mirror of https://gitee.com/Nocallback/glibc.git
Joe Ramsay
2 years ago
committed by
Szabolcs Nagy
Szabolcs Nagy
16 changed files with 572 additions and 0 deletions
@ -0,0 +1,121 @@ |
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/* Double-precision vector (Advanced SIMD) sinh function
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Copyright (C) 2024 Free Software Foundation, Inc. |
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This file is part of the GNU C Library. |
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|
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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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|
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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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|
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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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|
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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[11]; |
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float64x2_t inv_ln2, m_ln2, shift; |
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uint64x2_t halff; |
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int64x2_t onef; |
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#if WANT_SIMD_EXCEPT |
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uint64x2_t tiny_bound, thresh; |
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#else |
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uint64x2_t large_bound; |
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#endif |
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} data = { |
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/* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */ |
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.poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5), |
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V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10), |
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V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16), |
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V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22), |
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V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29), }, |
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.inv_ln2 = V2 (0x1.71547652b82fep0), |
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.m_ln2 = (float64x2_t) {-0x1.62e42fefa39efp-1, -0x1.abc9e3b39803fp-56}, |
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.shift = V2 (0x1.8p52), |
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.halff = V2 (0x3fe0000000000000), |
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.onef = V2 (0x3ff0000000000000), |
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#if WANT_SIMD_EXCEPT |
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/* 2^-26, below which sinh(x) rounds to x. */ |
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.tiny_bound = V2 (0x3e50000000000000), |
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/* asuint(large_bound) - asuint(tiny_bound). */ |
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.thresh = V2 (0x0230000000000000), |
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#else |
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/* 2^9. expm1 helper overflows for large input. */ |
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.large_bound = V2 (0x4080000000000000), |
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#endif |
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}; |
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static inline float64x2_t |
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expm1_inline (float64x2_t x) |
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{ |
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const struct data *d = ptr_barrier (&data); |
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/* Reduce argument:
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exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 |
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where i = round(x / ln2) |
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and f = x - i * ln2 (f in [-ln2/2, ln2/2]). */ |
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float64x2_t j = vsubq_f64 (vfmaq_f64 (d->shift, d->inv_ln2, x), d->shift); |
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int64x2_t i = vcvtq_s64_f64 (j); |
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float64x2_t f = vfmaq_laneq_f64 (x, j, d->m_ln2, 0); |
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f = vfmaq_laneq_f64 (f, j, d->m_ln2, 1); |
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/* Approximate expm1(f) using polynomial. */ |
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float64x2_t f2 = vmulq_f64 (f, f); |
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float64x2_t f4 = vmulq_f64 (f2, f2); |
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float64x2_t f8 = vmulq_f64 (f4, f4); |
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float64x2_t p = vfmaq_f64 (f, f2, v_estrin_10_f64 (f, f2, f4, f8, d->poly)); |
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/* t = 2^i. */ |
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float64x2_t t = vreinterpretq_f64_u64 ( |
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vreinterpretq_u64_s64 (vaddq_s64 (vshlq_n_s64 (i, 52), d->onef))); |
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/* expm1(x) ~= p * t + (t - 1). */ |
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return vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t); |
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} |
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static float64x2_t NOINLINE VPCS_ATTR |
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special_case (float64x2_t x) |
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{ |
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return v_call_f64 (sinh, x, x, v_u64 (-1)); |
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} |
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/* Approximation for vector double-precision sinh(x) using expm1.
