fix fmaf wrong result

if double precision r=x*y+z is not a half way case between two single
precision floats or it is an exact result then fmaf returns (float)r.

however the exactness check was wrong when |x*y| < |z| and could cause
incorrectly rounded result in nearest rounding mode when r is a half
way case.

fmaf(-0x1.26524ep-54, -0x1.cb7868p+11, 0x1.d10f5ep-29)
was incorrectly rounded up to 0x1.d117ap-29 instead of 0x1.d1179ep-29.
(exact result is 0x1.d1179efffffffecp-29, r is 0x1.d1179fp-29)

diff --git a/src/math/fmaf.c b/src/math/fmaf.c
index aa57feb..80f5cd8 100644 (file)
--- a/src/math/fmaf.c
+++ b/src/math/fmaf.c
@@ -50,7 +50,7 @@ float fmaf(float x, float y, float z)
        /* Common case: The double precision result is fine. */
        if ((u.i & 0x1fffffff) != 0x10000000 || /* not a halfway case */
                e == 0x7ff ||                   /* NaN */
-               result - xy == z ||                 /* exact */
+               (result - xy == z && result - z == xy) || /* exact */
                fegetround() != FE_TONEAREST)       /* not round-to-nearest */
        {
                /*