hx,hy; + GET_HIGH_WORD(hx,x); + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000)); + return x; +} + diff -urN dietlibc-0.30/libm/s_cos.c dietlibc-0.30-libm/libm/s_cos.c --- dietlibc-0.30/libm/s_cos.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_cos.c 2006-06-25 11:20:04.000000000 +0000 @@ -0,0 +1,82 @@ +/* @(#)s_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_cos.c,v 1.7 1995/05/10 20:47:02 jtc Exp $"; +#endif + +/* cos(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double cos(double x) +#else + double cos(x) + double x; +#endif +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_cos(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_cos(y[0],y[1]); + case 1: return -__kernel_sin(y[0],y[1],1); + case 2: return -__kernel_cos(y[0],y[1]); + default: + return __kernel_sin(y[0],y[1],1); + } + } +} diff -urN dietlibc-0.30/libm/s_erf.c dietlibc-0.30-libm/libm/s_erf.c --- dietlibc-0.30/libm/s_erf.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_erf.c 2006-06-25 11:20:05.000000000 +0000 @@ -0,0 +1,314 @@ +/* @(#)s_erf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; +#endif + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * where R = P/Q where P is an odd poly of degree 8 and + * Q is an odd poly of degree 10. + * -57.90 + * | R - (erf(x)-x)/x | <= 2 + * + * + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * That is, we use rational approximation to approximate + * erf(1+s) - (c = (single)0.84506291151) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * where + * P1(s) = degree 6 poly in s + * Q1(s) = degree 6 poly in s + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) + * erf(x) = 1 - erfc(x) + * where + * R1(z) = degree 7 poly in z, (z=1/x^2) + * S1(z) = degree 8 poly in z + * + * 4. For x in [1/0.35,28] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6 x >= 28 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +tiny = 1e-300, +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ + /* c = (float)0.84506291151 */ +erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ +efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ +pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ +pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ +pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ +pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ +pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ +qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ +qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ +qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ +qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ +qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ +pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ +pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ +pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ +pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ +pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ +pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ +qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ +qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ +qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ +qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ +qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ +qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ +ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ +ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ +ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ +ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ +ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ +ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ +ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ +sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ +sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ +sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ +sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ +sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ +sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ +sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ +sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ +rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ +rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ +rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ +rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ +rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ +rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ +sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ +sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ +sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ +sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ +sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ +sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ +sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ + +#ifdef __STDC__ + double erf(double x) +#else + double erf(x) + double x; +#endif +{ + int32_t hx,ix,i; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3e300000) { /* |x|<2**-28 */ + if (ix < 0x00800000) + return 0.125*(8.0*x+efx8*x); /*avoid underflow */ + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40180000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} + +#ifdef __STDC__ + double erfc(double x) +#else + double erfc(x) + double x; +#endif +{ + int32_t hx,ix; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (double)(((u_int32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3c700000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3fd00000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x403c0000) { /* |x|<28 */ + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)* + __ieee754_exp((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} diff -urN dietlibc-0.30/libm/s_expm1.c dietlibc-0.30-libm/libm/s_expm1.c --- dietlibc-0.30/libm/s_expm1.