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Date: Sat, 14 Jun 2014 21:17:13 -0400
From: Theodore Ts'o <tytso@....edu>
To: George Spelvin <linux@...izon.com>
Cc: hpa@...ux.intel.com, linux-kernel@...r.kernel.org,
mingo@...nel.org, price@....edu
Subject: Re: random: Benchamrking fast_mix2
On Sat, Jun 14, 2014 at 08:23:33PM -0400, George Spelvin wrote:
> The example I posted:
>
> // (29/66353) score = 49/121/123: 6 27 16 14
>
> a += b; c += d;
> b = rol32(a, 6); d = rol32(c, 27);
> d ^= a; b ^= c;
>
> a += b; c += d;
> b = rol32(a, 16); d = rol32(c, 14);
> d ^= a; b ^= c;
>
> has, after 2 rounds, a minimum avalanche of 49 bits, taken over all of
> the variables just mentioned. The only thing maximized over is the
> different starting values.
I'm seeing a minimum delta of 40 bits, actually. Which makes it
slightly better than your original fast_mix2 (which had a minimum
delta of 39) when using 1024 random samples using random(3) to
generate a starting pool and setting a single bit in each possible bit
position in the input array. So it's slightly better, and as I
mentioned, on my CPU, I'm really not seeing that much difference
between fast_mix2() and fast_mix3().
But I'm willing to go with this as being quite sufficient as a mixing
function.
- Ted
(Compile the following with -DANALYZE to see the analysis I did.)
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <string.h>
typedef unsigned int __u32;
typedef unsigned long long __u64;
struct fast_pool {
__u32 pool[4];
unsigned long last;
unsigned short count;
unsigned char rotate;
unsigned char last_timer_intr;
};
/**
* rol32 - rotate a 32-bit value left
* @word: value to rotate
* @shift: bits to roll
*/
static inline __u32 rol32(__u32 word, unsigned int shift)
{
return (word << shift) | (word >> (32 - shift));
}
static inline __u64 rol64(__u64 word, unsigned int shift)
{
return (word << shift) | (word >> (64 - shift));
}
static __u32 const twist_table[8] = {
0x00000000, 0x3b6e20c8, 0x76dc4190, 0x4db26158,
0xedb88320, 0xd6d6a3e8, 0x9b64c2b0, 0xa00ae278 };
extern void fast_mix(struct fast_pool *f, __u32 input[4])
{
__u32 w;
unsigned input_rotate = f->rotate;
w = rol32(input[0], input_rotate) ^ f->pool[0] ^ f->pool[3];
f->pool[0] = (w >> 3) ^ twist_table[w & 7];
input_rotate = (input_rotate + 14) & 31;
w = rol32(input[1], input_rotate) ^ f->pool[1] ^ f->pool[0];
f->pool[1] = (w >> 3) ^ twist_table[w & 7];
input_rotate = (input_rotate + 7) & 31;
w = rol32(input[2], input_rotate) ^ f->pool[2] ^ f->pool[1];
f->pool[2] = (w >> 3) ^ twist_table[w & 7];
input_rotate = (input_rotate + 7) & 31;
w = rol32(input[3], input_rotate) ^ f->pool[3] ^ f->pool[2];
f->pool[3] = (w >> 3) ^ twist_table[w & 7];
input_rotate = (input_rotate + 7) & 31;
f->rotate = input_rotate;
f->count++;
}
extern void fast_mix2(struct fast_pool *f, __u32 const input[4])
{
__u32 a = f->pool[0] ^ input[0], b = f->pool[1] ^ input[1];
__u32 c = f->pool[2] ^ input[2], d = f->pool[3] ^ input[3];
int i;
for (i = 0; i < 2; i++) {
/*
* Inspired by ChaCha's QuarterRound, but
* modified for much greater parallelism.
