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-rw-r--r--libm/src/e_j1f.c334
1 files changed, 0 insertions, 334 deletions
diff --git a/libm/src/e_j1f.c b/libm/src/e_j1f.c
deleted file mode 100644
index 539399e..0000000
--- a/libm/src/e_j1f.c
+++ /dev/null
@@ -1,334 +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.
- * ====================================================
- */
-
-#ifndef lint
-static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_j1f.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
-#endif
-
-#include "math.h"
-#include "math_private.h"
-
-static float ponef(float), qonef(float);
-
-static const float
-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 */
-
-static const float zero = 0.0;
-
-float
-__ieee754_j1f(float x)
-{
- 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>0x80000000) 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);
-}
-
-static const float U0[5] = {
- -1.9605709612e-01, /* 0xbe48c331 */
- 5.0443872809e-02, /* 0x3d4e9e3c */
- -1.9125689287e-03, /* 0xbafaaf2a */
- 2.3525259166e-05, /* 0x37c5581c */
- -9.1909917899e-08, /* 0xb3c56003 */
-};
-static const float V0[5] = {
- 1.9916731864e-02, /* 0x3ca3286a */
- 2.0255257550e-04, /* 0x3954644b */
- 1.3560879779e-06, /* 0x35b602d4 */
- 6.2274145840e-09, /* 0x31d5f8eb */
- 1.6655924903e-11, /* 0x2d9281cf */
-};
-
-float
-__ieee754_y1f(float x)
-{
- 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)
- */
-
-static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
- 0.0000000000e+00, /* 0x00000000 */
- 1.1718750000e-01, /* 0x3df00000 */
- 1.3239480972e+01, /* 0x4153d4ea */
- 4.1205184937e+02, /* 0x43ce06a3 */
- 3.8747453613e+03, /* 0x45722bed */
- 7.9144794922e+03, /* 0x45f753d6 */
-};
-static const float ps8[5] = {
- 1.1420736694e+02, /* 0x42e46a2c */
- 3.6509309082e+03, /* 0x45642ee5 */
- 3.6956207031e+04, /* 0x47105c35 */
- 9.7602796875e+04, /* 0x47bea166 */
- 3.0804271484e+04, /* 0x46f0a88b */
-};
-
-static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
- 1.3199052094e-11, /* 0x2d68333f */
- 1.1718749255e-01, /* 0x3defffff */
- 6.8027510643e+00, /* 0x40d9b023 */
- 1.0830818176e+02, /* 0x42d89dca */
- 5.1763616943e+02, /* 0x440168b7 */
- 5.2871520996e+02, /* 0x44042dc6 */
-};
-static const float ps5[5] = {
- 5.9280597687e+01, /* 0x426d1f55 */
- 9.9140142822e+02, /* 0x4477d9b1 */
- 5.3532670898e+03, /* 0x45a74a23 */
- 7.8446904297e+03, /* 0x45f52586 */
- 1.5040468750e+03, /* 0x44bc0180 */
-};
-
-static const float pr3[6] = {
- 3.0250391081e-09, /* 0x314fe10d */
- 1.1718686670e-01, /* 0x3defffab */
- 3.9329774380e+00, /* 0x407bb5e7 */
- 3.5119403839e+01, /* 0x420c7a45 */
- 9.1055007935e+01, /* 0x42b61c2a */
- 4.8559066772e+01, /* 0x42423c7c */
-};
-static const float ps3[5] = {
- 3.4791309357e+01, /* 0x420b2a4d */
- 3.3676245117e+02, /* 0x43a86198 */
- 1.0468714600e+03, /* 0x4482dbe3 */
- 8.9081134033e+02, /* 0x445eb3ed */
- 1.0378793335e+02, /* 0x42cf936c */
-};
-
