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authornsz <nsz@port70.net>2012-06-20 23:25:58 +0200
committernsz <nsz@port70.net>2012-06-20 23:25:58 +0200
commite5fb6820a42a1f675ba09c15273953e1ace65777 (patch)
tree19d075252fdb22352fd147e7c4333cfa015d3b21
parentac4fb51dde2f1fe9371a4cb51ff309d4868245ec (diff)
downloadmusl-e5fb6820a42a1f675ba09c15273953e1ace65777.tar.gz
math: fix fma bug on x86 (found by Bruno Haible with gnulib)
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.
-rw-r--r--src/math/fma.c12
1 files changed, 10 insertions, 2 deletions
diff --git a/src/math/fma.c b/src/math/fma.c
index 5fb95406..7076d4b9 100644
--- a/src/math/fma.c
+++ b/src/math/fma.c
@@ -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
-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)
{
@@ -55,17 +55,25 @@ static long double adjust(long double hi, long double lo)
ulo.x = lo;
if (uhi.bits.s == ulo.bits.s)
uhi.bits.m++;
- else
+ else {
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;
}
+/* adjusted add so the result is correct when rounded to double (or less) precision */
static long double dadd(long double x, long double y)
{
add(&x, &y, 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)
{
mul(&x, &y, x, y);