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95a01ea955
The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows better performance to the generic atanpif. The code was adapted to glibc style and to use the definition of math_config.h (to handle errno, overflow, and underflow). Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1, gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1): latency master patched improvement x86_64 66.3296 52.7558 20.46% x86_64v2 66.0429 51.4007 22.17% x86_64v3 60.6294 48.7876 19.53% aarch64 (Neoverse) 24.3163 20.9110 14.00% power8 16.5766 13.3620 19.39% power10 16.5115 13.4072 18.80% reciprocal-throughput master patched improvement x86_64 30.8599 16.0866 47.87% x86_64v2 29.2286 15.4688 47.08% x86_64v3 23.0960 12.8510 44.36% aarch64 (Neoverse) 15.4619 10.6752 30.96% power8 7.9200 5.2483 33.73% power10 6.8539 4.6262 32.50% Reviewed-by: DJ Delorie <dj@redhat.com>
110 lines
3.4 KiB
C
110 lines
3.4 KiB
C
/* Correctly-rounded half-revolution arc-tangent of binary32 value.
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Copyright (c) 2022-2025 Alexei Sibidanov.
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The original version of this file was copied from the CORE-MATH
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project (file src/binary32/atanpi/atanpif.c, revision e02000e).
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#include <errno.h>
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#include <math.h>
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#include <stdint.h>
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#include <libm-alias-float.h>
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#include "math_config.h"
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float
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__atanpif (float x)
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{
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uint32_t t = asuint (x);
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int32_t e = (t >> 23) & 0xff;
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bool gt = e >= 127;
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if (__glibc_unlikely (e > 127 + 24))
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{
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float f = copysignf (0.5f, x);
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if (__glibc_unlikely (e == 0xff))
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{
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if (t << 9)
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return x + x; /* nan */
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return f; /* inf */
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}
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/* Warning: 0x1.45f306p-2f / x underflows for |x| >= 0x1.45f306p+124 */
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if (fabsf (x) >= 0x1.45f306p+124f)
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return f - copysign (0x1p-26f, x);
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else
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return f - 0x1.45f306p-2f / x;
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}
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double z = x;
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if (__glibc_unlikely (e < 127 - 13))
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{
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double sx = z * 0x1.45f306dc9c883p-2;
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if (__glibc_unlikely (e < 127 - 25))
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{
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float rsx = sx;
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if (x != 0 && rsx == 0)
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__set_errno (ERANGE);
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return rsx;
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}
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return sx - (0x1.5555555555555p-2 * sx) * (x * x);
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}
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uint32_t ax = t & (~0u >> 1);
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if (__glibc_unlikely (ax == 0x3fa267ddu))
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return copysignf (0x1.267004p-2f, x) - copysignf (0x1p-55f, x);
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if (__glibc_unlikely (ax == 0x3f693531u))
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return copysignf (0x1.e1a662p-3f, x) + copysignf (0x1p-28f, x);
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if (__glibc_unlikely (ax == 0x3f800000u))
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return copysignf (0x1p-2f, x);
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if (gt)
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z = 1 / z;
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double z2 = z * z;
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double z4 = z2 * z2;
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double z8 = z4 * z4;
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static const double cn[] =
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{
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0x1.45f306dc9c882p-2, 0x1.733b561bc23d5p-1, 0x1.28d9805bdfbf2p-1,
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0x1.8c3ba966ae287p-3, 0x1.94a7f81ee634bp-6, 0x1.a6bbf6127a6dfp-11
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};
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static const double cd[] =
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{
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0x1p+0, 0x1.4e3b3ecc2518fp+1, 0x1.3ef4a360ff063p+1,
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0x1.0f1dc55bad551p+0, 0x1.8da0fecc018a4p-3, 0x1.8fa87803776bfp-7,
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0x1.dadf2ca0acb43p-14
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};
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double cn0 = cn[0] + z2 * cn[1];
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double cn2 = cn[2] + z2 * cn[3];
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double cn4 = cn[4] + z2 * cn[5];
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cn0 += z4 * cn2;
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cn0 += z8 * cn4;
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cn0 *= z;
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double cd0 = cd[0] + z2 * cd[1];
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double cd2 = cd[2] + z2 * cd[3];
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double cd4 = cd[4] + z2 * cd[5];
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double cd6 = cd[6];
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cd0 += z4 * cd2;
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cd4 += z4 * cd6;
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cd0 += z8 * cd4;
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double r = cn0 / cd0;
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if (gt)
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r = copysign (0.5, z) - r;
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return r;
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}
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libm_alias_float (__atanpi, atanpi)
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