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_expm1.c 2006-06-25 11:20:18.000000000 +0000 @@ -0,0 +1,229 @@ +/* @(#)s_expm1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; +#endif + +/* expm1(x) + * Returns exp(x)-1, the exponential of x minus 1. + * + * Method + * 1. Argument reduction: + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * + * Here a correction term c will be computed to compensate + * the error in r when rounded to a floating-point number. + * + * 2. Approximating expm1(r) by a special rational function on + * the interval [0,0.34658]: + * Since + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... + * we define R1(r*r) by + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) + * That is, + * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) + * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) + * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... + * We use a special Reme algorithm on [0,0.347] to generate + * a polynomial of degree 5 in r*r to approximate R1. The + * maximum error of this polynomial approximation is bounded + * by 2**-61. In other words, + * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 + * where Q1 = -1.6666666666666567384E-2, + * Q2 = 3.9682539681370365873E-4, + * Q3 = -9.9206344733435987357E-6, + * Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; + * (where z=r*r, and the values of Q1 to Q5 are listed below) + * with error bounded by + * | 5 | -61 + * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 + * | | + * + * expm1(r) = exp(r)-1 is then computed by the following + * specific way which minimize the accumulation rounding error: + * 2 3 + * r r [ 3 - (R1 + R1*r/2) ] + * expm1(r) = r + --- + --- * [--------------------] + * 2 2 [ 6 - r*(3 - R1*r/2) ] + * + * To compensate the error in the argument reduction, we use + * expm1(r+c) = expm1(r) + c + expm1(r)*c + * ~ expm1(r) + c + r*c + * Thus c+r*c will be added in as the correction terms for + * expm1(r+c). Now rearrange the term to avoid optimization + * screw up: + * ( 2 2 ) + * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) + * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) + * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) + * ( ) + * + * = r - E + * 3. Scale back to obtain expm1(x): + * From step 1, we have + * expm1(x) = either 2^k*[expm1(r)+1] - 1 + * = or 2^k*[expm1(r) + (1-2^-k)] + * 4. Implementation notes: + * (A). To save one multiplication, we scale the coefficient Qi + * to Qi*2^i, and replace z by (x^2)/2. + * (B). To achieve maximum accuracy, we compute expm1(x) by + * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) + * (ii) if k=0, return r-E + * (iii) if k=-1, return 0.5*(r-E)-0.5 + * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) + * else return 1.0+2.0*(r-E); + * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) + * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else + * (vii) return 2^k(1-((E+2^-k)-r)) + * + * Special cases: + * expm1(INF) is INF, expm1(NaN) is NaN; + * expm1(-INF) is -1, and + * for finite argument, only expm1(0)=0 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then expm1(x) overflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.0, +huge = 1.0e+300, +tiny = 1.0e-300, +o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ +ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ +ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */ + /* scaled coefficients related to expm1 */ +Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ +Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ +Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ +Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ +Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ + +#ifdef __STDC__ + double expm1(double x) +#else + double expm1(x) + double x; +#endif +{ + double y,hi,lo,c=0.0,t,e,hxs,hfx,r1; + int32_t k,xsb; + u_int32_t hx; + + GET_HIGH_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + if(xsb==0) y=x; else y= -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t low; + GET_LOW_WORD(low,x); + if(((hx&0xfffff)|low)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ + if(x+tiny<0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?0.5:-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + x = hi - lo; + c = (hi-x)-lo; + } + else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = 0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = 3.0-r1*hfx; + e = hxs*((r1-t)/(6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return 0.5*(x-e)-0.5; + if(k==1) { + if(x < -0.25) return -2.0*(e-(x+0.5)); + else return one+2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + u_int32_t high; + y = one-(e-x); + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + return y-one; + } + t = one; + if(k<20) { + u_int32_t high; + SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ + y = t-(e-x); + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + } else { + u_int32_t high; + SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ + y = x-(e+t); + y += one; + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + } + } + return y; +} diff -urN dietlibc-0.30/libm/s_fabs.c dietlibc-0.30-libm/libm/s_fabs.c --- dietlibc-0.30/libm/s_fabs.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_fabs.c 2006-06-25 11:20:17.000000000 +0000 @@ -0,0 +1,35 @@ +/* @(#)s_fabs.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_fabs.c,v 1.7 1995/05/10 20:47:13 jtc Exp $"; +#endif + +/* + * fabs(x) returns the absolute value of x. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double fabs(double x) +#else + double fabs(x) + double x; +#endif +{ + u_int32_t high; + GET_HIGH_WORD(high,x); + SET_HIGH_WORD(x,high&0x7fffffff); + return x; +} diff -urN dietlibc-0.30/libm/s_finite.c dietlibc-0.30-libm/libm/s_finite.c --- dietlibc-0.30/libm/s_finite.