The MMIX Supplement: Supplement to The Art of Computer Programming Volumes 1, 2, 3 by Donald E. Knuth

4.2.3. Double-Precision Calculations

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2. Only the two lowest bits in the hi-wyde of um are strictly needed during normalization. The hidden bit is tested in step N4, but this bit is set to 1, so there is no need to clear it. The bit left of the hidden bit is tested in step N1, line 37, so it needs to be cleared. Clearing the complete wyde, however, also simplifies the test for zero in line 38.

3. Program M will not cause an overflow exception because it uses “unsigned” instructions; there might be, however, a silent overflow. Working with exponents is safe because exponents are very small; the same holds for the upper 48 bits of the fraction parts. Whenever we work with 64-bit fraction parts, we determine an eventual carry and apply necessary ...