1 /* 2 * Double-precision SVE 2^x function. 3 * 4 * Copyright (c) 2023-2025, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "test_sig.h" 10 #include "test_defs.h" 11 12 #define N (1 << V_EXP_TABLE_BITS) 13 14 #define BigBound 1022 15 #define UOFlowBound 1280 16 17 static const struct data 18 { 19 double c0, c2; 20 double c1, c3; 21 double shift, big_bound, uoflow_bound; 22 } data = { 23 /* Coefficients are computed using Remez algorithm with 24 minimisation of the absolute error. */ 25 .c0 = 0x1.62e42fefa3686p-1, .c1 = 0x1.ebfbdff82c241p-3, 26 .c2 = 0x1.c6b09b16de99ap-5, .c3 = 0x1.3b2abf5571ad8p-7, 27 .shift = 0x1.8p52 / N, .uoflow_bound = UOFlowBound, 28 .big_bound = BigBound, 29 }; 30 31 #define SpecialOffset 0x6000000000000000 /* 0x1p513. */ 32 /* SpecialBias1 + SpecialBias1 = asuint(1.0). */ 33 #define SpecialBias1 0x7000000000000000 /* 0x1p769. */ 34 #define SpecialBias2 0x3010000000000000 /* 0x1p-254. */ 35 36 /* Update of both special and non-special cases, if any special case is 37 detected. */ 38 static inline svfloat64_t 39 special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n, 40 const struct data *d) 41 { 42 /* s=2^n may overflow, break it up into s=s1*s2, 43 such that exp = s + s*y can be computed as s1*(s2+s2*y) 44 and s1*s1 overflows only if n>0. */ 45 46 /* If n<=0 then set b to 0x6, 0 otherwise. */ 47 svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */ 48 svuint64_t b = svdup_u64_z (p_sign, SpecialOffset); 49 50 /* Set s1 to generate overflow depending on sign of exponent n. */ 51 svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1)); 52 /* Offset s to avoid overflow in final result if n is below threshold. */ 53 svfloat64_t s2 = svreinterpret_f64 ( 54 svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b)); 55 56 /* |n| > 1280 => 2^(n) overflows. */ 57 svbool_t p_cmp = svacgt (pg, n, d->uoflow_bound); 58 59 svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1); 60 svfloat64_t r2 = svmla_x (pg, s2, s2, y); 61 svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1); 62 63 return svsel (p_cmp, r1, r0); 64 } 65 66 /* Fast vector implementation of exp2. 67 Maximum measured error is 1.65 ulp. 68 _ZGVsMxv_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1 69 want 0x1.f8db0d4df721dp-1. */ 70 svfloat64_t SV_NAME_D1 (exp2) (svfloat64_t x, svbool_t pg) 71 { 72 const struct data *d = ptr_barrier (&data); 73 svbool_t no_big_scale = svacle (pg, x, d->big_bound); 74 svbool_t special = svnot_z (pg, no_big_scale); 75 76 /* Reduce x to k/N + r, where k is integer and r in [-1/2N, 1/2N]. */ 77 svfloat64_t shift = sv_f64 (d->shift); 78 svfloat64_t kd = svadd_x (pg, x, shift); 79 svuint64_t ki = svreinterpret_u64 (kd); 80 /* kd = k/N. */ 81 kd = svsub_x (pg, kd, shift); 82 svfloat64_t r = svsub_x (pg, x, kd); 83 84 /* scale ~= 2^(k/N). */ 85 svuint64_t idx = svand_x (pg, ki, N - 1); 86 svuint64_t sbits = svld1_gather_index (pg, __v_exp_data, idx); 87 /* This is only a valid scale when -1023*N < k < 1024*N. */ 88 svuint64_t top = svlsl_x (pg, ki, 52 - V_EXP_TABLE_BITS); 89 svfloat64_t scale = svreinterpret_f64 (svadd_x (pg, sbits, top)); 90 91 svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1); 92 /* Approximate exp2(r) using polynomial. */ 93 /* y = exp2(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4. */ 94 svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r); 95 svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r, c13, 0); 96 svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r, c13, 1); 97 svfloat64_t p = svmla_x (pg, p01, p23, r2); 98 svfloat64_t y = svmul_x (svptrue_b64 (), r, p); 99 /* Assemble exp2(x) = exp2(r) * scale. */ 100 if (unlikely (svptest_any (pg, special))) 101 return special_case (pg, scale, y, kd, d); 102 return svmla_x (pg, scale, scale, y); 103 } 104 105 TEST_SIG (SV, D, 1, exp2, -9.9, 9.9) 106 TEST_ULP (SV_NAME_D1 (exp2), 1.15) 107 TEST_DISABLE_FENV (SV_NAME_D1 (exp2)) 108 TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), 0, BigBound, 1000) 109 TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), BigBound, UOFlowBound, 100000) 110 TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), UOFlowBound, inf, 1000) 111 CLOSE_SVE_ATTR 112