1*072a4ba8SAndrew Turner /* 2*072a4ba8SAndrew Turner * Double-precision vector tanh(x) function. 3*072a4ba8SAndrew Turner * Copyright (c) 2023, Arm Limited. 4*072a4ba8SAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*072a4ba8SAndrew Turner */ 6*072a4ba8SAndrew Turner 7*072a4ba8SAndrew Turner #include "v_math.h" 8*072a4ba8SAndrew Turner #include "estrin.h" 9*072a4ba8SAndrew Turner #include "mathlib.h" 10*072a4ba8SAndrew Turner #include "pl_sig.h" 11*072a4ba8SAndrew Turner #include "pl_test.h" 12*072a4ba8SAndrew Turner 13*072a4ba8SAndrew Turner #if V_SUPPORTED 14*072a4ba8SAndrew Turner 15*072a4ba8SAndrew Turner #define AbsMask v_u64 (0x7fffffffffffffff) 16*072a4ba8SAndrew Turner #define InvLn2 v_f64 (0x1.71547652b82fep0) 17*072a4ba8SAndrew Turner #define MLn2hi v_f64 (-0x1.62e42fefa39efp-1) 18*072a4ba8SAndrew Turner #define MLn2lo v_f64 (-0x1.abc9e3b39803fp-56) 19*072a4ba8SAndrew Turner #define Shift v_f64 (0x1.8p52) 20*072a4ba8SAndrew Turner #define C(i) v_f64 (__expm1_poly[i]) 21*072a4ba8SAndrew Turner 22*072a4ba8SAndrew Turner #define BoringBound 0x403241bf835f9d5f /* asuint64 (0x1.241bf835f9d5fp+4). */ 23*072a4ba8SAndrew Turner #define TinyBound 0x3e40000000000000 /* asuint64 (0x1p-27). */ 24*072a4ba8SAndrew Turner #define One v_u64 (0x3ff0000000000000) 25*072a4ba8SAndrew Turner 26*072a4ba8SAndrew Turner static inline v_f64_t 27*072a4ba8SAndrew Turner expm1_inline (v_f64_t x) 28*072a4ba8SAndrew Turner { 29*072a4ba8SAndrew Turner /* Helper routine for calculating exp(x) - 1. Vector port of the helper from 30*072a4ba8SAndrew Turner the scalar variant of tanh. */ 31*072a4ba8SAndrew Turner 32*072a4ba8SAndrew Turner /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ 33*072a4ba8SAndrew Turner v_f64_t j = v_fma_f64 (InvLn2, x, Shift) - Shift; 34*072a4ba8SAndrew Turner v_s64_t i = v_to_s64_f64 (j); 35*072a4ba8SAndrew Turner v_f64_t f = v_fma_f64 (j, MLn2hi, x); 36*072a4ba8SAndrew Turner f = v_fma_f64 (j, MLn2lo, f); 37*072a4ba8SAndrew Turner 38*072a4ba8SAndrew Turner /* Approximate expm1(f) using polynomial. */ 39*072a4ba8SAndrew Turner v_f64_t f2 = f * f; 40*072a4ba8SAndrew Turner v_f64_t f4 = f2 * f2; 41*072a4ba8SAndrew Turner v_f64_t p = v_fma_f64 (f2, ESTRIN_10 (f, f2, f4, f4 * f4, C), f); 42*072a4ba8SAndrew Turner 43*072a4ba8SAndrew Turner /* t = 2 ^ i. */ 44*072a4ba8SAndrew Turner v_f64_t t = v_as_f64_u64 (v_as_u64_s64 (i << 52) + One); 45*072a4ba8SAndrew Turner /* expm1(x) = p * t + (t - 1). */ 46*072a4ba8SAndrew Turner return v_fma_f64 (p, t, t - 1); 47*072a4ba8SAndrew Turner } 48*072a4ba8SAndrew Turner 49*072a4ba8SAndrew Turner static NOINLINE v_f64_t 50*072a4ba8SAndrew Turner special_case (v_f64_t x, v_f64_t y, v_u64_t special) 51*072a4ba8SAndrew Turner { 52*072a4ba8SAndrew Turner return v_call_f64 (tanh, x, y, special); 53*072a4ba8SAndrew Turner } 54*072a4ba8SAndrew Turner 55*072a4ba8SAndrew Turner /* Vector approximation for double-precision tanh(x), using a simplified 56*072a4ba8SAndrew Turner version of expm1. The greatest observed error is 2.75 ULP: 57*072a4ba8SAndrew Turner __v_tanh(-0x1.c143c3a44e087p-3) got -0x1.ba31ba4691ab7p-3 58*072a4ba8SAndrew Turner want -0x1.ba31ba4691ab4p-3. */ 59*072a4ba8SAndrew Turner VPCS_ATTR v_f64_t V_NAME (tanh) (v_f64_t x) 60*072a4ba8SAndrew Turner { 61*072a4ba8SAndrew Turner v_u64_t ix = v_as_u64_f64 (x); 62*072a4ba8SAndrew Turner v_u64_t ia = ix & AbsMask; 63*072a4ba8SAndrew Turner 64*072a4ba8SAndrew Turner /* Trigger special-cases for tiny, boring and infinity/NaN. */ 65*072a4ba8SAndrew Turner v_u64_t special = v_cond_u64 ((ia - TinyBound) > (BoringBound - TinyBound)); 66*072a4ba8SAndrew Turner v_f64_t u; 67*072a4ba8SAndrew Turner 68*072a4ba8SAndrew Turner /* To trigger fp exceptions correctly, set special lanes to a neutral value. 69*072a4ba8SAndrew Turner They will be fixed up later by the special-case handler. */ 70*072a4ba8SAndrew Turner if (unlikely (v_any_u64 (special))) 71*072a4ba8SAndrew Turner u = v_sel_f64 (special, v_f64 (1), x) * 2; 72*072a4ba8SAndrew Turner else 73*072a4ba8SAndrew Turner u = x * 2; 74*072a4ba8SAndrew Turner 75*072a4ba8SAndrew Turner /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ 76*072a4ba8SAndrew Turner v_f64_t q = expm1_inline (u); 77*072a4ba8SAndrew Turner v_f64_t y = q / (q + 2); 78*072a4ba8SAndrew Turner 79*072a4ba8SAndrew Turner if (unlikely (v_any_u64 (special))) 80*072a4ba8SAndrew Turner return special_case (x, y, special); 81*072a4ba8SAndrew Turner return y; 82*072a4ba8SAndrew Turner } 83*072a4ba8SAndrew Turner VPCS_ALIAS 84*072a4ba8SAndrew Turner 85*072a4ba8SAndrew Turner PL_SIG (V, D, 1, tanh, -10.0, 10.0) 86*072a4ba8SAndrew Turner PL_TEST_ULP (V_NAME (tanh), 2.26) 87*072a4ba8SAndrew Turner PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (tanh)) 88*072a4ba8SAndrew Turner PL_TEST_INTERVAL (V_NAME (tanh), 0, TinyBound, 1000) 89*072a4ba8SAndrew Turner PL_TEST_INTERVAL (V_NAME (tanh), -0, -TinyBound, 1000) 90*072a4ba8SAndrew Turner PL_TEST_INTERVAL (V_NAME (tanh), TinyBound, BoringBound, 100000) 91*072a4ba8SAndrew Turner PL_TEST_INTERVAL (V_NAME (tanh), -TinyBound, -BoringBound, 100000) 92*072a4ba8SAndrew Turner PL_TEST_INTERVAL (V_NAME (tanh), BoringBound, inf, 1000) 93*072a4ba8SAndrew Turner PL_TEST_INTERVAL (V_NAME (tanh), -BoringBound, -inf, 1000) 94*072a4ba8SAndrew Turner #endif 95