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_finite.c 2006-06-25 11:19:58.000000000 +0000 @@ -0,0 +1,35 @@ +/* @(#)s_finite.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_finite.c,v 1.8 1995/05/10 20:47:17 jtc Exp $"; +#endif + +/* + * finite(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int finite(double x) +#else + int finite(x) + double x; +#endif +{ + int32_t hx; + GET_HIGH_WORD(hx,x); + return (int)((u_int32_t)((hx&0x7fffffff)-0x7ff00000)>>31); +} diff -urN dietlibc-0.30/libm/s_floor.c dietlibc-0.30-libm/libm/s_floor.c --- dietlibc-0.30/libm/s_floor.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_floor.c 2006-06-25 11:20:17.000000000 +0000 @@ -0,0 +1,81 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_floor.c,v 1.8 1995/05/10 20:47:20 jtc Exp $"; +#endif + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double huge = 1.0e300; +#else +static double huge = 1.0e300; +#endif + +#ifdef __STDC__ + double floor(double x) +#else + double floor(x) + double x; +#endif +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffff)|i1)!=0) + { i0=0xbff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) { + if(j0==20) i0+=1; + else { + j = i1+(1<<(52-j0)); + if(j>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffff)!=0) + { i0=0xbf800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} +weak_alias (__floorf, floorf) diff -urN dietlibc-0.30/libm/s_frexp.c dietlibc-0.30-libm/libm/s_frexp.c --- dietlibc-0.30/libm/s_frexp.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_frexp.c 2006-06-25 11:20:20.000000000 +0000 @@ -0,0 +1,60 @@ +/* @(#)s_frexp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_frexp.c,v 1.9 1995/05/10 20:47:24 jtc Exp $"; +#endif + +/* + * for non-zero x + * x = frexp(arg,&exp); + * return a double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */ + +#ifdef __STDC__ + double __frexp(double x, int *eptr) +#else + double __frexp(x, eptr) + double x; int *eptr; +#endif +{ + int32_t hx, ix, lx; + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */ + if (ix<0x00100000) { /* subnormal */ + x *= two54; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -54; + } + *eptr += (ix>>20)-1022; + hx = (hx&0x800fffff)|0x3fe00000; + SET_HIGH_WORD(x,hx); + return x; +} +weak_alias (__frexp, frexp) diff -urN dietlibc-0.30/libm/s_ilogb.c dietlibc-0.30-libm/libm/s_ilogb.c --- dietlibc-0.30/libm/s_ilogb.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_ilogb.c 2006-06-25 11:20:02.000000000 +0000 @@ -0,0 +1,51 @@ +/* @(#)s_ilogb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ilogb.c,v 1.9 1995/05/10 20:47:28 jtc Exp $"; +#endif + +/* ilogb(double x) + * return the binary exponent of non-zero x + * ilogb(0) = 0x80000001 + * ilogb(inf/NaN) = 0x7fffffff (no signal is raised) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int ilogb(double x) +#else + int ilogb(x) + double x; +#endif +{ + int32_t hx,lx,ix; + + GET_HIGH_WORD(hx,x); + hx &= 0x7fffffff; + if(hx<0x00100000) { + GET_LOW_WORD(lx,x); + if((hx|lx)==0) + return 0x80000001; /* ilogb(0) = 0x80000001 */ + else /* subnormal x */ + if(hx==0) { + for (ix = -1043; lx>0; lx<<=1) ix -=1; + } else { + for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1; + } + return ix; + } + else if (hx<0x7ff00000) return (hx>>20)-1023; + else return 0x7fffffff; +} diff -urN dietlibc-0.30/libm/s_ldexp.c dietlibc-0.30-libm/libm/s_ldexp.c --- dietlibc-0.30/libm/s_ldexp.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_ldexp.c 2006-06-25 11:20:12.000000000 +0000 @@ -0,0 +1,32 @@ +/* @(#)s_ldexp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_ldexp.c,v 1.6 1995/05/10 20:47:40 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" +#include + +#ifdef __STDC__ + double ldexp(double value, int exp) +#else + double ldexp(value, exp) + double value; int exp; +#endif +{ + if(!finite(value)||value==0.0) return value; + value = scalbn(value,exp); + if(!finite(value)||value==0.0) errno = ERANGE; + return value; +} diff -urN dietlibc-0.30/libm/s_lib_version.c dietlibc-0.30-libm/libm/s_lib_version.c --- dietlibc-0.30/libm/s_lib_version.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_lib_version.c 2006-06-25 11:20:09.000000000 +0000 @@ -0,0 +1,40 @@ +/* @(#)s_lib_ver.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_lib_version.c,v 1.6 1995/05/10 20:47:44 jtc Exp $"; +#endif + +/* + * MACRO for standards + */ + +#include "math.h" +#include "math_private.h" +#if 0 +/* + * define and initialize _LIB_VERSION + */ +#ifdef _POSIX_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_; +#else +#ifdef _XOPEN_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_; +#else +#ifdef _SVID3_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _SVID_; +#else /* default _IEEE_MODE */ +_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_; +#endif +#endif +#endif +#endif diff -urN dietlibc-0.30/libm/s_log1p.c dietlibc-0.30-libm/libm/s_log1p.c --- dietlibc-0.30/libm/s_log1p.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_log1p.c 2006-06-25 11:20:15.000000000 +0000 @@ -0,0 +1,174 @@ +/* @(#)s_log1p.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $"; +#endif + +/* double log1p(double x) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f + * may not be representable exactly. In that case, a correction + * term is need. Let u=1+x rounded. Let c = (1+x)-u, then + * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), + * and add back the correction term c/u. + * (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log1p(f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s + * (the values of Lp1 to Lp7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log1p(f) = f - (hfsq - s*(hfsq+R)). