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129 lines
4.7 KiB
C
129 lines
4.7 KiB
C
/* Single-precision AdvSIMD log1p
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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 "v_math.h"
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#include "poly_advsimd_f32.h"
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const static struct data
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{
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float32x4_t poly[8], ln2;
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uint32x4_t tiny_bound, minus_one, four, thresh;
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int32x4_t three_quarters;
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} data = {
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.poly = { /* Generated using FPMinimax in [-0.25, 0.5]. First two coefficients
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(1, -0.5) are not stored as they can be generated more
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efficiently. */
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V4 (0x1.5555aap-2f), V4 (-0x1.000038p-2f), V4 (0x1.99675cp-3f),
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V4 (-0x1.54ef78p-3f), V4 (0x1.28a1f4p-3f), V4 (-0x1.0da91p-3f),
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V4 (0x1.abcb6p-4f), V4 (-0x1.6f0d5ep-5f) },
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.ln2 = V4 (0x1.62e43p-1f),
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.tiny_bound = V4 (0x34000000), /* asuint32(0x1p-23). ulp=0.5 at 0x1p-23. */
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.thresh = V4 (0x4b800000), /* asuint32(INFINITY) - tiny_bound. */
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.minus_one = V4 (0xbf800000),
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.four = V4 (0x40800000),
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.three_quarters = V4 (0x3f400000)
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};
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static inline float32x4_t
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eval_poly (float32x4_t m, const float32x4_t *p)
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{
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/* Approximate log(1+m) on [-0.25, 0.5] using split Estrin scheme. */
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float32x4_t p_12 = vfmaq_f32 (v_f32 (-0.5), m, p[0]);
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float32x4_t p_34 = vfmaq_f32 (p[1], m, p[2]);
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float32x4_t p_56 = vfmaq_f32 (p[3], m, p[4]);
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float32x4_t p_78 = vfmaq_f32 (p[5], m, p[6]);
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float32x4_t m2 = vmulq_f32 (m, m);
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float32x4_t p_02 = vfmaq_f32 (m, m2, p_12);
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float32x4_t p_36 = vfmaq_f32 (p_34, m2, p_56);
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float32x4_t p_79 = vfmaq_f32 (p_78, m2, p[7]);
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float32x4_t m4 = vmulq_f32 (m2, m2);
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float32x4_t p_06 = vfmaq_f32 (p_02, m4, p_36);
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return vfmaq_f32 (p_06, m4, vmulq_f32 (m4, p_79));
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}
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static float32x4_t NOINLINE VPCS_ATTR
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special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
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{
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return v_call_f32 (log1pf, x, y, special);
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}
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/* Vector log1pf approximation using polynomial on reduced interval. Accuracy
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is roughly 2.02 ULP:
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log1pf(0x1.21e13ap-2) got 0x1.fe8028p-3 want 0x1.fe802cp-3. */
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VPCS_ATTR float32x4_t V_NAME_F1 (log1p) (float32x4_t x)
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{
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const struct data *d = ptr_barrier (&data);
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uint32x4_t ix = vreinterpretq_u32_f32 (x);
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uint32x4_t ia = vreinterpretq_u32_f32 (vabsq_f32 (x));
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uint32x4_t special_cases
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= vorrq_u32 (vcgeq_u32 (vsubq_u32 (ia, d->tiny_bound), d->thresh),
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vcgeq_u32 (ix, d->minus_one));
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float32x4_t special_arg = x;
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#if WANT_SIMD_EXCEPT
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if (__glibc_unlikely (v_any_u32 (special_cases)))
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/* Side-step special lanes so fenv exceptions are not triggered
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inadvertently. */
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x = v_zerofy_f32 (x, special_cases);
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#endif
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/* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
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is in [-0.25, 0.5]):
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log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
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We approximate log1p(m) with a polynomial, then scale by
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k*log(2). Instead of doing this directly, we use an intermediate
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scale factor s = 4*k*log(2) to ensure the scale is representable
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as a normalised fp32 number. */
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float32x4_t m = vaddq_f32 (x, v_f32 (1.0f));
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/* Choose k to scale x to the range [-1/4, 1/2]. */
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int32x4_t k
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= vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d->three_quarters),
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v_s32 (0xff800000));
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uint32x4_t ku = vreinterpretq_u32_s32 (k);
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/* Scale x by exponent manipulation. */
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float32x4_t m_scale
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= vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku));
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/* Scale up to ensure that the scale factor is representable as normalised
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fp32 number, and scale m down accordingly. */
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float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d->four, ku));
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m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s));
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/* Evaluate polynomial on the reduced interval. */
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float32x4_t p = eval_poly (m_scale, d->poly);
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/* The scale factor to be applied back at the end - by multiplying float(k)
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by 2^-23 we get the unbiased exponent of k. */
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float32x4_t scale_back = vcvtq_f32_s32 (vshrq_n_s32 (k, 23));
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/* Apply the scaling back. */
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float32x4_t y = vfmaq_f32 (p, scale_back, d->ln2);
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if (__glibc_unlikely (v_any_u32 (special_cases)))
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return special_case (special_arg, y, special_cases);
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return y;
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}
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