1 /* 2 * Single-precision vector log2 function. 3 * 4 * Copyright (c) 2022-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "v_math.h" 9 #include "pairwise_hornerf.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 #if V_SUPPORTED 13 14 #define C(i) v_f32 (__v_log2f_data.poly[i]) 15 16 #define Ln2 v_f32 (0x1.62e43p-1f) /* 0x3f317218 */ 17 #define Min v_u32 (0x00800000) 18 #define Max v_u32 (0x7f800000) 19 #define Mask v_u32 (0x007fffff) 20 #define Off v_u32 (0x3f2aaaab) /* 0.666667 */ 21 22 VPCS_ATTR 23 NOINLINE static v_f32_t 24 specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp) 25 { 26 /* Fall back to scalar code. */ 27 return v_call_f32 (log2f, x, y, cmp); 28 } 29 30 /* Fast implementation for single precision log2, 31 relies on same argument reduction as Neon logf. 32 Maximum error: 2.48 ULPs 33 __v_log2f(0x1.558174p+0) got 0x1.a9be84p-2 34 want 0x1.a9be8p-2. */ 35 VPCS_ATTR 36 v_f32_t V_NAME (log2f) (v_f32_t x) 37 { 38 v_u32_t u = v_as_u32_f32 (x); 39 v_u32_t cmp = v_cond_u32 (u - Min >= Max - Min); 40 41 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */ 42 u -= Off; 43 v_f32_t n = v_to_f32_s32 (v_as_s32_u32 (u) >> 23); /* signextend. */ 44 u &= Mask; 45 u += Off; 46 v_f32_t r = v_as_f32_u32 (u) - v_f32 (1.0f); 47 48 /* y = log2(1+r) + n. */ 49 v_f32_t r2 = r * r; 50 v_f32_t p = PAIRWISE_HORNER_8 (r, r2, C); 51 v_f32_t y = v_fma_f32 (p, r, n); 52 53 if (unlikely (v_any_u32 (cmp))) 54 return specialcase (x, y, cmp); 55 return y; 56 } 57 VPCS_ALIAS 58 59 PL_SIG (V, F, 1, log2, 0.01, 11.1) 60 PL_TEST_ULP (V_NAME (log2f), 1.99) 61 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (log2f)) 62 PL_TEST_INTERVAL (V_NAME (log2f), -0.0, -0x1p126, 100) 63 PL_TEST_INTERVAL (V_NAME (log2f), 0x1p-149, 0x1p-126, 4000) 64 PL_TEST_INTERVAL (V_NAME (log2f), 0x1p-126, 0x1p-23, 50000) 65 PL_TEST_INTERVAL (V_NAME (log2f), 0x1p-23, 1.0, 50000) 66 PL_TEST_INTERVAL (V_NAME (log2f), 1.0, 100, 50000) 67 PL_TEST_INTERVAL (V_NAME (log2f), 100, inf, 50000) 68 #endif 69