1 /* 2 * Single-precision e^x 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 EXP2F_TABLE_BITS = 5 16 EXP2F_POLY_ORDER = 3 17 18 ULP error: 0.502 (nearest rounding.) 19 Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.) 20 Wrong count: 170635 (all nearest rounding wrong results with fma.) 21 Non-nearest ULP error: 1 (rounded ULP error) 22 */ 23 24 #define N (1 << EXP2F_TABLE_BITS) 25 #define InvLn2N __exp2f_data.invln2_scaled 26 #define T __exp2f_data.tab 27 #define C __exp2f_data.poly_scaled 28 29 static inline uint32_t 30 top12 (float x) 31 { 32 return asuint (x) >> 20; 33 } 34 35 float 36 expf (float x) 37 { 38 uint32_t abstop; 39 uint64_t ki, t; 40 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ 41 double_t kd, xd, z, r, r2, y, s; 42 43 xd = (double_t) x; 44 abstop = top12 (x) & 0x7ff; 45 if (unlikely (abstop >= top12 (88.0f))) 46 { 47 /* |x| >= 88 or x is nan. */ 48 if (asuint (x) == asuint (-INFINITY)) 49 return 0.0f; 50 if (abstop >= top12 (INFINITY)) 51 return x + x; 52 if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */ 53 return __math_oflowf (0); 54 if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */ 55 return __math_uflowf (0); 56 #if WANT_ERRNO_UFLOW 57 if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */ 58 return __math_may_uflowf (0); 59 #endif 60 } 61 62 /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */ 63 z = InvLn2N * xd; 64 65 /* Round and convert z to int, the result is in [-150*N, 128*N] and 66 ideally nearest int is used, otherwise the magnitude of r can be 67 bigger which gives larger approximation error. */ 68 #if TOINT_INTRINSICS 69 kd = roundtoint (z); 70 ki = converttoint (z); 71 #else 72 # define SHIFT __exp2f_data.shift 73 kd = eval_as_double (z + SHIFT); 74 ki = asuint64 (kd); 75 kd -= SHIFT; 76 #endif 77 r = z - kd; 78 79 /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ 80 t = T[ki % N]; 81 t += ki << (52 - EXP2F_TABLE_BITS); 82 s = asdouble (t); 83 z = C[0] * r + C[1]; 84 r2 = r * r; 85 y = C[2] * r + 1; 86 y = z * r2 + y; 87 y = y * s; 88 return eval_as_float (y); 89 } 90 #if USE_GLIBC_ABI 91 strong_alias (expf, __expf_finite) 92 hidden_alias (expf, __ieee754_expf) 93 #endif 94 95 TEST_SIG (S, F, 1, exp, -9.9, 9.9) 96 TEST_ULP (expf, 0.01) 97 TEST_ULP_NONNEAREST (expf, 0.5) 98 TEST_INTERVAL (expf, 0, 0xffff0000, 10000) 99 TEST_SYM_INTERVAL (expf, 0x1p-14, 0x1p8, 500000) 100