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ziggurat-constants.c
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ziggurat-constants.c
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#include <float.h>
#include <math.h>
#include <stdio.h>
#define M_SQRTPI_OVER_SQRT2 1.253314137315500251207882642405522627L
#define M_1_OVER_SQRT2 0.707106781186547524400844362104849039L
#define ziggurat_f(x) expl(-0.5 * x * x)
#define ziggurat_f_inv(y) sqrtl(-2 * logl(y))
#define ziggurat_f_int_x_to_inf(x) \
-(M_SQRTPI_OVER_SQRT2 * (erfl(x * M_1_OVER_SQRT2) - 1))
int
main(void)
{
unsigned count = 0;
printf("#define ZIGGURAT_COUNT ");
scanf("%u", &count);
long double min = 0, max = 10, pmin, pmax;
long double area, R;
do {
int tobig = 0;
pmin = min;
pmax = max;
R = 0.5 * (min + max);
long double x = R;
area = R * ziggurat_f(R) + ziggurat_f_int_x_to_inf(R);
for (unsigned i = 1; i < count && !tobig; i++) {
x = area / x + ziggurat_f(x);
if (x > 1) tobig = 1;
else x = ziggurat_f_inv(x);
}
if (tobig)
min = R;
else
max = R;
} while (pmin < R && R < pmax);
printf("#define ZIGGURAT_R %.*Lg\n", DECIMAL_DIG, R);
printf("#define ZIGGURAT_AREA %.*Lg\n", DECIMAL_DIG, area);
}
/*
* Copyright (c) 2021 Olaf Berstein
* 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.
*/