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This chapter is from the book

This chapter is from the book

Hacker's Delight, 2nd EditionHacker's Delight, 2nd Edition

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This chapter is from the book

This chapter is from the book

Hacker's Delight, 2nd EditionHacker's Delight, 2nd Edition

Learn More Buy

2–16 Double-Length Add/Subtract

Using one of the expressions shown on page 31 for overflow of unsigned addition and subtraction, we can easily implement double-length addition and subtraction without accessing the machine’s carry bit. To illustrate with double-length addition, let the operands be (x1, x0) and (y1, y0), and the result be (z1, z0). Subscript 1 denotes the most significant half, and subscript 0 the least significant. We assume that all 32 bits of the registers are used. The less significant words are unsigned quantities.

038equ01.jpg

This executes in nine instructions. The second line can be 038fig01.jpg, permitting a four-instruction solution on machines that have this comparison operator in a form that gives the result as a 1 or 0 in a register, such as the “SLTU” (Set on Less Than Unsigned) instruction on MIPS [MIPS].

Similar code for double-length subtraction (x – y) is

038equ02.jpg

This executes in eight instructions on a machine that has a full set of logical instructions. The second line can be 039fig01.jpg, permitting a four-instruction solution on machines that have the “SLTU” instruction.

Double-length addition and subtraction can be done in five instructions on most machines by representing the multiple-length data using only 31 bits of the least significant words, with the high-order bit being 0 except momentarily when it contains a carry or borrow bit.

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