/* Double-Precision vector (Advanced SIMD) inverse tan2pi function Copyright (C) 2025 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see . */ #include "v_math.h" static const struct data { float64_t c2, c4, c6, c8, c10, c12, c14, c16, c18, c20; float64x2_t c0; uint64x2_t zeroinfnan; float64x2_t c1, c3, c5, c7, c9, c11, c13, c15, c17, c19; } data = { /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on [2**-1022, 1.0]. */ .c0 = V2 (0x1.45f306dc9c883p-2), .c1 = V2 (-0x1.b2995e7b7ba4ap-4), .c2 = 0x1.04c26be3d2c1p-4, .c3 = V2 (-0x1.7483759c17ea1p-5), .c4 = 0x1.21bb95c315d57p-5, .c5 = V2 (-0x1.da1bdc3d453f3p-6), .c6 = 0x1.912d20459b4bfp-6, .c7 = V2 (-0x1.5bbd4545cad1fp-6), .c8 = 0x1.331b83bec30a1p-6, .c9 = V2 (-0x1.13d6457f44de3p-6), .c10 = 0x1.f8e802974db94p-7, .c11 = V2 (-0x1.d7e173ab04a1ap-7), .c12 = 0x1.bdfa47d6a4f28p-7, .c13 = V2 (-0x1.9ba78f3232ceep-7), .c14 = 0x1.5e6044590ab4fp-7, .c15 = V2 (-0x1.01ccfdeb9f77fp-7), .c16 = 0x1.345cf0d4eb1c1p-8, .c17 = V2 (-0x1.19e5f00f67e3ap-9), .c18 = 0x1.6d3035ac7625bp-11, .c19 = V2 (-0x1.286bb9ae4ed79p-13), .c20 = 0x1.c37ec36da0e1ap-17, .zeroinfnan = V2 (2 * 0x7ff0000000000000ul - 1), }; #define SignMask v_u64 (0x8000000000000000) #define OneOverPi v_f64 (0x1.45f306dc9c883p-2) /* Special cases i.e. 0, infinity, NaN (fall back to scalar calls). */ static float64x2_t VPCS_ATTR NOINLINE special_case (float64x2_t y, float64x2_t x, float64x2_t ret, uint64x2_t sign_xy, uint64x2_t cmp) { /* Account for the sign of x and y. */ ret = vreinterpretq_f64_u64 ( veorq_u64 (vreinterpretq_u64_f64 (ret), sign_xy)); /* Since we have no scalar fallback for atan2pi, we can instead make a call to atan2f and divide by pi. */ ret = v_call2_f64 (atan2, y, x, ret, cmp); /* Only divide the special cases by pi, and leave the rest unchanged. */ return vbslq_f64 (cmp, vmulq_f64 (ret, OneOverPi), ret); } /* Returns 1 if input is the bit representation of 0, infinity or nan. */ static inline uint64x2_t zeroinfnan (uint64x2_t i, const struct data *d) { /* (2 * i - 1) >= (2 * asuint64 (INFINITY) - 1). */ return vcgeq_u64 (vsubq_u64 (vaddq_u64 (i, i), v_u64 (1)), d->zeroinfnan); } /* Fast implementation of vector atan2pi. Maximum observed error is 3.04 ulps: _ZGVnN2vv_atan2pi (0x1.1e0733532ce28p+5, 0x1.2d803379cca1fp+5) got 0x1.eed60c1e89317p-3 want 0x1.eed60c1e89314p-3. */ float64x2_t VPCS_ATTR V_NAME_D2 (atan2pi) (float64x2_t y, float64x2_t x) { const struct data *d = ptr_barrier (&data); uint64x2_t ix = vreinterpretq_u64_f64 (x); uint64x2_t iy = vreinterpretq_u64_f64 (y); uint64x2_t special_cases = vorrq_u64 (zeroinfnan (ix, d), zeroinfnan (iy, d)); uint64x2_t sign_x = vandq_u64 (ix, SignMask); uint64x2_t