3f7e4f1538
The threshold for not being tiny was confusing and too small. Use the usual 2**-12 threshold and simplify the algorithm slightly so that this threshold works (now use the threshold for sinhf() instead of one for 1+expm1()). This is just a small optimization. The magic number 22 is log(DBL_EPSILON)/2 plus slop. This is bogus for float precision. Use 9 (~log(FLT_EPSILON)/2 plus less slop than for double precision). The threshold for switching from returning exp(x)/2 to returning exp(x/2)^2/2 was a little smaller than necessary. This was not quite harmless since the exp(x/2)^2/2 case is inaccurate. Fixing it happens to avoid accuracy problems for 2*6 of the 2*151 args that were handled by the exp(x)/2 case. This leaves accuracy problems for about 2*19997 args near the overflow threshold (~89); the maximum error there is 2.5029 ulps. There are also accuracy probles for args in +-[0.5*ln2, 9] -- 2*188885 args with errors of more than 1 ulp, with a maximum error of 1.384 ulps. Fixed a syntax error and naming errors in pseudo-code in comments.
64 lines
1.5 KiB
C
64 lines
1.5 KiB
C
/* e_coshf.c -- float version of e_cosh.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.
|
|
* ====================================================
|
|
*/
|
|
|
|
#ifndef lint
|
|
static char rcsid[] = "$FreeBSD$";
|
|
#endif
|
|
|
|
#include "math.h"
|
|
#include "math_private.h"
|
|
|
|
static const float one = 1.0, half=0.5, huge = 1.0e30;
|
|
|
|
float
|
|
__ieee754_coshf(float x)
|
|
{
|
|
float t,w;
|
|
int32_t ix;
|
|
|
|
GET_FLOAT_WORD(ix,x);
|
|
ix &= 0x7fffffff;
|
|
|
|
/* x is INF or NaN */
|
|
if(ix>=0x7f800000) return x*x;
|
|
|
|
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
|
|
if(ix<0x3eb17218) {
|
|
t = expm1f(fabsf(x));
|
|
w = one+t;
|
|
if (ix<0x39800000) return one; /* cosh(tiny) = 1 */
|
|
return one+(t*t)/(w+w);
|
|
}
|
|
|
|
/* |x| in [0.5*ln2,9], return (exp(|x|)+1/exp(|x|))/2; */
|
|
if (ix < 0x41100000) {
|
|
t = __ieee754_expf(fabsf(x));
|
|
return half*t+half/t;
|
|
}
|
|
|
|
/* |x| in [9, log(maxfloat)] return half*exp(|x|) */
|
|
if (ix < 0x42b17217) return half*__ieee754_expf(fabsf(x));
|
|
|
|
/* |x| in [log(maxfloat), overflowthresold] */
|
|
if (ix<=0x42b2d4fc) {
|
|
w = __ieee754_expf(half*fabsf(x));
|
|
t = half*w;
|
|
return t*w;
|
|
}
|
|
|
|
/* |x| > overflowthresold, cosh(x) overflow */
|
|
return huge*huge;
|
|
}
|