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4 changed files with 291 additions and 1 deletions
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// This has the programs for computing the number of 1-bits
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// in a word, or byte, etc.
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// Max line length is 57, to fit in hacker.book.
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#include <stdio.h> |
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#include <stdlib.h> //To define "exit", req'd by XLC. |
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#include <ctime> |
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unsigned rotatel(unsigned x, int n) { |
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if ((unsigned)n > 63) {printf("rotatel, n out of range.\n"); exit(1);} |
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return (x << n) | (x >> (32 - n)); |
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} |
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int pop0(unsigned x) { |
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x = (x & 0x55555555) + ((x >> 1) & 0x55555555); |
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x = (x & 0x33333333) + ((x >> 2) & 0x33333333); |
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x = (x & 0x0F0F0F0F) + ((x >> 4) & 0x0F0F0F0F); |
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x = (x & 0x00FF00FF) + ((x >> 8) & 0x00FF00FF); |
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x = (x & 0x0000FFFF) + ((x >>16) & 0x0000FFFF); |
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return x; |
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} |
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int pop1(unsigned x) { |
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x = x - ((x >> 1) & 0x55555555); |
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x = (x & 0x33333333) + ((x >> 2) & 0x33333333); |
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x = (x + (x >> 4)) & 0x0F0F0F0F; |
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x = x + (x >> 8); |
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x = x + (x >> 16); |
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return x & 0x0000003F; |
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} |
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/* Note: an alternative to the last three executable lines above is:
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return x*0x01010101 >> 24; |
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if your machine has a fast multiplier (suggested by Jari Kirma). */ |
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int pop2(unsigned x) { |
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unsigned n; |
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n = (x >> 1) & 033333333333; // Count bits in
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x = x - n; // each 3-bit
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n = (n >> 1) & 033333333333; // field.
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x = x - n; |
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x = (x + (x >> 3)) & 030707070707; // 6-bit sums.
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return x%63; // Add 6-bit sums.
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} |
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/* An alternative to the "return" statement above is:
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return ((x * 0404040404) >> 26) + // Add 6-bit sums.
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(x >> 30); |
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which runs faster on most machines (suggested by Norbert Juffa). */ |
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int pop3(unsigned x) { |
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unsigned n; |
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n = (x >> 1) & 0x77777777; // Count bits in
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x = x - n; // each 4-bit
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n = (n >> 1) & 0x77777777; // field.
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x = x - n; |
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n = (n >> 1) & 0x77777777; |
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x = x - n; |
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x = (x + (x >> 4)) & 0x0F0F0F0F; // Get byte sums.
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x = x*0x01010101; // Add the bytes.
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return x >> 24; |
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} |
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int pop4(unsigned x) |
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{ |
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int n; |
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n = 0; |
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while (x != 0) { |
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n = n + 1; |
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x = x & (x - 1); |
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} |
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return n; |
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} |
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int pop5(unsigned x) |
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{ |
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int i, sum; |
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// Rotate and sum method // Shift right & subtract
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sum = x; // sum = x;
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for (i = 1; i <= 31; i++) { // while (x != 0) {
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x = rotatel(x, 1); // x = x >> 1;
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sum = sum + x; // sum = sum - x;
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} // }
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return -sum; // return sum;
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} |
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int pop5a(unsigned x) |
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{ |
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int sum; |
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// Shift right & subtract
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sum = x; |
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while (x != 0) { |
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x = x >> 1; |
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sum = sum - x; |
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} |
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return sum; |
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} |
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int pop6(unsigned x) { // Table lookup.
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static char table[256] = { |
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0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, |
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1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, |
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1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, |
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2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
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1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, |
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2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
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2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
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3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, |
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1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, |
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2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
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2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
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3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, |
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2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
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3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, |
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3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, |
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4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8}; |
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return table[x & 0xFF] + |
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table[(x >> 8) & 0xFF] + |
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table[(x >> 16) & 0xFF] + |
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table[(x >> 24)]; |
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} |
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// The following works only for 8-bit quantities.
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int pop7(unsigned x) { |
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x = x*0x08040201; // Make 4 copies.
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x = x >> 3; // So next step hits proper bits.
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x = x & 0x11111111; // Every 4th bit.
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x = x*0x11111111; // Sum the digits (each 0 or 1).
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x = x >> 28; // Position the result.
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return x; |
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} |
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// The following works only for 7-bit quantities.
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int pop8(unsigned x) { |
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x = x*0x02040810; // Make 4 copies, left-adjusted.
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x = x & 0x11111111; // Every 4th bit.
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x = x*0x11111111; // Sum the digits (each 0 or 1).
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x = x >> 28; // Position the result.
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return x; |
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} |
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// The following works only for 15-bit quantities.
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int pop9(unsigned x) { |
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unsigned long long y; |
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y = x * 0x0002000400080010ULL; |
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y = y & 0x1111111111111111ULL; |
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y = y * 0x1111111111111111ULL; |
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y = y >> 60; |
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return y; |
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} |
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int errors; |
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void error(int x, int y) { |
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errors = errors + 1; |
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printf("Error for x = %08x, got %08x\n", x, y); |
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} |
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int main() |
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{ |
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int i, n; |
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static int test[] = {0,0, 1,1, 2,1, 3,2, 4,1, 5,2, 6,2, 7,3, |
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8,1, 9,2, 10,2, 11,3, 12,2, 13,3, 14,3, 15,4, 16,1, 17,2, |
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0x3F,6, 0x40,1, 0x41,2, 0x7f,7, 0x80,1, 0x81,2, 0xfe,7, 0xff,8, |
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0x4000,1, 0x4001,2, 0x7000,3, 0x7fff,15, |
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0x55555555,16, 0xAAAAAAAA, 16, 0xFF000000,8, 0xC0C0C0C0,8, |
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0x0FFFFFF0,24, 0x80000000,1, 0xFFFFFFFF,32}; |
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std::size_t const Count = 10000000; |
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n = sizeof(test)/4; |
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std::clock_t TimestampBeg = 0; |
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std::clock_t TimestampEnd = 0; |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if (pop0(test[i]) != test[i+1]) error(test[i], pop0(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop0: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if (pop1(test[i]) != test[i+1]) error(test[i], pop1(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop1: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if (pop2(test[i]) != test[i+1]) error(test[i], pop2(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop2: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if (pop3(test[i]) != test[i+1]) error(test[i], pop3(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop3: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if (pop4(test[i]) != test[i+1]) error(test[i], pop4(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop4: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if (pop5(test[i]) != test[i+1]) error(test[i], pop5(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop5: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if (pop5a(test[i]) != test[i+1]) error(test[i], pop5a(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop5a: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if (pop6(test[i]) != test[i+1]) error(test[i], pop6(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop6: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if ((test[i] & 0xffffff00) == 0) |
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if (pop7(test[i]) != test[i+1]) error(test[i], pop7(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop7: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if ((test[i] & 0xffffff80) == 0) |
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if (pop8(test[i]) != test[i+1]) error(test[i], pop8(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop8: %d clocks\n", TimestampEnd - TimestampBeg); |
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TimestampBeg = std::clock(); |
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for (std::size_t k = 0; k < Count; ++k) |
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for (i = 0; i < n; i += 2) { |
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if ((test[i] & 0xffff8000) == 0) |
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if (pop9(test[i]) != test[i+1]) error(test[i], pop9(test[i]));} |
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TimestampEnd = std::clock(); |
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printf("pop9: %d clocks\n", TimestampEnd - TimestampBeg); |
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if (errors == 0) |
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printf("Passed all %d cases.\n", sizeof(test)/8); |
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} |
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