2 * Single-precision e^x function.
4 * Copyright (c) 2017-2019, Arm Limited.
5 * SPDX-License-Identifier: MIT
10 #include "math_config.h"
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)
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
27 static inline uint32_t
30 return asuint (x) >> 20;
38 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
39 double_t kd, xd, z, r, r2, y, s;
42 abstop = top12 (x) & 0x7ff;
43 if (unlikely (abstop >= top12 (88.0f)))
45 /* |x| >= 88 or x is nan. */
46 if (asuint (x) == asuint (-INFINITY))
48 if (abstop >= top12 (INFINITY))
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);
55 if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
56 return __math_may_uflowf (0);
60 /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
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. */
68 ki = converttoint (z);
70 # define SHIFT __exp2f_data.shift
71 kd = eval_as_double (z + SHIFT);
77 /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
79 t += ki << (52 - EXP2F_TABLE_BITS);
86 return eval_as_float (y);
89 strong_alias (expf, __expf_finite)
90 hidden_alias (expf, __ieee754_expf)