sign_y = vandq_u64 (iy, SignMask); uint64x2_t sign_xy = veorq_u64 (sign_x, sign_y); float64x2_t ax = vabsq_f64 (x); float64x2_t ay = vabsq_f64 (y); uint64x2_t pred_xlt0 = vcltzq_f64 (x); uint64x2_t pred_aygtax = vcgtq_f64 (ay, ax); /* Set up z for evaluation of atanpi. */ float64x2_t num = vbslq_f64 (pred_aygtax, vnegq_f64 (ax), ay); float64x2_t den = vbslq_f64 (pred_aygtax, ay, ax); float64x2_t z = vdivq_f64 (num, den); /* Work out the correct shift for atan2pi: -1.0 when x < 0 and ax < ay -0.5 when x < 0 and ax > ay 0 when x >= 0 and ax < ay 0.5 when x >= 0 and ax > ay. */ float64x2_t shift = vreinterpretq_f64_u64 ( vandq_u64 (pred_xlt0, vreinterpretq_u64_f64 (v_f64 (-1.0)))); float64x2_t shift2 = vreinterpretq_f64_u64 ( vandq_u64 (pred_aygtax, vreinterpretq_u64_f64 (v_f64 (0.5)))); shift = vaddq_f64 (shift, shift2); /* Calculate the polynomial approximation. */ float64x2_t z2 = vmulq_f64 (z, z); float64x2_t z3 = vmulq_f64 (z2, z); float64x2_t z4 = vmulq_f64 (z2, z2); float64x2_t z8 = vmulq_f64 (z4, z4); float64x2_t z16 = vmulq_f64 (z8, z8); float64x2_t c24 = vld1q_f64 (&d->c2); float64x2_t c68 = vld1q_f64 (&d->c6); /* Order-7 Estrin. */ float64x2_t p12 = vfmaq_laneq_f64 (d->c1, z2, c24, 0); float64x2_t p34 = vfmaq_laneq_f64 (d->c3, z2, c24, 1); float64x2_t p56 = vfmaq_laneq_f64 (d->c5, z2, c68, 0); float64x2_t p78 = vfmaq_laneq_f64 (d->c7, z2, c68, 1); float64x2_t p14 = vfmaq_f64 (p12, z4, p34); float64x2_t p58 = vfmaq_f64 (p56, z4, p78); float64x2_t p18 = vfmaq_f64 (p14, z8, p58); /* Order-11 Estrin. */ float64x2_t c1012 = vld1q_f64 (&d->c10); float64x2_t c1416 = vld1q_f64 (&d->c14); float64x2_t c1820 = vld1q_f64 (&d->c18); float64x2_t p910 = vfmaq_laneq_f64 (d->c9, z2, c1012, 0); float64x2_t p1112 = vfmaq_laneq_f64 (d->c11, z2, c1012, 1); float64x2_t p912 = vfmaq_f64 (p910, z4, p1112); float64x2_t p1314 = vfmaq_laneq_f64 (d->c13, z2, c1416, 0); float64x2_t p1516 = vfmaq_laneq_f64 (d->c15, z2, c1416, 1); float64x2_t p1316 = vfmaq_f64 (p1314, z4, p1516); float64x2_t p1718 = vfmaq_laneq_f64 (d->c17, z2, c1820, 0); float64x2_t p1920 = vfmaq_laneq_f64 (d->c19, z2, c1820, 1); float64x2_t p1720 = vfmaq_f64 (p1718, z4, p1920); float64x2_t p916 = vfmaq_f64 (p912, z8, p1316); float64x2_t p920 = vfmaq_f64 (p916, z16, p1720); float64x2_t poly = vfmaq_f64 (p18, z16, p920); /* y = shift + z * P(z^2). */ float64x2_t ret = vfmaq_f64 (shift, z, d->c0); ret = vfmaq_f64 (ret, z3, poly); if (__glibc_unlikely (v_any_u64 (special_cases))) return special_case (y, x, ret, sign_xy, special_cases); /* Account for the sign of x and y. */ return vreinterpretq_f64_u64 ( veorq_u64 (vreinterpretq_u64_f64 (ret), sign_xy)); }