bigmath.h

/*
 * Copyright © 2018 Intel Corporation
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice (including the next
 * paragraph) shall be included in all copies or substantial portions of the
 * Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
 * IN THE SOFTWARE.
 */

#ifndef UTIL_BIGMATH_H
#define UTIL_BIGMATH_H

#include "macros.h"

#include <assert.h>
#include <stdint.h>
#include <string.h>

static inline bool
_ubm_add_u32arr(uint32_t *dst, unsigned dst_len,
                uint32_t *a, unsigned a_len,
                uint32_t *b, unsigned b_len)
{
   uint32_t carry = 0;
   for (unsigned i = 0; i < dst_len; i++) {
      uint64_t sum = carry;
      if (i < a_len)
         sum += a[i];
      if (i < b_len)
         sum += b[i];
      dst[i] = sum;
      carry = sum >> 32;
   }

   /* Now compute overflow */

   for (unsigned i = dst_len; i < a_len; i++) {
      if (a[i])
         return true;
   }

   for (unsigned i = dst_len; i < b_len; i++) {
      if (b[i])
         return true;
   }

   return carry;
}
#define ubm_add_u32arr(dst, a, b) \
   _ubm_add_u32arr(dst, ARRAY_SIZE(dst), a, ARRAY_SIZE(a), b, ARRAY_SIZE(b))

static inline bool
_ubm_mul_u32arr(uint32_t *dst, unsigned dst_len,
                uint32_t *a, unsigned a_len,
                uint32_t *b, unsigned b_len)
{
   memset(dst, 0, dst_len * sizeof(*dst));

   bool overflow = false;

   for (unsigned i = 0; i < a_len; i++) {
      uint32_t carry = 0;
      for (unsigned j = 0; j < b_len; j++) {
         /* The maximum values of a[i] and b[i] are UINT32_MAX so the maximum
          * value of tmp is UINT32_MAX * UINT32_MAX.  The maximum value that
          * will fit in tmp is
          *
          *    UINT64_MAX = UINT32_MAX << 32 + UINT32_MAX
          *               = UINT32_MAX * (UINT32_MAX + 1) + UINT32_MAX
          *               = UINT32_MAX * UINT32_MAX + 2 * UINT32_MAX
          *
          * so we're guaranteed that we can add in two more 32-bit values
          * without overflowing tmp.
          */
         uint64_t tmp = (uint64_t)a[i] * (uint64_t)b[j];
         tmp += carry;
         if (i + j < dst_len) {
            tmp += dst[i + j];
            dst[i + j] = tmp;
            carry = tmp >> 32;
         } else {
            /* We're trying to write a value that doesn't fit */
            overflow = overflow || tmp > 0;
            break;
         }
      }
      if (i + b_len < dst_len)
         dst[i + b_len] = carry;
      else
         overflow = overflow || carry > 0;
   }

   return overflow;
}
#define ubm_mul_u32arr(dst, a, b) \
   _ubm_mul_u32arr(dst, ARRAY_SIZE(dst), a, ARRAY_SIZE(a), b, ARRAY_SIZE(b))

#endif /* UTIL_BIGMATH_H */