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From: Adhemerval Zanella <azanella@sourceware.org> To: glibc-cvs@sourceware.org Subject: [glibc] stdlib: Simplify arc4random_uniform Date: Mon, 1 Aug 2022 18:21:43 +0000 (GMT) [thread overview] Message-ID: <20220801182143.5E52C385842E@sourceware.org> (raw) https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=c622ac1b8662908b595ec1a19e401ad6a629f52c commit c622ac1b8662908b595ec1a19e401ad6a629f52c Author: Adhemerval Zanella <adhemerval.zanella@linaro.org> Date: Thu Jul 28 09:18:01 2022 -0300 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> Diff: --- stdlib/arc4random_uniform.c | 129 +++++++++++--------------------------------- 1 file changed, 30 insertions(+), 99 deletions(-) diff --git a/stdlib/arc4random_uniform.c b/stdlib/arc4random_uniform.c index 1326dfa593..5aa98d1c13 100644 --- a/stdlib/arc4random_uniform.c +++ b/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. */ -__attribute__ ((const)) -static uint32_t -byte_count (uint32_t n) -{ - if (n < (1U << 8)) - return 1; - else if (n < (1U << 16)) - return 2; - else if (n < (1U << 24)) - return 3; - else - return 4; -} +/* Return a uniformly distributed random number less than N. The algorithm + calculates a mask being the lowest power of two bounding the upper bound + N, successively queries new random values, and rejects values outside of + the request range. -/* Fill the lower bits of the result with randomness, according to the - number of bytes requested. */ -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); -} + For reject values, it also tries if the remaining entropy could fit on + the asked range after range adjustment. + 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); - - /* The general case. This algorithm follows Jérémie Lumbroso, - Optimal Discrete Uniform Generation from Coin Flips, and - Applications (2013), who credits Donald E. Knuth and Andrew - C. Yao, The complexity of nonuniform random number generation - (1976), for solving the general case. + return __arc4random () & (n - 1); - The implementation below unrolls the initialization stage of the - loop, where v is less than n. */ + /* mask is the smallest power of 2 minus 1 number larger than n. */ + int z = __builtin_clz (n); + uint32_t mask = ~UINT32_C(0) >> z; + int bits = CHAR_BIT * sizeof (uint32_t) - z; - /* 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) + while (1) { - if (v >= n) - { - /* 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. */ - if (bits_length == 0) - { - /* Overwrite the least significant byte. */ - random_bytes (&bits, 1); - bits_length = CHAR_BIT; - } - - /* Double the range. No overflow because v < n < 2**32. */ - v *= 2; - /* v < 2n here. */ - - /* Extract a bit and append it to c. c remains less than v and - thus 2**33. */ - c = (c << 1) | (bits & 1); - bits >>= 1; - --bits_length; - - /* At this point, c is uniformly distributed on [0, v) again, - and v < 2n < 2**33. */ + uint32_t value = __arc4random (); + + /* Return if the lower power of 2 minus 1 satisfy the condition. */ + uint32_t r = value & mask; + if (r < n) + return r; + + /* Otherwise check if remaining bits of entropy provides fits in the + bound. */ + for (int bits_left = z; bits_left >= bits; bits_left -= bits) + { + value >>= bits; + r = value & mask; + if (r < n) + return r; + } } } libc_hidden_def (__arc4random_uniform)

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