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90a6ca8b28
Previously many routines used * to load from vector types stored
in the data table. This is emitted as ldr, which byte-swaps the
entire vector register, and causes bugs for big-endian when not
all lanes contain the same value. When a vector is to be used
this way, it has been replaced with an array and the load with an
explicit ld1 intrinsic, which byte-swaps only within lanes.
As well, many routines previously used non-standard GCC syntax
for vector operations such as indexing into vectors types with []
and assembling vectors using {}. This syntax should not be mixed
with ACLE, as the former does not respect endianness whereas the
latter does. Such examples have been replaced with, for instance,
vcombine_* and vgetq_lane* intrinsics. Helpers which only use the
GCC syntax, such as the v_call helpers, do not need changing as
they do not use intrinsics.
Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com>
126 lines
4.6 KiB
C
126 lines
4.6 KiB
C
/* Double-precision vector (Advanced SIMD) tan function
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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 poly[9];
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double half_pi[2];
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float64x2_t two_over_pi, shift;
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#if !WANT_SIMD_EXCEPT
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float64x2_t range_val;
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#endif
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} data = {
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/* Coefficients generated using FPMinimax. */
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.poly = { V2 (0x1.5555555555556p-2), V2 (0x1.1111111110a63p-3),
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V2 (0x1.ba1ba1bb46414p-5), V2 (0x1.664f47e5b5445p-6),
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V2 (0x1.226e5e5ecdfa3p-7), V2 (0x1.d6c7ddbf87047p-9),
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V2 (0x1.7ea75d05b583ep-10), V2 (0x1.289f22964a03cp-11),
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V2 (0x1.4e4fd14147622p-12) },
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.half_pi = { 0x1.921fb54442d18p0, 0x1.1a62633145c07p-54 },
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.two_over_pi = V2 (0x1.45f306dc9c883p-1),
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.shift = V2 (0x1.8p52),
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#if !WANT_SIMD_EXCEPT
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.range_val = V2 (0x1p23),
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#endif
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};
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#define RangeVal 0x4160000000000000 /* asuint64(0x1p23). */
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#define TinyBound 0x3e50000000000000 /* asuint64(2^-26). */
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#define Thresh 0x310000000000000 /* RangeVal - TinyBound. */
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/* Special cases (fall back to scalar calls). */
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static float64x2_t VPCS_ATTR NOINLINE
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special_case (float64x2_t x)
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{
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return v_call_f64 (tan, x, x, v_u64 (-1));
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}
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/* Vector approximation for double-precision tan.
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Maximum measured error is 3.48 ULP:
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_ZGVnN2v_tan(0x1.4457047ef78d8p+20) got -0x1.f6ccd8ecf7dedp+37
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want -0x1.f6ccd8ecf7deap+37. */
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float64x2_t VPCS_ATTR V_NAME_D1 (tan) (float64x2_t x)
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{
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const struct data *dat = ptr_barrier (&data);
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/* Our argument reduction cannot calculate q with sufficient accuracy for
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very large inputs. Fall back to scalar routine for all lanes if any are
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too large, or Inf/NaN. If fenv exceptions are expected, also fall back for
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tiny input to avoid underflow. */
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#if WANT_SIMD_EXCEPT
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uint64x2_t iax = vreinterpretq_u64_f64 (vabsq_f64 (x));
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/* iax - tiny_bound > range_val - tiny_bound. */
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uint64x2_t special
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= vcgtq_u64 (vsubq_u64 (iax, v_u64 (TinyBound)), v_u64 (Thresh));
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if (__glibc_unlikely (v_any_u64 (special)))
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return special_case (x);
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#endif
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/* q = nearest integer to 2 * x / pi. */
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float64x2_t q
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= vsubq_f64 (vfmaq_f64 (dat->shift, x, dat->two_over_pi), dat->shift);
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int64x2_t qi = vcvtq_s64_f64 (q);
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/* Use q to reduce x to r in [-pi/4, pi/4], by:
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r = x - q * pi/2, in extended precision. */
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float64x2_t r = x;
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float64x2_t half_pi = vld1q_f64 (dat->half_pi);
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r = vfmsq_laneq_f64 (r, q, half_pi, 0);
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r = vfmsq_laneq_f64 (r, q, half_pi, 1);
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/* Further reduce r to [-pi/8, pi/8], to be reconstructed using double angle
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formula. */
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r = vmulq_n_f64 (r, 0.5);
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/* Approximate tan(r) using order 8 polynomial.
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tan(x) is odd, so polynomial has the form:
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tan(x) ~= x + C0 * x^3 + C1 * x^5 + C3 * x^7 + ...
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Hence we first approximate P(r) = C1 + C2 * r^2 + C3 * r^4 + ...
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Then compute the approximation by:
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tan(r) ~= r + r^3 * (C0 + r^2 * P(r)). */
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float64x2_t r2 = vmulq_f64 (r, r), r4 = vmulq_f64 (r2, r2),
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r8 = vmulq_f64 (r4, r4);
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/* Offset coefficients to evaluate from C1 onwards. */
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float64x2_t p = v_estrin_7_f64 (r2, r4, r8, dat->poly + 1);
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p = vfmaq_f64 (dat->poly[0], p, r2);
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p = vfmaq_f64 (r, r2, vmulq_f64 (p, r));
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/* Recombination uses double-angle formula:
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tan(2x) = 2 * tan(x) / (1 - (tan(x))^2)
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and reciprocity around pi/2:
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tan(x) = 1 / (tan(pi/2 - x))
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to assemble result using change-of-sign and conditional selection of
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numerator/denominator, dependent on odd/even-ness of q (hence quadrant).
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*/
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float64x2_t n = vfmaq_f64 (v_f64 (-1), p, p);
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float64x2_t d = vaddq_f64 (p, p);
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uint64x2_t no_recip = vtstq_u64 (vreinterpretq_u64_s64 (qi), v_u64 (1));
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#if !WANT_SIMD_EXCEPT
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uint64x2_t special = vcageq_f64 (x, dat->range_val);
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if (__glibc_unlikely (v_any_u64 (special)))
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return special_case (x);
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#endif
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return vdivq_f64 (vbslq_f64 (no_recip, n, vnegq_f64 (d)),
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vbslq_f64 (no_recip, d, n));
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}
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