Lisp: Why does (- 1e16 1) yield 10000000000000000 not 9999999999999999?

Question

Or rather, why does (= 1e16 (- 1e16 1)) return true? How can I receive more accurate answer?

[What Every Computer Scientist Should Know About Floating-Point Arithmetic](http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html) — sds, Mar 08 '15 at 00:05

score 8 · Accepted Answer · edited Mar 07 '15 at 23:46

1e16 is, in Scheme terms, an inexact number (or in more practical terms, a floating-point number). For (double-precision) floating point numbers above 2⁵³ (9007199254740992), the ulp is greater than 1, which means changes by 1 are too small to be represented.^†

10000000000000000, on the other hand, is an integer. If you do (- 10000000000000000 1), you will indeed get back 999999999999999. In Scheme, you can also write #e1e16 to represent the same quantity; the #e prefix makes the number exact (in Scheme terms; in practical terms, it means either an integer or rational).

† Try evaluating (+ 9007199254740992.0 1) and (- 9007199254740992.0 1), then try evaluating (+ 9007199254740992 1) and (- 9007199254740992 1) for contrast with integers.

Lisp: Why does (- 1e16 1) yield 10000000000000000 not 9999999999999999?

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