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sinh(x) = (exp(x) - exp(-x)) / 2. |
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The greatest observed error is 2.57 ULP: |
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_ZGVnN2v_sinh (0x1.9fb1d49d1d58bp-2) got 0x1.ab34e59d678dcp-2 |
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want 0x1.ab34e59d678d9p-2. */ |
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float64x2_t VPCS_ATTR V_NAME_D1 (sinh) (float64x2_t x) |
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{ |
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const struct data *d = ptr_barrier (&data); |
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float64x2_t ax = vabsq_f64 (x); |
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uint64x2_t sign |
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= veorq_u64 (vreinterpretq_u64_f64 (x), vreinterpretq_u64_f64 (ax)); |
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float64x2_t halfsign = vreinterpretq_f64_u64 (vorrq_u64 (sign, d->halff)); |
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#if WANT_SIMD_EXCEPT |
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uint64x2_t special = vcgeq_u64 ( |
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vsubq_u64 (vreinterpretq_u64_f64 (ax), d->tiny_bound), d->thresh); |
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#else |
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uint64x2_t special = vcgeq_u64 (vreinterpretq_u64_f64 (ax), d->large_bound); |
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#endif |
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/* Fall back to scalar variant for all lanes if any of them are special. */ |
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if (__glibc_unlikely (v_any_u64 (special))) |
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return special_case (x); |
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/* Up to the point that expm1 overflows, we can use it to calculate sinh
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using a slight rearrangement of the definition of sinh. This allows us to |
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retain acceptable accuracy for very small inputs. */ |
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float64x2_t t = expm1_inline (ax); |
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t = vaddq_f64 (t, vdivq_f64 (t, vaddq_f64 (t, v_f64 (1.0)))); |
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return vmulq_f64 (t, halfsign); |
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} |
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@ -0,0 +1,107 @@ |
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/* Double-precision vector (SVE) atanh function
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Copyright (C) 2024 Free Software Foundation, Inc. |
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This file is part of the GNU C Library. |
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|
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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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|
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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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|
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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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#include "poly_sve_f64.h" |
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static const struct data |
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{ |
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float64_t poly[11]; |
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float64_t inv_ln2, m_ln2_hi, m_ln2_lo, shift; |
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uint64_t halff; |
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int64_t onef; |
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uint64_t large_bound; |
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} data = { |
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/* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */ |
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.poly = { 0x1p-1, 0x1.5555555555559p-3, 0x1.555555555554bp-5, |
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0x1.111111110f663p-7, 0x1.6c16c16c1b5f3p-10, |
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0x1.a01a01affa35dp-13, 0x1.a01a018b4ecbbp-16, |
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0x1.71ddf82db5bb4p-19, 0x1.27e517fc0d54bp-22, |
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0x1.af5eedae67435p-26, 0x1.1f143d060a28ap-29, }, |
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.inv_ln2 = 0x1.71547652b82fep0, |
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.m_ln2_hi = -0x1.62e42fefa39efp-1, |
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.m_ln2_lo = -0x1.abc9e3b39803fp-56, |
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.shift = 0x1.8p52, |
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.halff = 0x3fe0000000000000, |
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.onef = 0x3ff0000000000000, |
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/* 2^9. expm1 helper overflows for large input. */ |
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.large_bound = 0x4080000000000000, |
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}; |
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static inline svfloat64_t |
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expm1_inline (svfloat64_t x, svbool_t pg) |
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{ |
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const struct data *d = ptr_barrier (&data); |
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|
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/* Reduce argument:
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exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 |
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where i = round(x / ln2) |
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and f = x - i * ln2 (f in [-ln2/2, ln2/2]). */ |
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svfloat64_t j |
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= svsub_x (pg, svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2), d->shift); |
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svint64_t i = svcvt_s64_x (pg, j); |
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svfloat64_t f = svmla_x (pg, x, j, d->m_ln2_hi); |
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f = svmla_x (pg, f, j, d->m_ln2_lo); |
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/* Approximate expm1(f) using polynomial. */ |
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svfloat64_t f2 = svmul_x (pg, f, f); |
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svfloat64_t f4 = svmul_x (pg, f2, f2); |
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svfloat64_t f8 = svmul_x (pg, f4, f4); |
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svfloat64_t p |
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= svmla_x (pg, f, f2, sv_estrin_10_f64_x (pg, f, f2, f4, f8, d->poly)); |
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/* t = 2^i. */ |
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svfloat64_t t = svscale_x (pg, sv_f64 (1), i); |
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/* expm1(x) ~= p * t + (t - 1). */ |
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return svmla_x (pg, svsub_x (pg, t, 1.0), p, t); |
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} |
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static svfloat64_t NOINLINE |
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special_case (svfloat64_t x, svbool_t pg) |
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{ |
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return sv_call_f64 (sinh, x, x, pg); |
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} |
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/* Approximation for SVE double-precision sinh(x) using expm1.
