mod_arith_64bit.h

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/* Copyright (C) 2010 The Trustees of Indiana University.                  */
/*                                                                         */
/* Use, modification and distribution is subject to the Boost Software     */
/* License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at */
/* http://www.boost.org/LICENSE_1_0.txt)                                   */
/*                                                                         */
/*  Authors: Jeremiah Willcock                                             */
/*           Andrew Lumsdaine                                              */
 
#ifndef MOD_ARITH_64BIT_H
#define MOD_ARITH_64BIT_H
 
#include <stdint.h>
#include <assert.h>
 
/* Various modular arithmetic operations for modulus 2^31-1 (0x7FFFFFFF).
 * These may need to be tweaked to get acceptable performance on some platforms
 * (especially ones without conditional moves). */
 
static inline uint_fast32_t mod_add(uint_fast32_t a, uint_fast32_t b) {
  assert (a <= 0x7FFFFFFE);
  assert (b <= 0x7FFFFFFE);
  return (a + b) % 0x7FFFFFFF;
}
 
static inline uint_fast32_t mod_mul(uint_fast32_t a, uint_fast32_t b) {
  assert (a <= 0x7FFFFFFE);
  assert (b <= 0x7FFFFFFE);
  return (uint_fast32_t)((uint_fast64_t)a * b % 0x7FFFFFFF);
}
 
static inline uint_fast32_t mod_mac(uint_fast32_t sum, uint_fast32_t a, uint_fast32_t b) {
  assert (sum <= 0x7FFFFFFE);
  assert (a <= 0x7FFFFFFE);
  assert (b <= 0x7FFFFFFE);
  return (uint_fast32_t)(((uint_fast64_t)a * b + sum) % 0x7FFFFFFF);
}
 
static inline uint_fast32_t mod_mac2(uint_fast32_t sum, uint_fast32_t a, uint_fast32_t b, uint_fast32_t c, uint_fast32_t d) {
  assert (sum <= 0x7FFFFFFE);
  assert (a <= 0x7FFFFFFE);
  assert (b <= 0x7FFFFFFE);
  assert (c <= 0x7FFFFFFE);
  assert (d <= 0x7FFFFFFE);
  return (uint_fast32_t)(((uint_fast64_t)a * b + (uint_fast64_t)c * d + sum) % 0x7FFFFFFF);
}
 
static inline uint_fast32_t mod_mac3(uint_fast32_t sum, uint_fast32_t a, uint_fast32_t b, uint_fast32_t c, uint_fast32_t d, uint_fast32_t e, uint_fast32_t f) {
  assert (sum <= 0x7FFFFFFE);
  assert (a <= 0x7FFFFFFE);
  assert (b <= 0x7FFFFFFE);
  assert (c <= 0x7FFFFFFE);
  assert (d <= 0x7FFFFFFE);
  assert (e <= 0x7FFFFFFE);
  assert (f <= 0x7FFFFFFE);
  return (uint_fast32_t)(((uint_fast64_t)a * b + (uint_fast64_t)c * d + (uint_fast64_t)e * f + sum) % 0x7FFFFFFF);
}
 
static inline uint_fast32_t mod_mac4(uint_fast32_t sum, uint_fast32_t a, uint_fast32_t b, uint_fast32_t c, uint_fast32_t d, uint_fast32_t e, uint_fast32_t f, uint_fast32_t g, uint_fast32_t h) {
  assert (sum <= 0x7FFFFFFE);
  assert (a <= 0x7FFFFFFE);
  assert (b <= 0x7FFFFFFE);
  assert (c <= 0x7FFFFFFE);
  assert (d <= 0x7FFFFFFE);
  assert (e <= 0x7FFFFFFE);
  assert (f <= 0x7FFFFFFE);
  assert (g <= 0x7FFFFFFE);
  assert (h <= 0x7FFFFFFE);
  return (uint_fast32_t)(((uint_fast64_t)a * b + (uint_fast64_t)c * d + (uint_fast64_t)e * f + (uint_fast64_t)g * h + sum) % 0x7FFFFFFF);
}
 
/* The two constants x and y are special cases because they are easier to
 * multiply by on 32-bit systems.  They are used as multipliers in the random
 * number generator.  The techniques for fast multiplication by these
 * particular values are in L'Ecuyer's papers; we don't use them yet. */
 
static inline uint_fast32_t mod_mul_x(uint_fast32_t a) {
  return mod_mul(a, 107374182);
}
 
static inline uint_fast32_t mod_mul_y(uint_fast32_t a) {
  return mod_mul(a, 104480);
}
 
static inline uint_fast32_t mod_mac_y(uint_fast32_t sum, uint_fast32_t a) {
  return mod_mac(sum, a, 104480);
}
 
#endif /* MOD_ARITH_64BIT_H */