You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
80 lines
1.7 KiB
80 lines
1.7 KiB
/* |
|
* Single-precision 2^x function. |
|
* |
|
* Copyright (c) 2017-2018, Arm Limited. |
|
* SPDX-License-Identifier: MIT |
|
*/ |
|
|
|
#include <math.h> |
|
#include <stdint.h> |
|
#include "math_config.h" |
|
|
|
/* |
|
EXP2F_TABLE_BITS = 5 |
|
EXP2F_POLY_ORDER = 3 |
|
|
|
ULP error: 0.502 (nearest rounding.) |
|
Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.) |
|
Wrong count: 168353 (all nearest rounding wrong results with fma.) |
|
Non-nearest ULP error: 1 (rounded ULP error) |
|
*/ |
|
|
|
#define N (1 << EXP2F_TABLE_BITS) |
|
#define T __exp2f_data.tab |
|
#define C __exp2f_data.poly |
|
#define SHIFT __exp2f_data.shift_scaled |
|
|
|
static inline uint32_t |
|
top12 (float x) |
|
{ |
|
return asuint (x) >> 20; |
|
} |
|
|
|
float |
|
exp2f (float x) |
|
{ |
|
uint32_t abstop; |
|
uint64_t ki, t; |
|
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ |
|
double_t kd, xd, z, r, r2, y, s; |
|
|
|
xd = (double_t) x; |
|
abstop = top12 (x) & 0x7ff; |
|
if (unlikely (abstop >= top12 (128.0f))) |
|
{ |
|
/* |x| >= 128 or x is nan. */ |
|
if (asuint (x) == asuint (-INFINITY)) |
|
return 0.0f; |
|
if (abstop >= top12 (INFINITY)) |
|
return x + x; |
|
if (x > 0.0f) |
|
return __math_oflowf (0); |
|
if (x <= -150.0f) |
|
return __math_uflowf (0); |
|
#if WANT_ERRNO_UFLOW |
|
if (x < -149.0f) |
|
return __math_may_uflowf (0); |
|
#endif |
|
} |
|
|
|
/* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */ |
|
kd = eval_as_double (xd + SHIFT); |
|
ki = asuint64 (kd); |
|
kd -= SHIFT; /* k/N for int k. */ |
|
r = xd - kd; |
|
|
|
/* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ |
|
t = T[ki % N]; |
|
t += ki << (52 - EXP2F_TABLE_BITS); |
|
s = asdouble (t); |
|
z = C[0] * r + C[1]; |
|
r2 = r * r; |
|
y = C[2] * r + 1; |
|
y = z * r2 + y; |
|
y = y * s; |
|
return eval_as_float (y); |
|
} |
|
#if USE_GLIBC_ABI |
|
strong_alias (exp2f, __exp2f_finite) |
|
hidden_alias (exp2f, __ieee754_exp2f) |
|
#endif
|
|
|