By Michael Welschenbach
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Extra info for Cryptography in C and C++, Second Edition - (May 25, 2005)
Sample text
If (carry & BASE) { *sptr_l = 1; SETDIGITS_L (ss_l, DIGITS_L (ss_l) + 1); } if (DIGITS_L (ss_l) > (USHORT)CLINTMAXDIGIT) /* overflow? */ { ANDMAX_L (ss_l); /* reduce modulo (Nmax + 1) */ OFL = E_CLINT_OFL; } cpy_l (s_l, ss_l); return OFL; } The run time t of all the procedures given here for addition and subtraction is t = O(n), and thus proportional to the number of digits of the larger of the two operands. 27 Chapter 4 Now that we have seen addition, we shall present the algorithm for subtraction of two numbers a and b with representations a = (am−1 am−2 .
1), the return value consists of status information or error messages. Parameters other than those involved with output are not changed by the function. Calls of the form f_l(a_l, b_l, a_l), where a_l and b_l are used 19 Chapter 3 as arguments and a_l is overwritten with the return value at the end of the computation, are always possible, since the return variable is written to with the return value only after the complete execution of the operation. From assembler programming one says in this case that the variable a_l is used as an accumulator.
6. Set pi+n ← c. 7. Set i ← i + 1; if i ≤ m − 1, go to step 3. 8. Output p = (pm+n−1 pm+n−2 . . p0 )B . The following implementation of multiplication contains at its core this main loop. Corresponding to the above estimate, in step 4 the lossless representation of a value less than B 2 in the variable t is required. Analogously to how we proceeded in the case of addition, the inner products t are thus represented as ULONG types. The variable t is nonetheless not used explicitly, and the setting of the result digits pi+j and the carry c occurs rather within a single expression, analogous to the process already mentioned in connection with the addition function (see page 25).