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Fix the double rounding problem with subnormals, and

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remove the XXX comments, which no longer apply.
This commit is contained in:
David Schultz 2005-03-18 02:27:59 +00:00
parent eb784d51c9
commit 2c2435825a
Notes: svn2git 2020-12-20 02:59:44 +00:00 
svn path=/head/; revision=143780
2 changed files with 36 additions and 16 deletions
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30
lib/msun/src/s_fma.c
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@ -45,15 +45,8 @@ __FBSDID("$FreeBSD$");
* to be stored in FP registers in order to avoid incorrect results.
* This is the default on FreeBSD, but not on many other systems.
*
* Tests on an Itanium 2 indicate that the hardware's FMA instruction
* is almost twice as fast as this implementation. The hardware
* instruction should be used on platforms that support it.
*
* XXX May incur an absolute error of 0x1p-1074 for subnormal results
* due to double rounding induced by the final scaling operation.
*
* XXX On machines supporting quad precision, we should use that, but
* see the caveat in s_fmaf.c.
* Hardware instructions should be used on architectures that support it,
* since this implementation will likely be several times slower.
*/
#if LDBL_MANT_DIG != 113
double
@ -174,8 +167,23 @@ fma(double x, double y, double z)
s = r - c;
rr = (c - (r - s)) + (zs - s) + cc;
fesetround(oround);
return (ldexp(r + rr, ex + ey));
spread = ex + ey;
if (spread + ilogb(r) > -1023) {
fesetround(oround);
r = r + rr;
} else {
/*
* The result is subnormal, so we round before scaling to
* avoid double rounding.
*/
p = ldexp(copysign(0x1p-1022, r), -spread);
c = r + p;
s = c - r;
cc = (r - (c - s)) + (p - s) + rr;
fesetround(oround);
r = (c + cc) - p;
}
return (ldexp(r, spread));
}
#else /* LDBL_MANT_DIG == 113 */
/*

22
lib/msun/src/s_fmal.c
View File

@ -39,9 +39,6 @@ __FBSDID("$FreeBSD$");
*
* Dekker, T. A Floating-Point Technique for Extending the
* Available Precision. Numer. Math. 18, 224-242 (1971).
*
* XXX May incur a small error for subnormal results due to double
* rounding induced by the final scaling operation.
*/
long double
fmal(long double x, long double y, long double z)
@ -165,6 +162,21 @@ fmal(long double x, long double y, long double z)
s = r - c;
rr = (c - (r - s)) + (zs - s) + cc;
fesetround(oround);
return (ldexpl(r + rr, ex + ey));
spread = ex + ey;
if (spread + ilogbl(r) > -16383) {
fesetround(oround);
r = r + rr;
} else {
/*
* The result is subnormal, so we round before scaling to
* avoid double rounding.
*/
p = ldexpl(copysignl(0x1p-16382L, r), -spread);
c = r + p;
s = c - r;
cc = (r - (c - s)) + (p - s) + rr;
fesetround(oround);
r = (c + cc) - p;
}
return (ldexpl(r, spread));
}