From bbb78d030efd87ec37f7599d0f014de598eceae7 Mon Sep 17 00:00:00 2001 From: Andreas Schwab Date: Mon, 5 Mar 2012 20:19:14 +0100 Subject: [PATCH] Fix loss of precision in cosh and sinh for IBM long double --- ChangeLog | 6 ++++++ sysdeps/ieee754/ldbl-128ibm/e_coshl.c | 10 +++++----- sysdeps/ieee754/ldbl-128ibm/e_sinhl.c | 10 +++++----- 3 files changed, 16 insertions(+), 10 deletions(-) diff --git a/ChangeLog b/ChangeLog index 6875313..5c9871b 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,9 @@ +2012-03-05 Andreas Schwab + + * sysdeps/ieee754/ldbl-128ibm/e_coshl.c: Drop exp(-x) term + only for |x| >= 40. + * sysdeps/ieee754/ldbl-128ibm/e_sinhl.c: Likewise. + 2012-03-05 H.J. Lu * sysdeps/unix/sysv/linux/x86_64/gettimeofday.c (gettimeofday_ifunc): diff --git a/sysdeps/ieee754/ldbl-128ibm/e_coshl.c b/sysdeps/ieee754/ldbl-128ibm/e_coshl.c index ebc9436..569b841 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_coshl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_coshl.c @@ -20,9 +20,9 @@ * 2*exp(x) * * exp(x) + 1/exp(x) - * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * ln2/2 <= x <= 40 : cosh(x) := ------------------- * 2 - * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * 40 <= x <= lnovft : cosh(x) := exp(x)/2 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) * ln2ovft < x : cosh(x) := huge*huge (overflow) * @@ -57,13 +57,13 @@ __ieee754_coshl (long double x) return one+(t*t)/(w+w); } - /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ - if (ix < 0x4036000000000000LL) { + /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x4044000000000000LL) { t = __ieee754_expl(fabsl(x)); return half*t+half/t; } - /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + /* |x| in [40, log(maxdouble)] return half*exp(|x|) */ if (ix < 0x40862e42fefa39efLL) return half*__ieee754_expl(fabsl(x)); /* |x| in [log(maxdouble), overflowthresold] */ diff --git a/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c b/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c index b8e86b1..4b53d90 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c @@ -16,10 +16,10 @@ * 1. Replace x by |x| (sinh(-x) = -sinh(x)). * 2. * E + E/(E+1) - * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 0 <= x <= 40 : sinh(x) := --------------, E=expm1(x) * 2 * - * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * 40 <= x <= lnovft : sinh(x) := exp(x)/2 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) * ln2ovft < x : sinh(x) := x*shuge (overflow) * @@ -48,8 +48,8 @@ __ieee754_sinhl(long double x) h = 0.5; if (jx<0) h = -h; - /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ - if (ix < 0x4036000000000000LL) { /* |x|<22 */ + /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x4044000000000000LL) { /* |x|<40 */ if (ix<0x3e20000000000000LL) /* |x|<2**-29 */ if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */ t = __expm1l(fabsl(x)); @@ -57,7 +57,7 @@ __ieee754_sinhl(long double x) return h*(t+t/(t+one)); } - /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */ if (ix < 0x40862e42fefa39efLL) return h*__ieee754_expl(fabsl(x)); /* |x| in [log(maxdouble), overflowthresold] */ -- 2.7.4