Re: musl libmath (implied algorithm issue)

[Szabolcs Nagy <nsz@port70.net>]

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* Alba Pompeo <albapompeo@gmail.com> [2018-04-01 10:54:54 -0300]:
> I found a commit elsewhere that implies musl's fma algorithm is wrong.
> You may be interested in investigating.
> https://git.eigenstate.org/npnth/mc.git/commit/?h=libmath&id=debd13efe12eaca072229e9859aaa6df8708a09f

thanks, it is a wrong result bug in fmaf, copied from freebsd.

near half way cases may get incorrectly rounded under some
circumstances, i didnt try to understand their fix, but
used a minimal change for now.


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From 2a38f5d89f7a69d03861a47a7f981136ee60630f Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <nsz@port70.net>
Date: Sun, 1 Apr 2018 20:02:01 +0000
Subject: [PATCH] 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)
this example was reported in
https://git.eigenstate.org/npnth/mc.git/commit/?h=libmath&id=debd13efe12eaca072229e9859aaa6df8708a09f
---
 src/math/fmaf.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/math/fmaf.c b/src/math/fmaf.c
index aa57feb6..80f5cd8a 100644
--- 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 */
 	{
 		/*
-- 
2.16.3