From 3f7e4f15381a1bfc788cd99f2dcc2cb8a8f5b460 Mon Sep 17 00:00:00 2001 From: bde Date: Sun, 13 Nov 2005 00:08:23 +0000 Subject: Fixed some magic numbers. 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. --- lib/msun/src/e_coshf.c | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) (limited to 'lib') diff --git a/lib/msun/src/e_coshf.c b/lib/msun/src/e_coshf.c index d2368a6..ebd659e 100644 --- a/lib/msun/src/e_coshf.c +++ b/lib/msun/src/e_coshf.c @@ -38,20 +38,20 @@ __ieee754_coshf(float x) if(ix<0x3eb17218) { t = expm1f(fabsf(x)); w = one+t; - if (ix<0x24000000) return w; /* cosh(tiny) = 1 */ + if (ix<0x39800000) return one; /* cosh(tiny) = 1 */ return one+(t*t)/(w+w); } - /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ - if (ix < 0x41b00000) { + /* |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 [22, log(maxdouble)] return half*exp(|x|) */ - if (ix < 0x42b17180) return half*__ieee754_expf(fabsf(x)); + /* |x| in [9, log(maxfloat)] return half*exp(|x|) */ + if (ix < 0x42b17217) return half*__ieee754_expf(fabsf(x)); - /* |x| in [log(maxdouble), overflowthresold] */ + /* |x| in [log(maxfloat), overflowthresold] */ if (ix<=0x42b2d4fc) { w = __ieee754_expf(half*fabsf(x)); t = half*w; -- cgit v1.1