From c599f4f4d705ba215a2672b92baa1c29d9dd0735 Mon Sep 17 00:00:00 2001 From: Szabolcs Nagy Date: Thu, 15 Aug 2013 10:14:46 +0000 Subject: math: fix asin, atan, log1p, tanh to raise underflow on subnormal for these functions f(x)=x for small inputs, because f(0)=0 and f'(0)=1, but for subnormal values they should raise the underflow flag (required by annex F), if they are approximated by a polynomial around 0 then spurious underflow should be avoided (not required by annex F) all these functions should raise inexact flag for small x if x!=0, but it's not required by the standard and it does not seem a worthy goal, so support for it is removed in some cases. raising underflow: - x*x may not raise underflow for subnormal x if FLT_EVAL_METHOD!=0 - x*x may raise spurious underflow for normal x if FLT_EVAL_METHOD==0 - in case of double subnormal x, store x as float - in case of float subnormal x, store x*x as float --- src/math/tanh.c | 14 +++++++++----- 1 file changed, 9 insertions(+), 5 deletions(-) (limited to 'src/math/tanh.c') diff --git a/src/math/tanh.c b/src/math/tanh.c index 0e766c5c..20d6dbcf 100644 --- a/src/math/tanh.c +++ b/src/math/tanh.c @@ -9,7 +9,7 @@ double tanh(double x) union {double f; uint64_t i;} u = {.f = x}; uint32_t w; int sign; - double t; + double_t t; /* x = |x| */ sign = u.i >> 63; @@ -22,8 +22,7 @@ double tanh(double x) if (w > 0x40340000) { /* |x| > 20 or nan */ /* note: this branch avoids raising overflow */ - /* raise inexact if x!=+-inf and handle nan */ - t = 1 + 0/(x + 0x1p-120f); + t = 1 - 0/x; } else { t = expm1(2*x); t = 1 - 2/(t+2); @@ -32,10 +31,15 @@ double tanh(double x) /* |x| > log(5/3)/2 ~= 0.2554 */ t = expm1(2*x); t = t/(t+2); - } else { - /* |x| is small, up to 2ulp error in [0.1,0.2554] */ + } else if (w >= 0x00100000) { + /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */ t = expm1(-2*x); t = -t/(t+2); + } else { + /* |x| is subnormal */ + /* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */ + FORCE_EVAL((float)x); + t = x; } return sign ? -t : t; } -- cgit v1.2.1