-static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
- 1.0771083225e-07, /* 0x33e74ea8 */
- 1.1717621982e-01, /* 0x3deffa16 */
- 2.3685150146e+00, /* 0x401795c0 */
- 1.2242610931e+01, /* 0x4143e1bc */
- 1.7693971634e+01, /* 0x418d8d41 */
- 5.0735230446e+00, /* 0x40a25a4d */
-};
-static const float ps2[5] = {
- 2.1436485291e+01, /* 0x41ab7dec */
- 1.2529022980e+02, /* 0x42fa9499 */
- 2.3227647400e+02, /* 0x436846c7 */
- 1.1767937469e+02, /* 0x42eb5bd7 */
- 8.3646392822e+00, /* 0x4105d590 */
-};
-
- static float ponef(float x)
-{
- const float *p,*q;
- 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)
- */
-
-static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
- 0.0000000000e+00, /* 0x00000000 */
- -1.0253906250e-01, /* 0xbdd20000 */
- -1.6271753311e+01, /* 0xc1822c8d */
- -7.5960174561e+02, /* 0xc43de683 */
- -1.1849806641e+04, /* 0xc639273a */
- -4.8438511719e+04, /* 0xc73d3683 */
-};
-static const float qs8[6] = {
- 1.6139537048e+02, /* 0x43216537 */
- 7.8253862305e+03, /* 0x45f48b17 */
- 1.3387534375e+05, /* 0x4802bcd6 */
- 7.1965775000e+05, /* 0x492fb29c */
- 6.6660125000e+05, /* 0x4922be94 */
- -2.9449025000e+05, /* 0xc88fcb48 */
-};
-
-static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
- -2.0897993405e-11, /* 0xadb7d219 */
- -1.0253904760e-01, /* 0xbdd1fffe */
- -8.0564479828e+00, /* 0xc100e736 */
- -1.8366960144e+02, /* 0xc337ab6b */
- -1.3731937256e+03, /* 0xc4aba633 */
- -2.6124443359e+03, /* 0xc523471c */
-};
-static const float qs5[6] = {
- 8.1276550293e+01, /* 0x42a28d98 */
- 1.9917987061e+03, /* 0x44f8f98f */
- 1.7468484375e+04, /* 0x468878f8 */
- 4.9851425781e+04, /* 0x4742bb6d */
- 2.7948074219e+04, /* 0x46da5826 */
- -4.7191835938e+03, /* 0xc5937978 */
-};
-
-static const float qr3[6] = {
- -5.0783124372e-09, /* 0xb1ae7d4f */
- -1.0253783315e-01, /* 0xbdd1ff5b */
- -4.6101160049e+00, /* 0xc0938612 */
- -5.7847221375e+01, /* 0xc267638e */
- -2.2824453735e+02, /* 0xc3643e9a */
- -2.1921012878e+02, /* 0xc35b35cb */
-};
-static const float qs3[6] = {
- 4.7665153503e+01, /* 0x423ea91e */
- 6.7386511230e+02, /* 0x4428775e */
- 3.3801528320e+03, /* 0x45534272 */
- 5.5477290039e+03, /* 0x45ad5dd5 */
- 1.9031191406e+03, /* 0x44ede3d0 */
- -1.3520118713e+02, /* 0xc3073381 */
-};
-
-static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
- -1.7838172539e-07, /* 0xb43f8932 */
- -1.0251704603e-01, /* 0xbdd1f475 */
- -2.7522056103e+00, /* 0xc0302423 */
- -1.9663616180e+01, /* 0xc19d4f16 */
- -4.2325313568e+01, /* 0xc2294d1f */
- -2.1371921539e+01, /* 0xc1aaf9b2 */
-};
-static const float qs2[6] = {
- 2.9533363342e+01, /* 0x41ec4454 */
- 2.5298155212e+02, /* 0x437cfb47 */
- 7.5750280762e+02, /* 0x443d602e */
- 7.3939318848e+02, /* 0x4438d92a */
- 1.5594900513e+02, /* 0x431bf2f2 */
- -4.9594988823e+00, /* 0xc09eb437 */
-};
-
- static float qonef(float x)
-{
- const float *p,*q;
- 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;
-}
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