From 4648909d56c1e9063017bcddd3271dffadef7cb5 Mon Sep 17 00:00:00 2001 From: Joseph Myers Date: Mon, 23 Jun 2014 20:20:10 +0000 Subject: Fix cosh spurious underflows from expm1 (bug 16354), inaccurate results near 0 (bug 17061). This patch fixes bug 16354, spurious underflows from cosh when a tiny argument is passed to expm1 and expm1 correctly underflows although the final result of cosh should be 1. As noted in that bug, some cases are latent because of expm1 implementations not raising underflow (bug 16353), but all the implementations are fixed similarly. They already contained checks for tiny arguments, but the checks were too late to avoid underflow from expm1 (although they would avoid underflow from subsequent squaring of the result of expm1); they are moved before the expm1 calls. The thresholds used for considering arguments tiny are not particularly consistent in how they relate to the precision of the floating-point format in question. They are, however, all sufficient to ensure that the round-to-nearest result of cosh is indeed 1 below the threshold (although sometimes they are smaller than necessary). But the previous logic did not return 1, but the previously computed 1 + expm1(abs(x)) value. And the thresholds in the ldbl-128 and ldbl-128ibm code (0x1p-71L - I suspect 0x3f8b was intended in the code instead of 0x3fb8 - and (roughly) 0x1p-55L) are not sufficient for that value to be 1. So by moving the test for tiny arguments, and consequently returning 1 directly now the expm1 value hasn't been computed by that point, this patch also fixes bug 17061, the (large number of ulps) inaccuracy for small arguments in those implementations. Tests for that bug are duly added. Tested x86_64 and x86 and ulps updated accordingly. Also tested for mips64 and powerpc32 to validate the ldbl-128 and ldbl-128ibm changes. [BZ #16354] [BZ #17061] * sysdeps/ieee754/dbl-64/e_cosh.c (__ieee754_cosh): Check for small arguments before calling __expm1. * sysdeps/ieee754/flt-32/e_coshf.c (__ieee754_coshf): Check for small arguments before calling __expm1f. * sysdeps/ieee754/ldbl-128/e_coshl.c (__ieee754_coshl): Check for small arguments before calling __expm1l. * sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl): Likewise. * sysdeps/ieee754/ldbl-96/e_coshl.c (__ieee754_coshl): Likewise. * math/auto-libm-test-in: Add more cosh tests. Do not allow spurious underflow for some cosh tests. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. --- sysdeps/ieee754/ldbl-96/e_coshl.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'sysdeps/ieee754/ldbl-96') diff --git a/sysdeps/ieee754/ldbl-96/e_coshl.c b/sysdeps/ieee754/ldbl-96/e_coshl.c index 995c9922cb..dd22cae363 100644 --- a/sysdeps/ieee754/ldbl-96/e_coshl.c +++ b/sysdeps/ieee754/ldbl-96/e_coshl.c @@ -54,9 +54,9 @@ __ieee754_coshl (long double x) if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { + if (ex<0x3fbc) return one; /* cosh(tiny) = 1 */ t = __expm1l(fabsl(x)); w = one+t; - if (ex<0x3fbc) return w; /* cosh(tiny) = 1 */ return one+(t*t)/(w+w); } -- cgit 1.4.1