presumably working bitmask with window of 64.

ver1-bitmask.c

@@ -0,0 +1,214 @@
+#define _GNU_SOURCE
+#include <assert.h>
+#include <limits.h>
+#include <stdbool.h>
+#include <stdio.h>
+#include <stdint.h>
+#include <string.h>
+#include <unistd.h>
+#include <linux/random.h>
+#include <sys/syscall.h>
+#include <sys/time.h>
+
+#include <gmp.h>
+
+
+#define INIT_TIMEIT() \
+  struct timeval __start, __end;                \
+  double __sdiff = 0, __udiff = 0
+
+#define START_TIMEIT()                          \
+  gettimeofday(&__start, NULL)
+
+#define END_TIMEIT()                                                    \
+  gettimeofday(&__end, NULL);                                           \
+  __sdiff += (__end.tv_sec - __start.tv_sec);                           \
+  __udiff += (__end.tv_usec - __start.tv_usec)
+
+#define GET_TIMEIT()                            \
+  __sdiff + __udiff * 1e-6
+
+#define TIMEIT_FORMAT "%lf"
+
+typedef __uint128_t uint128_t;
+
+/**
+ * p is our prime modulus, and is 2^n - g
+ * where g is referred to as "gamma" (built-in function in C, so transliterated)
+ */
+const static char* p_str =
+  "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+  "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+  "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+  "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+  "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+  "505CAF";
+const static char* g_str =
+  "11510609";
+
+mpz_t p, g;
+uint32_t gg = 11510609;
+uint128_t gg128 = 11510609;
+
+static uint8_t lookup[256];
+static uint8_t offset[256];
+
+static inline ssize_t
+getrandom(void *buffer, size_t length, unsigned int flags)
+{
+  return syscall(SYS_getrandom, buffer, length, flags);
+}
+
+
+INIT_TIMEIT();
+#define strip_size 16
+#define halfstrip_size ((strip_size)/2)
+
+size_t i;
+
+static inline
+void add_1(uint64_t *b, const size_t start, const size_t len, uint64_t a)
+{
+  for (i = start; a != 0; i = (i+1)%len) {
+    const uint64_t r = b[i] + a;
+    a = (r < a);
+    b[i] = r;
+  }
+  /** we don't check for overflows because performances and YOLO.
+      If it happens, buy a lottery ticket and retry.
+  */
+}
+
+uint32_t convert(uint64_t * nn)
+{
+  static const uint64_t topmask = ~(ULLONG_MAX >> halfstrip_size);
+  static const uint64_t topbigmask = ~(ULLONG_MAX >> strip_size);
+  static const uint64_t bottommask = (0x01  << halfstrip_size) -1;
+
+  uint32_t w;
+  uint32_t steps;
+  size_t head = 23;
+#define next_head  ((head + 23) % 24)
+#define tail       ((head + 1)  % 24)
+#define next_tail  ((head + 2)  % 24)
+
+  /** Check if x has a halfstrip starting from start */
+#define distinguished(x) (((x)[head] & topbigmask)) == 0
+
+  /** Check the most significant block */
+
+  const uint64_t x = nn[head];
+  for (uint32_t w2 = halfstrip_size; w2 < 64-halfstrip_size; w2 += halfstrip_size) {
+    if (!(x & (topmask >> w2))) {
+      for (w = w2-1; !(x & (topmask >> w)); w--);
+      ++w;
+      if (!(x & (topbigmask >> w))) return w;
+    }
+  }
+
+  for (steps = 64; !distinguished(nn); steps += 64) {
+    const uint64_t x = nn[head];
+    const uint64_t y = nn[next_head];
+
+    if (!(x & bottommask)) {
+      const uint8_t previous = (x >> halfstrip_size) & bottommask;
+      const size_t next = y >> (64 - halfstrip_size);
+      if (next <= lookup[previous]) return steps - halfstrip_size - offset[previous];
+    }
+
+    if (!(y & topmask)) {
+      const uint8_t previous = x & bottommask;
+      const size_t next = (y >> (64 - 2*halfstrip_size)) & bottommask;
+      if (next <= lookup[previous]) return steps - offset[previous];
+    }
+
+    for (uint32_t w2 = halfstrip_size; w2 < 64-halfstrip_size; w2 += halfstrip_size) {
+      if (!(y & (topmask >> w2))) {
+        for (w = w2-1; !(y & (topmask >> w)); w--);
+        ++w;
+        if (!(y & (topbigmask >> w)))  return steps + w;
+      }
+    }
+
+    /**
+     * We found no distinguished point.
+     */
+    const uint128_t a = x * gg128;
+    const uint64_t al = (uint64_t) a;
+    const uint64_t ah = (a >> 64);
+    head = next_head;
+    nn[tail] = al;
+    add_1(nn, next_tail, 24, ah);
+
+  }
+  return steps;
+}
+
+
+uint32_t naif_convert(mpz_t n)
+{
+  uint32_t i;
+  mpz_t t;
+  mpz_init_set_ui(t, 1);
+  mpz_mul_2exp(t, t, 1536-strip_size);
+
+
+  for (i = 0; mpz_cmp(n, t) > -1; i++) {
+    mpz_mul_2exp(n, n, 1);
+    mpz_mod(n, n, p);
+  }
+
+  mpz_clear(t);
+  return i;
+}
+
+int main()
+{
+  mpz_init_set_str(p, p_str, 0);
+  mpz_init_set_str(g, g_str, 10);
+
+  gmp_randstate_t _rstate;
+  unsigned long int _rseed;
+
+  gmp_randinit_default(_rstate);
+  getrandom(&_rseed, sizeof(unsigned long int), GRND_NONBLOCK);
+  gmp_randseed_ui(_rstate, _rseed);
+
+  mpz_t n, n0;
+  mpz_inits(n, n0, NULL);
+
+  for (size_t i = 0; i <= 0xFF; i++) {
+    uint32_t j = ffs(i) ? ffs(i) - 1 : 8;
+    lookup[i] = 0xFF >> (8-j);
+    offset[i] = j;
+  }
+
+  uint32_t converted;
+  for (int i=0; i < 1e5; i++) {
+    mpz_urandomm(n0, _rstate, p);
+    mpz_set(n, n0);
+    START_TIMEIT();
+    converted = convert(n->_mp_d);
+    END_TIMEIT();
+    mpz_set(n, n0);
+#ifndef NDEBUG
+    uint32_t expected = naif_convert(n);
+    printf("%d %d\n", converted, expected);
+    assert(converted == expected);
+#endif
+  }
+  printf(TIMEIT_FORMAT "\n", GET_TIMEIT());
+
+
+  /* memset(n->_mp_d, 0, 24*8); */
+  /* memset(n0->_mp_d, 0, 24*8); */
+  /* n0->_mp_d[0] = 13423523; */
+  /* n0->_mp_d[1] = 1; */
+  /* uint64_t v[64] = {0}; */
+  /* unpack(v, n->_mp_d); */
+  /* pack(n0, v); */
+
+  mpz_clears(n, n0, p, g, NULL);
+  return 0;
+
+}