1 /* 2 * Single-precision log 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 LOGF_TABLE_BITS = 4 16 LOGF_POLY_ORDER = 4 17 18 ULP error: 0.818 (nearest rounding.) 19 Relative error: 1.957 * 2^-26 (before rounding.) 20 */ 21 22 #define T __logf_data.tab 23 #define A __logf_data.poly 24 #define Ln2 __logf_data.ln2 25 #define N (1 << LOGF_TABLE_BITS) 26 #define OFF 0x3f330000 27 28 float 29 logf (float x) 30 { 31 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ 32 double_t z, r, r2, y, y0, invc, logc; 33 uint32_t ix, iz, tmp; 34 int k, i; 35 36 ix = asuint (x); 37 #if WANT_ROUNDING 38 /* Fix sign of zero with downward rounding when x==1. */ 39 if (unlikely (ix == 0x3f800000)) 40 return 0; 41 #endif 42 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000)) 43 { 44 /* x < 0x1p-126 or inf or nan. */ 45 if (ix * 2 == 0) 46 return __math_divzerof (1); 47 if (ix == 0x7f800000) /* log(inf) == inf. */ 48 return x; 49 if ((ix & 0x80000000) || ix * 2 >= 0xff000000) 50 return __math_invalidf (x); 51 /* x is subnormal, normalize it. */ 52 ix = asuint (x * 0x1p23f); 53 ix -= 23 << 23; 54 } 55 56 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. 57 The range is split into N subintervals. 58 The ith subinterval contains z and c is near its center. */ 59 tmp = ix - OFF; 60 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N; 61 k = (int32_t) tmp >> 23; /* arithmetic shift */ 62 iz = ix - (tmp & 0xff800000); 63 invc = T[i].invc; 64 logc = T[i].logc; 65 z = (double_t) asfloat (iz); 66 67 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */ 68 r = z * invc - 1; 69 y0 = logc + (double_t) k * Ln2; 70 71 /* Pipelined polynomial evaluation to approximate log1p(r). */ 72 r2 = r * r; 73 y = A[1] * r + A[2]; 74 y = A[0] * r2 + y; 75 y = y * r2 + (y0 + r); 76 return eval_as_float (y); 77 } 78 #if USE_GLIBC_ABI 79 strong_alias (logf, __logf_finite) 80 hidden_alias (logf, __ieee754_logf) 81 #endif 82 83 TEST_SIG (S, F, 1, log, 0.01, 11.1) 84 TEST_ULP (logf, 0.32) 85 TEST_ULP_NONNEAREST (logf, 0.5) 86 TEST_INTERVAL (logf, 0, 0xffff0000, 10000) 87 TEST_INTERVAL (logf, 0x1p-4, 0x1p4, 500000) 88 TEST_INTERVAL (logf, 0, inf, 50000) 89