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| From: Bradley Lucier <lucier@xxxxxxxxxxxxxxx> | Date: Wed, 18 May 2005 22:38:43 +0200 | | .., I sent document about proposed changes to numerics to | Marc Feeley last March to forward to the committee. Since then my | thinking has evolved a bit, but I thought I would just include my | comments verbatim here. | | Brad | | The first part deals with IEEE 754/854 arithmetic. If you don't | support this arithmetic, then things are still up in the air. | | 6.1 Equivalence predicates | ... | Note: This section does not state under which conditions eqv? | returns #t or #f for inexact numbers that are not in IEEE 754/854 | format. We recommend that numbers not in IEEE 754/854 format for | which a base, sign, number of exponent digits, exponent bias, | biased exponent, number of significand digits, and significand can | be defined follow the same rules as above. Why are you restricting the specification of inexacts to IEEE-754/854 arthmetic? | 6.2.5. Numerical operations | | (number? obj ) procedure | (complex? obj ) procedure | (real? obj ) procedure | (rational? obj ) procedure | (integer? obj ) procedure ... | <add this> | If an implementation uses IEEE 754/854 format for inexact numbers then: | | * If z is an inexact complex number, then (real? z) is true if and | only if both (exact? (imag-part z)) and (zero? (imag-part z)) are | true. ... | For implementations that allow (real z) and (imag z) to have different | exactness, then (exact? z) returns #t if and only if both (exact? | (real z)) and (exact? (imag z)) return #t. | <end of addition> A number is either exact or inexact; and a complex number (like a rational number) is one number, not two. Exactness thus applies to the whole complex number, not to its components. | <change the following predicates> | (zero? z) library procedure | (positive? x) library procedure | (negative? x) library procedure | (odd? n) library procedure | (even? n) library procedure | These numerical predicates test a number for a particular | property, returning #t or #f. | | If an implementation uses IEEE 754/854 format for its inexact numbers, | then zero?, positive?, and negative? return #f if called with a NaN | argument. The names of the arguments already restrict positive?, negative?, odd? and even? to argument types to which NaN does not belong. Passing NaN to them is an error. | <change the following procedures> | | (max x1 x2 : : : ) library procedure | (min x1 x2 : : : ) library procedure | | These procedures return the maximum or minimum of their arguments. | | (max 3 4) =) 4 ; exact | (max 3.9 4) =) 4.0 ; inexact | | If an implementation uses IEEE 754/854 format for its inexact numbers, | and any of the arguments to max and min are NaNs, then max and min | returns one of the NaN arguments as its result. IEEE NaN is not real, having no position in the well-ordered real-numbers. It is thus an illegal argument to MAX, MIN, <, <=, >, and >=. | <change the following procedures> | (+ z1 : : : ) procedure | (* z1 : : : ) procedure | | These procedures return the sum or product of their arguments. | | (+ 3 4) =) 7 | (+ 3) =) 3 | (+) =) 0 | (* 4) =) 4 | (*) =) 1 | | Note: We recommend that (+ 0 z) => z, (* 1 z) => z, and (* 0 z) => | 0 for all z. This simplifies some rules for addition and | multiplication for complex and inexact numbers if an | implementation uses IEEE 754/854 format for its inexact | arithmetic. Processors have either hardware to manipulate floating-point numbers, or library routines to emulate the hardware. Changing the IEEE-754 rules (so that 0 * NaN --> 0) will complicate, not simplify the implementation of numerics.