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math: Improve hypot performance with FMA

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Improve hypot performance significantly by using fma when available. The
fma version has twice the throughput of the previous version and 70% of
the latency.  The non-fma version has 30% higher throughput and 10%
higher latency.

Max ULP error is 0.949 with fma and 0.792 without fma.

Passes GLIBC testsuite.
This commit is contained in:
Wilco Dijkstra 2021-11-30 16:29:25 -03:00 committed by Adhemerval Zanella
parent 6c848d7038
commit ccfa865a82
1 changed files with 16 additions and 1 deletions
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17
sysdeps/ieee754/dbl-64/e_hypot.c
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@ -26,7 +26,11 @@
rounding mode.
- Handle required underflow exception for subnormal results.
The expected ULP is ~0.792.
The expected ULP is ~0.792 or ~0.948 if FMA is used. For FMA, the
correction is not used and the error of sqrt (x^2 + y^2) is below 1 ULP
if x^2 + y^2 is computed with less than 0.707 ULP error. If |x| >= |2y|,
fma (x, x, y^2) has ~0.625 ULP. If |x| < |2y|, fma (|2x|, |y|, (x - y)^2)
has ~0.625 ULP.
[1] https://arxiv.org/pdf/1904.09481.pdf */
@ -48,6 +52,16 @@ static inline double
kernel (double ax, double ay)
{
double t1, t2;
#ifdef __FP_FAST_FMA
t1 = ay + ay;
t2 = ax - ay;
if (t1 >= ax)
return sqrt (fma (t1, ax, t2 * t2));
else
return sqrt (fma (ax, ax, ay * ay));
#else
double h = sqrt (ax * ax + ay * ay);
if (h <= 2.0 * ay)
{
@ -64,6 +78,7 @@ kernel (double ax, double ay)
h -= (t1 + t2) / (2.0 * h);
return h;
#endif
}
double