mirror of git://sourceware.org/git/glibc.git
125 lines
4.5 KiB
C
125 lines
4.5 KiB
C
/* Double-precision vector (AdvSIMD) exp2 function
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Copyright (C) 2023-2025 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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static const struct data
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{
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uint64x2_t off, sign_exp_mask, offset_lower_bound;
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uint32x4_t special_bound;
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float64x2_t c0, c2;
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double c1, c3, invln2, c4;
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} data = {
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/* Each coefficient was generated to approximate log(r) for |r| < 0x1.fp-9
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and N = 128, then scaled by log2(e) in extended precision and rounded back
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to double precision. */
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.c0 = V2 (-0x1.71547652b8300p-1),
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.c1 = 0x1.ec709dc340953p-2,
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.c2 = V2 (-0x1.71547651c8f35p-2),
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.c3 = 0x1.2777ebe12dda5p-2,
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.c4 = -0x1.ec738d616fe26p-3,
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.invln2 = 0x1.71547652b82fep0,
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.off = V2 (0x3fe6900900000000),
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.sign_exp_mask = V2 (0xfff0000000000000),
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/* Lower bound is 0x0010000000000000. For
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optimised register use subnormals are detected after offset has been
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subtracted, so lower bound - offset (which wraps around). */
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.offset_lower_bound = V2 (0x0010000000000000 - 0x3fe6900900000000),
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.special_bound = V4 (0x7fe00000), /* asuint64(inf) - asuint64(0x1p-1022). */
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};
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#define N (1 << V_LOG2_TABLE_BITS)
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#define IndexMask (N - 1)
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struct entry
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{
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float64x2_t invc;
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float64x2_t log2c;
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};
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static inline struct entry
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lookup (uint64x2_t i)
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{
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struct entry e;
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uint64_t i0
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= (vgetq_lane_u64 (i, 0) >> (52 - V_LOG2_TABLE_BITS)) & IndexMask;
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uint64_t i1
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= (vgetq_lane_u64 (i, 1) >> (52 - V_LOG2_TABLE_BITS)) & IndexMask;
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float64x2_t e0 = vld1q_f64 (&__v_log2_data.table[i0].invc);
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float64x2_t e1 = vld1q_f64 (&__v_log2_data.table[i1].invc);
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e.invc = vuzp1q_f64 (e0, e1);
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e.log2c = vuzp2q_f64 (e0, e1);
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return e;
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}
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static float64x2_t VPCS_ATTR NOINLINE
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special_case (float64x2_t hi, uint64x2_t u_off, float64x2_t y, float64x2_t r2,
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uint32x2_t special, const struct data *d)
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{
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float64x2_t x = vreinterpretq_f64_u64 (vaddq_u64 (u_off, d->off));
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return v_call_f64 (log2, x, vfmaq_f64 (hi, y, r2), vmovl_u32 (special));
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}
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/* Double-precision vector log2 routine. Implements the same algorithm as
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vector log10, with coefficients and table entries scaled in extended
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precision. The maximum observed error is 2.58 ULP:
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_ZGVnN2v_log2(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
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want 0x1.fffb34198d9ddp-5. */
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float64x2_t VPCS_ATTR V_NAME_D1 (log2) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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/* To avoid having to mov x out of the way, keep u after offset has been
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applied, and recover x by adding the offset back in the special-case
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handler. */
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uint64x2_t u = vreinterpretq_u64_f64 (x);
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uint64x2_t u_off = vsubq_u64 (u, d->off);
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/* x = 2^k z; where z is in range [Off,2*Off) and exact.
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The range is split into N subintervals.
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The ith subinterval contains z and c is near its center. */
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int64x2_t k = vshrq_n_s64 (vreinterpretq_s64_u64 (u_off), 52);
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uint64x2_t iz = vsubq_u64 (u, vandq_u64 (u_off, d->sign_exp_mask));
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float64x2_t z = vreinterpretq_f64_u64 (iz);
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struct entry e = lookup (u_off);
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uint32x2_t special = vcge_u32 (vsubhn_u64 (u_off, d->offset_lower_bound),
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vget_low_u32 (d->special_bound));
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/* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */
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float64x2_t r = vfmaq_f64 (v_f64 (-1.0), z, e.invc);
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float64x2_t kd = vcvtq_f64_s64 (k);
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float64x2_t invln2_and_c4 = vld1q_f64 (&d->invln2);
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float64x2_t hi
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= vfmaq_laneq_f64 (vaddq_f64 (e.log2c, kd), r, invln2_and_c4, 0);
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float64x2_t r2 = vmulq_f64 (r, r);
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float64x2_t odd_coeffs = vld1q_f64 (&d->c1);
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float64x2_t y = vfmaq_laneq_f64 (d->c2, r, odd_coeffs, 1);
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float64x2_t p = vfmaq_laneq_f64 (d->c0, r, odd_coeffs, 0);
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y = vfmaq_laneq_f64 (y, r2, invln2_and_c4, 1);
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y = vfmaq_f64 (p, r2, y);
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if (__glibc_unlikely (v_any_u32h (special)))
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return special_case (hi, u_off, y, r2, special, d);
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return vfmaq_f64 (hi, y, r2);
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}
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