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/*
* Copyright (C) 2009-2011 Nick Johnson <nickbjohnson4224 at gmail.com>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
#include <stdint.h>
#include <float.h>
#include <errno.h>
#include <apps/math.h>
static float __sqrt_approx(float x) {
int32_t i;
// floats + bit manipulation = +inf fun!
i = *((int32_t*) &x);
i = 0x1FC00000 + (i >> 1);
x = *((float*) &i);
return x;
}
float sqrtf(float x) {
float y;
// filter out invalid/trivial inputs
if (x < 0.0) { errno = EDOM; return NAN; }
if (isnan(x)) return NAN;
if (isinf(x)) return INFINITY;
if (x == 0.0) return 0.0;
// guess square root (using bit manipulation)
y = __sqrt_approx(x);
// perform three iterations of approximation
// this number (3) is definitely optimal
y = 0.5 * (y + x / y);
y = 0.5 * (y + x / y);
y = 0.5 * (y + x / y);
return y;
}
double sqrt(double x) {
long double y, y1;
// filter out invalid/trivial inputs
if (x < 0.0) { errno = EDOM; return NAN; }
if (isnan(x)) return NAN;
if (isinf(x)) return INFINITY;
if (x == 0.0) return 0.0;
// guess square root (using bit manipulation)
y = __sqrt_approx(x);
// perform four iterations of approximation
// this number (4) is definitely optimal
y = 0.5 * (y + x / y);
y = 0.5 * (y + x / y);
y = 0.5 * (y + x / y);
y = 0.5 * (y + x / y);
// if guess was terribe (out of range of float)
// repeat approximation until convergence
if (y * y < x - 1.0 || y * y > x + 1.0) {
y1 = -1.0;
while (y != y1) {
y1 = y;
y = 0.5 * (y + x / y);
}
}
return y;
}
long double sqrtl(long double x) {
long double y, y1;
// filter out invalid/trivial inputs
if (x < 0.0) { errno = EDOM; return NAN; }
if (isnan(x)) return NAN;
if (isinf(x)) return INFINITY;
if (x == 0.0) return 0.0;
// guess square root (using bit manipulation)
y = __sqrt_approx(x);
// perform four iterations of approximation
// this number (4) is definitely optimal
y = 0.5 * (y + x / y);
y = 0.5 * (y + x / y);
y = 0.5 * (y + x / y);
y = 0.5 * (y + x / y);
// if guess was terribe (out of range of float)
// repeat approximation until convergence
if (y * y < x - 1.0 || y * y > x + 1.0) {
y1 = -1.0;
while (y != y1) {
y1 = y;
y = 0.5 * (y + x / y);
}
}
return y;
}
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