| /* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.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. |
| * ==================================================== |
| */ |
| |
| #define _GNU_SOURCE |
| #include "libm.h" |
| |
| static float ponef(float), qonef(float); |
| |
| static const float |
| invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */ |
| tpi = 6.3661974669e-01; /* 0x3f22f983 */ |
| |
| static float common(uint32_t ix, float x, int y1, int sign) |
| { |
| double z,s,c,ss,cc; |
| |
| s = sinf(x); |
| if (y1) |
| s = -s; |
| c = cosf(x); |
| cc = s-c; |
| if (ix < 0x7f000000) { |
| ss = -s-c; |
| z = cosf(2*x); |
| if (s*c > 0) |
| cc = z/ss; |
| else |
| ss = z/cc; |
| if (ix < 0x58800000) { |
| if (y1) |
| ss = -ss; |
| cc = ponef(x)*cc-qonef(x)*ss; |
| } |
| } |
| if (sign) |
| cc = -cc; |
| return invsqrtpi*cc/sqrtf(x); |
| } |
| |
| /* R0/S0 on [0,2] */ |
| static const float |
| 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 */ |
| |
| float j1f(float x) |
| { |
| float z,r,s; |
| uint32_t ix; |
| int sign; |
| |
| GET_FLOAT_WORD(ix, x); |
| sign = ix>>31; |
| ix &= 0x7fffffff; |
| if (ix >= 0x7f800000) |
| return 1/(x*x); |
| if (ix >= 0x40000000) /* |x| >= 2 */ |
| return common(ix, fabsf(x), 0, sign); |
| if (ix >= 0x39000000) { /* |x| >= 2**-13 */ |
| z = x*x; |
| r = z*(r00+z*(r01+z*(r02+z*r03))); |
| s = 1+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); |
| z = 0.5f + r/s; |
| } else |
| z = 0.5f; |
| return z*x; |
| } |
| |
| 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 y1f(float x) |
| { |
| float z,u,v; |
| uint32_t ix; |
| |
| GET_FLOAT_WORD(ix, x); |
| if ((ix & 0x7fffffff) == 0) |
| return -1/0.0f; |
| if (ix>>31) |
| return 0/0.0f; |
| if (ix >= 0x7f800000) |
| return 1/x; |
| if (ix >= 0x40000000) /* |x| >= 2.0 */ |
| return common(ix,x,1,0); |
| if (ix < 0x33000000) /* x < 2**-25 */ |
| return -tpi/x; |
| z = x*x; |
| u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); |
| v = 1.0f+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); |
| return x*(u/v) + tpi*(j1f(x)*logf(x)-1.0f/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_t z,r,s; |
| uint32_t ix; |
| |
| GET_FLOAT_WORD(ix, x); |
| ix &= 0x7fffffff; |
| if (ix >= 0x41000000){p = pr8; q = ps8;} |
| else if (ix >= 0x409173eb){p = pr5; q = ps5;} |
| else if (ix >= 0x4036d917){p = pr3; q = ps3;} |
| else /*ix >= 0x40000000*/ {p = pr2; q = ps2;} |
| z = 1.0f/(x*x); |
| r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
| s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); |
| return 1.0f + 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_t s,r,z; |
| uint32_t ix; |
| |
| GET_FLOAT_WORD(ix, x); |
| ix &= 0x7fffffff; |
| if (ix >= 0x41000000){p = qr8; q = qs8;} |
| else if (ix >= 0x409173eb){p = qr5; q = qs5;} |
| else if (ix >= 0x4036d917){p = qr3; q = qs3;} |
| else /*ix >= 0x40000000*/ {p = qr2; q = qs2;} |
| z = 1.0f/(x*x); |
| r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
| s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); |
| return (.375f + r/s)/x; |
| } |
