1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision vector 2^x function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2019-2024, 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 "v_poly_f64.h" 10*f3087befSAndrew Turner #include "test_sig.h" 11*f3087befSAndrew Turner #include "test_defs.h" 12*f3087befSAndrew Turner 13*f3087befSAndrew Turner #define N (1 << V_EXP_TABLE_BITS) 14*f3087befSAndrew Turner #define IndexMask (N - 1) 15*f3087befSAndrew Turner #define BigBound 1022.0 16*f3087befSAndrew Turner #define UOFlowBound 1280.0 17*f3087befSAndrew Turner #define TinyBound 0x2000000000000000 /* asuint64(0x1p-511). */ 18*f3087befSAndrew Turner 19*f3087befSAndrew Turner static const struct data 20*f3087befSAndrew Turner { 21*f3087befSAndrew Turner float64x2_t poly[4]; 22*f3087befSAndrew Turner float64x2_t shift, scale_big_bound, scale_uoflow_bound; 23*f3087befSAndrew Turner } data = { 24*f3087befSAndrew Turner /* Coefficients are computed using Remez algorithm with 25*f3087befSAndrew Turner minimisation of the absolute error. */ 26*f3087befSAndrew Turner .poly = { V2 (0x1.62e42fefa3686p-1), V2 (0x1.ebfbdff82c241p-3), 27*f3087befSAndrew Turner V2 (0x1.c6b09b16de99ap-5), V2 (0x1.3b2abf5571ad8p-7) }, 28*f3087befSAndrew Turner .shift = V2 (0x1.8p52 / N), 29*f3087befSAndrew Turner .scale_big_bound = V2 (BigBound), 30*f3087befSAndrew Turner .scale_uoflow_bound = V2 (UOFlowBound), 31*f3087befSAndrew Turner }; 32*f3087befSAndrew Turner 33*f3087befSAndrew Turner static inline uint64x2_t 34*f3087befSAndrew Turner lookup_sbits (uint64x2_t i) 35*f3087befSAndrew Turner { 36*f3087befSAndrew Turner return (uint64x2_t){ __v_exp_data[i[0] & IndexMask], 37*f3087befSAndrew Turner __v_exp_data[i[1] & IndexMask] }; 38*f3087befSAndrew Turner } 39*f3087befSAndrew Turner 40*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 41*f3087befSAndrew Turner 42*f3087befSAndrew Turner # define Thres 0x2080000000000000 /* asuint64(512.0) - TinyBound. */ 43*f3087befSAndrew Turner 44*f3087befSAndrew Turner /* Call scalar exp2 as a fallback. */ 45*f3087befSAndrew Turner static float64x2_t VPCS_ATTR NOINLINE 46*f3087befSAndrew Turner special_case (float64x2_t x, float64x2_t y, uint64x2_t is_special) 47*f3087befSAndrew Turner { 48*f3087befSAndrew Turner return v_call_f64 (exp2, x, y, is_special); 49*f3087befSAndrew Turner } 50*f3087befSAndrew Turner 51*f3087befSAndrew Turner #else 52*f3087befSAndrew Turner 53*f3087befSAndrew Turner # define SpecialOffset 0x6000000000000000 /* 0x1p513. */ 54*f3087befSAndrew Turner /* SpecialBias1 + SpecialBias1 = asuint(1.0). */ 55*f3087befSAndrew Turner # define SpecialBias1 0x7000000000000000 /* 0x1p769. */ 56*f3087befSAndrew Turner # define SpecialBias2 0x3010000000000000 /* 0x1p-254. */ 57*f3087befSAndrew Turner 58*f3087befSAndrew Turner static inline float64x2_t VPCS_ATTR 59*f3087befSAndrew Turner special_case (float64x2_t s, float64x2_t y, float64x2_t n, 60*f3087befSAndrew Turner const struct data *d) 61*f3087befSAndrew Turner { 62*f3087befSAndrew Turner /* 2^(n/N) may overflow, break it up into s1*s2. */ 63*f3087befSAndrew Turner uint64x2_t b = vandq_u64 (vclezq_f64 (n), v_u64 (SpecialOffset)); 64*f3087befSAndrew Turner float64x2_t s1 = vreinterpretq_f64_u64 (vsubq_u64 (v_u64 (SpecialBias1), b)); 65*f3087befSAndrew Turner float64x2_t s2 = vreinterpretq_f64_u64 (vaddq_u64 ( 66*f3087befSAndrew Turner vsubq_u64 (vreinterpretq_u64_f64 (s), v_u64 (SpecialBias2)), b)); 67*f3087befSAndrew Turner uint64x2_t cmp = vcagtq_f64 (n, d->scale_uoflow_bound); 68*f3087befSAndrew Turner float64x2_t r1 = vmulq_f64 (s1, s1); 69*f3087befSAndrew Turner float64x2_t r0 = vmulq_f64 (vfmaq_f64 (s2, s2, y), s1); 70*f3087befSAndrew Turner return vbslq_f64 (cmp, r1, r0); 71*f3087befSAndrew Turner } 72*f3087befSAndrew Turner 73*f3087befSAndrew Turner #endif 74*f3087befSAndrew Turner 75*f3087befSAndrew Turner /* Fast vector implementation of exp2. 