1 /* 2 * Single-precision vector exp(x) - 1 function. 3 * 4 * Copyright (c) 2023-2024, 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 /* Largest value of x for which expm1(x) should round to -1. */ 13 #define SpecialBound 0x1.5ebc4p+6f 14 15 static const struct data 16 { 17 /* These 4 are grouped together so they can be loaded as one quadword, then 18 used with _lane forms of svmla/svmls. */ 19 float c2, c4, ln2_hi, ln2_lo; 20 float c0, inv_ln2, c1, c3, special_bound; 21 } data = { 22 /* Generated using fpminimax. */ 23 .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, 24 .c2 = 0x1.555736p-5, .c3 = 0x1.12287cp-7, 25 .c4 = 0x1.6b55a2p-10, .inv_ln2 = 0x1.715476p+0f, 26 .special_bound = SpecialBound, .ln2_lo = 0x1.7f7d1cp-20f, 27 .ln2_hi = 0x1.62e4p-1f, 28 29 }; 30 31 static svfloat32_t NOINLINE 32 special_case (svfloat32_t x, svbool_t pg) 33 { 34 return sv_call_f32 (expm1f, x, x, pg); 35 } 36 37 /* Single-precision SVE exp(x) - 1. Maximum error is 1.52 ULP: 38 _ZGVsMxv_expm1f(0x1.8f4ebcp-2) got 0x1.e859dp-2 39 want 0x1.e859d4p-2. */ 40 svfloat32_t SV_NAME_F1 (expm1) (svfloat32_t x, svbool_t pg) 41 { 42 const struct data *d = ptr_barrier (&data); 43 44 /* Large, NaN/Inf. */ 45 svbool_t special = svnot_z (pg, svaclt (pg, x, d->special_bound)); 46 47 if (unlikely (svptest_any (pg, special))) 48 return special_case (x, pg); 49 50 /* This vector is reliant on layout of data - it contains constants 51 that can be used with _lane forms of svmla/svmls. Values are: 52 [ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */ 53 svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2); 54 55 /* Reduce argument to smaller range: 56 Let i = round(x / ln2) 57 and f = x - i * ln2, then f is in [-ln2/2, ln2/2]. 58 exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 59 where 2^i is exact because i is an integer. */ 60 svfloat32_t j = svmul_x (svptrue_b32 (), x, d->inv_ln2); 61 j = svrinta_x (pg, j); 62 63 svfloat32_t f = svmls_lane (x, j, lane_constants, 2); 64 f = svmls_lane (f, j, lane_constants, 3); 65 66 /* Approximate expm1(f) using polynomial. 67 Taylor expansion for expm1(x) has the form: 68 x + ax^2 + bx^3 + cx^4 .... 69 So we calculate the polynomial P(f) = a + bf + cf^2 + ... 70 and assemble the approximation expm1(f) ~= f + f^2 * P(f). */ 71 svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), f, lane_constants, 0); 72 svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), f, lane_constants, 1); 73 svfloat32_t f2 = svmul_x (svptrue_b32 (), f, f); 74 svfloat32_t p = svmla_x (pg, p12, f2, p34); 75 76 p = svmla_x (pg, sv_f32 (d->c0), f, p); 77 p = svmla_x (pg, f, f2, p); 78 79 /* Assemble the result. 80 expm1(x) ~= 2^i * (p + 1) - 1 81 Let t = 2^i. */ 82 svfloat32_t t = svscale_x (pg, sv_f32 (1.0f), svcvt_s32_x (pg, j)); 83 return svmla_x (pg, svsub_x (pg, t, 1.0f), p, t); 84 } 85 86 TEST_SIG (SV, F, 1, expm1, -9.9, 9.9) 87 TEST_ULP (SV_NAME_F1 (expm1), 1.02) 88 TEST_DISABLE_FENV (SV_NAME_F1 (expm1)) 89 TEST_SYM_INTERVAL (SV_NAME_F1 (expm1), 0, SpecialBound, 100000) 90 TEST_SYM_INTERVAL (SV_NAME_F1 (expm1), SpecialBound, inf, 1000) 91 CLOSE_SVE_ATTR 92