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sinh(x) = (exp(x) - exp(-x)) / 2. |
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The greatest observed error is 2.57 ULP: |
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_ZGVsMxv_sinh (0x1.a008538399931p-2) got 0x1.ab929fc64bd66p-2 |
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want 0x1.ab929fc64bd63p-2. */ |
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svfloat64_t SV_NAME_D1 (sinh) (svfloat64_t x, svbool_t pg) |
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{ |
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const struct data *d = ptr_barrier (&data); |
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svfloat64_t ax = svabs_x (pg, x); |
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svuint64_t sign |
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= sveor_x (pg, svreinterpret_u64 (x), svreinterpret_u64 (ax)); |
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svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, d->halff)); |
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svbool_t special = svcmpge (pg, svreinterpret_u64 (ax), d->large_bound); |
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/* Fall back to scalar variant for all lanes if any are special. */ |
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if (__glibc_unlikely (svptest_any (pg, special))) |
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return special_case (x, pg); |
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/* Up to the point that expm1 overflows, we can use it to calculate sinh
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using a slight rearrangement of the definition of sinh. This allows us to |
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retain acceptable accuracy for very small inputs. */ |
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svfloat64_t t = expm1_inline (ax, pg); |
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t = svadd_x (pg, t, svdiv_x (pg, t, svadd_x (pg, t, 1.0))); |
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return svmul_x (pg, t, halfsign); |
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} |
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@ -0,0 +1,88 @@ |
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/* Single-precision vector (Advanced SIMD) sinh function
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Copyright (C) 2024 Free Software Foundation, Inc. |
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This file is part of the GNU C Library. |
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|
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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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|
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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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|
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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 "v_expm1f_inline.h" |
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static const struct data |
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{ |
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struct v_expm1f_data expm1f_consts; |
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uint32x4_t halff; |
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#if WANT_SIMD_EXCEPT |
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uint32x4_t tiny_bound, thresh; |
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#else |
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uint32x4_t oflow_bound; |
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#endif |
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} data = { |
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.expm1f_consts = V_EXPM1F_DATA, |
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.halff = V4 (0x3f000000), |
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#if WANT_SIMD_EXCEPT |
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/* 0x1.6a09e8p-32, below which expm1f underflows. */ |
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.tiny_bound = V4 (0x2fb504f4), |
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/* asuint(oflow_bound) - asuint(tiny_bound). */ |
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.thresh = V4 (0x12fbbbb3), |
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#else |
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/* 0x1.61814ep+6, above which expm1f helper overflows. */ |
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.oflow_bound = V4 (0x42b0c0a7), |
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#endif |
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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 (sinhf, x, y, special); |
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} |
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|
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/* Approximation for vector single-precision sinh(x) using expm1.
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sinh(x) = (exp(x) - exp(-x)) / 2. |
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The maximum error is 2.26 ULP: |
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_ZGVnN4v_sinhf (0x1.e34a9ep-4) got 0x1.e469ep-4 |
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want 0x1.e469e4p-4. */ |
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float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (sinh) (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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float32x4_t ax = vabsq_f32 (x); |
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uint32x4_t iax = vreinterpretq_u32_f32 (ax); |
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uint32x4_t sign = veorq_u32 (ix, iax); |
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float32x4_t halfsign = vreinterpretq_f32_u32 (vorrq_u32 (sign, d->halff)); |
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#if WANT_SIMD_EXCEPT |
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uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, d->tiny_bound), d->thresh); |
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ax = v_zerofy_f32 (ax, special); |
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#else |
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uint32x4_t special = vcgeq_u32 (iax, d->oflow_bound); |
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#endif |
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/* Up to the point that expm1f overflows, we can use it to calculate sinhf
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using a slight rearrangement of the definition of asinh. This allows us |
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to retain acceptable accuracy for very small inputs. */ |
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float32x4_t t = expm1f_inline (ax, &d->expm1f_consts); |
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t = vaddq_f32 (t, vdivq_f32 (t, vaddq_f32 (t, v_f32 (1.0)))); |
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/* Fall back to the scalar variant for any lanes that should trigger an
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exception. */ |
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if (__glibc_unlikely (v_any_u32 (special))) |
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return special_case (x, vmulq_f32 (t, halfsign), special); |
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return vmulq_f32 (t, halfsign); |
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} |
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libmvec_hidden_def (V_NAME_F1 (sinh)) |
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HALF_WIDTH_ALIAS_F1 (sinh) |
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@ -0,0 +1,67 @@ |
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/* Single-precision vector (SVE) sinh function
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|
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Copyright (C) 2024 Free Software Foundation, Inc. |
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This file is part of the GNU C Library. |
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|
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The GNU C Library is free software; you can redistribute it and/or |
|||
modify it under the terms of the GNU Lesser General Public |
|||
License as published by the Free Software Foundation; either |
|||
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, |
|||
but WITHOUT ANY WARRANTY; without even the implied warranty of |
|||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
|||
Lesser General Public License for more details. |
|||
|
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You should have received a copy of the GNU Lesser General Public |
|||
License along with the GNU C Library; if not, see |
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<https://www.gnu.org/licenses/>. */
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|
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#include "sv_expm1f_inline.h" |
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#include "sv_math.h" |
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static const struct data |
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{ |
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struct sv_expm1f_data expm1f_consts; |
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uint32_t halff, large_bound; |
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} data = { |
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.expm1f_consts = SV_EXPM1F_DATA, |
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.halff = 0x3f000000, |
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/* 0x1.61814ep+6, above which expm1f helper overflows. */ |
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.large_bound = 0x42b0c0a7, |
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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 pg) |
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{ |
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return sv_call_f32 (sinhf, x, y, pg); |
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} |
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|
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/* Approximation for SVE single-precision sinh(x) using expm1.
