1 /* 2 * Double-precision vector 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 "v_math.h" 8 #include "poly_advsimd_f64.h" 9 #include "mathlib.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 static const struct data 14 { 15 float64x2_t poly[11]; 16 float64x2_t inv_ln2, ln2_hi, ln2_lo, shift; 17 uint64x2_t onef; 18 uint64x2_t thresh, tiny_bound; 19 } data = { 20 /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */ 21 .poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5), 22 V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10), 23 V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16), 24 V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22), 25 V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29), }, 26 27 .inv_ln2 = V2 (0x1.71547652b82fep0), 28 .ln2_hi = V2 (-0x1.62e42fefa39efp-1), 29 .ln2_lo = V2 (-0x1.abc9e3b39803fp-56), 30 .shift = V2 (0x1.8p52), 31 32 .onef = V2 (0x3ff0000000000000), 33 .tiny_bound = V2 (0x3e40000000000000), /* asuint64 (0x1p-27). */ 34 /* asuint64(0x1.241bf835f9d5fp+4) - asuint64(tiny_bound). */ 35 .thresh = V2 (0x01f241bf835f9d5f), 36 }; 37 38 static inline float64x2_t 39 expm1_inline (float64x2_t x, const struct data *d) 40 { 41 /* Helper routine for calculating exp(x) - 1. Vector port of the helper from 42 the scalar variant of tanh. */ 43 44 /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ 45 float64x2_t j = vsubq_f64 (vfmaq_f64 (d->shift, d->inv_ln2, x), d->shift); 46 int64x2_t i = vcvtq_s64_f64 (j); 47 float64x2_t f = vfmaq_f64 (x, j, d->ln2_hi); 48 f = vfmaq_f64 (f, j, d->ln2_lo); 49 50 /* Approximate expm1(f) using polynomial. */ 51 float64x2_t f2 = vmulq_f64 (f, f); 52 float64x2_t f4 = vmulq_f64 (f2, f2); 53 float64x2_t p = vfmaq_f64 ( 54 f, f2, v_estrin_10_f64 (f, f2, f4, vmulq_f64 (f4, f4), d->poly)); 55 56 /* t = 2 ^ i. */ 57 float64x2_t t = vreinterpretq_f64_u64 ( 58 vaddq_u64 (vreinterpretq_u64_s64 (i << 52), d->onef)); 59 /* expm1(x) = p * t + (t - 1). */ 60 return vfmaq_f64 (vsubq_f64 (t, v_f64 (1)), p, t); 61 } 62 63 static float64x2_t NOINLINE VPCS_ATTR 64 special_case (float64x2_t x, float64x2_t y, uint64x2_t special) 65 { 66 return v_call_f64 (tanh, x, y, special); 67 } 68 69 /* Vector approximation for double-precision tanh(x), using a simplified 70 version of expm1. The greatest observed error is 2.77 ULP: 71 _ZGVnN2v_tanh(-0x1.c4a4ca0f9f3b7p-3) got -0x1.bd6a21a163627p-3 72 want -0x1.bd6a21a163624p-3. */ 73 float64x2_t VPCS_ATTR V_NAME_D1 (tanh) (float64x2_t x) 74 { 75 const struct data *d = ptr_barrier (&data); 76 77 uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x)); 78 79 float64x2_t u = x; 80 81 /* Trigger special-cases for tiny, boring and infinity/NaN. */ 82 uint64x2_t special = vcgtq_u64 (vsubq_u64 (ia, d->tiny_bound), d->thresh); 83 #if WANT_SIMD_EXCEPT 84 /* To trigger fp exceptions correctly, set special lanes to a neutral value. 85 They will be fixed up later by the special-case handler. */ 86 if (unlikely (v_any_u64 (special))) 87 u = v_zerofy_f64 (u, special); 88 #endif 89 90 u = vaddq_f64 (u, u); 91 92 /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ 93 float64x2_t q = expm1_inline (u, d); 94 float64x2_t qp2 = vaddq_f64 (q, v_f64 (2)); 95 96 if (unlikely (v_any_u64 (special))) 97 return special_case (x, vdivq_f64 (q, qp2), special); 98 return vdivq_f64 (q, qp2); 99 } 100 101 PL_SIG (V, D, 1, tanh, -10.0, 10.0) 102 PL_TEST_ULP (V_NAME_D1 (tanh), 2.27) 103 PL_TEST_EXPECT_FENV (V_NAME_D1 (tanh), WANT_SIMD_EXCEPT) 104 PL_TEST_SYM_INTERVAL (V_NAME_D1 (tanh), 0, 0x1p-27, 5000) 105 PL_TEST_SYM_INTERVAL (V_NAME_D1 (tanh), 0x1p-27, 0x1.241bf835f9d5fp+4, 50000) 106 PL_TEST_SYM_INTERVAL (V_NAME_D1 (tanh), 0x1.241bf835f9d5fp+4, inf, 1000) 107