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(+INF) is +INF; log1p(-1) is -INF with signal; + * log1p(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + * + * Note: Assuming log() return accurate answer, the following + * algorithm can be used to compute log1p(x) to within a few ULP: + * + * u = 1+x; + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double log1p(double x) +#else + double log1p(x) + double x; +#endif +{ + double hfsq,f=0,c=0,s,z,R,u; + int32_t k,hx,hu=0,ax; + + GET_HIGH_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3FDA827A) { /* x < 0.41422 */ + if(ax>=0x3ff00000) { /* x <= -1.0 */ + if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x3e200000) { /* |x| < 2**-29 */ + if(two54+x>zero /* raise inexact */ + &&ax<0x3c900000) /* |x| < 2**-54 */ + return x; + else + return x - x*x*0.5; + } + if(hx>0||hx<=((int32_t)0xbfd2bec3)) { + k=0;f=x;hu=1;} /* -0.2929= 0x7ff00000) return x+x; + if(k!=0) { + if(hx<0x43400000) { + u = 1.0+x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ + c /= u; + } else { + u = x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = 0; + } + hu &= 0x000fffff; + if(hu<0x6a09e) { + SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ + } else { + k += 1; + SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ + hu = (0x00100000-hu)>>2; + } + f = u-1.0; + } + hfsq=0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) {if(k==0) return zero; + else {c += k*ln2_lo; return k*ln2_hi+c;} + } + R = hfsq*(1.0-0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/(2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} diff -urN dietlibc-0.30/libm/s_logb.c dietlibc-0.30-libm/libm/s_logb.c --- dietlibc-0.30/libm/s_logb.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_logb.c 2006-06-25 11:20:20.000000000 +0000 @@ -0,0 +1,42 @@ +/* @(#)s_logb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_logb.c,v 1.8 1995/05/10 20:47:50 jtc Exp $"; +#endif + +/* + * double logb(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double logb(double x) +#else + double logb(x) + double x; +#endif +{ + int32_t lx,ix; + EXTRACT_WORDS(ix,lx,x); + ix &= 0x7fffffff; /* high |x| */ + if((ix|lx)==0) return -1.0/fabs(x); + if(ix>=0x7ff00000) return x*x; + if((ix>>=20)==0) /* IEEE 754 logb */ + return -1022.0; + else + return (double) (ix-1023); +} diff -urN dietlibc-0.30/libm/s_matherr.c dietlibc-0.30-libm/libm/s_matherr.c --- dietlibc-0.30/libm/s_matherr.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_matherr.c 2006-06-25 11:20:08.000000000 +0000 @@ -0,0 +1,30 @@ +/* @(#)s_matherr.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_matherr.c,v 1.6 1995/05/10 20:47:53 jtc Exp $"; +#endif + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + int matherr(struct exception *x) +#else + int matherr(x) + struct exception *x; +#endif +{ + int n=0; + if(x->arg1!=x->arg1) return 0; + return n; +} diff -urN dietlibc-0.30/libm/s_modf.c dietlibc-0.30-libm/libm/s_modf.c --- dietlibc-0.30/libm/s_modf.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_modf.c 2006-06-25 11:20:21.000000000 +0000 @@ -0,0 +1,83 @@ +/* @(#)s_modf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_modf.c,v 1.8 1995/05/10 20:47:55 jtc Exp $"; +#endif + +/* + * modf(double x, double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one = 1.0; +#else +static double one = 1.0; +#endif + +#ifdef __STDC__ + double modf(double x, double *iptr) +#else + double modf(x, iptr) + double x,*iptr; +#endif +{ + int32_t i0,i1,j0; + u_int32_t i; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent of x */ + if(j0<20) { /* integer part in high x */ + if(j0<0) { /* |x|<1 */ + INSERT_WORDS(*iptr,i0&0x80000000,0); /* *iptr = +-0 */ + return x; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) { /* x is integral */ + u_int32_t high; + *iptr = x; + GET_HIGH_WORD(high,x); + INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */ + return x; + } else { + INSERT_WORDS(*iptr,i0&(~i),0); + return x - *iptr; + } + } + } else if (j0>51) { /* no fraction part */ + u_int32_t high; + *iptr = x*one; + GET_HIGH_WORD(high,x); + INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */ + return x; + } else { /* fraction part in low x */ + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) { /* x is integral */ + u_int32_t high; + *iptr = x; + GET_HIGH_WORD(high,x); + INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */ + return x; + } else { + INSERT_WORDS(*iptr,i0,i1&(~i)); + return x - *iptr; + } + } +} diff -urN dietlibc-0.30/libm/s_nextafter.c dietlibc-0.30-libm/libm/s_nextafter.c --- dietlibc-0.30/libm/s_nextafter.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_nextafter.c 2006-06-25 11:20:08.000000000 +0000 @@ -0,0 +1,79 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_nextafter.c,v 1.8 1995/05/10 20:47:58 jtc Exp $"; +#endif + +/* IEEE functions + * nextafter(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double nextafter(double x, double y) +#else + double nextafter(x,y) + double x,y; +#endif +{ + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */ + return x+y; + if(x==y) return x; /* x=y, return x */ + if((ix|lx)==0) { /* x == 0 */ + INSERT_WORDS(x,hy&0x80000000,1); /* return +-minsubnormal */ + y = x*x; + if(y==x) return y; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) return x+x; /* overflow */ + if(hy<0x00100000) { /* underflow */ + y = x*x; + if(y!=x) { /* raise underflow flag */ + INSERT_WORDS(y,hx,lx); + return y; + } + } + INSERT_WORDS(x,hx,lx); + return x; +} diff -urN dietlibc-0.30/libm/s_rint.c dietlibc-0.30-libm/libm/s_rint.c --- dietlibc-0.30/libm/s_rint.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_rint.c 2006-06-25 11:20:22.000000000 +0000 @@ -0,0 +1,86 @@ +/* @(#)s_rint.