1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision vector tanh(x) function. 3*f3087befSAndrew Turner * Copyright (c) 2023-2024, Arm Limited. 4*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*f3087befSAndrew Turner */ 6*f3087befSAndrew Turner 7*f3087befSAndrew Turner #include "v_math.h" 8*f3087befSAndrew Turner #include "test_sig.h" 9*f3087befSAndrew Turner #include "test_defs.h" 10*f3087befSAndrew Turner #include "v_expm1_inline.h" 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner static const struct data 13*f3087befSAndrew Turner { 14*f3087befSAndrew Turner struct v_expm1_data d; 15*f3087befSAndrew Turner uint64x2_t thresh, tiny_bound; 16*f3087befSAndrew Turner } data = { 17*f3087befSAndrew Turner .d = V_EXPM1_DATA, 18*f3087befSAndrew Turner .tiny_bound = V2 (0x3e40000000000000), /* asuint64 (0x1p-27). */ 19*f3087befSAndrew Turner /* asuint64(0x1.241bf835f9d5fp+4) - asuint64(tiny_bound). */ 20*f3087befSAndrew Turner .thresh = V2 (0x01f241bf835f9d5f), 21*f3087befSAndrew Turner }; 22*f3087befSAndrew Turner 23*f3087befSAndrew Turner static float64x2_t NOINLINE VPCS_ATTR 24*f3087befSAndrew Turner special_case (float64x2_t x, float64x2_t q, float64x2_t qp2, 25*f3087befSAndrew Turner uint64x2_t special) 26*f3087befSAndrew Turner { 27*f3087befSAndrew Turner return v_call_f64 (tanh, x, vdivq_f64 (q, qp2), special); 28*f3087befSAndrew Turner } 29*f3087befSAndrew Turner 30*f3087befSAndrew Turner /* Vector approximation for double-precision tanh(x), using a simplified 31*f3087befSAndrew Turner version of expm1. The greatest observed error is 2.70 ULP: 32*f3087befSAndrew Turner _ZGVnN2v_tanh(-0x1.c59aa220cb177p-3) got -0x1.be5452a6459fep-3 33*f3087befSAndrew Turner want -0x1.be5452a6459fbp-3. */ 34*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (tanh) (float64x2_t x) 35*f3087befSAndrew Turner { 36*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data); 37*f3087befSAndrew Turner 38*f3087befSAndrew Turner uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x)); 39*f3087befSAndrew Turner 40*f3087befSAndrew Turner float64x2_t u = x; 41*f3087befSAndrew Turner 42*f3087befSAndrew Turner /* Trigger special-cases for tiny, boring and infinity/NaN. */ 43*f3087befSAndrew Turner uint64x2_t special = vcgtq_u64 (vsubq_u64 (ia, d->tiny_bound), d->thresh); 44*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 45*f3087befSAndrew Turner /* To trigger fp exceptions correctly, set special lanes to a neutral value. 46*f3087befSAndrew Turner They will be fixed up later by the special-case handler. */ 47*f3087befSAndrew Turner if (unlikely (v_any_u64 (special))) 48*f3087befSAndrew Turner u = v_zerofy_f64 (u, special); 49*f3087befSAndrew Turner #endif 50*f3087befSAndrew Turner 51*f3087befSAndrew Turner u = vaddq_f64 (u, u); 52*f3087befSAndrew Turner 53*f3087befSAndrew Turner /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ 54*f3087befSAndrew Turner float64x2_t q = expm1_inline (u, &d->d); 55*f3087befSAndrew Turner float64x2_t qp2 = vaddq_f64 (q, v_f64 (2.0)); 56*f3087befSAndrew Turner 57*f3087befSAndrew Turner if (unlikely (v_any_u64 (special))) 58*f3087befSAndrew Turner return special_case (x, q, qp2, special); 59*f3087befSAndrew Turner return vdivq_f64 (q, qp2); 60*f3087befSAndrew Turner } 61*f3087befSAndrew Turner 62*f3087befSAndrew Turner TEST_SIG (V, D, 1, tanh, -10.0, 10.0) 63*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (tanh), 2.21) 64*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (tanh), WANT_SIMD_EXCEPT) 65*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (tanh), 0, 0x1p-27, 5000) 66*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (tanh), 0x1p-27, 0x1.241bf835f9d5fp+4, 50000) 67*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (tanh), 0x1.241bf835f9d5fp+4, inf, 1000) 68