1 /* 2 * Single-precision e^x function. 3 * 4 * Copyright (c) 2017-2019, Arm Limited. 5 * SPDX-License-Identifier: MIT 6 */ 7 8 #include <math.h> 9 #include <stdint.h> 10 #include "math_config.h" 11 12 /* 13 EXP2F_TABLE_BITS = 5 14 EXP2F_POLY_ORDER = 3 15 16 ULP error: 0.502 (nearest rounding.) 17 Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.) 18 Wrong count: 170635 (all nearest rounding wrong results with fma.) 19 Non-nearest ULP error: 1 (rounded ULP error) 20 */ 21 22 #define N (1 << EXP2F_TABLE_BITS) 23 #define InvLn2N __exp2f_data.invln2_scaled 24 #define T __exp2f_data.tab 25 #define C __exp2f_data.poly_scaled 26 27 static inline uint32_t 28 top12 (float x) 29 { 30 return asuint (x) >> 20; 31 } 32 33 float 34 expf (float x) 35 { 36 uint32_t abstop; 37 uint64_t ki, t; 38 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ 39 double_t kd, xd, z, r, r2, y, s; 40 41 xd = (double_t) x; 42 abstop = top12 (x) & 0x7ff; 43 if (unlikely (abstop >= top12 (88.0f))) 44 { 45 /* |x| >= 88 or x is nan. */ 46 if (asuint (x) == asuint (-INFINITY)) 47 return 0.0f; 48 if (abstop >= top12 (INFINITY)) 49 return x + x; 50 if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */ 51 return __math_oflowf (0); 52 if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */ 53 return __math_uflowf (0); 54 #if WANT_ERRNO_UFLOW 55 if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */ 56 return __math_may_uflowf (0); 57 #endif 58 } 59 60 /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */ 61 z = InvLn2N * xd; 62 63 /* Round and convert z to int, the result is in [-150*N, 128*N] and 64 ideally nearest int is used, otherwise the magnitude of r can be 65 bigger which gives larger approximation error. */ 66 #if TOINT_INTRINSICS 67 kd = roundtoint (z); 68 ki = converttoint (z); 69 #else 70 # define SHIFT __exp2f_data.shift 71 kd = eval_as_double (z + SHIFT); 72 ki = asuint64 (kd); 73 kd -= SHIFT; 74 #endif 75 r = z - kd; 76 77 /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ 78 t = T[ki % N]; 79 t += ki << (52 - EXP2F_TABLE_BITS); 80 s = asdouble (t); 81 z = C[0] * r + C[1]; 82 r2 = r * r; 83 y = C[2] * r + 1; 84 y = z * r2 + y; 85 y = y * s; 86 return eval_as_float (y); 87 } 88 #if USE_GLIBC_ABI 89 strong_alias (expf, __expf_finite) 90 hidden_alias (expf, __ieee754_expf) 91 #endif 92