5-1. Counting 1-Bits
The IBM Stretch computer (ca. 1960) had a means of counting the number of 1-bits in a word as well as the number of leading 0’s. It produced these two quantities as a by-product of all logical operations! The former function is sometimes called population count (e.g., on Stretch and the SPARCv9).
For machines that don’t have this instruction, a good way to count the number of 1-bits is to first set each 2-bit field equal to the sum of the two single bits that were originally in the field, and then sum adjacent 2-bit fields, putting the results in each 4-bit field, and so on. A more complete discussion of this trick is in [RND]. The method is illustrated in Figure 5-1, in which the first row shows a computer word whose 1-bits ...
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