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math: fix fma bug on x86 (found by Bruno Haible with gnulib)

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The long double adjustment was wrong:
The usual check is
  mant_bits & 0x7ff == 0x400
before doing a mant_bits++ or mant_bits-- adjustment since
this is the only case when rounding an inexact ld80 into
double can go wrong. (only in nearest rounding mode)

After such a check the ++ and -- is ok (the mantissa will end
in 0x401 or 0x3ff).

fma is a bit different (we need to add 3 numbers with correct
rounding: hi_xy + lo_xy + z so we should survive two roundings
at different places without precision loss)

The adjustment in fma only checks for zero low bits
  mant_bits & 0x3ff == 0
this way the adjusted value is correct when rounded to
double or *less* precision.
(this is an important piece in the fma puzzle)

Unfortunately in this case the -- is not a correct adjustment
because mant_bits might underflow so further checks are needed
and this was the source of the bug.
This commit is contained in:
nsz 2012-06-20 23:25:58 +02:00
commit e5fb6820a4
1 changed files with 10 additions and 2 deletions
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12
src/math/fma.c
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@ -41,7 +41,7 @@ static void mul(long double *hi, long double *lo, long double x, long double y)
/* /*
assume (long double)(hi+lo) == hi assume (long double)(hi+lo) == hi
return an adjusted hi so that rounding it to double is correct return an adjusted hi so that rounding it to double (or less) precision is correct
*/ */
static long double adjust(long double hi, long double lo) static long double adjust(long double hi, long double lo)
{ {
@ -55,17 +55,25 @@ static long double adjust(long double hi, long double lo)
ulo.x = lo; ulo.x = lo;
if (uhi.bits.s == ulo.bits.s) if (uhi.bits.s == ulo.bits.s)
uhi.bits.m++; uhi.bits.m++;
else else {
uhi.bits.m--; uhi.bits.m--;
/* handle underflow and take care of ld80 implicit msb */
if (uhi.bits.m == (uint64_t)-1/2) {
uhi.bits.m *= 2;
uhi.bits.e--;
}
}
return uhi.x; return uhi.x;
} }
/* adjusted add so the result is correct when rounded to double (or less) precision */
static long double dadd(long double x, long double y) static long double dadd(long double x, long double y)
{ {
add(&x, &y, x, y); add(&x, &y, x, y);
return adjust(x, y); return adjust(x, y);
} }
/* adjusted mul so the result is correct when rounded to double (or less) precision */
static long double dmul(long double x, long double y) static long double dmul(long double x, long double y)
{ {
mul(&x, &y, x, y); mul(&x, &y, x, y);