ClickHouse/libs/libglibc-compatibility/musl/exp2f.c

70 lines
1.5 KiB
C
Raw Normal View History

2019-09-28 14:36:56 +00:00
/*
* Single-precision 2^x function.
2018-05-11 11:54:25 +00:00
*
2019-09-28 14:36:56 +00:00
* Copyright (c) 2017-2018, Arm Limited.
* SPDX-License-Identifier: MIT
2018-05-11 11:54:25 +00:00
*/
#include <math.h>
#include <stdint.h>
2019-09-28 14:36:56 +00:00
#include "libm.h"
#include "exp2f_data.h"
2018-05-11 11:54:25 +00:00
2019-09-28 14:36:56 +00:00
/*
EXP2F_TABLE_BITS = 5
EXP2F_POLY_ORDER = 3
2018-05-11 11:54:25 +00:00
2019-09-28 14:36:56 +00:00
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)
*/
2018-05-11 11:54:25 +00:00
2019-09-28 14:36:56 +00:00
#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;
}
2018-05-11 11:54:25 +00:00
float exp2f(float x)
{
2019-09-28 14:36:56 +00:00
uint32_t abstop;
uint64_t ki, t;
double_t kd, xd, z, r, r2, y, s;
2018-05-11 11:54:25 +00:00
2019-09-28 14:36:56 +00:00
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);
2018-05-11 11:54:25 +00:00
}
2019-09-28 14:36:56 +00:00
/* 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;
2018-05-11 11:54:25 +00:00
2019-09-28 14:36:56 +00:00
/* 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);
2018-05-11 11:54:25 +00:00
}