1 /* 2 * Single-precision 2^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 [-1/64, 1/64] (before rounding.) 20 Wrong count: 168353 (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 T __exp2f_data.tab 26 #define C __exp2f_data.poly 27 #define SHIFT __exp2f_data.shift_scaled 28 29 static inline uint32_t 30 top12 (float x) 31 { 32 return asuint (x) >> 20; 33 } 34 35 float 36 exp2f (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 (128.0f))) 46 { 47 /* |x| >= 128 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 > 0.0f) 53 return __math_oflowf (0); 54 if (x <= -150.0f) 55 return __math_uflowf (0); 56 #if WANT_ERRNO_UFLOW 57 if (x < -149.0f) 58 return __math_may_uflowf (0); 59 #endif 60 } 61 62 /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */ 63 kd = eval_as_double (xd + SHIFT); 64 ki = asuint64 (kd); 65 kd -= SHIFT; /* k/N for int k. */ 66 r = xd - kd; 67 68 /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ 69 t = T[ki % N]; 70 t += ki << (52 - EXP2F_TABLE_BITS); 71 s = asdouble (t); 72 z = C[0] * r + C[1]; 73 r2 = r * r; 74 y = C[2] * r + 1; 75 y = z * r2 + y; 76 y = y * s; 77 return eval_as_float (y); 78 } 79 #if USE_GLIBC_ABI 80 strong_alias (exp2f, __exp2f_finite) 81 hidden_alias (exp2f, __ieee754_exp2f) 82 #endif 83 84 TEST_SIG (S, F, 1, exp2, -9.9, 9.9) 85 TEST_ULP (exp2f, 0.01) 86 TEST_ULP_NONNEAREST (exp2f, 0.5) 87 TEST_INTERVAL (exp2f, 0, 0xffff0000, 10000) 88 TEST_SYM_INTERVAL (exp2f, 0x1p-14, 0x1p8, 50000) 89