The End of Error

13 Fused operations (single-use expressions)

Standard library routines for performing complex arithmetic are crippled by a fear of “falling off the edge of the world,” since straightforward arithmetic can overflow or underflow in the scratch calculations. These routines typically disassemble the float inputs into exponent and fraction parts to avoid this problem, which destroys most of the speed advantage of having hardware for float operations. This chapter presents a better way to avoid “falling off the edge” of the set of representable real numbers, by declaring fused operations and making their use explicit.

13.1 Standardizing a set of ...