1 /* 2 * Single-precision vector log 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 /* 3.34 ulp error */ 14 -0x1.3e737cp-3f, 0x1.5a9aa2p-3f, -0x1.4f9934p-3f, 0x1.961348p-3f, 15 -0x1.00187cp-2f, 0x1.555d7cp-2f, -0x1.ffffc8p-2f, 16 }; 17 #define P7 v_f32 (Poly[0]) 18 #define P6 v_f32 (Poly[1]) 19 #define P5 v_f32 (Poly[2]) 20 #define P4 v_f32 (Poly[3]) 21 #define P3 v_f32 (Poly[4]) 22 #define P2 v_f32 (Poly[5]) 23 #define P1 v_f32 (Poly[6]) 24 25 #define Ln2 v_f32 (0x1.62e43p-1f) /* 0x3f317218 */ 26 #define Min v_u32 (0x00800000) 27 #define Max v_u32 (0x7f800000) 28 #define Mask v_u32 (0x007fffff) 29 #define Off v_u32 (0x3f2aaaab) /* 0.666667 */ 30 31 VPCS_ATTR 32 __attribute__ ((noinline)) static v_f32_t 33 specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp) 34 { 35 /* Fall back to scalar code. */ 36 return v_call_f32 (logf, x, y, cmp); 37 } 38 39 VPCS_ATTR 40 v_f32_t 41 V_NAME(logf) (v_f32_t x) 42 { 43 v_f32_t n, p, q, r, r2, y; 44 v_u32_t u, cmp; 45 46 u = v_as_u32_f32 (x); 47 cmp = v_cond_u32 (u - Min >= Max - Min); 48 49 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3 */ 50 u -= Off; 51 n = v_to_f32_s32 (v_as_s32_u32 (u) >> 23); /* signextend */ 52 u &= Mask; 53 u += Off; 54 r = v_as_f32_u32 (u) - v_f32 (1.0f); 55 56 /* y = log(1+r) + n*ln2. */ 57 r2 = r * r; 58 /* n*ln2 + r + r2*(P1 + r*P2 + r2*(P3 + r*P4 + r2*(P5 + r*P6 + r2*P7))). */ 59 p = v_fma_f32 (P6, r, P5); 60 q = v_fma_f32 (P4, r, P3); 61 y = v_fma_f32 (P2, r, P1); 62 p = v_fma_f32 (P7, r2, p); 63 q = v_fma_f32 (p, r2, q); 64 y = v_fma_f32 (q, r2, y); 65 p = v_fma_f32 (Ln2, n, r); 66 y = v_fma_f32 (y, r2, p); 67 68 if (unlikely (v_any_u32 (cmp))) 69 return specialcase (x, y, cmp); 70 return y; 71 } 72 VPCS_ALIAS 73 #endif 74