glibc/sysdeps/ieee754/flt-32/s_sincosf.c
Wilco Dijkstra ea5c662c62 Improve performance of sincosf
This patch is a complete rewrite of sincosf.  The new version is
significantly faster, as well as simple and accurate.
The worst-case ULP is 0.5607, maximum relative error is 0.5303 * 2^-23 over
all 4 billion inputs.  In non-nearest rounding modes the error is 1ULP.

The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction.  The code uses approximate integer
comparisons to quickly decide between these cases.

The small range reducer uses a single reduction step to handle values up to
120.0.  It is fastest on targets which support inlined round instructions.

The large range reducer uses integer arithmetic for simplicity.  It does a
32x96 bit multiply to compute a 64-bit modulo result.  This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4.  It could be further optimized, however it is
already much faster than necessary.

sincosf throughput gains on Cortex-A72:
* |x| < 0x1p-12 : 1.6x
* |x| < M_PI_4  : 1.7x
* |x| < 2 * M_PI: 1.5x
* |x| < 120.0   : 1.8x
* |x| < Inf     : 2.3x

	* math/Makefile: Add s_sincosf_data.c.
	* sysdeps/ia64/fpu/s_sincosf_data.c: New file.
	* sysdeps/ieee754/flt-32/s_sincosf.h (abstop12): Add new function.
	(sincosf_poly): Likewise.
	(reduce_small): Likewise.
	(reduce_large): Likewise.
	* sysdeps/ieee754/flt-32/s_sincosf.c (sincosf): Rewrite.
	* sysdeps/ieee754/flt-32/s_sincosf_data.c: New file with sincosf data.
	* sysdeps/m68k/m680x0/fpu/s_sincosf_data.c: New file.
	* sysdeps/x86_64/fpu/s_sincosf_data.c: New file.
2018-08-10 17:34:39 +01:00

104 lines
2.8 KiB
C

/* Compute sine and cosine of argument.
Copyright (C) 2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include <errno.h>
#include <stdint.h>
#include <math.h>
#include <math-barriers.h>
#include <libm-alias-float.h>
#include "math_config.h"
#include "s_sincosf.h"
#ifndef SINCOSF
# define SINCOSF_FUNC __sincosf
#else
# define SINCOSF_FUNC SINCOSF
#endif
/* Fast sincosf implementation. Worst-case ULP is 0.5607, maximum relative
error is 0.5303 * 2^-23. A single-step range reduction is used for
small values. Large inputs have their range reduced using fast integer
arithmetic. */
void
SINCOSF_FUNC (float y, float *sinp, float *cosp)
{
double x = y;
double s;
int n;
const sincos_t *p = &__sincosf_table[0];
if (abstop12 (y) < abstop12 (pio4))
{
double x2 = x * x;
if (__glibc_unlikely (abstop12 (y) < abstop12 (0x1p-12f)))
{
/* Force underflow for tiny y. */
if (__glibc_unlikely (abstop12 (y) < abstop12 (0x1p-126f)))
math_force_eval ((float)x2);
*sinp = y;
*cosp = 1.0f;
return;
}
sincosf_poly (x, x2, p, 0, sinp, cosp);
}
else if (abstop12 (y) < abstop12 (120.0f))
{
x = reduce_fast (x, p, &n);
/* Setup the signs for sin and cos. */
s = p->sign[n & 3];
if (n & 2)
p = &__sincosf_table[1];
sincosf_poly (x * s, x * x, p, n, sinp, cosp);
}
else if (__glibc_likely (abstop12 (y) < abstop12 (INFINITY)))
{
uint32_t xi = asuint (y);
int sign = xi >> 31;
x = reduce_large (xi, &n);
/* Setup signs for sin and cos - include original sign. */
s = p->sign[(n + sign) & 3];
if ((n + sign) & 2)
p = &__sincosf_table[1];
sincosf_poly (x * s, x * x, p, n, sinp, cosp);
}
else
{
/* Return NaN if Inf or NaN for both sin and cos. */
*sinp = *cosp = y - y;
#if WANT_ERRNO
/* Needed to set errno for +-Inf, the add is a hack to work
around a gcc register allocation issue: just passing y
affects code generation in the fast path (PR86901). */
__math_invalidf (y + y);
#endif
}
}
#ifndef SINCOSF
libm_alias_float (__sincos, sincos)
#endif