mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-26 15:00:06 +00:00
ea5c662c62
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.
75 lines
2.2 KiB
C
75 lines
2.2 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 <stdint.h>
|
|
#include <math.h>
|
|
#include "math_config.h"
|
|
#include "s_sincosf.h"
|
|
|
|
/* The constants and polynomials for sine and cosine. The 2nd entry
|
|
computes -cos (x) rather than cos (x) to get negation for free. */
|
|
const sincos_t __sincosf_table[2] =
|
|
{
|
|
{
|
|
{ 1.0, -1.0, -1.0, 1.0 },
|
|
#if TOINT_INTRINSICS
|
|
0x1.45F306DC9C883p-1,
|
|
#else
|
|
0x1.45F306DC9C883p+23,
|
|
#endif
|
|
0x1.921FB54442D18p0,
|
|
0x1p0,
|
|
-0x1.ffffffd0c621cp-2,
|
|
0x1.55553e1068f19p-5,
|
|
-0x1.6c087e89a359dp-10,
|
|
0x1.99343027bf8c3p-16,
|
|
-0x1.555545995a603p-3,
|
|
0x1.1107605230bc4p-7,
|
|
-0x1.994eb3774cf24p-13
|
|
},
|
|
{
|
|
{ 1.0, -1.0, -1.0, 1.0 },
|
|
#if TOINT_INTRINSICS
|
|
0x1.45F306DC9C883p-1,
|
|
#else
|
|
0x1.45F306DC9C883p+23,
|
|
#endif
|
|
0x1.921FB54442D18p0,
|
|
-0x1p0,
|
|
0x1.ffffffd0c621cp-2,
|
|
-0x1.55553e1068f19p-5,
|
|
0x1.6c087e89a359dp-10,
|
|
-0x1.99343027bf8c3p-16,
|
|
-0x1.555545995a603p-3,
|
|
0x1.1107605230bc4p-7,
|
|
-0x1.994eb3774cf24p-13
|
|
}
|
|
};
|
|
|
|
/* Table with 4/PI to 192 bit precision. To avoid unaligned accesses
|
|
only 8 new bits are added per entry, making the table 4 times larger. */
|
|
const uint32_t __inv_pio4[24] =
|
|
{
|
|
0xa2, 0xa2f9, 0xa2f983, 0xa2f9836e,
|
|
0xf9836e4e, 0x836e4e44, 0x6e4e4415, 0x4e441529,
|
|
0x441529fc, 0x1529fc27, 0x29fc2757, 0xfc2757d1,
|
|
0x2757d1f5, 0x57d1f534, 0xd1f534dd, 0xf534ddc0,
|
|
0x34ddc0db, 0xddc0db62, 0xc0db6295, 0xdb629599,
|
|
0x6295993c, 0x95993c43, 0x993c4390, 0x3c439041
|
|
};
|