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_rint.c,v 1.8 1995/05/10 20:48:04 jtc Exp $"; +#endif + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +#ifdef __STDC__ + double rint(double x) +#else + double rint(x) + double x; +#endif +{ + int32_t i0,j0,sx; + u_int32_t i,i1; + double w,t; + EXTRACT_WORDS(i0,i1,x); + sx = (i0>>31)&1; + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { + if(((i0&0x7fffffff)|i1)==0) return x; + i1 |= (i0&0x0fffff); + i0 &= 0xfffe0000; + i0 |= ((i1|-i1)>>12)&0x80000; + SET_HIGH_WORD(x,i0); + w = TWO52[sx]+x; + t = w-TWO52[sx]; + GET_HIGH_WORD(i0,t); + SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if(j0==19) i1 = 0x40000000; else + i0 = (i0&(~i))|((0x20000)>>j0); + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20)); + } + INSERT_WORDS(x,i0,i1); + w = TWO52[sx]+x; + return w-TWO52[sx]; +} diff -urN dietlibc-0.30/libm/s_scalbn.c dietlibc-0.30-libm/libm/s_scalbn.c --- dietlibc-0.30/libm/s_scalbn.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_scalbn.c 2006-06-25 11:20:21.000000000 +0000 @@ -0,0 +1,67 @@ +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_scalbn.c,v 1.8 1995/05/10 20:48:08 jtc Exp $"; +#endif + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +#ifdef __STDC__ + double scalbn (double x, int n) +#else + double scalbn (x,n) + double x; int n; +#endif +{ + int32_t k,hx,lx; + EXTRACT_WORDS(hx,lx,x); + k = (hx&0x7ff00000)>>20; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD(hx,x); + k = ((hx&0x7ff00000)>>20) - 54; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0x7ff) return x+x; /* NaN or Inf */ + k = k+n; + if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;} + if (k <= -54) { + if (n > 50000) /* in case integer overflow in n+k */ + return huge*copysign(huge,x); /*overflow*/ + else return tiny*copysign(tiny,x); /*underflow*/ + } + k += 54; /* subnormal result */ + SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); + return x*twom54; +} diff -urN dietlibc-0.30/libm/s_signgam.c dietlibc-0.30-libm/libm/s_signgam.c --- dietlibc-0.30/libm/s_signgam.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_signgam.c 2006-06-25 11:20:20.000000000 +0000 @@ -0,0 +1,3 @@ +#include "math.h" +#include "math_private.h" +int signgam = 0; diff -urN dietlibc-0.30/libm/s_significand.c dietlibc-0.30-libm/libm/s_significand.c --- dietlibc-0.30/libm/s_significand.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_significand.c 2006-06-25 11:19:59.000000000 +0000 @@ -0,0 +1,34 @@ +/* @(#)s_signif.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_significand.c,v 1.6 1995/05/10 20:48:11 jtc Exp $"; +#endif + +/* + * significand(x) computes just + * scalb(x, (double) -ilogb(x)), + * for exercising the fraction-part(F) IEEE 754-1985 test vector. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double significand(double x) +#else + double significand(x) + double x; +#endif +{ + return __ieee754_scalb(x,(double) -ilogb(x)); +} diff -urN dietlibc-0.30/libm/s_sin.c dietlibc-0.30-libm/libm/s_sin.c --- dietlibc-0.30/libm/s_sin.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_sin.c 2006-06-25 11:20:05.000000000 +0000 @@ -0,0 +1,82 @@ +/* @(#)s_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_sin.c,v 1.7 1995/05/10 20:48:15 jtc Exp $"; +#endif + +/* sin(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double sin(double x) +#else + double sin(x) + double x; +#endif +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_sin(y[0],y[1],1); + case 1: return __kernel_cos(y[0],y[1]); + case 2: return -__kernel_sin(y[0],y[1],1); + default: + return -__kernel_cos(y[0],y[1]); + } + } +} diff -urN dietlibc-0.30/libm/s_tan.c dietlibc-0.30-libm/libm/s_tan.c --- dietlibc-0.30/libm/s_tan.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_tan.c 2006-06-25 11:20:06.000000000 +0000 @@ -0,0 +1,76 @@ +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $"; +#endif + +/* tan(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tan ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double tan(double x) +#else + double tan(x) + double x; +#endif +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} diff -urN dietlibc-0.30/libm/s_tanh.c dietlibc-0.30-libm/libm/s_tanh.c --- dietlibc-0.30/libm/s_tanh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/s_tanh.c 2006-06-25 11:20:22.000000000 +0000 @@ -0,0 +1,86 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $"; +#endif + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 22.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double one=1.0, two=2.0, tiny = 1.0e-300; +#else +static double one=1.0, two=2.0, tiny = 1.0e-300; +#endif + +#ifdef __STDC__ + double tanh(double x) +#else + double tanh(x) + double x; +#endif +{ + double t,z; + int32_t jx,ix; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3c800000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3ff00000) { /* |x|>=1 */ + t = expm1(two*fabs(x)); + z = one - two/(t+two); + } else { + t = expm1(-two*fabs(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} diff -urN dietlibc-0.30/libm/sinh.c dietlibc-0.30-libm/libm/sinh.c --- dietlibc-0.30/libm/sinh.c 2001-07-27 20:30:34.000000000 +0000 +++ dietlibc-0.30-libm/libm/sinh.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,9 +0,0 @@ -#include - -extern const float __half; - -double sinh ( double x ) -{ - long double y = exp (x); - return (y - 1./y) * __half; -} diff -urN dietlibc-0.30/libm/tanh.c dietlibc-0.30-libm/libm/tanh.c --- dietlibc-0.30/libm/tanh.c 2001-07-27 20:30:34.000000000 +0000 +++ dietlibc-0.30-libm/libm/tanh.c 1970-01-01 00:00:00.000000000 +0000 @@ -1,7 +0,0 @@ -#include - -double tanh ( double x ) -{ - long double y = exp (x + x); - return (y - 1.) / (y + 1.); -} diff -urN dietlibc-0.30/libm/w_acos.c dietlibc-0.30-libm/libm/w_acos.c --- dietlibc-0.30/libm/w_acos.