|
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sinh(x) = (exp(x) - exp(-x)) / 2. |
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The maximum error is 2.26 ULP: |
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_ZGVsMxv_sinhf (0x1.e34a9ep-4) got 0x1.e469ep-4 |
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want 0x1.e469e4p-4. */ |
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svfloat32_t SV_NAME_F1 (sinh) (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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svfloat32_t ax = svabs_x (pg, x); |
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svuint32_t sign |
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= sveor_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (ax)); |
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svfloat32_t halfsign = svreinterpret_f32 (svorr_x (pg, sign, d->halff)); |
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svbool_t special = svcmpge (pg, svreinterpret_u32 (ax), d->large_bound); |
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|
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/* Up to the point that expm1f overflows, we can use it to calculate sinhf
|
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using a slight rearrangement of the definition of asinh. This allows us to |
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retain acceptable accuracy for very small inputs. */ |
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svfloat32_t t = expm1f_inline (ax, pg, &d->expm1f_consts); |
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t = svadd_x (pg, t, svdiv_x (pg, t, svadd_x (pg, t, 1.0))); |
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|
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/* Fall back to the scalar variant for any lanes which would cause
|
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expm1f to overflow. */ |
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if (__glibc_unlikely (svptest_any (pg, special))) |
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return special_case (x, svmul_x (pg, t, halfsign), special); |
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|
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return svmul_x (pg, t, halfsign); |
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} |
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@ -0,0 +1,84 @@ |
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/* Single-precision inline helper for vector (SVE) expm1 function
|
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|
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Copyright (C) 2024 Free Software Foundation, Inc. |
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This file is part of the GNU C Library. |
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|
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The GNU C Library is free software; you can redistribute it and/or |
|||
modify it under the terms of the GNU Lesser General Public |
|||
License as published by the Free Software Foundation; either |
|||
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, |
|||
but WITHOUT ANY WARRANTY; without even the implied warranty of |
|||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
|||
Lesser General Public License for more details. |
|||
|
|||
You should have received a copy of the GNU Lesser General Public |
|||
License along with the GNU C Library; if not, see |
|||
<https://www.gnu.org/licenses/>. */
|
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|
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#ifndef AARCH64_FPU_SV_EXPM1F_INLINE_H |
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#define AARCH64_FPU_SV_EXPM1F_INLINE_H |
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|
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#include "sv_math.h" |
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|
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struct sv_expm1f_data |
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{ |
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/* These 4 are grouped together so they can be loaded as one quadword, then
|
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used with _lane forms of svmla/svmls. */ |
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float32_t c2, c4, ln2_hi, ln2_lo; |
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float32_t c0, c1, c3, inv_ln2, shift; |
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}; |
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|
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/* Coefficients generated using fpminimax. */ |
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#define SV_EXPM1F_DATA \ |
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{ \ |
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.c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .c2 = 0x1.555736p-5, \ |
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.c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \ |
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\ |
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.shift = 0x1.8p23f, .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \ |
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.ln2_lo = 0x1.7f7d1cp-20f, \ |
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} |
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|
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#define C(i) sv_f32 (d->c##i) |
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|
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static inline svfloat32_t |
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expm1f_inline (svfloat32_t x, svbool_t pg, const struct sv_expm1f_data *d) |
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{ |
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/* This vector is reliant on layout of data - it contains constants
|
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that can be used with _lane forms of svmla/svmls. Values are: |
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[ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */ |
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svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2); |
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|
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/* Reduce argument to smaller range:
|
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Let i = round(x / ln2) |
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and f = x - i * ln2, then f is in [-ln2/2, ln2/2]. |
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exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 |
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where 2^i is exact because i is an integer. */ |
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svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2); |
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j = svsub_x (pg, j, d->shift); |
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svint32_t i = svcvt_s32_x (pg, j); |
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|
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svfloat32_t f = svmls_lane (x, j, lane_constants, 2); |
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f = svmls_lane (f, j, lane_constants, 3); |
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|
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/* Approximate expm1(f) using polynomial.
