mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-12 22:30:12 +00:00
46a3d3c7d6
This patch fixes bug 17050, missing errno setting for y1 overflow (for small positive arguments). An appropriate check is added for overflow directly in the __ieee754_y1 implementation, similar to the check present for yn (doing it there rather than in the wrapper also avoids yn needing to repeat the check when called for order 1 or -1 and it uses __ieee754_y1). Tested x86_64 and x86; no ulps update needed. Also tested for mips64 to verify the ldbl-128 fix (the ldbl-128ibm code just #includes the ldbl-128 file). [BZ #17050] * sysdeps/ieee754/dbl-64/e_j1.c: Include <errno.h>. (__ieee754_y1): Set errno if return value overflows. * sysdeps/ieee754/flt-32/e_j1f.c: Include <errno.h>. (__ieee754_y1f): Set errno if return value overflows. * sysdeps/ieee754/ldbl-128/e_j1l.c: Include <errno.h>. (__ieee754_y1l): Set errno if return value overflows. * sysdeps/ieee754/ldbl-96/e_j1l.c: Include <errno.h>. (__ieee754_y1l): Set errno if return value overflows. * math/auto-libm-test-in: Add more tests of y0, y1 and yn. * math/auto-libm-test-out: Regenerated.
339 lines
9.8 KiB
C
339 lines
9.8 KiB
C
/* 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.
|
|
* ====================================================
|
|
*/
|
|
|
|
#include <errno.h>
|
|
#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(__builtin_expect(ix>=0x7f800000, 0)) return one/x;
|
|
y = fabsf(x);
|
|
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
|
__sincosf (y, &s, &c);
|
|
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)/__ieee754_sqrtf(y);
|
|
else {
|
|
u = ponef(y); v = qonef(y);
|
|
z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y);
|
|
}
|
|
if(hx<0) return -z;
|
|
else return z;
|
|
}
|
|
if(__builtin_expect(ix<0x32000000, 0)) { /* |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);
|
|
}
|
|
strong_alias (__ieee754_j1f, __j1f_finite)
|
|
|
|
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(__builtin_expect(ix>=0x7f800000, 0)) return one/(x+x*x);
|
|
if(__builtin_expect(ix==0, 0))
|
|
return -HUGE_VALF+x; /* -inf and overflow exception. */
|
|
if(__builtin_expect(hx<0, 0)) return zero/(zero*x);
|
|
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
|
SET_RESTORE_ROUNDF (FE_TONEAREST);
|
|
__sincosf (x, &s, &c);
|
|
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)/__ieee754_sqrtf(x);
|
|
else {
|
|
u = ponef(x); v = qonef(x);
|
|
z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
|
|
}
|
|
return z;
|
|
}
|
|
if(__builtin_expect(ix<=0x33000000, 0)) { /* x < 2**-25 */
|
|
z = -tpi / x;
|
|
if (__isinff (z))
|
|
__set_errno (ERANGE);
|
|
return z;
|
|
}
|
|
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));
|
|
}
|
|
strong_alias (__ieee754_y1f, __y1f_finite)
|
|
|
|
/* 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;
|
|
}
|