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122 lines
4.4 KiB
C
122 lines
4.4 KiB
C
/* Double-precision AdvSIMD atan2
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Copyright (C) 2023-2024 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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#include "poly_advsimd_f64.h"
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static const struct data
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{
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float64x2_t pi_over_2;
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float64x2_t poly[20];
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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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the interval [2**-1022, 1.0]. */
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.poly = { V2 (-0x1.5555555555555p-2), V2 (0x1.99999999996c1p-3),
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V2 (-0x1.2492492478f88p-3), V2 (0x1.c71c71bc3951cp-4),
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V2 (-0x1.745d160a7e368p-4), V2 (0x1.3b139b6a88ba1p-4),
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V2 (-0x1.11100ee084227p-4), V2 (0x1.e1d0f9696f63bp-5),
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V2 (-0x1.aebfe7b418581p-5), V2 (0x1.842dbe9b0d916p-5),
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V2 (-0x1.5d30140ae5e99p-5), V2 (0x1.338e31eb2fbbcp-5),
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V2 (-0x1.00e6eece7de8p-5), V2 (0x1.860897b29e5efp-6),
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V2 (-0x1.0051381722a59p-6), V2 (0x1.14e9dc19a4a4ep-7),
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V2 (-0x1.d0062b42fe3bfp-9), V2 (0x1.17739e210171ap-10),
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V2 (-0x1.ab24da7be7402p-13), V2 (0x1.358851160a528p-16), },
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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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/* Special cases i.e. 0, infinity, NaN (fall back to scalar calls). */
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static float64x2_t VPCS_ATTR NOINLINE
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special_case (float64x2_t y, float64x2_t x, float64x2_t ret, uint64x2_t cmp)
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{
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return v_call2_f64 (atan2, y, x, ret, cmp);
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}
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/* Returns 1 if input is the bit representation of 0, infinity or nan. */
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static inline uint64x2_t
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zeroinfnan (uint64x2_t i)
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{
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/* (2 * i - 1) >= (2 * asuint64 (INFINITY) - 1). */
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return vcgeq_u64 (vsubq_u64 (vaddq_u64 (i, i), v_u64 (1)),
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v_u64 (2 * asuint64 (INFINITY) - 1));
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}
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/* Fast implementation of vector atan2.
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Maximum observed error is 2.8 ulps:
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_ZGVnN2vv_atan2 (0x1.9651a429a859ap+5, 0x1.953075f4ee26p+5)
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got 0x1.92d628ab678ccp-1
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want 0x1.92d628ab678cfp-1. */
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float64x2_t VPCS_ATTR V_NAME_D2 (atan2) (float64x2_t y, float64x2_t x)
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{
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const struct data *data_ptr = ptr_barrier (&data);
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uint64x2_t ix = vreinterpretq_u64_f64 (x);
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uint64x2_t iy = vreinterpretq_u64_f64 (y);
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uint64x2_t special_cases = vorrq_u64 (zeroinfnan (ix), zeroinfnan (iy));
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uint64x2_t sign_x = vandq_u64 (ix, SignMask);
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uint64x2_t sign_y = vandq_u64 (iy, SignMask);
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uint64x2_t sign_xy = veorq_u64 (sign_x, sign_y);
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float64x2_t ax = vabsq_f64 (x);
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float64x2_t ay = vabsq_f64 (y);
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uint64x2_t pred_xlt0 = vcltzq_f64 (x);
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uint64x2_t pred_aygtax = vcgtq_f64 (ay, ax);
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/* Set up z for call to atan. */
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float64x2_t n = vbslq_f64 (pred_aygtax, vnegq_f64 (ax), ay);
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float64x2_t d = vbslq_f64 (pred_aygtax, ay, ax);
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float64x2_t z = vdivq_f64 (n, d);
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/* Work out the correct shift. */
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float64x2_t shift = vreinterpretq_f64_u64 (
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vandq_u64 (pred_xlt0, vreinterpretq_u64_f64 (v_f64 (-2.0))));
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shift = vbslq_f64 (pred_aygtax, vaddq_f64 (shift, v_f64 (1.0)), shift);
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shift = vmulq_f64 (shift, data_ptr->pi_over_2);
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/* Calculate the polynomial approximation.
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Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of
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full scheme to avoid underflow in x^16.
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The order 19 polynomial P approximates
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(atan(sqrt(x))-sqrt(x))/x^(3/2). */
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float64x2_t z2 = vmulq_f64 (z, z);
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float64x2_t x2 = vmulq_f64 (z2, z2);
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float64x2_t x4 = vmulq_f64 (x2, x2);
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float64x2_t x8 = vmulq_f64 (x4, x4);
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float64x2_t ret
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= vfmaq_f64 (v_estrin_7_f64 (z2, x2, x4, data_ptr->poly),
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v_estrin_11_f64 (z2, x2, x4, x8, data_ptr->poly + 8), x8);
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/* Finalize. y = shift + z + z^3 * P(z^2). */
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ret = vfmaq_f64 (z, ret, vmulq_f64 (z2, z));
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ret = vaddq_f64 (ret, shift);
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/* Account for the sign of x and y. */
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ret = vreinterpretq_f64_u64 (
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veorq_u64 (vreinterpretq_u64_f64 (ret), sign_xy));
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if (__glibc_unlikely (v_any_u64 (special_cases)))
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return special_case (y, x, ret, special_cases);
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return ret;
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}
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