|
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Taylor expansion for expm1(x) has the form: |
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x + ax^2 + bx^3 + cx^4 .... |
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So we calculate the polynomial P(f) = a + bf + cf^2 + ... |
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and assemble the approximation expm1(f) ~= f + f^2 * P(f). */ |
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svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0); |
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svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1); |
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svfloat32_t f2 = svmul_x (pg, f, f); |
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svfloat32_t p = svmla_x (pg, p12, f2, p34); |
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p = svmla_x (pg, C (0), f, p); |
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p = svmla_x (pg, f, f2, p); |
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|
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/* Assemble the result.
|
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expm1(x) ~= 2^i * (p + 1) - 1 |
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Let t = 2^i. */ |
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svfloat32_t t = svscale_x (pg, sv_f32 (1), i); |
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return svmla_x (pg, svsub_x (pg, t, 1), p, t); |
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} |
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|
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#endif |
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@ -0,0 +1,73 @@ |
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/* Single-precision inline helper for vector (Advanced SIMD) expm1 function
|
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|
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Copyright (C) 2024 Free Software Foundation, Inc. |
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This file is part of the GNU C Library. |
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|
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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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|
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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 |
|||
Lesser General Public License for more details. |
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|
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You should have received a copy of the GNU Lesser General Public |
|||
License along with the GNU C Library; if not, see |
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<https://www.gnu.org/licenses/>. */
|
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|
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#ifndef AARCH64_FPU_V_EXPM1F_INLINE_H |
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#define AARCH64_FPU_V_EXPM1F_INLINE_H |
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|
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#include "v_math.h" |
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#include "poly_advsimd_f32.h" |
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|
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struct v_expm1f_data |
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{ |
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float32x4_t poly[5]; |
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float32x4_t invln2_and_ln2, shift; |
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int32x4_t exponent_bias; |
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}; |
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|
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/* Coefficients generated using fpminimax with degree=5 in [-log(2)/2,
|
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log(2)/2]. Exponent bias is asuint(1.0f). |
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invln2_and_ln2 Stores constants: invln2, ln2_lo, ln2_hi, 0. */ |
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#define V_EXPM1F_DATA \ |
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{ \ |
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.poly = { V4 (0x1.fffffep-2), V4 (0x1.5554aep-3), V4 (0x1.555736p-5), \ |
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V4 (0x1.12287cp-7), V4 (0x1.6b55a2p-10) }, \ |
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.shift = V4 (0x1.8p23f), .exponent_bias = V4 (0x3f800000), \ |
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.invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 }, \ |
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} |
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|
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static inline float32x4_t |
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expm1f_inline (float32x4_t x, const struct v_expm1f_data *d) |
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{ |
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/* Helper routine for calculating exp(x) - 1.
|
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Copied from v_expm1f_1u6.c, with all special-case handling removed - the |
|||
calling routine should handle special values if required. */ |
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|
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/* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ |
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float32x4_t j = vsubq_f32 ( |
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vfmaq_laneq_f32 (d->shift, x, d->invln2_and_ln2, 0), d->shift); |
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int32x4_t i = vcvtq_s32_f32 (j); |
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float32x4_t f = vfmsq_laneq_f32 (x, j, d->invln2_and_ln2, 1); |
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f = vfmsq_laneq_f32 (f, j, d->invln2_and_ln2, 2); |
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|
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/* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f).
|
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Uses Estrin scheme, where the main _ZGVnN4v_expm1f routine uses |
|||
Horner. */ |
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float32x4_t f2 = vmulq_f32 (f, f); |
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float32x4_t f4 = vmulq_f32 (f2, f2); |
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float32x4_t p = v_estrin_4_f32 (f, f2, f4, d->poly); |
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p = vfmaq_f32 (f, f2, p); |
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|
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/* t = 2^i. */ |
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int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias); |
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float32x4_t t = vreinterpretq_f32_s32 (u); |
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/* expm1(x) ~= p * t + (t - 1). */ |
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return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t); |
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} |
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|
|||
#endif |
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