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 "estrin.h" 9 #include "mathlib.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 #if V_SUPPORTED 14 15 #define AbsMask v_u64 (0x7fffffffffffffff) 16 #define InvLn2 v_f64 (0x1.71547652b82fep0) 17 #define MLn2hi v_f64 (-0x1.62e42fefa39efp-1) 18 #define MLn2lo v_f64 (-0x1.abc9e3b39803fp-56) 19 #define Shift v_f64 (0x1.8p52) 20 #define C(i) v_f64 (__expm1_poly[i]) 21 22 #define BoringBound 0x403241bf835f9d5f /* asuint64 (0x1.241bf835f9d5fp+4). */ 23 #define TinyBound 0x3e40000000000000 /* asuint64 (0x1p-27). */ 24 #define One v_u64 (0x3ff0000000000000) 25 26 static inline v_f64_t 27 expm1_inline (v_f64_t x) 28 { 29 /* Helper routine for calculating exp(x) - 1. Vector port of the helper from 30 the scalar variant of tanh. */ 31 32 /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ 33 v_f64_t j = v_fma_f64 (InvLn2, x, Shift) - Shift; 34 v_s64_t i = v_to_s64_f64 (j); 35 v_f64_t f = v_fma_f64 (j, MLn2hi, x); 36 f = v_fma_f64 (j, MLn2lo, f); 37 38 /* Approximate expm1(f) using polynomial. */ 39 v_f64_t f2 = f * f; 40 v_f64_t f4 = f2 * f2; 41 v_f64_t p = v_fma_f64 (f2, ESTRIN_10 (f, f2, f4, f4 * f4, C), f); 42 43 /* t = 2 ^ i. */ 44 v_f64_t t = v_as_f64_u64 (v_as_u64_s64 (i << 52) + One); 45 /* expm1(x) = p * t + (t - 1). */ 46 return v_fma_f64 (p, t, t - 1); 47 } 48 49 static NOINLINE v_f64_t 50 special_case (v_f64_t x, v_f64_t y, v_u64_t special) 51 { 52 return v_call_f64 (tanh, x, y, special); 53 } 54 55 /* Vector approximation for double-precision tanh(x), using a simplified 56 version of expm1. The greatest observed error is 2.75 ULP: 57 __v_tanh(-0x1.c143c3a44e087p-3) got -0x1.ba31ba4691ab7p-3 58 want -0x1.ba31ba4691ab4p-3. */ 59 VPCS_ATTR v_f64_t V_NAME (tanh) (v_f64_t x) 60 { 61 v_u64_t ix = v_as_u64_f64 (x); 62 v_u64_t ia = ix & AbsMask; 63 64 /* Trigger special-cases for tiny, boring and infinity/NaN. */ 65 v_u64_t special = v_cond_u64 ((ia - TinyBound) > (BoringBound - TinyBound)); 66 v_f64_t u; 67 68 /* To trigger fp exceptions correctly, set special lanes to a neutral value. 69 They will be fixed up later by the special-case handler. */ 70 if (unlikely (v_any_u64 (special))) 71 u = v_sel_f64 (special, v_f64 (1), x) * 2; 72 else 73 u = x * 2; 74 75 /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ 76 v_f64_t q = expm1_inline (u); 77 v_f64_t y = q / (q + 2); 78 79 if (unlikely (v_any_u64 (special))) 80 return special_case (x, y, special); 81 return y; 82 } 83 VPCS_ALIAS 84 85 PL_SIG (V, D, 1, tanh, -10.0, 10.0) 86 PL_TEST_ULP (V_NAME (tanh), 2.26) 87 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (tanh)) 88 PL_TEST_INTERVAL (V_NAME (tanh), 0, TinyBound, 1000) 89 PL_TEST_INTERVAL (V_NAME (tanh), -0, -TinyBound, 1000) 90 PL_TEST_INTERVAL (V_NAME (tanh), TinyBound, BoringBound, 100000) 91 PL_TEST_INTERVAL (V_NAME (tanh), -TinyBound, -BoringBound, 100000) 92 PL_TEST_INTERVAL (V_NAME (tanh), BoringBound, inf, 1000) 93 PL_TEST_INTERVAL (V_NAME (tanh), -BoringBound, -inf, 1000) 94 #endif 95