mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 11:37:35 +00:00
108 lines
4.3 KiB
C
108 lines
4.3 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
|
||
│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
|
||
╚──────────────────────────────────────────────────────────────────────────────╝
|
||
│ │
|
||
│ Musl Libc │
|
||
│ Copyright © 2005-2014 Rich Felker, et al. │
|
||
│ │
|
||
│ Permission is hereby granted, free of charge, to any person obtaining │
|
||
│ a copy of this software and associated documentation files (the │
|
||
│ "Software"), to deal in the Software without restriction, including │
|
||
│ without limitation the rights to use, copy, modify, merge, publish, │
|
||
│ distribute, sublicense, and/or sell copies of the Software, and to │
|
||
│ permit persons to whom the Software is furnished to do so, subject to │
|
||
│ the following conditions: │
|
||
│ │
|
||
│ The above copyright notice and this permission notice shall be │
|
||
│ included in all copies or substantial portions of the Software. │
|
||
│ │
|
||
│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
|
||
│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
|
||
│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
|
||
│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
|
||
│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
|
||
│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
|
||
│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
|
||
│ │
|
||
╚─────────────────────────────────────────────────────────────────────────────*/
|
||
#include "libc/bits/likely.h"
|
||
#include "libc/math.h"
|
||
#include "libc/tinymath/exp2f_data.internal.h"
|
||
#include "libc/tinymath/internal.h"
|
||
#ifndef TINY
|
||
|
||
asm(".ident\t\"\\n\\n\
|
||
Double-precision math functions (MIT License)\\n\
|
||
Copyright 2018 ARM Limited\"");
|
||
asm(".include \"libc/disclaimer.inc\"");
|
||
/* clang-format off */
|
||
|
||
/*
|
||
* Single-precision 2^x function.
|
||
*
|
||
* Copyright (c) 2017-2018, Arm Limited.
|
||
* SPDX-License-Identifier: MIT
|
||
*/
|
||
|
||
/*
|
||
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;
|
||
}
|
||
|
||
/**
|
||
* Returns 2^𝑥.
|
||
*/
|
||
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 (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);
|
||
}
|
||
|
||
/* 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);
|
||
}
|
||
|
||
#endif /* !TINY */
|