User:VIxen/Code - Revision history

VIxen: no sense in if...break when I can add the condition to the for-clause, smh

2023-03-05T13:23:57Z

no sense in if...break when I can add the condition to the for-clause, smh

← Older revision		Revision as of 13:23, 5 March 2023
Line 92:		Line 92:
	to omit boring 0-(2k+1)-4k triads for large k */		to omit boring 0-(2k+1)-4k triads for large k */

	for (mid = top - (top/6) - 3; mid >= minmid; mid--){		for (mid = top - (top/6) - 3; (mid >= minmid) && (x > MINX); mid--){
	/* mid starts a bit lower than top to omit boring triads like 0-4k-4(k+1) */		/* mid starts a bit lower than top to omit boring triads like 0-4k-4(k+1) */

Line 107:		Line 107:
	val = log2(x);		val = log2(x);
	fprintf(res, "%d,%d,%f,%.3f,%.3f\n", mid, top, 1200.val, 1./val, val top);		fprintf(res, "%d,%d,%f,%.3f,%.3f\n", mid, top, 1200.val, 1./val, val top);
	~~if (x < MINX) break;~~
	}		}
	}		}

VIxen: 10x speedup of printIsodiffTriads by keeping it simple

2023-03-05T13:12:01Z

10x speedup of printIsodiffTriads by keeping it simple

← Older revision		Revision as of 13:12, 5 March 2023
Line 71:		Line 71:
	int printIsodiffTriads(){		int printIsodiffTriads(){
	/* Find triads in ETs that satisfy the frequency relation bottom + top == 2 * middle.		/* Find triads in ETs that satisfy the frequency relation bottom + top == 2 * middle.
	The root of x^{top} - 2 * x^{mid} + 1 is found by the Newton-Raphson method		The root of x^{top} - 2 * x^{mid} + 1 is found by the Newton-Raphson method. */
	~~after dividing the polynomial by x-1~~. */

	const int MINDEG = 12;		const int MINDEG = 12;
Line 96:		Line 95:
	/* mid starts a bit lower than top to omit boring triads like 0-4k-4(k+1) */		/* mid starts a bit lower than top to omit boring triads like 0-4k-4(k+1) */

	do{ /* Step of Newton-Raphson~~. TODO: avoid summing lots of powers,~~		do{ /* Step of Newton-Raphson */
	~~differentiate (x^k-1)/(x-1) like a fraction instead.~~ */		pwr = pow(x, mid);
	pwr = x;		val = 1. - 2. * pwr;
	val = -~~x - 1~~.;		der = -2. * mid * pwr / x;
	der = -1.;		pwr *= pow(x, top - mid);
	~~for (p = 2; p <~~ mid~~; p++){~~		val += pwr;
	pwr *= x;		der += top * pwr / x;
	~~val -=~~ pwr;
	~~der -~~= ~~pwr * p;~~
	}
	~~for~~ (~~; p <~~ top~~; p++~~){
	~~pwr *= x~~;
	val += pwr;
	der += pwr * p;
	}
	x -= val / der;		x -= val / der;
	} while (val > 1e-5);		} while (val > 1e-5);

VIxen: DR triad finder code

2023-03-04T20:31:14Z

DR triad finder code

New page

<syntaxhighlight lang="c">
/* This is free and unencumbered software released into the public domain.

Anyone is free to copy, modify, publish, use, compile, sell, or
distribute this software, either in source code form or as a compiled
binary, for any purpose, commercial or non-commercial, and by any
means.

In jurisdictions that recognize copyright laws, the author or authors
of this software dedicate any and all copyright interest in the
software to the public domain. We make this dedication for the benefit
of the public at large and to the detriment of our heirs and
successors. We intend this dedication to be an overt act of
relinquishment in perpetuity of all present and future rights to this
software under copyright law.

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 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.

For more information, please refer to <http://unlicense.org/> */

#include<stdio.h>
#include<math.h>

int printAdditiveTriads(){
/* Find triads in ETs that satisfy the frequency relation bottom + middle == top.
The root of x^{top} - x^{mid} - 1 is found by the Newton-Raphson method. */

const int MINDEG = 5;
const int MAXDEG = 1400; /* so that .csv have <1M lines */
/* const double MINX = 1.0002714; */
const double MAXX = 1.3248; /* plastic number */
const char* respath = "res.csv";

int mid, minmid, top, p;
double x, val, der, pwr;

FILE *res = fopen(respath, "w");
/* if (!res) printf ("File open error\n"); */
fprintf(res, "mid,top,gencents,ed2,octaves\n");

for (top = MINDEG; top <= MAXDEG; top++){
x = MAXX;
minmid = (top>>4);
for (mid = top - 1; mid > minmid; mid--){
do{ /* Step of Newton-Raphson */
pwr = pow(x, mid);
val = -1. - pwr;
der = -mid * pwr / x;
pwr *= pow(x, top - mid);
val += pwr;
der += top * pwr / x;
x -= val / der;
} while (val > 1e-5);

val = log2(x);
fprintf(res, "%d,%d,%f,%.3f,%.3f\n", mid, top, 1200.*val, 1./val, val * top);
/* if (x < MINX) break; */
}
}

fclose(res);
return 0;
}

int printIsodiffTriads(){
/* Find triads in ETs that satisfy the frequency relation bottom + top == 2 * middle.
The root of x^{top} - 2 * x^{mid} + 1 is found by the Newton-Raphson method
after dividing the polynomial by x-1. */

const int MINDEG = 12;
const int MAXDEG = 2009; /* to fit 6.46 octaves of 311ed2 */
const double MINX = 1.0002714; /* 2554ed2 */
const double MAXX = 1.1487; /* 5ed2 */
const char* respath = "res1.csv";

int mid, minmid, top, p;
double x, val, der, pwr;

FILE *res = fopen(respath, "w");
/* if (!res) printf ("File open error\n"); */
fprintf(res, "mid,top,gencents,ed2,octaves\n");

for (top = MINDEG; top <= MAXDEG; top++){
x = MAXX;
minmid = (top>>1) + (top>>6) + 1;
/* mid stops substantially higher than top/2
to omit boring 0-(2k+1)-4k triads for large k */

for (mid = top - (top/6) - 3; mid >= minmid; mid--){
/* mid starts a bit lower than top to omit boring triads like 0-4k-4(k+1) */

do{ /* Step of Newton-Raphson. TODO: avoid summing lots of powers,
differentiate (x^k-1)/(x-1) like a fraction instead. */
pwr = x;
val = -x - 1.;
der = -1.;
for (p = 2; p < mid; p++){
pwr *= x;
val -= pwr;
der -= pwr * p;
}
for (; p < top; p++){
pwr *= x;
val += pwr;
der += pwr * p;
}
x -= val / der;
} while (val > 1e-5);

val = log2(x);
fprintf(res, "%d,%d,%f,%.3f,%.3f\n", mid, top, 1200.*val, 1./val, val * top);
if (x < MINX) break;
}
}

fclose(res);
return 0;
}
</syntaxhighlight>