mirror of git://sourceware.org/git/glibc.git
121 lines
4.7 KiB
C
121 lines
4.7 KiB
C
/* Double-precision SVE inverse tan
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Copyright (C) 2023-2025 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "sv_math.h"
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static const struct data
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{
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float64_t c0, c2, c4, c6, c8, c10, c12, c14, c16, c18;
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float64_t c1, c3, c5, c7, c9, c11, c13, c15, c17, c19;
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float64_t shift_val, neg_one;
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} data = {
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/* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
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[2**-1022, 1.0]. */
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.c0 = -0x1.555555555552ap-2, .c1 = 0x1.9999999995aebp-3,
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.c2 = -0x1.24924923923f6p-3, .c3 = 0x1.c71c7184288a2p-4,
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.c4 = -0x1.745d11fb3d32bp-4, .c5 = 0x1.3b136a18051b9p-4,
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.c6 = -0x1.110e6d985f496p-4, .c7 = 0x1.e1bcf7f08801dp-5,
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.c8 = -0x1.ae644e28058c3p-5, .c9 = 0x1.82eeb1fed85c6p-5,
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.c10 = -0x1.59d7f901566cbp-5, .c11 = 0x1.2c982855ab069p-5,
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.c12 = -0x1.eb49592998177p-6, .c13 = 0x1.69d8b396e3d38p-6,
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.c14 = -0x1.ca980345c4204p-7, .c15 = 0x1.dc050eafde0b3p-8,
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.c16 = -0x1.7ea70755b8eccp-9, .c17 = 0x1.ba3da3de903e8p-11,
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.c18 = -0x1.44a4b059b6f67p-13, .c19 = 0x1.c4a45029e5a91p-17,
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.shift_val = 0x1.490fdaa22168cp+1, .neg_one = -1,
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};
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/* Useful constants. */
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#define SignMask (0x8000000000000000)
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/* Fast implementation of SVE atan.
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Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
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z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed
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error is 2.08 ulps:
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_ZGVsMxv_atan (0x1.000a7c56975e8p+0) got 0x1.922a3163e15c2p-1
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want 0x1.922a3163e15c4p-1. */
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svfloat64_t SV_NAME_D1 (atan) (svfloat64_t x, const svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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svbool_t ptrue = svptrue_b64 ();
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svuint64_t ix = svreinterpret_u64 (x);
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svuint64_t sign = svand_x (pg, ix, SignMask);
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/* Argument reduction:
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y := arctan(x) for x < 1
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y := pi/2 + arctan(-1/x) for x > 1
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Hence, use z=-1/a if x>=1, otherwise z=a. */
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svbool_t red = svacgt (pg, x, d->neg_one);
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svfloat64_t z = svsel (red, svdiv_x (pg, sv_f64 (d->neg_one), x), x);
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/* Reuse of -1.0f to reduce constant loads,
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We need a shift value of 1/2, which is created via -1 + (1 + 1/2). */
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svfloat64_t shift
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= svadd_z (red, sv_f64 (d->neg_one), sv_f64 (d->shift_val));
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/* Reinserts the sign bit of the argument to handle the case of x < -1. */
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shift = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (shift), sign));
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/* Use split Estrin scheme for P(z^2) with deg(P)=19. */
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svfloat64_t z2 = svmul_x (ptrue, z, z);
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svfloat64_t z4 = svmul_x (ptrue, z2, z2);
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svfloat64_t z8 = svmul_x (ptrue, z4, z4);
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svfloat64_t z16 = svmul_x (ptrue, z8, z8);
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/* Order-7 Estrin. */
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svfloat64_t c13 = svld1rq (ptrue, &d->c1);
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svfloat64_t c57 = svld1rq (ptrue, &d->c5);
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svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), z2, c13, 0);
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svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), z2, c13, 1);
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svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), z2, c57, 0);
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svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), z2, c57, 1);
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svfloat64_t p03 = svmla_x (pg, p01, z4, p23);
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svfloat64_t p47 = svmla_x (pg, p45, z4, p67);
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svfloat64_t p07 = svmla_x (pg, p03, z8, p47);
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/* Order-11 Estrin. */
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svfloat64_t c911 = svld1rq (ptrue, &d->c9);
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svfloat64_t c1315 = svld1rq (ptrue, &d->c13);
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svfloat64_t c1719 = svld1rq (ptrue, &d->c17);
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svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), z2, c911, 0);
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svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), z2, c911, 1);
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svfloat64_t p811 = svmla_x (pg, p89, z4, p1011);
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svfloat64_t p1213 = svmla_lane (sv_f64 (d->c12), z2, c1315, 0);
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svfloat64_t p1415 = svmla_lane (sv_f64 (d->c14), z2, c1315, 1);
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svfloat64_t p1215 = svmla_x (pg, p1213, z4, p1415);
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svfloat64_t p1617 = svmla_lane (sv_f64 (d->c16), z2, c1719, 0);
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svfloat64_t p1819 = svmla_lane (sv_f64 (d->c18), z2, c1719, 1);
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svfloat64_t p1619 = svmla_x (pg, p1617, z4, p1819);
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svfloat64_t p815 = svmla_x (pg, p811, z8, p1215);
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svfloat64_t p819 = svmla_x (pg, p815, z16, p1619);
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svfloat64_t y = svmla_x (pg, p07, z16, p819);
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/* y = shift + z + z^3 * P(z^2). */
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shift = svadd_m (red, z, shift);
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y = svmul_x (pg, z2, y);
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return svmla_x (pg, shift, z, y);
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}
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