From: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
To: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Cc: 'GNU C Library' <libc-alpha@sourceware.org>
Subject: RFC: Improve hypot performance
Date: Wed, 17 Nov 2021 15:58:53 +0000 [thread overview]
Message-ID: <VE1PR08MB5599C92B47C5EE081422D0DE839A9@VE1PR08MB5599.eurprd08.prod.outlook.com> (raw)
Hi Adhemerval,
Here is an early version of a much faster hypot implementation. It uses fma
to significantly outperform the powerpc version both in throughput and
latency. It has a worst-case ULP of ~0.949 and passes the testsuite. The
powerpc version has a worst-case ULP of ~1.21 and several test failures.
It applies on top of your hypot patch series. I didn't optimize the non-fma
case since modern targets have fma. It'll be interesting to compare it on
Power. You'll need to correctly set FAST_FMINMAX to indicate support for
inlined fmin/fmax instructions (this will be added to math_private.h for
targets that have it), without it the code tries to use a conditional move
since using a branch here is really bad for performance.
Cheers,
Wilco
---
diff --git a/sysdeps/ieee754/dbl-64/e_hypot.c b/sysdeps/ieee754/dbl-64/e_hypot.c
index d20bc3e3657e350a1103a8f8477db35ee60399e0..3906711788cff5d66725e5879bb4d6c36dd24dc7 100644
--- a/sysdeps/ieee754/dbl-64/e_hypot.c
+++ b/sysdeps/ieee754/dbl-64/e_hypot.c
@@ -37,73 +37,40 @@
#include <math-svid-compat.h>
#include <errno.h>
+#define FAST_FMINMAX 1
+//#undef __FP_FAST_FMA
+
+#define SCALE 0x1p-600
+#define LARGE_VAL 0x1p+511
+#define TINY_VAL 0x1p-459
+#define EPS 0x1p-54
+
+
static inline double
handle_errno (double r)
{
+ r = math_narrow_eval (r);
if (isinf (r))
__set_errno (ERANGE);
return r;
}
-/* sqrt (DBL_EPSILON / 2.0) */
-#define SQRT_EPS_DIV_2 0x1.6a09e667f3bcdp-27
-/* DBL_MIN / (sqrt (DBL_EPSILON / 2.0)) */
-#define DBL_MIN_THRESHOLD 0x1.6a09e667f3bcdp-996
-/* eps (double) * sqrt (DBL_MIN)) */
-#define SCALE 0x1p-563
-/* 1 / eps (sqrt (DBL_MIN) */
-#define INV_SCALE 0x1p+563
-/* sqrt (DBL_MAX) */
-#define SQRT_DBL_MAX 0x1.6a09e667f3bccp+511
-/* sqrt (DBL_MIN) */
-#define SQRT_DBL_MIN 0x1p-511
-
-double
-__hypot (double x, double y)
+static inline double
+kernel (double ax, double ay)
{
- if ((isinf (x) || isinf (y))
- && !issignaling (x) && !issignaling (y))
- return INFINITY;
- if (isnan (x) || isnan (y))
- return x + y;
-
- double ax = fabs (x);
- double ay = fabs (y);
- if (ay > ax)
- {
- double tmp = ax;
- ax = ay;
- ay = tmp;
- }
-
- /* Widely varying operands. The DBL_MIN_THRESHOLD check is used to avoid
- a spurious underflow from the multiplication. */
- if (ax >= DBL_MIN_THRESHOLD && ay <= ax * SQRT_EPS_DIV_2)
- return (ay == 0.0)
- ? ax
- : handle_errno (math_narrow_eval (ax + DBL_TRUE_MIN));
+ double t1, t2;
+#ifdef __FP_FAST_FMA
+ t1 = ay + ay;
+ t2 = ax - ay;
- double scale = SCALE;
- if (ax > SQRT_DBL_MAX)
- {
- ax *= scale;
- ay *= scale;
- scale = INV_SCALE;
- }
- else if (ay < SQRT_DBL_MIN)
- {
- ax /= scale;
- ay /= scale;
- }
+ if (t1 >= ax)
+ return sqrt (fma (t1, ax, t2 * t2));
else
- scale = 1.0;
-
+ return sqrt (fma (ax, ax, ay * ay));
+#else
double h = sqrt (ax * ax + ay * ay);
- double t1, t2;
- if (h == 0.0)
- return h;
- else if (h <= 2.0 * ay)
+ if (h <= 2.0 * ay)
{
double delta = h - ay;
t1 = ax * (2.0 * delta - ax);
@@ -112,14 +79,57 @@ __hypot (double x, double y)
else
{
double delta = h - ax;
- t1 = 2.0 * delta * (ax - 2 * ay);
+ t1 = 2.0 * delta * (ax - 2.0 * ay);
t2 = (4.0 * delta - ay) * ay + delta * delta;
}
h -= (t1 + t2) / (2.0 * h);
- h = math_narrow_eval (h * scale);
- math_check_force_underflow_nonneg (h);
- return handle_errno (h);
+ return h;
+#endif
+}
+
+
+double
+__hypot (double x, double y)
+{
+ if (!isfinite (x) || !isfinite (y))
+ {
+ if ((isinf (x) || isinf (y))
+ && !issignaling_inline (x) && !issignaling_inline (y))
+ return INFINITY;
+ return x + y;
+ }
+
+ x = fabs (x);
+ y = fabs (y);
+
+ double ax = FAST_FMINMAX ? fmax (x, y) : (x < y ? y : x);
+ double ay = FAST_FMINMAX ? fmin (x, y) : (x < y ? x : y);
+
+ if (__glibc_unlikely (ax > LARGE_VAL))
+ {
+ if (__glibc_unlikely (ay <= ax * EPS))
+ return handle_errno (ax + ay);
+
+ return handle_errno (kernel (ax * SCALE, ay * SCALE) / SCALE);
+ }
+
+ if (__glibc_unlikely (ay < TINY_VAL))
+ {
+ if (__glibc_unlikely (ax >= ay / EPS))
+ return math_narrow_eval (ax + ay);
+
+ ax = math_narrow_eval (kernel (ax / SCALE, ay / SCALE) * SCALE);
+ math_check_force_underflow_nonneg (ax);
+ return ax;
+ }
+
+ /* Common case: ax is not huge and ay is not tiny. */
+ if (__glibc_unlikely (ay <= ax * EPS))
+ return math_narrow_eval (ax + ay);
+
+ return math_narrow_eval (kernel (ax, ay));
}
+
strong_alias (__hypot, __ieee754_hypot)
libm_alias_finite (__ieee754_hypot, __hypot)
#if LIBM_SVID_COMPAT
next reply other threads:[~2021-11-17 15:59 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2021-11-17 15:58 Wilco Dijkstra [this message]
2021-11-17 19:02 ` Paul A. Clarke
2021-11-18 12:37 ` Wilco Dijkstra
2021-11-18 15:43 ` Paul A. Clarke
2021-11-18 16:15 ` Paul A. Clarke
2021-11-18 17:39 ` Wilco Dijkstra
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