1 /* 2 * Single-precision log2 function. 3 * 4 * Copyright (c) 2017-2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include <math.h> 9 #include <stdint.h> 10 #include "math_config.h" 11 #include "test_defs.h" 12 #include "test_sig.h" 13 14 /* 15 LOG2F_TABLE_BITS = 4 16 LOG2F_POLY_ORDER = 4 17 18 ULP error: 0.752 (nearest rounding.) 19 Relative error: 1.9 * 2^-26 (before rounding.) 20 */ 21 22 #define N (1 << LOG2F_TABLE_BITS) 23 #define T __log2f_data.tab 24 #define A __log2f_data.poly 25 #define OFF 0x3f330000 26 27 float 28 log2f (float x) 29 { 30 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ 31 double_t z, r, r2, p, y, y0, invc, logc; 32 uint32_t ix, iz, top, tmp; 33 int k, i; 34 35 ix = asuint (x); 36 #if WANT_ROUNDING 37 /* Fix sign of zero with downward rounding when x==1. */ 38 if (unlikely (ix == 0x3f800000)) 39 return 0; 40 #endif 41 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000)) 42 { 43 /* x < 0x1p-126 or inf or nan. */ 44 if (ix * 2 == 0) 45 return __math_divzerof (1); 46 if (ix == 0x7f800000) /* log2(inf) == inf. */ 47 return x; 48 if ((ix & 0x80000000) || ix * 2 >= 0xff000000) 49 return __math_invalidf (x); 50 /* x is subnormal, normalize it. */ 51 ix = asuint (x * 0x1p23f); 52 ix -= 23 << 23; 53 } 54 55 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. 56 The range is split into N subintervals. 57 The ith subinterval contains z and c is near its center. */ 58 tmp = ix - OFF; 59 i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N; 60 top = tmp & 0xff800000; 61 iz = ix - top; 62 k = (int32_t) tmp >> 23; /* arithmetic shift */ 63 invc = T[i].invc; 64 logc = T[i].logc; 65 z = (double_t) asfloat (iz); 66 67 /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */ 68 r = z * invc - 1; 69 y0 = logc + (double_t) k; 70 71 /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */ 72 r2 = r * r; 73 y = A[1] * r + A[2]; 74 y = A[0] * r2 + y; 75 p = A[3] * r + y0; 76 y = y * r2 + p; 77 return eval_as_float (y); 78 } 79 #if USE_GLIBC_ABI 80 strong_alias (log2f, __log2f_finite) 81 hidden_alias (log2f, __ieee754_log2f) 82 #endif 83 84 TEST_SIG (S, F, 1, log2, 0.01, 11.1) 85 TEST_ULP (log2f, 0.26) 86 TEST_ULP_NONNEAREST (log2f, 0.5) 87 TEST_INTERVAL (log2f, 0, 0xffff0000, 10000) 88 TEST_INTERVAL (log2f, 0x1p-4, 0x1p4, 50000) 89 TEST_INTERVAL (log2f, 0, inf, 50000) 90