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_acos.c 2006-06-25 11:19:58.000000000 +0000 @@ -0,0 +1,43 @@ +/* @(#)w_acos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_acos.c,v 1.6 1995/05/10 20:48:26 jtc Exp $"; +#endif + +/* + * wrap_acos(x) + */ + +#include "math.h" +#include "math_private.h" + + +#ifdef __STDC__ + double acos(double x) /* wrapper acos */ +#else + double acos(x) /* wrapper acos */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_acos(x); +#else + double z; + z = __ieee754_acos(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>1.0) { + return __kernel_standard(x,x,1); /* acos(|x|>1) */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_acosh.c dietlibc-0.30-libm/libm/w_acosh.c --- dietlibc-0.30/libm/w_acosh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_acosh.c 2006-06-25 11:20:01.000000000 +0000 @@ -0,0 +1,42 @@ +/* @(#)w_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_acosh.c,v 1.6 1995/05/10 20:48:31 jtc Exp $"; +#endif + +/* + * wrapper acosh(x) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double acosh(double x) /* wrapper acosh */ +#else + double acosh(x) /* wrapper acosh */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_acosh(x); +#else + double z; + z = __ieee754_acosh(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<1.0) { + return __kernel_standard(x,x,29); /* acosh(x<1) */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_asin.c dietlibc-0.30-libm/libm/w_asin.c --- dietlibc-0.30/libm/w_asin.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_asin.c 2006-06-25 11:19:58.000000000 +0000 @@ -0,0 +1,44 @@ +/* @(#)w_asin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_asin.c,v 1.6 1995/05/10 20:48:35 jtc Exp $"; +#endif + +/* + * wrapper asin(x) + */ + + +#include "math.h" +#include "math_private.h" + + +#ifdef __STDC__ + double asin(double x) /* wrapper asin */ +#else + double asin(x) /* wrapper asin */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_asin(x); +#else + double z; + z = __ieee754_asin(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>1.0) { + return __kernel_standard(x,x,2); /* asin(|x|>1) */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_atan2.c dietlibc-0.30-libm/libm/w_atan2.c --- dietlibc-0.30/libm/w_atan2.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_atan2.c 2006-06-25 11:20:08.000000000 +0000 @@ -0,0 +1,42 @@ +/* @(#)w_atan2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_atan2.c,v 1.6 1995/05/10 20:48:39 jtc Exp $"; +#endif + +/* + * wrapper atan2(y,x) + */ +#include "math.h" +#include "math_private.h" + + +#ifdef __STDC__ + double atan2(double y, double x) /* wrapper atan2 */ +#else + double atan2(y,x) /* wrapper atan2 */ + double y,x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_atan2(y,x); +#else + double z; + z = __ieee754_atan2(y,x); + if(_LIB_VERSION == _IEEE_||isnan(x)||isnan(y)) return z; + if(x==0.0&&y==0.0) { + return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_atanh.c dietlibc-0.30-libm/libm/w_atanh.c --- dietlibc-0.30/libm/w_atanh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_atanh.c 2006-06-25 11:20:09.000000000 +0000 @@ -0,0 +1,47 @@ +/* @(#)w_atanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_atanh.c,v 1.6 1995/05/10 20:48:43 jtc Exp $"; +#endif + +/* + * wrapper atanh(x) + */ + +#include "math.h" +#include "math_private.h" + + +#ifdef __STDC__ + double atanh(double x) /* wrapper atanh */ +#else + double atanh(x) /* wrapper atanh */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_atanh(x); +#else + double z,y; + z = __ieee754_atanh(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + y = fabs(x); + if(y>=1.0) { + if(y>1.0) + return __kernel_standard(x,x,30); /* atanh(|x|>1) */ + else + return __kernel_standard(x,x,31); /* atanh(|x|==1) */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_cabs.c dietlibc-0.30-libm/libm/w_cabs.c --- dietlibc-0.30/libm/w_cabs.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_cabs.c 2006-06-25 11:19:59.000000000 +0000 @@ -0,0 +1,18 @@ +/* + * cabs() wrapper for hypot(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + */ + +#include + +struct complex { + double x; + double y; +}; + +double cabs(struct complex z) +{ + return hypot(z.x, z.y); +} diff -urN dietlibc-0.30/libm/w_cosh.c dietlibc-0.30-libm/libm/w_cosh.c --- dietlibc-0.30/libm/w_cosh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_cosh.c 2006-06-25 11:19:59.000000000 +0000 @@ -0,0 +1,42 @@ +/* @(#)w_cosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_cosh.c,v 1.6 1995/05/10 20:48:47 jtc Exp $"; +#endif + +/* + * wrapper cosh(x) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double cosh(double x) /* wrapper cosh */ +#else + double cosh(x) /* wrapper cosh */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_cosh(x); +#else + double z; + z = __ieee754_cosh(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>7.10475860073943863426e+02) { + return __kernel_standard(x,x,5); /* cosh overflow */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_drem.c dietlibc-0.30-libm/libm/w_drem.c --- dietlibc-0.30/libm/w_drem.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_drem.c 2006-06-25 11:20:00.000000000 +0000 @@ -0,0 +1,15 @@ +/* + * drem() wrapper for remainder(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + */ + +#include + +double +drem(x, y) + double x, y; +{ + return remainder(x, y); +} diff -urN dietlibc-0.30/libm/w_exp.c dietlibc-0.30-libm/libm/w_exp.c --- dietlibc-0.30/libm/w_exp.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_exp.c 2006-06-25 11:20:19.000000000 +0000 @@ -0,0 +1,54 @@ +/* @(#)w_exp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_exp.c,v 1.6 1995/05/10 20:48:51 jtc Exp $"; +#endif + +/* + * wrapper exp(x) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */ + +#ifdef __STDC__ + double __exp(double x) /* wrapper exp */ +#else + double __exp(x) /* wrapper exp */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_exp(x); +#else + double z; + z = __ieee754_exp(x); + if(_LIB_VERSION == _IEEE_) return z; + if(finite(x)) { + if(x>o_threshold) + return __kernel_standard(x,x,6); /* exp overflow */ + else if(xX_TLOSS) { + return __kernel_standard(x,x,34); /* j0(|x|>X_TLOSS) */ + } else + return z; +#endif +} + +#ifdef __STDC__ + double y0(double x) /* wrapper y0 */ +#else + double y0(x) /* wrapper y0 */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_y0(x); +#else + double z; + z = __ieee754_y0(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(x <= 0.0){ + if(x==0.0) + /* d= -one/(x-x); */ + return __kernel_standard(x,x,8); + else + /* d = zero/(x-x); */ + return __kernel_standard(x,x,9); + } + if(x>X_TLOSS) { + return __kernel_standard(x,x,35); /* y0(x>X_TLOSS) */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_j1.c dietlibc-0.30-libm/libm/w_j1.c --- dietlibc-0.30/libm/w_j1.