1 /* 2 * Single-precision vector e^x function. 3 * 4 * Copyright (c) 2019-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 12 static const struct data 13 { 14 float poly[5]; 15 float inv_ln2, ln2_hi, ln2_lo, shift, thres; 16 } data = { 17 /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for 18 compatibility with polynomial helpers. */ 19 .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f, 20 0x1.0e4020p-7f }, 21 .inv_ln2 = 0x1.715476p+0f, 22 .ln2_hi = 0x1.62e4p-1f, 23 .ln2_lo = 0x1.7f7d1cp-20f, 24 /* 1.5*2^17 + 127. */ 25 .shift = 0x1.903f8p17f, 26 /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled 27 correctly by FEXPA. */ 28 .thres = 0x1.5d5e2ap+6f, 29 }; 30 31 #define C(i) sv_f32 (d->poly[i]) 32 #define ExponentBias 0x3f800000 33 34 static svfloat32_t NOINLINE 35 special_case (svfloat32_t x, svfloat32_t y, svbool_t special) 36 { 37 return sv_call_f32 (expf, x, y, special); 38 } 39 40 /* Optimised single-precision SVE exp function. 41 Worst-case error is 1.04 ulp: 42 SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4 43 want 0x1.ba74bap+4. */ 44 svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg) 45 { 46 const struct data *d = ptr_barrier (&data); 47 48 /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)] 49 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ 50 51 /* Load some constants in quad-word chunks to minimise memory access (last 52 lane is wasted). */ 53 svfloat32_t invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->inv_ln2); 54 55 /* n = round(x/(ln2/N)). */ 56 svfloat32_t z = svmla_lane (sv_f32 (d->shift), x, invln2_and_ln2, 0); 57 svfloat32_t n = svsub_x (pg, z, d->shift); 58 59 /* r = x - n*ln2/N. */ 60 svfloat32_t r = svmls_lane (x, n, invln2_and_ln2, 1); 61 r = svmls_lane (r, n, invln2_and_ln2, 2); 62 63 /* scale = 2^(n/N). */ 64 svbool_t is_special_case = svacgt (pg, x, d->thres); 65 svfloat32_t scale = svexpa (svreinterpret_u32 (z)); 66 67 /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */ 68 svfloat32_t p12 = svmla_x (pg, C (1), C (2), r); 69 svfloat32_t p34 = svmla_x (pg, C (3), C (4), r); 70 svfloat32_t r2 = svmul_x (pg, r, r); 71 svfloat32_t p14 = svmla_x (pg, p12, p34, r2); 72 svfloat32_t p0 = svmul_x (pg, r, C (0)); 73 svfloat32_t poly = svmla_x (pg, p0, r2, p14); 74 75 if (unlikely (svptest_any (pg, is_special_case))) 76 return special_case (x, svmla_x (pg, scale, scale, poly), is_special_case); 77 78 return svmla_x (pg, scale, scale, poly); 79 } 80 81 PL_SIG (SV, F, 1, exp, -9.9, 9.9) 82 PL_TEST_ULP (SV_NAME_F1 (exp), 0.55) 83 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 0, 0x1p-23, 40000) 84 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 0x1p-23, 1, 50000) 85 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 1, 0x1p23, 50000) 86 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 0x1p23, inf, 50000) 87