glibc/sysdeps/ieee754/flt-32/e_j1f.c
Joseph Myers 09220e6634 Avoid uninitialized warnings in Bessel functions.
math/Makefile currently has:

  # The fdlibm code generates a lot of these warnings but is otherwise clean.
  override CFLAGS += -Wno-uninitialized

This is of course undesirable; warnings should be disabled as narrowly
as possible.  To remove this override, we need to fix files that
generate such warnings, or put warning-disabling pragmas in them.
This patch does so for Bessel function implementations, one of the
cases that have the warnings if the override is removed.  The warnings
arise because functions set pointer variables p and q only for certain
values of the function argument, then use them unconditionally.  As
the static functions in question only get called for arguments that
satisfy the last condition in the if/else chain, the natural fix is to
change the last "else if" to just "else", which this patch does.  (The
ldbl-128 / ldbl-128ibm implementation of these functions is
substantially different and looks like it already does use "else" in
the last case in the nearest corresponding code.)

Tested for x86_64 and x86.

	* sysdeps/ieee754/dbl-64/e_j0.c (pzero): Change last case for
	setting p and q from "else if" to "else".
	(qzero): Likewise.
	* sysdeps/ieee754/dbl-64/e_j1.c (pone): Likewise.
	(qone): Likewise.
	* sysdeps/ieee754/flt-32/e_j0f.c (pzerof): Likewise.
	(qzerof): Likewise.
	* sysdeps/ieee754/flt-32/e_j1f.c (ponef): Likewise.
	(qonef): Likewise.
	* sysdeps/ieee754/ldbl-96/e_j0l.c (pzero): Likewise.
	(qzero): Likewise.
	* sysdeps/ieee754/ldbl-96/e_j1l.c (pone): Likewise.
	(qone): Likewise.
2015-02-26 21:49:19 +00:00

341 lines
9.9 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;
/* ix >= 0x40000000 for all calls to this function. */
if(ix>=0x41000000) {p = pr8; q= ps8;}
else if(ix>=0x40f71c58){p = pr5; q= ps5;}
else if(ix>=0x4036db68){p = pr3; q= ps3;}
else {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;
/* ix >= 0x40000000 for all calls to this function. */
if(ix>=0x40200000) {p = qr8; q= qs8;}
else if(ix>=0x40f71c58){p = qr5; q= qs5;}
else if(ix>=0x4036db68){p = qr3; q= qs3;}
else {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;
}