*/
a += b; c += d;
d ^= a; b ^= c;
a = rol32(a, 15); c = rol32(c, 21);
a += b; c += d;
d ^= a; b ^= c;
a = rol32(a, 3); c = rol32(c, 7);
}
f->pool[0] = a; f->pool[1] = b;
f->pool[2] = c; f->pool[3] = d;
f->count++;
}
extern void fast_mix3(struct fast_pool *f, __u32 const input[4])
{
__u32 a = f->pool[0] ^ input[0], b = f->pool[1] ^ input[1];
__u32 c = f->pool[2] ^ input[2], d = f->pool[3] ^ input[3];
int i;
for (i = 0; i < 2; i++) {
a += b; c += d;
a = rol32(a, 6); c = rol32(c, 27);
d ^= a; b ^= c;
a += b; c += d;
a = rol32(a, 16); c = rol32(c, 14);
d ^= a; b ^= c;
}
f->pool[0] = a; f->pool[1] = b;
f->pool[2] = c; f->pool[3] = d;
f->count++;
}
extern void fast_mix4(struct fast_pool *f, __u32 const input[4])
{
__u64 a = ((__u64 *)f->pool)[0] ^ ((__u64 const *)input)[0];
__u64 b = ((__u64 *)f->pool)[1] ^ ((__u64 const *)input)[1];
int i;
for (i = 0; i < 2; i++) {
a += b; b = rol64(b, 52);
b ^= a; a = rol64(a, 10);
a += b; b = rol64(b, 47);
b ^= a; a = rol64(a, 17);
}
((__u64 *)f->pool)[0] = a;
((__u64 *)f->pool)[1] = b;
f->count++;
}
static void rotate(__u32 a[4])
{
int i;
int carry = 0;
__u32 tmp;
for (i=0; i < 4; i++) {
tmp = a[i];
a[i] = (tmp << 1) + carry;
carry = (tmp & 0x80000000) ? 1 : 0;
}
if (carry)
a[0]++;
}
int global_min = 9999;
void analyze(void)
{
struct fast_pool f;
int i, pc;
int sum = 0, max = 0, min=9999;
__u32 input[4];
__u32 start[4];
start[0] = random();
start[1] = random();
start[2] = random();
start[3] = random();
memset(&f, 0, sizeof(f));
memset(&input, 0, sizeof(input));
input[0] = 1;
for (i=0; i < 32; i++) {
memcpy(f.pool, start, sizeof(start));
fast_mix3(&f, input);
pc = (__builtin_popcount(f.pool[0] ^ start[0]) +
__builtin_popcount(f.pool[1] ^ start[1]) +
__builtin_popcount(f.pool[2] ^ start[2]) +
__builtin_popcount(f.pool[3] ^ start[3]));
sum += pc;
if (pc > max)
max = pc;
if (pc < min)
min = pc;
if (pc < global_min)
global_min = pc;
rotate(input);
// printf("%d ", pc);
}
// printf("\n");
// printf("average popcount: %d, max: %d min %d\n", sum / 128, max, min);
}
static __inline__ unsigned long long rdtsc(void)
{
unsigned long long int x;
__asm__ volatile (".byte 0x0f, 0x31" : "=A" (x));
return x;
}
int main(int argc, char **argv)
{
struct fast_pool f;
int i;
__u32 input[4];
unsigned volatile long long start_time, end_time;
#ifdef ANALYZE
for (i=0; i < 1024; i++)
analyze();
printf("Global minimum: %d\n", global_min);
return 0;
#endif
#if !defined(BENCH_FASTMIX) && !defined(BENCH_FASTMIX2)
for (i=0; i < 20; i++) {
usleep(50000);
start_time = rdtsc();
fast_mix2(&f, input);
end_time = rdtsc();
printf("fast_mix2: %llu\t", end_time - start_time);
#if 0
usleep(50000);
start_time = rdtsc();
fast_mix2(&f, input);
end_time = rdtsc();
printf("fast_mix2: %llu\t", end_time - start_time);
usleep(50000);
start_time = rdtsc();
fast_mix3(&f, input);
end_time = rdtsc();
printf("fast_mix3: %llu\t", end_time - start_time);
#endif
fputc('\n', stdout);
}
#endif
#ifdef BENCH_FASTMIX
for (i=0; i < 10240000; i++) {
fast_mix(&f, input);
}
#endif
#ifdef BENCH_FASTMIX2
for (i=0; i < 10240000; i++) {
fast_mix2(&f, input);
}
#endif
return 0;
}
--
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