76*f3087befSAndrew Turner Maximum measured error is 1.65 ulp. 77*f3087befSAndrew Turner _ZGVnN2v_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1 78*f3087befSAndrew Turner want 0x1.f8db0d4df721dp-1. */ 79*f3087befSAndrew Turner VPCS_ATTR 80*f3087befSAndrew Turner float64x2_t V_NAME_D1 (exp2) (float64x2_t x) 81*f3087befSAndrew Turner { 82*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data); 83*f3087befSAndrew Turner uint64x2_t cmp; 84*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 85*f3087befSAndrew Turner uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x)); 86*f3087befSAndrew Turner cmp = vcgeq_u64 (vsubq_u64 (ia, v_u64 (TinyBound)), v_u64 (Thres)); 87*f3087befSAndrew Turner /* Mask special lanes and retain a copy of x for passing to special-case 88*f3087befSAndrew Turner handler. */ 89*f3087befSAndrew Turner float64x2_t xc = x; 90*f3087befSAndrew Turner x = v_zerofy_f64 (x, cmp); 91*f3087befSAndrew Turner #else 92*f3087befSAndrew Turner cmp = vcagtq_f64 (x, d->scale_big_bound); 93*f3087befSAndrew Turner #endif 94*f3087befSAndrew Turner 95*f3087befSAndrew Turner /* n = round(x/N). */ 96*f3087befSAndrew Turner float64x2_t z = vaddq_f64 (d->shift, x); 97*f3087befSAndrew Turner uint64x2_t u = vreinterpretq_u64_f64 (z); 98*f3087befSAndrew Turner float64x2_t n = vsubq_f64 (z, d->shift); 99*f3087befSAndrew Turner 100*f3087befSAndrew Turner /* r = x - n/N. */ 101*f3087befSAndrew Turner float64x2_t r = vsubq_f64 (x, n); 102*f3087befSAndrew Turner 103*f3087befSAndrew Turner /* s = 2^(n/N). */ 104*f3087befSAndrew Turner uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS); 105*f3087befSAndrew Turner u = lookup_sbits (u); 106*f3087befSAndrew Turner float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e)); 107*f3087befSAndrew Turner 108*f3087befSAndrew Turner /* y ~ exp2(r) - 1. */ 109*f3087befSAndrew Turner float64x2_t r2 = vmulq_f64 (r, r); 110*f3087befSAndrew Turner float64x2_t y = v_pairwise_poly_3_f64 (r, r2, d->poly); 111*f3087befSAndrew Turner y = vmulq_f64 (r, y); 112*f3087befSAndrew Turner 113*f3087befSAndrew Turner if (unlikely (v_any_u64 (cmp))) 114*f3087befSAndrew Turner #if !WANT_SIMD_EXCEPT 115*f3087befSAndrew Turner return special_case (s, y, n, d); 116*f3087befSAndrew Turner #else 117*f3087befSAndrew Turner return special_case (xc, vfmaq_f64 (s, s, y), cmp); 118*f3087befSAndrew Turner #endif 119*f3087befSAndrew Turner return vfmaq_f64 (s, s, y); 120*f3087befSAndrew Turner } 121*f3087befSAndrew Turner 122*f3087befSAndrew Turner TEST_SIG (V, D, 1, exp2, -9.9, 9.9) 123*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (exp2), 1.15) 124*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (exp2), WANT_SIMD_EXCEPT) 125*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (exp2), 0, TinyBound, 5000) 126*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (exp2), TinyBound, BigBound, 10000) 127*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (exp2), BigBound, UOFlowBound, 5000) 128*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (exp2), UOFlowBound, inf, 10000) 129