int tz = Long.numberOfTrailingZeros(num);
      long normalizedNum = num >> tz;
      shift += tz;
      // Adjust floor(log2(num)) + 1.
      int normalizedBits = bits - tz;
      // If it won't fit in a long, then we store off the intermediate product.
      if (normalizedBits + productBits >= Long.SIZE) {
        bignums.add(BigInteger.valueOf(product));
        product = 1;
        productBits = 0;
      }

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