1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision vector exp(x) - 1 function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited. 5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6*f3087befSAndrew Turner */ 7*f3087befSAndrew Turner 8*f3087befSAndrew Turner #include "v_math.h" 9*f3087befSAndrew Turner #include "test_sig.h" 10*f3087befSAndrew Turner #include "test_defs.h" 11*f3087befSAndrew Turner #include "v_expm1_inline.h" 12*f3087befSAndrew Turner 13*f3087befSAndrew Turner static const struct data 14*f3087befSAndrew Turner { 15*f3087befSAndrew Turner struct v_expm1_data d; 16*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 17*f3087befSAndrew Turner uint64x2_t thresh, tiny_bound; 18*f3087befSAndrew Turner #else 19*f3087befSAndrew Turner float64x2_t oflow_bound; 20*f3087befSAndrew Turner #endif 21*f3087befSAndrew Turner } data = { 22*f3087befSAndrew Turner .d = V_EXPM1_DATA, 23*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 24*f3087befSAndrew Turner /* asuint64(oflow_bound) - asuint64(0x1p-51), shifted left by 1 for abs 25*f3087befSAndrew Turner compare. */ 26*f3087befSAndrew Turner .thresh = V2 (0x78c56fa6d34b552), 27*f3087befSAndrew Turner /* asuint64(0x1p-51) << 1. */ 28*f3087befSAndrew Turner .tiny_bound = V2 (0x3cc0000000000000 << 1), 29*f3087befSAndrew Turner #else 30*f3087befSAndrew Turner /* Value above which expm1(x) should overflow. Absolute value of the 31*f3087befSAndrew Turner underflow bound is greater than this, so it catches both cases - there is 32*f3087befSAndrew Turner a small window where fallbacks are triggered unnecessarily. */ 33*f3087befSAndrew Turner .oflow_bound = V2 (0x1.62b7d369a5aa9p+9), 34*f3087befSAndrew Turner #endif 35*f3087befSAndrew Turner }; 36*f3087befSAndrew Turner 37*f3087befSAndrew Turner static float64x2_t VPCS_ATTR NOINLINE 38*f3087befSAndrew Turner special_case (float64x2_t x, uint64x2_t special, const struct data *d) 39*f3087befSAndrew Turner { 40*f3087befSAndrew Turner return v_call_f64 (expm1, x, expm1_inline (v_zerofy_f64 (x, special), &d->d), 41*f3087befSAndrew Turner special); 42*f3087befSAndrew Turner } 43*f3087befSAndrew Turner 44*f3087befSAndrew Turner /* Double-precision vector exp(x) - 1 function. 45*f3087befSAndrew Turner The maximum error observed error is 2.05 ULP: 46*f3087befSAndrew Turner _ZGVnN2v_expm1(0x1.6329669eb8c87p-2) got 0x1.a8897eef87b34p-2 47*f3087befSAndrew Turner want 0x1.a8897eef87b32p-2. */ 48*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (expm1) (float64x2_t x) 49*f3087befSAndrew Turner { 50*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data); 51*f3087befSAndrew Turner 52*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 53*f3087befSAndrew Turner uint64x2_t ix = vreinterpretq_u64_f64 (x); 54*f3087befSAndrew Turner /* If fp exceptions are to be triggered correctly, fall back to scalar for 55*f3087befSAndrew Turner |x| < 2^-51, |x| > oflow_bound, Inf & NaN. Add ix to itself for 56*f3087befSAndrew Turner shift-left by 1, and compare with thresh which was left-shifted offline - 57*f3087befSAndrew Turner this is effectively an absolute compare. */ 58*f3087befSAndrew Turner uint64x2_t special 59*f3087befSAndrew Turner = vcgeq_u64 (vsubq_u64 (vaddq_u64 (ix, ix), d->tiny_bound), d->thresh); 60*f3087befSAndrew Turner #else 61*f3087befSAndrew Turner /* Large input, NaNs and Infs. */ 62*f3087befSAndrew Turner uint64x2_t special = vcageq_f64 (x, d->oflow_bound); 63*f3087befSAndrew Turner #endif 64*f3087befSAndrew Turner 65*f3087befSAndrew Turner if (unlikely (v_any_u64 (special))) 66*f3087befSAndrew Turner return special_case (x, special, d); 67*f3087befSAndrew Turner 68*f3087befSAndrew Turner /* expm1(x) ~= p * t + (t - 1). */ 69*f3087befSAndrew Turner return expm1_inline (x, &d->d); 70*f3087befSAndrew Turner } 71*f3087befSAndrew Turner 72*f3087befSAndrew Turner TEST_SIG (V, D, 1, expm1, -9.9, 9.9) 73*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (expm1), 1.56) 74*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (expm1), WANT_SIMD_EXCEPT) 75*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (expm1), 0, 0x1p-51, 1000) 76*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (expm1), 0x1p-51, 0x1.62b7d369a5aa9p+9, 100000) 77*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (expm1), 0x1.62b7d369a5aa9p+9, inf, 100) 78