mirror of git://sourceware.org/git/glibc.git
121 lines
4.8 KiB
C
121 lines
4.8 KiB
C
/* Double-precision AdvSIMD 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 "v_math.h"
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static const struct data
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{
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float64x2_t c0, c2, c4, c6, c8, c10, c12, c14, c16, c18;
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float64x2_t pi_over_2;
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double c1, c3, c5, c7, c9, c11, c13, c15, c17, c19;
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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 = V2 (-0x1.555555555552ap-2), .c1 = 0x1.9999999995aebp-3,
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.c2 = V2 (-0x1.24924923923f6p-3), .c3 = 0x1.c71c7184288a2p-4,
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.c4 = V2 (-0x1.745d11fb3d32bp-4), .c5 = 0x1.3b136a18051b9p-4,
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.c6 = V2 (-0x1.110e6d985f496p-4), .c7 = 0x1.e1bcf7f08801dp-5,
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.c8 = V2 (-0x1.ae644e28058c3p-5), .c9 = 0x1.82eeb1fed85c6p-5,
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.c10 = V2 (-0x1.59d7f901566cbp-5), .c11 = 0x1.2c982855ab069p-5,
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.c12 = V2 (-0x1.eb49592998177p-6), .c13 = 0x1.69d8b396e3d38p-6,
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.c14 = V2 (-0x1.ca980345c4204p-7), .c15 = 0x1.dc050eafde0b3p-8,
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.c16 = V2 (-0x1.7ea70755b8eccp-9), .c17 = 0x1.ba3da3de903e8p-11,
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.c18 = V2 (-0x1.44a4b059b6f67p-13), .c19 = 0x1.c4a45029e5a91p-17,
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.pi_over_2 = V2 (0x1.921fb54442d18p+0),
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};
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#define SignMask v_u64 (0x8000000000000000)
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#define TinyBound 0x3e10000000000000 /* asuint64(0x1p-30). */
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#define BigBound 0x4340000000000000 /* asuint64(0x1p53). */
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/* Fast implementation of vector 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. Maximum observed error is 2.45 ulps:
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_ZGVnN2v_atan (0x1.0008d737eb3e6p+0) got 0x1.92288c551a4c1p-1
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want 0x1.92288c551a4c3p-1. */
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float64x2_t VPCS_ATTR V_NAME_D1 (atan) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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float64x2_t c13 = vld1q_f64 (&d->c1);
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float64x2_t c57 = vld1q_f64 (&d->c5);
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float64x2_t c911 = vld1q_f64 (&d->c9);
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float64x2_t c1315 = vld1q_f64 (&d->c13);
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float64x2_t c1719 = vld1q_f64 (&d->c17);
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/* Small cases, infs and nans are supported by our approximation technique,
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but do not set fenv flags correctly. Only trigger special case if we need
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fenv. */
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uint64x2_t ix = vreinterpretq_u64_f64 (x);
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uint64x2_t sign = vandq_u64 (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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uint64x2_t red = vcagtq_f64 (x, v_f64 (-1.0));
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/* Avoid dependency in abs(x) in division (and comparison). */
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float64x2_t z = vbslq_f64 (red, vdivq_f64 (v_f64 (-1.0), x), x);
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float64x2_t shift = vreinterpretq_f64_u64 (
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vandq_u64 (red, vreinterpretq_u64_f64 (d->pi_over_2)));
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/* Reinsert sign bit from argument into the shift value. */
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shift = vreinterpretq_f64_u64 (
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veorq_u64 (vreinterpretq_u64_f64 (shift), sign));
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/* Calculate polynomial approximation P(z^2) with deg(P)=19. */
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float64x2_t z2 = vmulq_f64 (z, z);
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float64x2_t z4 = vmulq_f64 (z2, z2);
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float64x2_t z8 = vmulq_f64 (z4, z4);
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float64x2_t z16 = vmulq_f64 (z8, z8);
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/* Order-7 Estrin. */
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float64x2_t p01 = vfmaq_laneq_f64 (d->c0, z2, c13, 0);
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float64x2_t p23 = vfmaq_laneq_f64 (d->c2, z2, c13, 1);
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float64x2_t p03 = vfmaq_f64 (p01, z4, p23);
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float64x2_t p45 = vfmaq_laneq_f64 (d->c4, z2, c57, 0);
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float64x2_t p67 = vfmaq_laneq_f64 (d->c6, z2, c57, 1);
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float64x2_t p47 = vfmaq_f64 (p45, z4, p67);
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float64x2_t p07 = vfmaq_f64 (p03, z8, p47);
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/* Order-11 Estrin. */
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float64x2_t p89 = vfmaq_laneq_f64 (d->c8, z2, c911, 0);
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float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, z2, c911, 1);
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float64x2_t p811 = vfmaq_f64 (p89, z4, p1011);
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float64x2_t p1213 = vfmaq_laneq_f64 (d->c12, z2, c1315, 0);
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float64x2_t p1415 = vfmaq_laneq_f64 (d->c14, z2, c1315, 1);
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float64x2_t p1215 = vfmaq_f64 (p1213, z4, p1415);
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float64x2_t p1617 = vfmaq_laneq_f64 (d->c16, z2, c1719, 0);
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float64x2_t p1819 = vfmaq_laneq_f64 (d->c18, z2, c1719, 1);
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float64x2_t p1619 = vfmaq_f64 (p1617, z4, p1819);
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float64x2_t p815 = vfmaq_f64 (p811, z8, p1215);
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float64x2_t p819 = vfmaq_f64 (p815, z16, p1619);
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float64x2_t y = vfmaq_f64 (p07, p819, z16);
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/* Finalize. y = shift + z + z^3 * P(z^2). */
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y = vfmsq_f64 (v_f64 (-1.0), z2, y);
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return vfmsq_f64 (shift, z, y);
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}
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