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* Use the volatile qualifier for 'tiny' to prevent compilers

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from erronously constant folding expressions of the form
  '1 - tiny'.  This allows erf[f](x) to raise INEXACT.

* Use 0.5, 1, and 2, which are exactly representable in radix-2
  floating point formats.  This reduces diffs between s_erf[fl].c.

* While here, add a comment about efx and efx8.
This commit is contained in:
Steve Kargl 2014-07-13 15:45:45 +00:00
parent f2c0cd942c
commit 019ffb5df8
2 changed files with 21 additions and 10 deletions
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15
lib/msun/src/s_erf.c
View File

@ -111,13 +111,20 @@ __FBSDID("$FreeBSD$");
#include "math.h"
#include "math_private.h"
/* XXX Prevent compilers from erroneously constant folding: */
static const volatile double tiny= 1e-300;
static const double
tiny = 1e-300,
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
half= 0.5,
one = 1,
two = 2,
/* c = (float)0.84506291151 */
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
/*
* In the domain [0, 2**-28], only the first term in the power series
* expansion of erf(x) is used. The magnitude of the first neglected
* terms is less than 2**-84.
*/
efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
/*

16
lib/msun/src/s_erff.c
View File

@ -19,13 +19,18 @@ __FBSDID("$FreeBSD$");
#include "math.h"
#include "math_private.h"
/* XXX Prevent compilers from erroneously constant folding: */
static const volatile float tiny = 1e-30;
static const float
tiny = 1e-30,
half= 5.0000000000e-01, /* 0x3F000000 */
one = 1.0000000000e+00, /* 0x3F800000 */
two = 2.0000000000e+00, /* 0x40000000 */
half= 0.5,
one = 1,
two = 2,
erx = 8.42697144e-01, /* 0x3f57bb00 */
/*
* Coefficients for approximation to erf on [0,0.84375]
* In the domain [0, 2**-14], only the first term in the power series
* expansion of erf(x) is used. The magnitude of the first neglected
* terms is less than 2**-42.
*/
efx = 1.2837916613e-01, /* 0x3e0375d4 */
efx8= 1.0270333290e+00, /* 0x3f8375d4 */
@ -43,7 +48,6 @@ qq3 = -1.98859419e-03F, /* -0x1.04a626p-9 */
* Domain [0.84375, 1.25], range ~[-1.953e-11,1.940e-11]:
* |(erf(x) - erx) - p(x)/q(x)| < 2**-36.
*/
erx = 8.42697144e-01F, /* 0x1.af7600p-1. erf(1) rounded to 16 bits. */
pa0 = 3.64939137e-06F, /* 0x1.e9d022p-19 */
pa1 = 4.15109694e-01F, /* 0x1.a91284p-2 */
pa2 = -1.65179938e-01F, /* -0x1.5249dcp-3 */