1 /* 2 * Single-precision 2^x function. 3 * 4 * Copyright (c) 2017-2018, 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 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 [-1/64, 1/64] (before rounding.) 18 Wrong count: 168353 (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 T __exp2f_data.tab 24 #define C __exp2f_data.poly 25 #define SHIFT __exp2f_data.shift_scaled 26 27 static inline uint32_t 28 top12 (float x) 29 { 30 return asuint (x) >> 20; 31 } 32 33 float 34 exp2f (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 (128.0f))) 44 { 45 /* |x| >= 128 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 > 0.0f) 51 return __math_oflowf (0); 52 if (x <= -150.0f) 53 return __math_uflowf (0); 54 #if WANT_ERRNO_UFLOW 55 if (x < -149.0f) 56 return __math_may_uflowf (0); 57 #endif 58 } 59 60 /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */ 61 kd = eval_as_double (xd + SHIFT); 62 ki = asuint64 (kd); 63 kd -= SHIFT; /* k/N for int k. */ 64 r = xd - kd; 65 66 /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ 67 t = T[ki % N]; 68 t += ki << (52 - EXP2F_TABLE_BITS); 69 s = asdouble (t); 70 z = C[0] * r + C[1]; 71 r2 = r * r; 72 y = C[2] * r + 1; 73 y = z * r2 + y; 74 y = y * s; 75 return eval_as_float (y); 76 } 77 #if USE_GLIBC_ABI 78 strong_alias (exp2f, __exp2f_finite) 79 hidden_alias (exp2f, __ieee754_exp2f) 80 #endif 81