stdlib: Simplify arc4random_uniform

It uses the bitmask with rejection [1], which calculates a mask
being the lowest power of two bounding the request upper bound,
successively queries new random values, and rejects values
outside the requested range.

Performance-wise, there is no much gain in trying to conserve
bits since arc4random is wrapper on getrandom syscall.  It should
be cheaper to just query a uint32_t value.  The algorithm also
avoids modulo and divide operations, which might be costly
depending of the architecture.

[1] https://www.pcg-random.org/posts/bounded-rands.html

Reviewed-by: Yann Droneaud <ydroneaud@opteya.com>

stdlib/arc4random_uniform.c

@@ -17,38 +17,19 @@
    License along with the GNU C Library; if not, see
    <https://www.gnu.org/licenses/>.  */
 
-#include <endian.h>
-#include <libc-lock.h>
 #include <stdlib.h>
 #include <sys/param.h>
 
-/* Return the number of bytes which cover values up to the limit.  */
+/* Return a uniformly distributed random number less than N.  The algorithm
-__attribute__ ((const))
+   calculates a mask being the lowest power of two bounding the upper bound
-static uint32_t
+   N, successively queries new random values, and rejects values outside of
-byte_count (uint32_t n)
+   the request range.
-{
-  if (n < (1U << 8))
-    return 1;
-  else if (n < (1U << 16))
-    return 2;
-  else if (n < (1U << 24))
-    return 3;
-  else
-    return 4;
-}
 
-/* Fill the lower bits of the result with randomness, according to the
+   For reject values, it also tries if the remaining entropy could fit on
-   number of bytes requested.  */
+   the asked range after range adjustment.
-static void
-random_bytes (uint32_t *result, uint32_t byte_count)
-{
-  *result = 0;
-  unsigned char *ptr = (unsigned char *) result;
-  if (__BYTE_ORDER == __BIG_ENDIAN)
-    ptr += 4 - byte_count;
-  __arc4random_buf (ptr, byte_count);
-}
 
+   The algorithm avoids modulo and divide operations, which might be costly
+   depending on the architecture.  */
 uint32_t
 __arc4random_uniform (uint32_t n)
 {
@@ -57,83 +38,33 @@ __arc4random_uniform (uint32_t n)
        only possible result for limit 1.  */
     return 0;
 
-  /* The bits variable serves as a source for bits.  Prefetch the
-     minimum number of bytes needed.  */
-  uint32_t count = byte_count (n);
-  uint32_t bits_length = count * CHAR_BIT;
-  uint32_t bits;
-  random_bytes (&bits, count);
-
   /* Powers of two are easy.  */
   if (powerof2 (n))
-    return bits & (n - 1);
+    return __arc4random () & (n - 1);
 
-  /* The general case.  This algorithm follows Jérémie Lumbroso,
+  /* mask is the smallest power of 2 minus 1 number larger than n.  */
-     Optimal Discrete Uniform Generation from Coin Flips, and
+  int z = __builtin_clz (n);
-     Applications (2013), who credits Donald E. Knuth and Andrew
+  uint32_t mask = ~UINT32_C(0) >> z;
-     C. Yao, The complexity of nonuniform random number generation
+  int bits = CHAR_BIT * sizeof (uint32_t) - z;
-     (1976), for solving the general case.
 
-     The implementation below unrolls the initialization stage of the
+  while (1)
-     loop, where v is less than n.  */
-
-  /* Use 64-bit variables even though the intermediate results are
-     never larger than 33 bits.  This ensures the code is easier to
-     compile on 64-bit architectures.  */
-  uint64_t v;
-  uint64_t c;
-
-  /* Initialize v and c.  v is the smallest power of 2 which is larger
-     than n.*/
-  {
-    uint32_t log2p1 = 32 - __builtin_clz (n);
-    v = 1ULL << log2p1;
-    c = bits & (v - 1);
-    bits >>= log2p1;
-    bits_length -= log2p1;
-  }
-
-  /* At the start of the loop, c is uniformly distributed within the
-     half-open interval [0, v), and v < 2n < 2**33.  */
-  while (true)
     {
-      if (v >= n)
+      uint32_t value = __arc4random ();
-        {
-          /* If the candidate is less than n, accept it.  */
-          if (c < n)
-            /* c is uniformly distributed on [0, n).  */
-            return c;
-          else
-            {
-              /* c is uniformly distributed on [n, v).  */
-              v -= n;
-              c -= n;
-              /* The distribution was shifted, so c is uniformly
-                 distributed on [0, v) again.  */
-            }
-        }
-      /* v < n here.  */
 
-      /* Replenish the bit source if necessary.  */
+      /* Return if the lower power of 2 minus 1 satisfy the condition.  */
-      if (bits_length == 0)
+      uint32_t r = value & mask;
-        {
+      if (r < n)
-          /* Overwrite the least significant byte.  */
+	return r;
-	  random_bytes (&bits, 1);
-	  bits_length = CHAR_BIT;
-        }
 
-      /* Double the range.  No overflow because v < n < 2**32.  */
+      /* Otherwise check if remaining bits of entropy provides fits in the
-      v *= 2;
+	 bound.  */
-      /* v < 2n here.  */
+      for (int bits_left = z; bits_left >= bits; bits_left -= bits)
-
+	{
-      /* Extract a bit and append it to c.  c remains less than v and
+	  value >>= bits;
-         thus 2**33.  */
+	  r = value & mask;
-      c = (c << 1) | (bits & 1);
+	  if (r < n)
-      bits >>= 1;
+	    return r;
-      --bits_length;
+	}
-
-      /* At this point, c is uniformly distributed on [0, v) again,
-         and v < 2n < 2**33.  */
     }
 }
 libc_hidden_def (__arc4random_uniform)