mirror of git://sourceware.org/git/glibc.git
93 lines
3.3 KiB
C
93 lines
3.3 KiB
C
/* Single-Precision vector (Advanced SIMD) inverse tanpi function
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Copyright (C) 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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uint32x4_t half;
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float32x4_t neg_one;
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float32x4_t c0, c1, c3, c5, c7;
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float c2, c4, c6, c8;
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} data = {
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/* Polynomial coefficients generated using Remez algorithm,
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see atanpi.sollya for details. */
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.c0 = V4 (0x1.45f306p-2), .c1 = V4 (-0x1.b2975ep-4),
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.c2 = 0x1.0490e4p-4, .c3 = V4 (-0x1.70c272p-5),
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.c4 = 0x1.0eef52p-5, .c5 = V4 (-0x1.6abbbap-6),
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.c6 = 0x1.78157p-7, .c7 = V4 (-0x1.f0b406p-9),
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.c8 = 0x1.2ae7fep-11, .half = V4 (0x3f000000),
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.neg_one = V4 (-1.0f),
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};
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#define SignMask v_u32 (0x80000000)
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/* Fast implementation of vector atanpif based on
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atanpi(x) ~ shift + z * P(z^2) with reduction to [0,1]
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using z=-1/x and shift = +-1/2.
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Maximum observed error is 2.59ulps:
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_ZGVnN4v_atanpif (0x1.f2a89cp-1) got 0x1.f76524p-3
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want 0x1.f7651ep-3. */
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float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (atanpi) (float32x4_t x)
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{
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const struct data *d = ptr_barrier (&data);
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uint32x4_t ix = vreinterpretq_u32_f32 (x);
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uint32x4_t sign = vandq_u32 (ix, SignMask);
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/* Argument Reduction:
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y := arctanpi(x) for |x| < 1
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y := arctanpi(-1/x) + 1/2 for x > 1
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y := arctanpi(-1/x) - 1/2 for x < -1
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Hence, use z=-1/a if |x|>=|-1|, otherwise z=a. */
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uint32x4_t red = vcagtq_f32 (x, d->neg_one);
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float32x4_t z = vbslq_f32 (red, vdivq_f32 (d->neg_one, x), x);
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/* Shift is calculated as +1/2 or 0, depending on the argument case. */
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float32x4_t shift = vreinterpretq_f32_u32 (vandq_u32 (red, d->half));
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/* Reinsert sign bit from argument into the shift value. */
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shift = vreinterpretq_f32_u32 (
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veorq_u32 (vreinterpretq_u32_f32 (shift), sign));
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/* Uses an Estrin scheme for polynomial approximation. */
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float32x4_t z2 = vmulq_f32 (z, z);
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float32x4_t z4 = vmulq_f32 (z2, z2);
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float32x4_t z8 = vmulq_f32 (z4, z4);
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float32x4_t even_coeffs = vld1q_f32 (&d->c2);
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float32x4_t p12 = vfmaq_laneq_f32 (d->c1, z2, even_coeffs, 0);
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float32x4_t p34 = vfmaq_laneq_f32 (d->c3, z2, even_coeffs, 1);
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float32x4_t p56 = vfmaq_laneq_f32 (d->c5, z2, even_coeffs, 2);
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float32x4_t p78 = vfmaq_laneq_f32 (d->c7, z2, even_coeffs, 3);
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float32x4_t p14 = vfmaq_f32 (p12, z4, p34);
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float32x4_t p58 = vfmaq_f32 (p56, z4, p78);
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float32x4_t y = vfmaq_f32 (p14, z8, p58);
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y = vfmaq_f32 (d->c0, z2, y);
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/* y = shift + z * P(z^2). */
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return vfmaq_f32 (shift, z, y);
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}
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libmvec_hidden_def (V_NAME_F1 (atanpi))
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HALF_WIDTH_ALIAS_F1 (atanpi)
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