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Message-ID: <20230818211738.GF3448312@port70.net>
Date: Fri, 18 Aug 2023 23:17:38 +0200
From: Szabolcs Nagy <nsz@...t70.net>
To: Paul Zimmermann <Paul.Zimmermann@...ia.fr>
Cc: musl@...ts.openwall.com
Subject: [PATCH 2/2] math: fix ld80 powl(x,huge) and powl(LDBL_MAX,small)
powl used >= LDBL_MAX as infinity check, but LDBL_MAX is finite, so
this can cause wrong results e.g. powl(LDBL_MAX, 0.5) returned inf
or powl(2, LDBL_MAX) returned inf without raising overflow.
huge y values (close to LDBL_MAX) could cause intermediate results to
overflow (computing y * log2(x) with more than long double precision)
and e.g. powl(0.5, 0x1p16380L) or powl(10, 0x1p16380L) returned nan.
this is fixed by handling huge y early since that always overflows or
underflows.
reported by Paul Zimmermann against expl10 (which uses powl).
---
src/math/powl.c | 34 +++++++++++++++++++++-------------
1 file changed, 21 insertions(+), 13 deletions(-)
diff --git a/src/math/powl.c b/src/math/powl.c
index 5b6da07b..6f64ea71 100644
--- a/src/math/powl.c
+++ b/src/math/powl.c
@@ -212,25 +212,33 @@ long double powl(long double x, long double y)
}
if (x == 1.0)
return 1.0; /* 1**y = 1, even if y is nan */
- if (x == -1.0 && !isfinite(y))
- return 1.0; /* -1**inf = 1 */
if (y == 0.0)
return 1.0; /* x**0 = 1, even if x is nan */
if (y == 1.0)
return x;
- if (y >= LDBL_MAX) {
- if (x > 1.0 || x < -1.0)
- return INFINITY;
- if (x != 0.0)
- return 0.0;
- }
- if (y <= -LDBL_MAX) {
- if (x > 1.0 || x < -1.0)
+ /* if y*log2(x) < log2(LDBL_TRUE_MIN)-1 then x^y uflows to 0
+ if y*log2(x) > -log2(LDBL_TRUE_MIN)+1 > LDBL_MAX_EXP then x^y oflows
+ if |x|!=1 then |log2(x)| > |log(x)| > LDBL_EPSILON/2 so
+ x^y oflows/uflows if |y|*LDBL_EPSILON/2 > -log2(LDBL_TRUE_MIN)+1 */
+ if (fabsl(y) > 2*(-LDBL_MIN_EXP+LDBL_MANT_DIG+1)/LDBL_EPSILON) {
+ /* y is not an odd int */
+ if (x == -1.0)
+ return 1.0;
+ if (y == INFINITY) {
+ if (x > 1.0 || x < -1.0)
+ return INFINITY;
return 0.0;
- if (x != 0.0 || y == -INFINITY)
+ }
+ if (y == -INFINITY) {
+ if (x > 1.0 || x < -1.0)
+ return 0.0;
return INFINITY;
+ }
+ if ((x > 1.0 || x < -1.0) == (y > 0))
+ return huge * huge;
+ return twom10000 * twom10000;
}
- if (x >= LDBL_MAX) {
+ if (x == INFINITY) {
if (y > 0.0)
return INFINITY;
return 0.0;
@@ -253,7 +261,7 @@ long double powl(long double x, long double y)
yoddint = 1;
}
- if (x <= -LDBL_MAX) {
+ if (x == -INFINITY) {
if (y > 0.0) {
if (yoddint)
return -INFINITY;
--
2.41.0
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