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pop.c.txt
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// This has the programs for computing the number of 1-bits
// in a word, or byte, etc.
// Max line length is 57, to fit in hacker.book.
#include <stdio.h>
#include <stdlib.h> //To define "exit", req'd by XLC.
unsigned rotatel(unsigned x, int n) {
if ((unsigned)n > 63) {printf("rotatel, n out of range.\n"); exit(1);}
return (x << n) | (x >> (32 - n));
}
int pop0(unsigned x) {
x = (x & 0x55555555) + ((x >> 1) & 0x55555555);
x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
x = (x & 0x0F0F0F0F) + ((x >> 4) & 0x0F0F0F0F);
x = (x & 0x00FF00FF) + ((x >> 8) & 0x00FF00FF);
x = (x & 0x0000FFFF) + ((x >>16) & 0x0000FFFF);
return x;
}
int pop1(unsigned x) {
x = x - ((x >> 1) & 0x55555555);
x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
x = (x + (x >> 4)) & 0x0F0F0F0F;
x = x + (x >> 8);
x = x + (x >> 16);
return x & 0x0000003F;
}
/* Note: an alternative to the last three executable lines above is:
return x*0x01010101 >> 24;
if your machine has a fast multiplier (suggested by Jari Kirma). */
int pop2(unsigned x) {
unsigned n;
n = (x >> 1) & 033333333333; // Count bits in
x = x - n; // each 3-bit
n = (n >> 1) & 033333333333; // field.
x = x - n;
x = (x + (x >> 3)) & 030707070707; // 6-bit sums.
return x%63; // Add 6-bit sums.
}
/* An alternative to the "return" statement above is:
return ((x * 0404040404) >> 26) + // Add 6-bit sums.
(x >> 30);
which runs faster on most machines (suggested by Norbert Juffa). */
int pop3(unsigned x) {
unsigned n;
n = (x >> 1) & 0x77777777; // Count bits in
x = x - n; // each 4-bit
n = (n >> 1) & 0x77777777; // field.
x = x - n;
n = (n >> 1) & 0x77777777;
x = x - n;
x = (x + (x >> 4)) & 0x0F0F0F0F; // Get byte sums.
x = x*0x01010101; // Add the bytes.
return x >> 24;
}
int pop4(unsigned x) {
int n;
n = 0;
while (x != 0) {
n = n + 1;
x = x & (x - 1);
}
return n;
}
int pop5(unsigned x) {
int i, sum;
// Rotate and sum method // Shift right & subtract
sum = x; // sum = x;
for (i = 1; i <= 31; i++) { // while (x != 0) {
x = rotatel(x, 1); // x = x >> 1;
sum = sum + x; // sum = sum - x;
} // }
return -sum; // return sum;
}
int pop5a(unsigned x) {
int sum;
// Shift right & subtract
sum = x;
while (x != 0) {
x = x >> 1;
sum = sum - x;
}
return sum;
}
int pop6(unsigned x) { // Table lookup.
static char table[256] = {
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8};
return table[x & 0xFF] +
table[(x >> 8) & 0xFF] +
table[(x >> 16) & 0xFF] +
table[(x >> 24)];
}
// The following works only for 8-bit quantities.
int pop7(unsigned x) {
x = x*0x08040201; // Make 4 copies.
x = x >> 3; // So next step hits proper bits.
x = x & 0x11111111; // Every 4th bit.
x = x*0x11111111; // Sum the digits (each 0 or 1).
x = x >> 28; // Position the result.
return x;
}
// The following works only for 7-bit quantities.
int pop8(unsigned x) {
x = x*0x02040810; // Make 4 copies, left-adjusted.
x = x & 0x11111111; // Every 4th bit.
x = x*0x11111111; // Sum the digits (each 0 or 1).
x = x >> 28; // Position the result.
return x;
}
// The following works only for 15-bit quantities.
int pop9(unsigned x) {
unsigned long long y;
y = x * 0x0002000400080010ULL;
y = y & 0x1111111111111111ULL;
y = y * 0x1111111111111111ULL;
y = y >> 60;
return y;
}
int errors;
void error(int x, int y) {
errors = errors + 1;
printf("Error for x = %08x, got %08x\n", x, y);
}
int main() {
int i, n;
static int test[] = {0,0, 1,1, 2,1, 3,2, 4,1, 5,2, 6,2, 7,3,
8,1, 9,2, 10,2, 11,3, 12,2, 13,3, 14,3, 15,4, 16,1, 17,2,
0x3F,6, 0x40,1, 0x41,2, 0x7f,7, 0x80,1, 0x81,2, 0xfe,7, 0xff,8,
0x4000,1, 0x4001,2, 0x7000,3, 0x7fff,15,
0x55555555,16, 0xAAAAAAAA, 16, 0xFF000000,8, 0xC0C0C0C0,8,
0x0FFFFFF0,24, 0x80000000,1, 0xFFFFFFFF,32};
n = sizeof(test)/4;
printf("pop0:\n");
for (i = 0; i < n; i += 2) {
if (pop0(test[i]) != test[i+1]) error(test[i], pop0(test[i]));}
printf("pop1:\n");
for (i = 0; i < n; i += 2) {
if (pop1(test[i]) != test[i+1]) error(test[i], pop1(test[i]));}
printf("pop2:\n");
for (i = 0; i < n; i += 2) {
if (pop2(test[i]) != test[i+1]) error(test[i], pop2(test[i]));}
printf("pop3:\n");
for (i = 0; i < n; i += 2) {
if (pop3(test[i]) != test[i+1]) error(test[i], pop3(test[i]));}
printf("pop4:\n");
for (i = 0; i < n; i += 2) {
if (pop4(test[i]) != test[i+1]) error(test[i], pop4(test[i]));}
printf("pop5:\n");
for (i = 0; i < n; i += 2) {
if (pop5(test[i]) != test[i+1]) error(test[i], pop5(test[i]));}
printf("pop5a:\n");
for (i = 0; i < n; i += 2) {
if (pop5a(test[i]) != test[i+1]) error(test[i], pop5a(test[i]));}
printf("pop6:\n");
for (i = 0; i < n; i += 2) {
if (pop6(test[i]) != test[i+1]) error(test[i], pop6(test[i]));}
printf("pop7:\n");
for (i = 0; i < n; i += 2) {
if ((test[i] & 0xffffff00) == 0)
if (pop7(test[i]) != test[i+1]) error(test[i], pop7(test[i]));}
printf("pop8:\n");
for (i = 0; i < n; i += 2) {
if ((test[i] & 0xffffff80) == 0)
if (pop8(test[i]) != test[i+1]) error(test[i], pop8(test[i]));}
printf("pop9:\n");
for (i = 0; i < n; i += 2) {
if ((test[i] & 0xffff8000) == 0)
if (pop9(test[i]) != test[i+1]) error(test[i], pop9(test[i]));}
if (errors == 0)
printf("Passed all %d cases.\n", sizeof(test)/8);
}