1 /* 2 * Single-precision SVE 2^x 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 #define Thres 0x1.5d5e2ap+6f 13 14 static const struct data 15 { 16 float c0, c2, c4, c1, c3; 17 float shift, thres; 18 } data = { 19 /* Coefficients copied from the polynomial in AdvSIMD variant. */ 20 .c0 = 0x1.62e422p-1f, 21 .c1 = 0x1.ebf9bcp-3f, 22 .c2 = 0x1.c6bd32p-5f, 23 .c3 = 0x1.3ce9e4p-7f, 24 .c4 = 0x1.59977ap-10f, 25 /* 1.5*2^17 + 127. */ 26 .shift = 0x1.803f8p17f, 27 /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled 28 correctly by FEXPA. */ 29 .thres = Thres, 30 }; 31 32 static inline svfloat32_t 33 sv_exp2f_inline (svfloat32_t x, const svbool_t pg, const struct data *d) 34 { 35 /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)] 36 x = n + r, with r in [-1/2, 1/2]. */ 37 svfloat32_t z = svadd_x (svptrue_b32 (), x, d->shift); 38 svfloat32_t n = svsub_x (svptrue_b32 (), z, d->shift); 39 svfloat32_t r = svsub_x (svptrue_b32 (), x, n); 40 41 svfloat32_t scale = svexpa (svreinterpret_u32 (z)); 42 43 /* Polynomial evaluation: poly(r) ~ exp2(r)-1. 44 Evaluate polynomial use hybrid scheme - offset ESTRIN by 1 for 45 coefficients 1 to 4, and apply most significant coefficient directly. */ 46 svfloat32_t even_coeffs = svld1rq (svptrue_b32 (), &d->c0); 47 svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r); 48 svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, even_coeffs, 1); 49 svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, even_coeffs, 2); 50 svfloat32_t p14 = svmla_x (pg, p12, r2, p34); 51 svfloat32_t p0 = svmul_lane (r, even_coeffs, 0); 52 svfloat32_t poly = svmla_x (pg, p0, r2, p14); 53 54 return svmla_x (pg, scale, scale, poly); 55 } 56 57 static svfloat32_t NOINLINE 58 special_case (svfloat32_t x, svbool_t special, const struct data *d) 59 { 60 return sv_call_f32 (exp2f, x, sv_exp2f_inline (x, svptrue_b32 (), d), 61 special); 62 } 63 64 /* Single-precision SVE exp2f routine. Implements the same algorithm 65 as AdvSIMD exp2f. 66 Worst case error is 1.04 ULPs. 67 _ZGVsMxv_exp2f(-0x1.af994ap-3) got 0x1.ba6a66p-1 68 want 0x1.ba6a64p-1. */ 69 svfloat32_t SV_NAME_F1 (exp2) (svfloat32_t x, const svbool_t pg) 70 { 71 const struct data *d = ptr_barrier (&data); 72 svbool_t special = svacgt (pg, x, d->thres); 73 if (unlikely (svptest_any (special, special))) 74 return special_case (x, special, d); 75 return sv_exp2f_inline (x, pg, d); 76 } 77 78 TEST_SIG (SV, F, 1, exp2, -9.9, 9.9) 79 TEST_ULP (SV_NAME_F1 (exp2), 0.54) 80 TEST_DISABLE_FENV (SV_NAME_F1 (exp2)) 81 TEST_SYM_INTERVAL (SV_NAME_F1 (exp2), 0, Thres, 50000) 82 TEST_SYM_INTERVAL (SV_NAME_F1 (exp2), Thres, inf, 50000) 83 CLOSE_SVE_ATTR 84