glibc/sysdeps/ieee754/flt-32/e_jnf.c
Joseph Myers be25493251 Fix yn overflow handling in non-default rounding modes (bug 16561, bug 16562).
This patch fixes bugs 16561 and 16562, bad results of yn in overflow
cases in non-default rounding modes, both because an intermediate
overflow in the recurrence does not get detected if the result is not
an infinity and because an overflowing result may occur in the wrong
sign.  The fix is to set FE_TONEAREST mode internally for the parts of
the function where such overflows can occur (which includes the call
to y1 - where yn is used to compute a Bessel function of order -1,
negating the result of y1 isn't correct for overflowing results in
directed rounding modes) and then compute an overflowing value in the
original rounding mode if the to-nearest result was an infinity.

Tested x86_64 and x86 and ulps updated accordingly.  Also tested for
mips64 and powerpc32 to test the ldbl-128 and ldbl-128ibm changes.

(The tests for these bugs were added in my previous y1 patch, so the
only thing this patch has to do with the testsuite is enable yn
testing in all rounding modes.)

	[BZ #16561]
	[BZ #16562]
	* sysdeps/ieee754/dbl-64/e_jn.c: Include <float.h>.
	(__ieee754_yn): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/flt-32/e_jnf.c: Include <float.h>.
	(__ieee754_ynf): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/ldbl-128/e_jnl.c: Include <float.h>.
	(__ieee754_ynl): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/ldbl-128ibm/e_jnl.c: Include <float.h>.
	(__ieee754_ynl): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/ldbl-96/e_jnl.c: Include <float.h>.
	(__ieee754_ynl): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/i386/fpu/fenv_private.h [!__SSE2_MATH__]
	(libc_feholdsetround_ctx): New macro.
	* math/libm-test.inc (yn_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps : Likewise.
2014-06-27 14:52:13 +00:00

221 lines
5.3 KiB
C

/* e_jnf.c -- float version of e_jn.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 <float.h>
#include <math.h>
#include <math_private.h>
static const float
two = 2.0000000000e+00, /* 0x40000000 */
one = 1.0000000000e+00; /* 0x3F800000 */
static const float zero = 0.0000000000e+00;
float
__ieee754_jnf(int n, float x)
{
int32_t i,hx,ix, sgn;
float a, b, temp, di;
float z, w;
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
* Thus, J(-n,x) = J(n,-x)
*/
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* if J(n,NaN) is NaN */
if(__builtin_expect(ix>0x7f800000, 0)) return x+x;
if(n<0){
n = -n;
x = -x;
hx ^= 0x80000000;
}
if(n==0) return(__ieee754_j0f(x));
if(n==1) return(__ieee754_j1f(x));
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
x = fabsf(x);
if(__builtin_expect(ix==0||ix>=0x7f800000, 0)) /* if x is 0 or inf */
b = zero;
else if((float)n<=x) {
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
a = __ieee754_j0f(x);
b = __ieee754_j1f(x);
for(i=1;i<n;i++){
temp = b;
b = b*((double)(i+i)/x) - a; /* avoid underflow */
a = temp;
}
} else {
if(ix<0x30800000) { /* x < 2**-29 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if(n>33) /* underflow */
b = zero;
else {
temp = x*(float)0.5; b = temp;
for (a=one,i=2;i<=n;i++) {
a *= (float)i; /* a = n! */
b *= temp; /* b = (x/2)^n */
}
b = b/a;
}
} else {
/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
float t,v;
float q0,q1,h,tmp; int32_t k,m;
w = (n+n)/(float)x; h = (float)2.0/(float)x;
q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1;
while(q1<(float)1.0e9) {
k += 1; z += h;
tmp = z*q1 - q0;
q0 = q1;
q1 = tmp;
}
m = n+n;
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
a = t;
b = one;
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = n;
v = two/x;
tmp = tmp*__ieee754_logf(fabsf(v*tmp));
if(tmp<(float)8.8721679688e+01) {
for(i=n-1,di=(float)(i+i);i>0;i--){
temp = b;
b *= di;
b = b/x - a;
a = temp;
di -= two;
}
} else {
for(i=n-1,di=(float)(i+i);i>0;i--){
temp = b;
b *= di;
b = b/x - a;
a = temp;
di -= two;
/* scale b to avoid spurious overflow */
if(b>(float)1e10) {
a /= b;
t /= b;
b = one;
}
}
}
/* j0() and j1() suffer enormous loss of precision at and
* near zero; however, we know that their zero points never
* coincide, so just choose the one further away from zero.
*/
z = __ieee754_j0f (x);
w = __ieee754_j1f (x);
if (fabsf (z) >= fabsf (w))
b = (t * z / b);
else
b = (t * w / a);
}
}
if(sgn==1) return -b; else return b;
}
strong_alias (__ieee754_jnf, __jnf_finite)
float
__ieee754_ynf(int n, float x)
{
float ret;
{
int32_t i,hx,ix;
u_int32_t ib;
int32_t sign;
float a, b, temp;
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
/* if Y(n,NaN) is NaN */
if(__builtin_expect(ix>0x7f800000, 0)) return 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);
sign = 1;
if(n<0){
n = -n;
sign = 1 - ((n&1)<<1);
}
if(n==0) return(__ieee754_y0f(x));
SET_RESTORE_ROUNDF (FE_TONEAREST);
if(n==1) {
ret = sign*__ieee754_y1f(x);
goto out;
}
if(__builtin_expect(ix==0x7f800000, 0)) return zero;
a = __ieee754_y0f(x);
b = __ieee754_y1f(x);
/* quit if b is -inf */
GET_FLOAT_WORD(ib,b);
for(i=1;i<n&&ib!=0xff800000;i++){
temp = b;
b = ((double)(i+i)/x)*b - a;
GET_FLOAT_WORD(ib,b);
a = temp;
}
/* If B is +-Inf, set up errno accordingly. */
if (! __finitef (b))
__set_errno (ERANGE);
if(sign>0) ret = b; else ret = -b;
}
out:
if (__isinff (ret))
ret = __copysignf (FLT_MAX, ret) * FLT_MAX;
return ret;
}
strong_alias (__ieee754_ynf, __ynf_finite)