70 lines
1.5 KiB
C
70 lines
1.5 KiB
C
/* clang-format off */
|
|
/*
|
|
* Single-precision 2^x function.
|
|
*
|
|
* Copyright (c) 2017-2018, Arm Limited.
|
|
* SPDX-License-Identifier: MIT
|
|
*/
|
|
|
|
#include "libc/math/math.h"
|
|
#include "libc/math/libm.h"
|
|
#include "libc/math/exp2f_data.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 kd, xd, z, r, r2, y, s;
|
|
|
|
xd = (double_t)x;
|
|
abstop = top12(x) & 0x7ff;
|
|
if (predict_false(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);
|
|
}
|
|
|
|
/* 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);
|
|
}
|