Szabolcs Nagy
5bb6b24952
a common code path in j1 and y1 was factored out so the resulting object code is a bit smaller unsigned int arithmetics is used for bit manipulation j1(-inf) now returns 0 instead of -0 an incorrect threshold in the common code of j1f and y1f got fixed (this caused spurious overflow and underflow exceptions) the else branch in pone and pzero functions are fixed (so code analyzers dont warn about uninitialized values)
311 lines
8.4 KiB
C
311 lines
8.4 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.c */
|
|
/*
|
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
|
|
*/
|
|
/*
|
|
* ====================================================
|
|
* 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.
|
|
* ====================================================
|
|
*/
|
|
|
|
#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 >= 0x32000000) { /* |x| >= 2**-27 */
|
|
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
|
|
/* raise inexact if x!=0 */
|
|
z = 0.5f + x;
|
|
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 < 0x32000000) /* x < 2**-27 */
|
|
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 z,r,s;
|
|
uint32_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 /*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 s,r,z;
|
|
uint32_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 /*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;
|
|
}
|