1 /* 2 * Single-precision vector e^x function. 3 * 4 * Copyright (c) 2019, Arm Limited. 5 * SPDX-License-Identifier: MIT 6 */ 7 8 #include "mathlib.h" 9 #include "v_math.h" 10 #if V_SUPPORTED 11 12 static const float Poly[] = { 13 /* maxerr: 1.45358 +0.5 ulp. */ 14 0x1.0e4020p-7f, 15 0x1.573e2ep-5f, 16 0x1.555e66p-3f, 17 0x1.fffdb6p-2f, 18 0x1.ffffecp-1f, 19 }; 20 #define C0 v_f32 (Poly[0]) 21 #define C1 v_f32 (Poly[1]) 22 #define C2 v_f32 (Poly[2]) 23 #define C3 v_f32 (Poly[3]) 24 #define C4 v_f32 (Poly[4]) 25 26 #define Shift v_f32 (0x1.8p23f) 27 #define InvLn2 v_f32 (0x1.715476p+0f) 28 #define Ln2hi v_f32 (0x1.62e4p-1f) 29 #define Ln2lo v_f32 (0x1.7f7d1cp-20f) 30 31 VPCS_ATTR 32 static v_f32_t 33 specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale) 34 { 35 /* 2^n may overflow, break it up into s1*s2. */ 36 v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000); 37 v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b); 38 v_f32_t s2 = v_as_f32_u32 (e - b); 39 v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f)); 40 v_u32_t r2 = v_as_u32_f32 (s1 * s1); 41 v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1); 42 /* Similar to r1 but avoids double rounding in the subnormal range. */ 43 v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale)); 44 return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0)); 45 } 46 47 VPCS_ATTR 48 v_f32_t 49 V_NAME(expf) (v_f32_t x) 50 { 51 v_f32_t n, r, r2, scale, p, q, poly, absn, z; 52 v_u32_t cmp, e; 53 54 /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)] 55 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ 56 #if 1 57 z = v_fma_f32 (x, InvLn2, Shift); 58 n = z - Shift; 59 r = v_fma_f32 (n, -Ln2hi, x); 60 r = v_fma_f32 (n, -Ln2lo, r); 61 e = v_as_u32_f32 (z) << 23; 62 #else 63 z = x * InvLn2; 64 n = v_round_f32 (z); 65 r = v_fma_f32 (n, -Ln2hi, x); 66 r = v_fma_f32 (n, -Ln2lo, r); 67 e = v_as_u32_s32 (v_round_s32 (z)) << 23; 68 #endif 69 scale = v_as_f32_u32 (e + v_u32 (0x3f800000)); 70 absn = v_abs_f32 (n); 71 cmp = v_cond_u32 (absn > v_f32 (126.0f)); 72 r2 = r * r; 73 p = v_fma_f32 (C0, r, C1); 74 q = v_fma_f32 (C2, r, C3); 75 q = v_fma_f32 (p, r2, q); 76 p = C4 * r; 77 poly = v_fma_f32 (q, r2, p); 78 if (unlikely (v_any_u32 (cmp))) 79 return specialcase (poly, n, e, absn, cmp, scale); 80 return v_fma_f32 (poly, scale, scale); 81 } 82 VPCS_ALIAS 83 #endif 84