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/*
* lfsr.c
*
*/
#include <stdio.h>
#include "datatypes.h"
uint32_t
parity(uint32_t x) {
x ^= (x >> 16);
x ^= (x >> 8);
x ^= (x >> 4);
x ^= (x >> 2);
x ^= (x >> 1);
return x & 1;
}
/* typedef struct { */
/* uint32_t register[8]; */
/* } lfsr_t; */
void
compute_period(uint32_t feedback_polynomial) {
int i;
v32_t lfsr;
v32_t mask;
mask.value = feedback_polynomial;
lfsr.value = 1;
printf("polynomial: %s\t", v32_bit_string(mask));
for (i=0; i < 256; i++) {
/* printf("%s\n", v32_bit_string(lfsr)); */
if (parity(mask.value & lfsr.value))
lfsr.value = ((lfsr.value << 1) | 1) & 0xff;
else
lfsr.value = (lfsr.value << 1) & 0xff;
/* now halt if we're back at the initial state */
if (lfsr.value == 1) {
printf("period: %d\n", i);
break;
}
}
}
uint32_t poly0 = 223;
uint32_t polynomials[39] = {
31,
47,
55,
59,
61,
79,
87,
91,
103,
107,
109,
115,
117,
121,
143,
151,
157,
167,
171,
173,
179,
181,
185,
199,
203,
205,
211,
213,
227,
229,
233,
241,
127,
191,
223,
239,
247,
251,
253
};
char binary_string[32];
char *
u32_bit_string(uint32_t x, unsigned int length) {
unsigned int mask;
int index;
mask = 1 << length;
index = 0;
for (; mask > 0; mask >>= 1)
if ((x & mask) == 0)
binary_string[index++] = '0';
else
binary_string[index++] = '1';
binary_string[index++] = 0; /* NULL terminate string */
return binary_string;
}
extern int octet_weight[256];
unsigned int
weight(uint32_t poly) {
int wt = 0;
/* note: endian-ness makes no difference */
wt += octet_weight[poly & 0xff];
wt += octet_weight[(poly >> 8) & 0xff];
wt += octet_weight[(poly >> 16) & 0xff];
wt += octet_weight[(poly >> 24)];
return wt;
}
#define MAX_PERIOD 65535
#define debug_print 0
int
period(uint32_t poly) {
int i;
uint32_t x;
/* set lfsr to 1 */
x = 1;
#if debug_print
printf("%d:\t%s\n", 0, u32_bit_string(x,8));
#endif
for (i=1; i < MAX_PERIOD; i++) {
if (x & 1)
x = (x >> 1) ^ poly;
else
x = (x >> 1);
#if debug_print
/* print for a sanity check */
printf("%d:\t%s\n", i, u32_bit_string(x,8));
#endif
/* check for return to original value */
if (x == 1)
return i;
}
return i;
}
/*
* weight distribution computes the weight distribution of the
* code generated by the polynomial poly
*/
#define MAX_LEN 8
#define MAX_WEIGHT (1 << MAX_LEN)
int A[MAX_WEIGHT+1];
void
weight_distribution2(uint32_t poly, int *A) {
int i;
uint32_t x;
/* zeroize array */
for (i=0; i < MAX_WEIGHT+1; i++)
A[i] = 0;
/* loop over all input sequences */
/* set lfsr to 1 */
x = 1;
#if debug_print
printf("%d:\t%s\n", 0, u32_bit_string(x,8));
#endif
for (i=1; i < MAX_PERIOD; i++) {
if (x & 1)
x = (x >> 1) ^ poly;
else
x = (x >> 1);
#if debug_print
/* print for a sanity check */
printf("%d:\t%s\n", i, u32_bit_string(x,8));
#endif
/* increment weight */
wt += (x & 1);
/* check for return to original value */
if (x == 1)
break;
}
/* set zero */
A[0] = 0;
}
void
weight_distribution(uint32_t poly, int *A) {
int i;
uint32_t x;
/* zeroize array */
for (i=0; i < MAX_WEIGHT+1; i++)
A[i] = 0;
/* set lfsr to 1 */
x = 1;
#if debug_print
printf("%d:\t%s\n", 0, u32_bit_string(x,8));
#endif
for (i=1; i < MAX_PERIOD; i++) {
if (x & 1)
x = (x >> 1) ^ poly;
else
x = (x >> 1);
#if debug_print
/* print for a sanity check */
printf("%d:\t%s\n", i, u32_bit_string(x,8));
#endif
/* compute weight, increment proper element */
A[weight(x)]++;
/* check for return to original value */
if (x == 1)
break;
}
/* set zero */
A[0] = 0;
}
int
main () {
int i,j;
v32_t x;
v32_t p;
/* originally 0xaf */
p.value = 0x9;
printf("polynomial: %s\tperiod: %d\n",
u32_bit_string(p.value,8), period(p.value));
/* compute weight distribution */
weight_distribution(p.value, A);
/* print weight distribution */
for (i=0; i <= 8; i++) {
printf("A[%d]: %d\n", i, A[i]);
}
#if 0
for (i=0; i < 39; i++) {
printf("polynomial: %s\tperiod: %d\n",
u32_bit_string(polynomials[i],8), period(polynomials[i]));
/* compute weight distribution */
weight_distribution(p.value, A);
/* print weight distribution */
for (j=0; j <= 8; j++) {
printf("A[%d]: %d\n", j, A[j]);
}
}
#endif
{
int bits = 8;
uint32_t y;
for (y=0; y < (1 << bits); y++) {
printf("polynomial: %s\tweight: %d\tperiod: %d\n",
u32_bit_string(y,bits), weight(y), period(y));
/* compute weight distribution */
weight_distribution(y, A);
/* print weight distribution */
for (j=0; j <= 8; j++) {
printf("A[%d]: %d\n", j, A[j]);
}
}
}
return 0;
}
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