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a357d6273f
The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows slight better performance to the generic atanf. 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 56.8265 53.6842 5.53% x86_64v2 54.8177 53.6842 2.07% x86_64v3 46.2915 48.7034 -5.21% i686 158.3760 108.9560 31.20% aarch64 (Neoverse) 21.687 20.5893 5.06% power10 13.1903 13.5012 -2.36% reciprocal-throughput master patched improvement x86_64 16.6787 16.7601 -0.49% x86_64v2 16.6983 16.7601 -0.37% x86_64v3 16.2268 12.1391 25.19% i686 138.6840 36.0640 74.00% aarch64 (Neoverse) 11.8012 10.3565 12.24% power10 5.3212 4.2894 19.39% Signed-off-by: Alexei Sibidanov <sibid@uvic.ca> Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr> Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org> Reviewed-by: DJ Delorie <dj@redhat.com>
113 lines
3.9 KiB
C
113 lines
3.9 KiB
C
/* Correctly-rounded arc-tangent of binary32 value.
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Copyright (c) 2022-2024 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/atan/atanf.c, revision a8066a5).
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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 <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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__atanf (float x)
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{
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const double pi2 = 0x1.921fb54442d18p+0;
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uint32_t t = asuint (x);
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int e = (t >> 23) & 0xff;
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bool gt = e >= 127;
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uint32_t ta = t & 0x7fffffff;
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if (__glibc_unlikely (ta >= 0x4c700518u)) /* |x| > 0x1.e00a3p+25 */
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{
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if (ta > 0x7f800000u)
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return x + x; /* nan */
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return copysign (pi2, (double) x);
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}
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if (__glibc_unlikely (e < 127 - 13))
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{
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if (__glibc_unlikely (e < 127 - 25))
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{
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if (!(t << 1))
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return x;
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return fmaf (-x, fabsf (x), x);
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}
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return fmaf (-0x1.5555555555555p-2f * x, x * x, x);
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}
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/* now |x| >= 0x1p-13 */
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double z = x;
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if (gt)
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z = 1 / z; /* gt is non-zero for |x| >= 1 */
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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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/* polynomials generated using rminimax
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(https://gitlab.inria.fr/sfilip/rminimax) with the following command:
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./ratapprox --function="atan(x)" --dom=[0.000122070,1]
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--num=[x,x^3,x^5,x^7,x^9,x^11,x^13] --den=[1,x^2,x^4,x^6,x^8,x^10,x^12]
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--output=atanf.sollya --log (see output atanf.sollya) The coefficient
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cd[0] was slightly reduced from the original value 0x1.51eccde075d67p-2 to
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avoid an exceptional case for |x| = 0x1.1ad646p-4 and rounding to nearest.
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*/
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static const double cn[] =
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{
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0x1.51eccde075d67p-2, 0x1.a76bb5637f2f2p-1, 0x1.81e0eed20de88p-1,
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0x1.376c8ca67d11dp-2, 0x1.aec7b69202ac6p-5, 0x1.9561899acc73ep-9,
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0x1.bf9fa5b67e6p-16
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};
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static const double cd[] =
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{
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0x1.51eccde075d66p-2, 0x1.dfbdd7b392d28p-1, 0x1p+0,
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0x1.fd22bf0e89b54p-2, 0x1.d91ff8b576282p-4, 0x1.653ea99fc9bbp-7,
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0x1.1e7fcc202340ap-12
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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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double cn6 = cn[6];
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cn0 += z4 * cn2;
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cn4 += z4 * cn6;
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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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return r; /* for |x| < 1, (float) r is correctly rounded */
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#define PI_OVER2_H 0x1.9p0
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#define PI_OVER2_L 0x1.0fdaa22168c23p-7
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/* now r approximates atan(1/x), we use atan(x) + atan(1/x) = sign(x)*pi/2,
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where PI_OVER2_H + PI_OVER2_L approximates pi/2.
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With sign(z)*L + (-r + sign(z)*H), it fails for x=0x1.98c252p+12 and
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rounding upward.
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With sign(z)*PI - r, where PI is a double approximation of pi to nearest,
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it fails for x=0x1.ddf9f6p+0 and rounding upward. */
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r = copysign (PI_OVER2_L, z) - r + copysign (PI_OVER2_H, z);
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return r;
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}
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libm_alias_float (__atan, atan)
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