From patchwork Mon Jun 16 21:38:47 2014 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: Joseph Myers X-Patchwork-Id: 1514 Received: (qmail 4224 invoked by alias); 16 Jun 2014 21:39:09 -0000 Mailing-List: contact libc-alpha-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Unsubscribe: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: libc-alpha-owner@sourceware.org Delivered-To: mailing list libc-alpha@sourceware.org Received: (qmail 4211 invoked by uid 89); 16 Jun 2014 21:39:08 -0000 Authentication-Results: sourceware.org; auth=none X-Virus-Found: No X-Spam-SWARE-Status: No, score=-1.9 required=5.0 tests=AWL, BAYES_00 autolearn=ham version=3.3.2 X-HELO: relay1.mentorg.com Date: Mon, 16 Jun 2014 21:38:47 +0000 From: "Joseph S. Myers" To: Subject: Fix cosh spurious underflows from expm1 (bug 16354), inaccurate results near 0 (bug 17061) Message-ID: MIME-Version: 1.0 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. (auto-libm-test-out diffs omitted below.) 2014-06-16 Joseph Myers [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. diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in index 6edad5a..c29abbf 100644 --- a/math/auto-libm-test-in +++ b/math/auto-libm-test-in @@ -624,11 +624,14 @@ cosh 50 # GCC bug 59666: results on directed rounding may be incorrect. cosh max no-test-inline xfail-rounding:ldbl-128ibm cosh -max no-test-inline xfail-rounding:ldbl-128ibm -# Bug 16354: spurious underflow may occur. -cosh min spurious-underflow -cosh -min spurious-underflow -cosh min_subnorm spurious-underflow -cosh -min_subnorm spurious-underflow +cosh min +cosh -min +cosh min_subnorm +cosh -min_subnorm +cosh 0x1p-56 +cosh -0x1p-56 +cosh 0x1p-72 +cosh -0x1p-72 # Test values either side of overflow for each floating-point format. cosh 0x5.96a7ep+4 cosh 0x5.96a7e8p+4 diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index d7424a6..148584e 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -895,6 +895,7 @@ ldouble: 2 Function: "cosh_upward": double: 1 +float: 1 idouble: 1 ifloat: 1 ildouble: 2 diff --git a/sysdeps/ieee754/dbl-64/e_cosh.c b/sysdeps/ieee754/dbl-64/e_cosh.c index 6caf943..af3910d 100644 --- a/sysdeps/ieee754/dbl-64/e_cosh.c +++ b/sysdeps/ieee754/dbl-64/e_cosh.c @@ -53,10 +53,10 @@ __ieee754_cosh (double x) /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if (ix < 0x3fd62e43) { + if (ix < 0x3c800000) + return one; /* cosh(tiny) = 1 */ t = __expm1 (fabs (x)); w = one + t; - if (ix < 0x3c800000) - return w; /* cosh(tiny) = 1 */ return one + (t * t) / (w + w); } diff --git a/sysdeps/ieee754/flt-32/e_coshf.c b/sysdeps/ieee754/flt-32/e_coshf.c index 7eeea4d..dedda47 100644 --- a/sysdeps/ieee754/flt-32/e_coshf.c +++ b/sysdeps/ieee754/flt-32/e_coshf.c @@ -33,9 +33,9 @@ __ieee754_coshf (float x) if (ix < 0x41b00000) { /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if(ix<0x3eb17218) { + if (ix<0x24000000) return one; /* cosh(tiny) = 1 */ t = __expm1f(fabsf(x)); w = one+t; - if (ix<0x24000000) return w; /* cosh(tiny) = 1 */ return one+(t*t)/(w+w); } diff --git a/sysdeps/ieee754/ldbl-128/e_coshl.c b/sysdeps/ieee754/ldbl-128/e_coshl.c index 59f2030..488c318 100644 --- a/sysdeps/ieee754/ldbl-128/e_coshl.c +++ b/sysdeps/ieee754/ldbl-128/e_coshl.c @@ -77,10 +77,10 @@ __ieee754_coshl (long double x) /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ if (ex < 0x3ffd62e4) /* 0.3465728759765625 */ { + if (ex < 0x3fb80000) /* |x| < 2^-116 */ + return one; /* cosh(tiny) = 1 */ t = __expm1l (u.value); w = one + t; - if (ex < 0x3fb80000) /* |x| < 2^-116 */ - return w; /* cosh(tiny) = 1 */ return one + (t * t) / (w + w); } diff --git a/sysdeps/ieee754/ldbl-128ibm/e_coshl.c b/sysdeps/ieee754/ldbl-128ibm/e_coshl.c index 92313e2..327b2ab 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_coshl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_coshl.c @@ -53,9 +53,9 @@ __ieee754_coshl (long double x) /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if(ix<0x3fd62e42fefa39efLL) { + if (ix<0x3c80000000000000LL) return one; /* cosh(tiny) = 1 */ t = __expm1l(fabsl(x)); w = one+t; - if (ix<0x3c80000000000000LL) return w; /* cosh(tiny) = 1 */ return one+(t*t)/(w+w); } diff --git a/sysdeps/ieee754/ldbl-96/e_coshl.c b/sysdeps/ieee754/ldbl-96/e_coshl.c index 995c992..dd22cae 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); }