1 /* 2 * Single-precision vector log10 function. 3 * 4 * Copyright (c) 2020-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "v_math.h" 9 #include "mathlib.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 #if V_SUPPORTED 14 15 #define P(i) v_f32 (__v_log10f_poly[i]) 16 17 #define Ln2 v_f32 (0x1.62e43p-1f) /* 0x3f317218. */ 18 #define InvLn10 v_f32 (0x1.bcb7b2p-2f) 19 #define Min v_u32 (0x00800000) 20 #define Max v_u32 (0x7f800000) 21 #define Mask v_u32 (0x007fffff) 22 #define Off v_u32 (0x3f2aaaab) /* 0.666667. */ 23 24 VPCS_ATTR 25 NOINLINE static v_f32_t 26 specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp) 27 { 28 /* Fall back to scalar code. */ 29 return v_call_f32 (log10f, x, y, cmp); 30 } 31 32 /* Our fast implementation of v_log10f uses a similar approach as v_logf. 33 With the same offset as v_logf (i.e., 2/3) it delivers about 3.3ulps with 34 order 9. This is more efficient than using a low order polynomial computed in 35 double precision. 36 Maximum error: 3.305ulps (nearest rounding.) 37 __v_log10f(0x1.555c16p+0) got 0x1.ffe2fap-4 38 want 0x1.ffe2f4p-4 -0.304916 ulp err 2.80492. */ 39 VPCS_ATTR 40 v_f32_t V_NAME (log10f) (v_f32_t x) 41 { 42 v_f32_t n, o, p, q, r, r2, y; 43 v_u32_t u, cmp; 44 45 u = v_as_u32_f32 (x); 46 cmp = v_cond_u32 (u - Min >= Max - Min); 47 48 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */ 49 u -= Off; 50 n = v_to_f32_s32 (v_as_s32_u32 (u) >> 23); /* signextend. */ 51 u &= Mask; 52 u += Off; 53 r = v_as_f32_u32 (u) - v_f32 (1.0f); 54 55 /* y = log10(1+r) + n*log10(2). */ 56 r2 = r * r; 57 /* (n*ln2 + r)*InvLn10 + r2*(P0 + r*P1 + r2*(P2 + r*P3 + r2*(P4 + r*P5 + 58 r2*(P6+r*P7))). */ 59 o = v_fma_f32 (P (7), r, P (6)); 60 p = v_fma_f32 (P (5), r, P (4)); 61 q = v_fma_f32 (P (3), r, P (2)); 62 y = v_fma_f32 (P (1), r, P (0)); 63 p = v_fma_f32 (o, r2, p); 64 q = v_fma_f32 (p, r2, q); 65 y = v_fma_f32 (q, r2, y); 66 /* Using p = Log10(2)*n + r*InvLn(10) is slightly faster 67 but less accurate. */ 68 p = v_fma_f32 (Ln2, n, r); 69 y = v_fma_f32 (y, r2, p * InvLn10); 70 71 if (unlikely (v_any_u32 (cmp))) 72 return specialcase (x, y, cmp); 73 return y; 74 } 75 VPCS_ALIAS 76 77 PL_SIG (V, F, 1, log10, 0.01, 11.1) 78 PL_TEST_ULP (V_NAME (log10f), 2.81) 79 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (log10f)) 80 PL_TEST_INTERVAL (V_NAME (log10f), 0, 0xffff0000, 10000) 81 PL_TEST_INTERVAL (V_NAME (log10f), 0x1p-4, 0x1p4, 500000) 82 #endif 83