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Implementation of TI Basic's PRNG
/**
* Implementation of the TI BASIC PRNG
*
* Copyright (C) 2009, Tim Hentenaar
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
/* These are test results from runs of the GPL Rand function in a TI emulator */
uint16_t gpl_rand_test_results[][2] = {
{ 0x34, 0xe8dc },
{ 0x5b, 0x2b85 },
{ 0x57, 0x13b2 },
{ 0x4e, 0x46f3 },
{ 0x17, 0x4f18 },
{ 0x07, 0xa331 },
{ 0x20, 0xb48e }
};
/* The first ten sequences generated from RND */
const char *rnd_test_results[10] = {
".5291877823",
".3913360723",
".5343438556",
".3894551053",
".2555008073",
".5621974824",
".2553391677",
".5882911741",
".7000201301",
".0010849577",
};
/* Value of the seed after RANDOMIZE */
int32_t randomize_test_results[14][2] = {
{ 0, 0 },
{ 1, 0x4001 },
{ 2, 0x4002 },
{ 100, 0x4101 },
{ 200, 0x4102 },
{ 256, 0x4102 },
{ 1000, 0x410a },
{ 1500, 0x410f },
{ 10000, 0x4201 },
{ 100000, 0x420a },
{ 1000000, 0x4301 },
{ 1506631, 0x4301 },
{ -1, 0xbfff },
{ -100, 0xbeff }
};
/* The initial seed */
uint16_t seed = 0x3567;
/* RAND: Generate a pseudo-random number */
uint8_t gpl_rand(uint8_t divisor) {
/* Update the seed */
seed = ((uint32_t)(seed * 0x6fe5) & 0xffff) + 0x7ab9;
/* Swap bytes, and compute modulus */
return ((((seed & 0xff00) >> 8) | ((seed & 0x00ff) << 8)) % (!divisor ? 1 : divisor));
}
/* Equivalent to PRINT RND in TI Basic */
char *rnd() {
uint8_t rnds[7]; int i; char *n;
/* Try up to 64 times to come up with a non-zero pseudo-random integer */
for (i=0;i<63;i++) if ((rnds[0] = gpl_rand(100)) != 0) break;
if (rnds[0] == 0) return strdup("0");
/* Generate the rest of the set */
for (i=1;i<7;i++) rnds[i] = gpl_rand(100);
/* PRINT rounds up if the 6th number generated is >= 0x32 (50) */
if (rnds[5] >= 0x32) rnds[4]++;
/* PRINT prepends a leading zero if the first byte is < 0x10 */
if (rnds[0] < 0x10) {
memmove(&rnds[1],&rnds[0],6);
rnds[0] = 0;
}
/* Convert to string */
n = malloc(22);
snprintf(n,22,".%02d%02d%02d%02d%02d",rnds[0],rnds[1],rnds[2],rnds[3],rnds[4]);
return n;
}
/* TI Basic RANDOMIZE */
void randomize(int32_t s) {
/* Randomize appears to compute the seed this way */
int ex = 0; uint32_t x = (s < 0) ? (~s+1) : s;
if (s == 0) { seed = 0; return; }
/* The seed is: 0x4000 + (exponent << 8) + (s / 100^exponent) */
while ((x / 100) > 0) { ex++; x /= 100; }
seed = 0x4000 + (ex << 8) + x;
/* Handle negative numbers */
if (s < 0) seed = ~(seed-1);
}
int main() {
int i,x; char *f;
/* Test the GPL 'RAND' function */
printf("RAND:\n");
for (i=1;i<8;i++) {
x = gpl_rand(100);
printf("\tIteration: %02d, Modulus: %02d (0x%02x), Seed: 0x%04x [%s]\n",i,x,x,seed,
((x == gpl_rand_test_results[i-1][0] &&
seed == gpl_rand_test_results[i-1][1]) ? "PASS" : "FAIL"));
}
/* Reset seed */
seed = 0x3567;
/* Test TI Basic RND function */
printf("\nBasic RND():\n");
for (i=1;i<11;i++) {
f = rnd();
printf("\tIteration: %02d, Number: %s [%s]\n",i,f,
((!strncmp(f,rnd_test_results[i-1],strlen(rnd_test_results[i-1]))) ? "PASS" : "FAIL"));
free(f);
}
/* Test TI Basic RANDOMIZE function */
printf("\nBasic RANDOMIZE():\n");
for (i=1;i<15;i++) {
randomize(randomize_test_results[i-1][0]);
printf("\tIteration: %02d, Number: %d, Seed: 0x%04x [%s]\n",i,randomize_test_results[i-1][0],seed,
((seed == (uint16_t)randomize_test_results[i-1][1]) ? "PASS" : "FAIL"));
}
return 0;
}
/* vi:set ts=4 sw=4 expandtab sta: */
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