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_j1.c 2006-06-25 11:20:18.000000000 +0000 @@ -0,0 +1,70 @@ +/* @(#)w_j1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_j1.c,v 1.6 1995/05/10 20:49:15 jtc Exp $"; +#endif + +/* + * wrapper of j1,y1 + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double j1(double x) /* wrapper j1 */ +#else + double j1(x) /* wrapper j1 */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_j1(x); +#else + double z; + z = __ieee754_j1(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(fabs(x)>X_TLOSS) { + return __kernel_standard(x,x,36); /* j1(|x|>X_TLOSS) */ + } else + return z; +#endif +} + +#ifdef __STDC__ + double y1(double x) /* wrapper y1 */ +#else + double y1(x) /* wrapper y1 */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_y1(x); +#else + double z; + z = __ieee754_y1(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(x <= 0.0){ + if(x==0.0) + /* d= -one/(x-x); */ + return __kernel_standard(x,x,10); + else + /* d = zero/(x-x); */ + return __kernel_standard(x,x,11); + } + if(x>X_TLOSS) { + return __kernel_standard(x,x,37); /* y1(x>X_TLOSS) */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_jn.c dietlibc-0.30-libm/libm/w_jn.c --- dietlibc-0.30/libm/w_jn.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_jn.c 2006-06-25 11:20:18.000000000 +0000 @@ -0,0 +1,92 @@ +/* @(#)w_jn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_jn.c,v 1.6 1995/05/10 20:49:19 jtc Exp $"; +#endif + +/* + * wrapper jn(int n, double x), yn(int n, double x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for nx, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double jn(int n, double x) /* wrapper jn */ +#else + double jn(n,x) /* wrapper jn */ + double x; int n; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_jn(n,x); +#else + double z; + z = __ieee754_jn(n,x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(fabs(x)>X_TLOSS) { + return __kernel_standard((double)n,x,38); /* jn(|x|>X_TLOSS,n) */ + } else + return z; +#endif +} + +#ifdef __STDC__ + double yn(int n, double x) /* wrapper yn */ +#else + double yn(n,x) /* wrapper yn */ + double x; int n; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_yn(n,x); +#else + double z; + z = __ieee754_yn(n,x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(x <= 0.0){ + if(x==0.0) + /* d= -one/(x-x); */ + return __kernel_standard((double)n,x,12); + else + /* d = zero/(x-x); */ + return __kernel_standard((double)n,x,13); + } + if(x>X_TLOSS) { + return __kernel_standard((double)n,x,39); /* yn(x>X_TLOSS,n) */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_lgamma.c dietlibc-0.30-libm/libm/w_lgamma.c --- dietlibc-0.30/libm/w_lgamma.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_lgamma.c 2006-06-25 11:20:03.000000000 +0000 @@ -0,0 +1,49 @@ +/* @(#)w_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_lgamma.c,v 1.6 1995/05/10 20:49:24 jtc Exp $"; +#endif + +/* double lgamma(double x) + * Return the logarithm of the Gamma function of x. + * + * Method: call __ieee754_lgamma_r + */ + +#include "math.h" +#include "math_private.h" + +extern int signgam; + +#ifdef __STDC__ + double lgamma(double x) +#else + double lgamma(x) + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_lgamma_r(x,&signgam); +#else + double y; + y = __ieee754_lgamma_r(x,&signgam); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { + if(floor(x)==x&&x<=0.0) + return __kernel_standard(x,x,15); /* lgamma pole */ + else + return __kernel_standard(x,x,14); /* lgamma overflow */ + } else + return y; +#endif +} diff -urN dietlibc-0.30/libm/w_lgamma_r.c dietlibc-0.30-libm/libm/w_lgamma_r.c --- dietlibc-0.30/libm/w_lgamma_r.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_lgamma_r.c 2006-06-25 11:20:11.000000000 +0000 @@ -0,0 +1,46 @@ +/* @(#)wr_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_lgamma_r.c,v 1.6 1995/05/10 20:49:27 jtc Exp $"; +#endif + +/* + * wrapper double lgamma_r(double x, int *signgamp) + */ + +#include "math.h" +#include "math_private.h" + + +#ifdef __STDC__ + double lgamma_r(double x, int *signgamp) /* wrapper lgamma_r */ +#else + double lgamma_r(x,signgamp) /* wrapper lgamma_r */ + double x; int *signgamp; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_lgamma_r(x,signgamp); +#else + double y; + y = __ieee754_lgamma_r(x,signgamp); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { + if(floor(x)==x&&x<=0.0) + return __kernel_standard(x,x,15); /* lgamma pole */ + else + return __kernel_standard(x,x,14); /* lgamma overflow */ + } else + return y; +#endif +} diff -urN dietlibc-0.30/libm/w_log.c dietlibc-0.30-libm/libm/w_log.c --- dietlibc-0.30/libm/w_log.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_log.c 2006-06-25 11:20:19.000000000 +0000 @@ -0,0 +1,43 @@ +/* @(#)w_log.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_log.c,v 1.6 1995/05/10 20:49:33 jtc Exp $"; +#endif + +/* + * wrapper log(x) + */ + +#include "math.h" +#include "math_private.h" + + +#ifdef __STDC__ + double log(double x) /* wrapper log */ +#else + double log(x) /* wrapper log */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_log(x); +#else + double z; + z = __ieee754_log(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z; + if(x==0.0) + return __kernel_standard(x,x,16); /* log(0) */ + else + return __kernel_standard(x,x,17); /* log(x<0) */ +#endif +} diff -urN dietlibc-0.30/libm/w_log10.c dietlibc-0.30-libm/libm/w_log10.c --- dietlibc-0.30/libm/w_log10.