65 lines
2.1 KiB
Plaintext
65 lines
2.1 KiB
Plaintext
;; Function To Be Tested: RATIONAL
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;;
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;; Source: Guy L Steele's CLTL
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;; Section: 12.6 Type Conversions and Component Extractions on Numbers
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;; Page: 214
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;;
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;; Created By: Kelly Roach, John Park
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;;
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;; Creation Date: July 12,1986
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;;
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;; Last Update: Jan 28, 1987 - Jim Blum - Substitued (= ...) for (eq.. ...)
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;;
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;; Filed As: {ERIS}<LISPCORE>CML>TEST>12-6-RATIONAL.TEST
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;;
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;;
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;; Syntax: (RATIONAL NUMBER)
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;;
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;; Function Description:
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;; Each of these functions converts any non-complex number to be a rational
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;; number. If the argument is already rational, it is returned.
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;; The two functions differ in their treatment of floating-point numbers.
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;;
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;; RATIONAL assumes that the floating-point number is completely accurate
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;; and returns a rational number mathematically equal to the precise
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;; value of the floating-point number.
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;;
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;; RATIONALIZE assumes that the
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;; floating-point number is accurate only to the precision of the
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;; floating-point representation, and may return any rational number for
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;; which the floating-point number is the best available approximation of
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;; its format; in doing this it attempts to keep both numerator and
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;; denominator small.
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;;
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;; It is always the case that
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;;
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;; (FLOAT (RATIONAL X) X) = X
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;;
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;; and
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;;
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;; (FLOAT (RATIONALIZE X) X) = X
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;;
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;; That is, rationalizing a floating-point number by either method
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;; and then converting it back
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;; to a floating-point number of the same format produces the original number.
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;; What distinguishes the two functions is that RATIONAL typically
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;; has a simple, inexpensive implementation, whereas RATIONALIZE goes
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;; to more trouble to produce a result that is more pleasant to view and
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;; simpler for some purposes to compute with.
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;;
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;; Argument(s): NUMBER - a number
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;;
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;; Returns: a number
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;;
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(do-test rational-test
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(and (= (rational 10) 10)
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(= (float (rational 3.1)) (/ 31 10))
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(rationalp (rational 3.1))
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(= (float (rational 3.1)) 3.1)
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(= (float (rational (/ 3 10))) (/ 3 10))
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(rationalp (rational (/ 3 10)))
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(= (rational 3E3) 3000)))
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STOP
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