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119 lines
4.2 KiB
C
119 lines
4.2 KiB
C
/* Single-precision vector (SVE) tan function
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Copyright (C) 2023 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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float pio2_1, pio2_2, pio2_3, invpio2;
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float c1, c3, c5;
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float c0, c2, c4, range_val, shift;
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} data = {
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/* Coefficients generated using:
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poly = fpminimax((tan(sqrt(x))-sqrt(x))/x^(3/2),
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deg,
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[|single ...|],
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[a*a;b*b]);
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optimize relative error
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final prec : 23 bits
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deg : 5
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a : 0x1p-126 ^ 2
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b : ((pi) / 0x1p2) ^ 2
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dirty rel error: 0x1.f7c2e4p-25
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dirty abs error: 0x1.f7c2ecp-25. */
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.c0 = 0x1.55555p-2, .c1 = 0x1.11166p-3,
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.c2 = 0x1.b88a78p-5, .c3 = 0x1.7b5756p-6,
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.c4 = 0x1.4ef4cep-8, .c5 = 0x1.0e1e74p-7,
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.pio2_1 = 0x1.921fb6p+0f, .pio2_2 = -0x1.777a5cp-25f,
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.pio2_3 = -0x1.ee59dap-50f, .invpio2 = 0x1.45f306p-1f,
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.range_val = 0x1p15f, .shift = 0x1.8p+23f
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};
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static svfloat32_t NOINLINE
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special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
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{
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return sv_call_f32 (tanf, x, y, cmp);
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}
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/* Fast implementation of SVE tanf.
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Maximum error is 3.45 ULP:
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SV_NAME_F1 (tan)(-0x1.e5f0cap+13) got 0x1.ff9856p-1
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want 0x1.ff9850p-1. */
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svfloat32_t SV_NAME_F1 (tan) (svfloat32_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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/* Determine whether input is too large to perform fast regression. */
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svbool_t cmp = svacge (pg, x, d->range_val);
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svfloat32_t odd_coeffs = svld1rq (svptrue_b32 (), &d->c1);
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svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->pio2_1);
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/* n = rint(x/(pi/2)). */
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svfloat32_t q = svmla_lane (sv_f32 (d->shift), x, pi_vals, 3);
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svfloat32_t n = svsub_x (pg, q, d->shift);
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/* n is already a signed integer, simply convert it. */
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svint32_t in = svcvt_s32_x (pg, n);
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/* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
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svint32_t alt = svand_x (pg, in, 1);
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svbool_t pred_alt = svcmpne (pg, alt, 0);
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/* r = x - n * (pi/2) (range reduction into 0 .. pi/4). */
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svfloat32_t r;
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r = svmls_lane (x, n, pi_vals, 0);
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r = svmls_lane (r, n, pi_vals, 1);
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r = svmls_lane (r, n, pi_vals, 2);
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/* If x lives in an interval, where |tan(x)|
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- is finite, then use a polynomial approximation of the form
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tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
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- grows to infinity then use symmetries of tangent and the identity
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tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
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the same polynomial approximation of tan as above. */
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/* Perform additional reduction if required. */
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svfloat32_t z = svneg_m (r, pred_alt, r);
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/* Evaluate polynomial approximation of tangent on [-pi/4, pi/4],
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using Estrin on z^2. */
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svfloat32_t z2 = svmul_x (pg, z, z);
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svfloat32_t p01 = svmla_lane (sv_f32 (d->c0), z2, odd_coeffs, 0);
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svfloat32_t p23 = svmla_lane (sv_f32 (d->c2), z2, odd_coeffs, 1);
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svfloat32_t p45 = svmla_lane (sv_f32 (d->c4), z2, odd_coeffs, 2);
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svfloat32_t z4 = svmul_x (pg, z2, z2);
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svfloat32_t p = svmla_x (pg, p01, z4, p23);
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svfloat32_t z8 = svmul_x (pg, z4, z4);
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p = svmla_x (pg, p, z8, p45);
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svfloat32_t y = svmla_x (pg, z, p, svmul_x (pg, z, z2));
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/* Transform result back, if necessary. */
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svfloat32_t inv_y = svdivr_x (pg, y, 1.0f);
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/* No need to pass pg to specialcase here since cmp is a strict subset,
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guaranteed by the cmpge above. */
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if (__glibc_unlikely (svptest_any (pg, cmp)))
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return special_case (x, svsel (pred_alt, inv_y, y), cmp);
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return svsel (pred_alt, inv_y, y);
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}
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