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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>
134 lines
5.0 KiB
C
134 lines
5.0 KiB
C
/* Single-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_f32.h"
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static const struct data
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{
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float32x4_t poly[6];
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float pi_consts[4];
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float32x4_t shift;
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#if !WANT_SIMD_EXCEPT
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float32x4_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 = { V4 (0x1.55555p-2f), V4 (0x1.11166p-3f), V4 (0x1.b88a78p-5f),
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V4 (0x1.7b5756p-6f), V4 (0x1.4ef4cep-8f), V4 (0x1.0e1e74p-7f) },
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/* Stores constants: (-pi/2)_high, (-pi/2)_mid, (-pi/2)_low, and 2/pi. */
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.pi_consts
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= { -0x1.921fb6p+0f, 0x1.777a5cp-25f, 0x1.ee59dap-50f, 0x1.45f306p-1f },
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.shift = V4 (0x1.8p+23f),
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#if !WANT_SIMD_EXCEPT
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.range_val = V4 (0x1p15f),
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#endif
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};
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#define RangeVal v_u32 (0x47000000) /* asuint32(0x1p15f). */
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#define TinyBound v_u32 (0x30000000) /* asuint32 (0x1p-31f). */
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#define Thresh v_u32 (0x16000000) /* asuint32(RangeVal) - TinyBound. */
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/* Special cases (fall back to scalar calls). */
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static float32x4_t VPCS_ATTR NOINLINE
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special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
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{
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return v_call_f32 (tanf, x, y, cmp);
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}
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/* Use a full Estrin scheme to evaluate polynomial. */
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static inline float32x4_t
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eval_poly (float32x4_t z, const struct data *d)
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{
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float32x4_t z2 = vmulq_f32 (z, z);
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#if WANT_SIMD_EXCEPT
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/* Tiny z (<= 0x1p-31) will underflow when calculating z^4.
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If fp exceptions are to be triggered correctly,
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sidestep this by fixing such lanes to 0. */
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uint32x4_t will_uflow
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= vcleq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (z)), TinyBound);
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if (__glibc_unlikely (v_any_u32 (will_uflow)))
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z2 = vbslq_f32 (will_uflow, v_f32 (0), z2);
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#endif
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float32x4_t z4 = vmulq_f32 (z2, z2);
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return v_estrin_5_f32 (z, z2, z4, d->poly);
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}
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/* Fast implementation of AdvSIMD tanf.
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Maximum error is 3.45 ULP:
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__v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
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want 0x1.ff9850p-1. */
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float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (tan) (float32x4_t x)
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{
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const struct data *d = ptr_barrier (&data);
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float32x4_t special_arg = x;
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/* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
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regression. */
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#if WANT_SIMD_EXCEPT
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uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x));
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/* If fp exceptions are to be triggered correctly, also special-case tiny
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input, as this will load to overflow later. Fix any special lanes to 1 to
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prevent any exceptions being triggered. */
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uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, TinyBound), Thresh);
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if (__glibc_unlikely (v_any_u32 (special)))
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x = vbslq_f32 (special, v_f32 (1.0f), x);
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#else
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/* Otherwise, special-case large and special values. */
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uint32x4_t special = vcageq_f32 (x, d->range_val);
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#endif
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/* n = rint(x/(pi/2)). */
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float32x4_t pi_consts = vld1q_f32 (d->pi_consts);
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float32x4_t q = vfmaq_laneq_f32 (d->shift, x, pi_consts, 3);
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float32x4_t n = vsubq_f32 (q, d->shift);
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/* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
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uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1));
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/* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */
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float32x4_t r;
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r = vfmaq_laneq_f32 (x, n, pi_consts, 0);
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r = vfmaq_laneq_f32 (r, n, pi_consts, 1);
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r = vfmaq_laneq_f32 (r, n, pi_consts, 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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/* Invert sign of r if odd quadrant. */
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float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1)));
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/* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */
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float32x4_t z2 = vmulq_f32 (r, r);
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float32x4_t p = eval_poly (z2, d);
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float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p);
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/* Compute reciprocal and apply if required. */
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float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y);
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if (__glibc_unlikely (v_any_u32 (special)))
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return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special);
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return vbslq_f32 (pred_alt, inv_y, y);
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}
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libmvec_hidden_def (V_NAME_F1 (tan))
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HALF_WIDTH_ALIAS_F1 (tan)
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