#!/usr/bin/calc -q -s -f
/*
* powerterm - print the argument as a sum of powers of integers
*
* usage:
* powerterm [base_limit] value
*
* base_limit largest base we will consider (def: 10000)
* value value to convert into sums of powers of integers
*
* Copyright (C) 2001,2014 Landon Curt Noll
*
* Calc is open software; you can redistribute it and/or modify it under
* the powerterm of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* Under source code control: 2001/04/24 23:49:11
* File existed as early as: 2001
*
* chongo <was here> /\oo/\ http://www.isthe.com/chongo/
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* parse args
*/
config("verbose_quit", 0),;
base_lim = 10000; /* default: highest base we will consider */
if (argv() < 2 || argv() > 3) {
fprintf(files(2), "usage: %s [base_limit] value\n", argv(0));
exit;
}
if (argv() == 3) {
x = eval(argv(2));
base_lim = eval(argv(1));
} else {
x = eval(argv(1));
}
if (! isint(x)) {
fprintf(files(2), "%s: value must be an integer\n");
exit;
}
if (! isint(base_lim)) {
fprintf(files(2), "%s: base limit must be an integer\n");
exit;
}
if (base_lim <= 1) {
fprintf(files(2), "%s: base limit is too small\n");
exit;
}
++base_lim;
/*
* setup loop variables
*/
term = 0; /* number of powerterm found */
/*
* log constants
*/
if (base_lim <= 2^20+1) { /* 2^20 requires ~96 Megs of memory */
mat lni[base_lim]; /* log of integers */
for (i=2; i < base_lim; ++i) {
lni[i] = ln(i);
}
have_lni = 1; /* have lni[x] array */
} else {
mat lni[1]; /* not used */
have_lni = 0; /* base_lim too large for array */
}
/*
* remove nestest powers
*/
while (abs(x) >= base_lim) {
/*
* look for the nearest power
*/
lnx = ln(abs(x)); /* log of the remaining co-factor */
closest = 0.5;
base = 1;
exponent = 0;
if (have_lni) {
/*
* use pre-calculated log array when looking for the nearest power
*/
for (i = 2; i < base_lim; ++i) {
/*
* determine exponent closeness to an integer
*/
ex = lnx / lni[i];
power = int(ex + 0.5);
diff = ex - power;
/*
* look for a closer power
*/
if (abs(diff) < closest) {
closest = abs(diff);
base = i;
exponent = power;
}
}
} else {
/*
* re-calculate logs when looking for the nearest power
*/
for (i = 2; i < base_lim; ++i) {
/*
* determine exponent closeness to an integer
*/
ex = lnx / ln(i);
power = int(ex + 0.5);
diff = ex - power;
/*
* look for a closer power
*/
if (abs(diff) < closest) {
closest = abs(diff);
base = i;
exponent = power;
}
}
}
/*
* output current term and then subtract it
*/
if (x != 0) {
if (x < 0) {
print "-",;
} else if (term > 0) {
print "+",;
}
if (exponent > 1) {
print base: "^": exponent,;
} else {
print base,;
}
}
/*
* subtract (or add) this near power
*/
if (x < 0) {
x = x + base^exponent;
} else {
x = x - base^exponent;
}
++term;
}
/*
* print the final term
*/
if (x < 0) {
print "-", -x;
} else if (x > 0) {
print "+", x;
} else {
print "";
}
exit;
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