1 /* 2 * Double-precision SVE tanh(x) function. 3 * Copyright (c) 2023, Arm Limited. 4 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5 */ 6 7 #include "sv_math.h" 8 #include "poly_sve_f64.h" 9 #include "mathlib.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 static const struct data 14 { 15 float64_t poly[11]; 16 float64_t inv_ln2, ln2_hi, ln2_lo, shift; 17 uint64_t thresh, tiny_bound; 18 } data = { 19 /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */ 20 .poly = { 0x1p-1, 0x1.5555555555559p-3, 0x1.555555555554bp-5, 21 0x1.111111110f663p-7, 0x1.6c16c16c1b5f3p-10, 22 0x1.a01a01affa35dp-13, 0x1.a01a018b4ecbbp-16, 23 0x1.71ddf82db5bb4p-19, 0x1.27e517fc0d54bp-22, 24 0x1.af5eedae67435p-26, 0x1.1f143d060a28ap-29, }, 25 26 .inv_ln2 = 0x1.71547652b82fep0, 27 .ln2_hi = -0x1.62e42fefa39efp-1, 28 .ln2_lo = -0x1.abc9e3b39803fp-56, 29 .shift = 0x1.8p52, 30 31 .tiny_bound = 0x3e40000000000000, /* asuint64 (0x1p-27). */ 32 /* asuint64(0x1.241bf835f9d5fp+4) - asuint64(tiny_bound). */ 33 .thresh = 0x01f241bf835f9d5f, 34 }; 35 36 static inline svfloat64_t 37 expm1_inline (svfloat64_t x, const svbool_t pg, const struct data *d) 38 { 39 /* Helper routine for calculating exp(x) - 1. Vector port of the helper from 40 the scalar variant of tanh. */ 41 42 /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ 43 svfloat64_t j 44 = svsub_x (pg, svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2), d->shift); 45 svint64_t i = svcvt_s64_x (pg, j); 46 svfloat64_t f = svmla_x (pg, x, j, d->ln2_hi); 47 f = svmla_x (pg, f, j, d->ln2_lo); 48 49 /* Approximate expm1(f) using polynomial. */ 50 svfloat64_t f2 = svmul_x (pg, f, f); 51 svfloat64_t f4 = svmul_x (pg, f2, f2); 52 svfloat64_t p = svmla_x ( 53 pg, f, f2, 54 sv_estrin_10_f64_x (pg, f, f2, f4, svmul_x (pg, f4, f4), d->poly)); 55 56 /* t = 2 ^ i. */ 57 svfloat64_t t = svscale_x (pg, sv_f64 (1), i); 58 /* expm1(x) = p * t + (t - 1). */ 59 return svmla_x (pg, svsub_x (pg, t, 1), p, t); 60 } 61 62 static svfloat64_t NOINLINE 63 special_case (svfloat64_t x, svfloat64_t y, svbool_t special) 64 { 65 return sv_call_f64 (tanh, x, y, special); 66 } 67 68 /* SVE approximation for double-precision tanh(x), using a simplified 69 version of expm1. The greatest observed error is 2.77 ULP: 70 _ZGVsMxv_tanh(-0x1.c4a4ca0f9f3b7p-3) got -0x1.bd6a21a163627p-3 71 want -0x1.bd6a21a163624p-3. */ 72 svfloat64_t SV_NAME_D1 (tanh) (svfloat64_t x, svbool_t pg) 73 { 74 const struct data *d = ptr_barrier (&data); 75 76 svuint64_t ia = svreinterpret_u64 (svabs_x (pg, x)); 77 78 /* Trigger special-cases for tiny, boring and infinity/NaN. */ 79 svbool_t special = svcmpgt (pg, svsub_x (pg, ia, d->tiny_bound), d->thresh); 80 81 svfloat64_t u = svadd_x (pg, x, x); 82 83 /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ 84 svfloat64_t q = expm1_inline (u, pg, d); 85 svfloat64_t qp2 = svadd_x (pg, q, 2); 86 87 if (unlikely (svptest_any (pg, special))) 88 return special_case (x, svdiv_x (pg, q, qp2), special); 89 return svdiv_x (pg, q, qp2); 90 } 91 92 PL_SIG (SV, D, 1, tanh, -10.0, 10.0) 93 PL_TEST_ULP (SV_NAME_D1 (tanh), 2.27) 94 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (tanh), 0, 0x1p-27, 5000) 95 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (tanh), 0x1p-27, 0x1.241bf835f9d5fp+4, 50000) 96 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (tanh), 0x1.241bf835f9d5fp+4, inf, 1000) 97