2 * Single-precision 2^x function.
4 * Copyright (c) 2017-2018, Arm Limited.
5 * SPDX-License-Identifier: MIT
11 #include "exp2f_data.h"
17 ULP error: 0.502 (nearest rounding.)
18 Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
19 Wrong count: 168353 (all nearest rounding wrong results with fma.)
20 Non-nearest ULP error: 1 (rounded ULP error)
23 #define N (1 << EXP2F_TABLE_BITS)
24 #define T __exp2f_data.tab
25 #define C __exp2f_data.poly
26 #define SHIFT __exp2f_data.shift_scaled
28 static inline uint32_t top12(float x
)
30 return asuint(x
) >> 20;
37 double_t kd
, xd
, z
, r
, r2
, y
, s
;
40 abstop
= top12(x
) & 0x7ff;
41 if (predict_false(abstop
>= top12(128.0f
))) {
42 /* |x| >= 128 or x is nan. */
43 if (asuint(x
) == asuint(-INFINITY
))
45 if (abstop
>= top12(INFINITY
))
48 return __math_oflowf(0);
50 return __math_uflowf(0);
53 /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */
54 kd
= eval_as_double(xd
+ SHIFT
);
56 kd
-= SHIFT
; /* k/N for int k. */
59 /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
61 t
+= ki
<< (52 - EXP2F_TABLE_BITS
);
68 return eval_as_float(y
);