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author | Ulrich Drepper <drepper@redhat.com> | 1999-07-14 00:54:57 +0000 |
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committer | Ulrich Drepper <drepper@redhat.com> | 1999-07-14 00:54:57 +0000 |
commit | abfbdde177c3a7155070dda1b2cdc8292054cc26 (patch) | |
tree | e021306b596381fbf8311d2b7eb294e918ff17c8 /sysdeps/libm-ieee754/e_j1f.c | |
parent | 86421aa57ecfd70963ae66848bd6a6dd3b8e0fe6 (diff) | |
download | glibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.tar.gz glibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.tar.xz glibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.zip |
Update.
Diffstat (limited to 'sysdeps/libm-ieee754/e_j1f.c')
-rw-r--r-- | sysdeps/libm-ieee754/e_j1f.c | 444 |
1 files changed, 0 insertions, 444 deletions
diff --git a/sysdeps/libm-ieee754/e_j1f.c b/sysdeps/libm-ieee754/e_j1f.c deleted file mode 100644 index e6f14a16ac..0000000000 --- a/sysdeps/libm-ieee754/e_j1f.c +++ /dev/null @@ -1,444 +0,0 @@ -/* e_j1f.c -- float version of e_j1.c. - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ - -/* - * ==================================================== - * 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_j1f.c,v 1.4 1995/05/10 20:45:31 jtc Exp $"; -#endif - -#include "math.h" -#include "math_private.h" - -#ifdef __STDC__ -static float ponef(float), qonef(float); -#else -static float ponef(), qonef(); -#endif - -#ifdef __STDC__ -static const float -#else -static float -#endif -huge = 1e30, -one = 1.0, -invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ -tpi = 6.3661974669e-01, /* 0x3f22f983 */ - /* R0/S0 on [0,2] */ -r00 = -6.2500000000e-02, /* 0xbd800000 */ -r01 = 1.4070566976e-03, /* 0x3ab86cfd */ -r02 = -1.5995563444e-05, /* 0xb7862e36 */ -r03 = 4.9672799207e-08, /* 0x335557d2 */ -s01 = 1.9153760746e-02, /* 0x3c9ce859 */ -s02 = 1.8594678841e-04, /* 0x3942fab6 */ -s03 = 1.1771846857e-06, /* 0x359dffc2 */ -s04 = 5.0463624390e-09, /* 0x31ad6446 */ -s05 = 1.2354227016e-11; /* 0x2d59567e */ - -#ifdef __STDC__ -static const float zero = 0.0; -#else -static float zero = 0.0; -#endif - -#ifdef __STDC__ - float __ieee754_j1f(float x) -#else - float __ieee754_j1f(x) - float x; -#endif -{ - float z, s,c,ss,cc,r,u,v,y; - int32_t hx,ix; - - GET_FLOAT_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix>=0x7f800000) return one/x; - y = fabsf(x); - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = __sinf(y); - c = __cosf(y); - ss = -s-c; - cc = s-c; - if(ix<0x7f000000) { /* make sure y+y not overflow */ - z = __cosf(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)/__sqrtf(y); - else { - u = ponef(y); v = qonef(y); - z = invsqrtpi*(u*cc-v*ss)/__sqrtf(y); - } - if(hx<0) return -z; - else return z; - } - if(ix<0x32000000) { /* |x|<2**-27 */ - if(huge+x>one) return (float)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*(float)0.5+r/s); -} - -#ifdef __STDC__ -static const float U0[5] = { -#else -static float U0[5] = { -#endif - -1.9605709612e-01, /* 0xbe48c331 */ - 5.0443872809e-02, /* 0x3d4e9e3c */ - -1.9125689287e-03, /* 0xbafaaf2a */ - 2.3525259166e-05, /* 0x37c5581c */ - -9.1909917899e-08, /* 0xb3c56003 */ -}; -#ifdef __STDC__ -static const float V0[5] = { -#else -static float V0[5] = { -#endif - 1.9916731864e-02, /* 0x3ca3286a */ - 2.0255257550e-04, /* 0x3954644b */ - 1.3560879779e-06, /* 0x35b602d4 */ - 6.2274145840e-09, /* 0x31d5f8eb */ - 1.6655924903e-11, /* 0x2d9281cf */ -}; - -#ifdef __STDC__ - float __ieee754_y1f(float x) -#else - float __ieee754_y1f(x) - float x; -#endif -{ - float z, s,c,ss,cc,u,v; - int32_t hx,ix; - - GET_FLOAT_WORD(hx,x); - ix = 0x7fffffff&hx; - /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ - if(ix>=0x7f800000) return one/(x+x*x); - if(ix==0) return -one/zero; - if(hx<0) return zero/zero; - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = __sinf(x); - c = __cosf(x); - ss = -s-c; - cc = s-c; - if(ix<0x7f000000) { /* make sure x+x not overflow */ - z = __cosf(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)/__sqrtf(x); - else { - u = ponef(x); v = qonef(x); - z = invsqrtpi*(u*ss+v*cc)/__sqrtf(x); - } - return z; - } - if(ix<=0x24800000) { /* 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_j1f(x)*__ieee754_logf(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 float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.0000000000e+00, /* 0x00000000 */ - 1.1718750000e-01, /* 0x3df00000 */ - 1.3239480972e+01, /* 0x4153d4ea */ - 4.1205184937e+02, /* 0x43ce06a3 */ - 3.8747453613e+03, /* 0x45722bed */ - 7.9144794922e+03, /* 0x45f753d6 */ -}; -#ifdef __STDC__ -static const float ps8[5] = { -#else -static float ps8[5] = { -#endif - 1.1420736694e+02, /* 0x42e46a2c */ - 3.6509309082e+03, /* 0x45642ee5 */ - 3.6956207031e+04, /* 0x47105c35 */ - 9.7602796875e+04, /* 0x47bea166 */ - 3.0804271484e+04, /* 0x46f0a88b */ -}; - -#ifdef __STDC__ -static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - 1.3199052094e-11, /* 0x2d68333f */ - 1.1718749255e-01, /* 0x3defffff */ - 6.8027510643e+00, /* 0x40d9b023 */ - 1.0830818176e+02, /* 0x42d89dca */ - 5.1763616943e+02, /* 0x440168b7 */ - 5.2871520996e+02, /* 0x44042dc6 */ -}; -#ifdef __STDC__ -static const float ps5[5] = { -#else -static float ps5[5] = { -#endif - 5.9280597687e+01, /* 0x426d1f55 */ - 9.9140142822e+02, /* 0x4477d9b1 */ - 5.3532670898e+03, /* 0x45a74a23 */ - 7.8446904297e+03, /* 0x45f52586 */ - 1.5040468750e+03, /* 0x44bc0180 */ -}; - -#ifdef __STDC__ -static const float pr3[6] = { -#else -static float pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - 3.0250391081e-09, /* 0x314fe10d */ - 1.1718686670e-01, /* 0x3defffab */ - 3.9329774380e+00, /* 0x407bb5e7 */ - 3.5119403839e+01, /* 0x420c7a45 */ - 9.1055007935e+01, /* 0x42b61c2a */ - 4.8559066772e+01, /* 0x42423c7c */ -}; -#ifdef __STDC__ -static const float ps3[5] = { -#else -static float ps3[5] = { -#endif - 3.4791309357e+01, /* 0x420b2a4d */ - 3.3676245117e+02, /* 0x43a86198 */ - 1.0468714600e+03, /* 0x4482dbe3 */ - 8.9081134033e+02, /* 0x445eb3ed */ - 1.0378793335e+02, /* 0x42cf936c */ -}; - -#ifdef __STDC__ -static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - 1.0771083225e-07, /* 0x33e74ea8 */ - 1.1717621982e-01, /* 0x3deffa16 */ - 2.3685150146e+00, /* 0x401795c0 */ - 1.2242610931e+01, /* 0x4143e1bc */ - 1.7693971634e+01, /* 0x418d8d41 */ - 5.0735230446e+00, /* 0x40a25a4d */ -}; -#ifdef __STDC__ -static const float ps2[5] = { -#else -static float ps2[5] = { -#endif - 2.1436485291e+01, /* 0x41ab7dec */ - 1.2529022980e+02, /* 0x42fa9499 */ - 2.3227647400e+02, /* 0x436846c7 */ - 1.1767937469e+02, /* 0x42eb5bd7 */ - 8.3646392822e+00, /* 0x4105d590 */ -}; - -#ifdef __STDC__ - static float ponef(float x) -#else - static float ponef(x) - float x; -#endif -{ -#ifdef __STDC__ - const float *p,*q; -#else - float *p,*q; -#endif - float z,r,s; - int32_t ix; - GET_FLOAT_WORD(ix,x); - ix &= 0x7fffffff; - if(ix>=0x41000000) {p = pr8; q= ps8;} - else if(ix>=0x40f71c58){p = pr5; q= ps5;} - else if(ix>=0x4036db68){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 float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.0000000000e+00, /* 0x00000000 */ - -1.0253906250e-01, /* 0xbdd20000 */ - -1.6271753311e+01, /* 0xc1822c8d */ - -7.5960174561e+02, /* 0xc43de683 */ - -1.1849806641e+04, /* 0xc639273a */ - -4.8438511719e+04, /* 0xc73d3683 */ -}; -#ifdef __STDC__ -static const float qs8[6] = { -#else -static float qs8[6] = { -#endif - 1.6139537048e+02, /* 0x43216537 */ - 7.8253862305e+03, /* 0x45f48b17 */ - 1.3387534375e+05, /* 0x4802bcd6 */ - 7.1965775000e+05, /* 0x492fb29c */ - 6.6660125000e+05, /* 0x4922be94 */ - -2.9449025000e+05, /* 0xc88fcb48 */ -}; - -#ifdef __STDC__ -static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - -2.0897993405e-11, /* 0xadb7d219 */ - -1.0253904760e-01, /* 0xbdd1fffe */ - -8.0564479828e+00, /* 0xc100e736 */ - -1.8366960144e+02, /* 0xc337ab6b */ - -1.3731937256e+03, /* 0xc4aba633 */ - -2.6124443359e+03, /* 0xc523471c */ -}; -#ifdef __STDC__ -static const float qs5[6] = { -#else -static float qs5[6] = { -#endif - 8.1276550293e+01, /* 0x42a28d98 */ - 1.9917987061e+03, /* 0x44f8f98f */ - 1.7468484375e+04, /* 0x468878f8 */ - 4.9851425781e+04, /* 0x4742bb6d */ - 2.7948074219e+04, /* 0x46da5826 */ - -4.7191835938e+03, /* 0xc5937978 */ -}; - -#ifdef __STDC__ -static const float qr3[6] = { -#else -static float qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - -5.0783124372e-09, /* 0xb1ae7d4f */ - -1.0253783315e-01, /* 0xbdd1ff5b */ - -4.6101160049e+00, /* 0xc0938612 */ - -5.7847221375e+01, /* 0xc267638e */ - -2.2824453735e+02, /* 0xc3643e9a */ - -2.1921012878e+02, /* 0xc35b35cb */ -}; -#ifdef __STDC__ -static const float qs3[6] = { -#else -static float qs3[6] = { -#endif - 4.7665153503e+01, /* 0x423ea91e */ - 6.7386511230e+02, /* 0x4428775e */ - 3.3801528320e+03, /* 0x45534272 */ - 5.5477290039e+03, /* 0x45ad5dd5 */ - 1.9031191406e+03, /* 0x44ede3d0 */ - -1.3520118713e+02, /* 0xc3073381 */ -}; - -#ifdef __STDC__ -static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - -1.7838172539e-07, /* 0xb43f8932 */ - -1.0251704603e-01, /* 0xbdd1f475 */ - -2.7522056103e+00, /* 0xc0302423 */ - -1.9663616180e+01, /* 0xc19d4f16 */ - -4.2325313568e+01, /* 0xc2294d1f */ - -2.1371921539e+01, /* 0xc1aaf9b2 */ -}; -#ifdef __STDC__ -static const float qs2[6] = { -#else -static float qs2[6] = { -#endif - 2.9533363342e+01, /* 0x41ec4454 */ - 2.5298155212e+02, /* 0x437cfb47 */ - 7.5750280762e+02, /* 0x443d602e */ - 7.3939318848e+02, /* 0x4438d92a */ - 1.5594900513e+02, /* 0x431bf2f2 */ - -4.9594988823e+00, /* 0xc09eb437 */ -}; - -#ifdef __STDC__ - static float qonef(float x) -#else - static float qonef(x) - float x; -#endif -{ -#ifdef __STDC__ - const float *p,*q; -#else - float *p,*q; -#endif - float s,r,z; - int32_t ix; - GET_FLOAT_WORD(ix,x); - ix &= 0x7fffffff; - if(ix>=0x40200000) {p = qr8; q= qs8;} - else if(ix>=0x40f71c58){p = qr5; q= qs5;} - else if(ix>=0x4036db68){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 ((float).375 + r/s)/x; -} |