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_log10.c 2006-06-25 11:20:21.000000000 +0000 @@ -0,0 +1,46 @@ +/* @(#)w_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_log10.c,v 1.6 1995/05/10 20:49:35 jtc Exp $"; +#endif + +/* + * wrapper log10(X) + */ + +#include "math.h" +#include "math_private.h" + + +#ifdef __STDC__ + double log10(double x) /* wrapper log10 */ +#else + double log10(x) /* wrapper log10 */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_log10(x); +#else + double z; + z = __ieee754_log10(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<=0.0) { + if(x==0.0) + return __kernel_standard(x,x,18); /* log10(0) */ + else + return __kernel_standard(x,x,19); /* log10(x<0) */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_pow.c dietlibc-0.30-libm/libm/w_pow.c --- dietlibc-0.30/libm/w_pow.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_pow.c 2006-06-25 11:20:19.000000000 +0000 @@ -0,0 +1,61 @@ + + +/* @(#)w_pow.c 5.2 93/10/01 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * wrapper pow(x,y) return x**y + */ + +#include "math.h" +#include "math_private.h" + + +#ifdef __STDC__ + double pow(double x, double y) /* wrapper pow */ +#else + double pow(x,y) /* wrapper pow */ + double x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_pow(x,y); +#else + double z; + z=__ieee754_pow(x,y); + if(_LIB_VERSION == _IEEE_|| isnan(y)) return z; + if(isnan(x)) { + if(y==0.0) + return __kernel_standard(x,y,42); /* pow(NaN,0.0) */ + else + return z; + } + if(x==0.0){ + if(y==0.0) + return __kernel_standard(x,y,20); /* pow(0.0,0.0) */ + if(finite(y)&&y<0.0) + return __kernel_standard(x,y,23); /* pow(0.0,negative) */ + return z; + } + if(!finite(z)) { + if(finite(x)&&finite(y)) { + if(isnan(z)) + return __kernel_standard(x,y,24); /* pow neg**non-int */ + else + return __kernel_standard(x,y,21); /* pow overflow */ + } + } + if(z==0.0&&finite(x)&&finite(y)) + return __kernel_standard(x,y,22); /* pow underflow */ + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_remainder.c dietlibc-0.30-libm/libm/w_remainder.c --- dietlibc-0.30/libm/w_remainder.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_remainder.c 2006-06-25 11:20:14.000000000 +0000 @@ -0,0 +1,42 @@ +/* @(#)w_remainder.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_remainder.c,v 1.6 1995/05/10 20:49:44 jtc Exp $"; +#endif + +/* + * wrapper remainder(x,p) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double remainder(double x, double y) /* wrapper remainder */ +#else + double remainder(x,y) /* wrapper remainder */ + double x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_remainder(x,y); +#else + double z; + z = __ieee754_remainder(x,y); + if(_LIB_VERSION == _IEEE_ || isnan(y)) return z; + if(y==0.0) + return __kernel_standard(x,y,28); /* remainder(x,0) */ + else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_scalb.c dietlibc-0.30-libm/libm/w_scalb.c --- dietlibc-0.30/libm/w_scalb.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_scalb.c 2006-06-25 11:20:19.000000000 +0000 @@ -0,0 +1,60 @@ +/* @(#)w_scalb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_scalb.c,v 1.6 1995/05/10 20:49:48 jtc Exp $"; +#endif + +/* + * wrapper scalb(double x, double fn) is provide for + * passing various standard test suite. One + * should use scalbn() instead. + */ + +#include "math.h" +#include "math_private.h" + +#include + +#ifdef __STDC__ +#ifdef _SCALB_INT + double scalb(double x, int fn) /* wrapper scalb */ +#else + double scalb(double x, double fn) /* wrapper scalb */ +#endif +#else + double scalb(x,fn) /* wrapper scalb */ +#ifdef _SCALB_INT + double x; int fn; +#else + double x,fn; +#endif +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_scalb(x,fn); +#else + double z; + z = __ieee754_scalb(x,fn); + if(_LIB_VERSION == _IEEE_) return z; + if(!(finite(z)||isnan(z))&&finite(x)) { + return __kernel_standard(x,(double)fn,32); /* scalb overflow */ + } + if(z==0.0&&z!=x) { + return __kernel_standard(x,(double)fn,33); /* scalb underflow */ + } +#ifndef _SCALB_INT + if(!finite(fn)) errno = ERANGE; +#endif + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_sinh.c dietlibc-0.30-libm/libm/w_sinh.c --- dietlibc-0.30/libm/w_sinh.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_sinh.c 2006-06-25 11:20:07.000000000 +0000 @@ -0,0 +1,42 @@ +/* @(#)w_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_sinh.c,v 1.6 1995/05/10 20:49:51 jtc Exp $"; +#endif + +/* + * wrapper sinh(x) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double sinh(double x) /* wrapper sinh */ +#else + double sinh(x) /* wrapper sinh */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_sinh(x); +#else + double z; + z = __ieee754_sinh(x); + if(_LIB_VERSION == _IEEE_) return z; + if(!finite(z)&&finite(x)) { + return __kernel_standard(x,x,25); /* sinh overflow */ + } else + return z; +#endif +} diff -urN dietlibc-0.30/libm/w_sqrt.c dietlibc-0.30-libm/libm/w_sqrt.c --- dietlibc-0.30/libm/w_sqrt.c 1970-01-01 00:00:00.000000000 +0000 +++ dietlibc-0.30-libm/libm/w_sqrt.c 2006-06-25 11:20:08.000000000 +0000 @@ -0,0 +1,42 @@ +/* @(#)w_sqrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#if defined(LIBM_SCCS) && !defined(lint) +static char rcsid[] = "$NetBSD: w_sqrt.c,v 1.6 1995/05/10 20:49:55 jtc Exp $"; +#endif + +/* + * wrapper sqrt(x) + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ + double sqrt(double x) /* wrapper sqrt */ +#else + double sqrt(x) /* wrapper sqrt */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_sqrt(x); +#else + double z; + z = __ieee754_sqrt(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<0.0) { + return __kernel_standard(x,x,26); /* sqrt(negative) */ + } else + return z; +#endif +}