;;;; numbers.test --- tests guile's numbers -*- scheme -*-
-;;;; Copyright (C) 2000, 2001, 2003, 2004, 2005, 2006, 2009, 2010 Free Software Foundation, Inc.
+;;;; Copyright (C) 2000, 2001, 2003, 2004, 2005, 2006, 2009, 2010, 2011,
+;;;; 2012, 2013 Free Software Foundation, Inc.
;;;;
;;;; This library is free software; you can redistribute it and/or
;;;; modify it under the terms of the GNU Lesser General Public
(define-module (test-suite test-numbers)
#:use-module (test-suite lib)
- #:use-module (ice-9 documentation))
+ #:use-module (ice-9 documentation)
+ #:use-module (srfi srfi-1) ; list library
+ #:use-module (srfi srfi-11)) ; let-values
;;;
;;; miscellaneous
(not (not (object-documentation object))))
(define fixnum-bit
- (inexact->exact (+ (/ (log (+ most-positive-fixnum 1)) (log 2)) 1)))
+ (do ((i 0 (+ 1 i))
+ (n 1 (* 2 n)))
+ ((> n most-positive-fixnum)
+ (+ 1 i))))
(define fixnum-min most-negative-fixnum)
(define fixnum-max most-positive-fixnum)
;; the usual 53.
;;
(define dbl-mant-dig
- (let more ((i 1)
- (d 2.0))
- (if (> i 1024)
- (error "Oops, cannot determine number of bits in mantissa of inexact"))
- (let* ((sum (+ 1.0 d))
- (diff (- sum d)))
- (if (= diff 1.0)
- (more (1+ i) (* 2.0 d))
- i))))
+ (do ((prec 0 (+ prec 1))
+ (eps 1.0 (/ eps 2.0)))
+ ((begin (when (> prec 1000000)
+ (error "Unable to determine dbl-mant-dig"))
+ (= 1.0 (+ 1.0 eps)))
+ prec)))
+
+(define dbl-epsilon
+ (expt 0.5 (- dbl-mant-dig 1)))
+
+(define dbl-epsilon-exact
+ (expt 1/2 (- dbl-mant-dig 1)))
+
+(define dbl-min-exp
+ (do ((x 1.0 (/ x 2.0))
+ (y (+ 1.0 dbl-epsilon) (/ y 2.0))
+ (e 2 (- e 1)))
+ ((begin (when (< e -100000000)
+ (error "Unable to determine dbl-min-exp"))
+ (= x y))
+ e)))
+
+(define dbl-max-exp
+ (do ((x 1.0 (* x 2.0))
+ (e 0 (+ e 1)))
+ ((begin (when (> e 100000000)
+ (error "Unable to determine dbl-max-exp"))
+ (inf? x))
+ e)))
;; like ash, but working on a flonum
(define (ash-flo x n)
(negative? obj)
(inf? obj)))
+;;
+;; Tolerance used by test-eqv? for inexact numbers.
+;;
+(define test-epsilon 1e-10)
+
+;;
+;; Like eqv?, except that inexact finite numbers need only be within
+;; test-epsilon (1e-10) to be considered equal. For non-real complex
+;; numbers, each component is tested according to these rules. The
+;; intent is that the known-correct value will be the first parameter.
+;;
+(define (test-eqv? x y)
+ (cond ((real? x)
+ (and (real? y) (test-real-eqv? x y)))
+ ((complex? x)
+ (and (not (real? y))
+ (test-real-eqv? (real-part x) (real-part y))
+ (test-real-eqv? (imag-part x) (imag-part y))))
+ (else (eqv? x y))))
+
+;; Auxiliary predicate used by test-eqv?
+(define (test-real-eqv? x y)
+ (cond ((or (exact? x) (nan? x) (inf? x))
+ (eqv? x y))
+ (else (and (inexact? y) (> test-epsilon (abs (- x y)))))))
+
+;; return true if OBJ is a real NaN
+(define (real-nan? obj)
+ (and (real? obj)
+ (nan? obj)))
+
+;; return true if OBJ is a non-real complex number
+;; whose real part is a nan, and whose imaginary
+;; part is an inexact zero.
+(define (almost-real-nan? obj)
+ (and (not (real? obj))
+ (nan? (real-part obj))
+ (zero? (imag-part obj))))
+
+;; return true if both the real and imaginary
+;; parts of OBJ are NaNs
+(define (complex-nan? obj)
+ (and (nan? (real-part obj))
+ (nan? (imag-part obj))))
+
+;; return true if the real part of OBJ is zero
+;; and the imaginary part is a NaN.
+(define (imaginary-nan? obj)
+ (and (zero? (real-part obj))
+ (nan? (imag-part obj))))
+
+;; return true if OBJ is a non-real complex zero
+(define (complex-zero? obj)
+ (and (zero? obj)
+ (complex? obj)
+ (not (real? obj))))
+
(define const-e 2.7182818284590452354)
(define const-e^2 7.3890560989306502274)
(define const-1/e 0.3678794411714423215)
(pass-if "1- fixnum = bignum (64-bit)"
(eqv? -2305843009213693953 (1- -2305843009213693952))))
-;;;
-;;; ash
-;;;
-
-(with-test-prefix "ash"
-
- (pass-if "documented?"
- (documented? ash))
-
- (pass-if (eqv? 0 (ash 0 0)))
- (pass-if (eqv? 0 (ash 0 1)))
- (pass-if (eqv? 0 (ash 0 1000)))
- (pass-if (eqv? 0 (ash 0 -1)))
- (pass-if (eqv? 0 (ash 0 -1000)))
-
- (pass-if (eqv? 1 (ash 1 0)))
- (pass-if (eqv? 2 (ash 1 1)))
- (pass-if (eqv? 340282366920938463463374607431768211456 (ash 1 128)))
- (pass-if (eqv? 0 (ash 1 -1)))
- (pass-if (eqv? 0 (ash 1 -1000)))
-
- (pass-if (eqv? -1 (ash -1 0)))
- (pass-if (eqv? -2 (ash -1 1)))
- (pass-if (eqv? -340282366920938463463374607431768211456 (ash -1 128)))
- (pass-if (eqv? -1 (ash -1 -1)))
- (pass-if (eqv? -1 (ash -1 -1000)))
-
- (pass-if (eqv? -3 (ash -3 0)))
- (pass-if (eqv? -6 (ash -3 1)))
- (pass-if (eqv? -1020847100762815390390123822295304634368 (ash -3 128)))
- (pass-if (eqv? -2 (ash -3 -1)))
- (pass-if (eqv? -1 (ash -3 -1000)))
-
- (pass-if (eqv? -6 (ash -23 -2)))
-
- (pass-if (eqv? most-positive-fixnum (ash most-positive-fixnum 0)))
- (pass-if (eqv? (* 2 most-positive-fixnum) (ash most-positive-fixnum 1)))
- (pass-if (eqv? (* 4 most-positive-fixnum) (ash most-positive-fixnum 2)))
- (pass-if
- (eqv? (* most-positive-fixnum 340282366920938463463374607431768211456)
- (ash most-positive-fixnum 128)))
- (pass-if (eqv? (quotient most-positive-fixnum 2)
- (ash most-positive-fixnum -1)))
- (pass-if (eqv? 0 (ash most-positive-fixnum -1000)))
-
- (let ((mpf4 (quotient most-positive-fixnum 4)))
- (pass-if (eqv? (* 2 mpf4) (ash mpf4 1)))
- (pass-if (eqv? (* 4 mpf4) (ash mpf4 2)))
- (pass-if (eqv? (* 8 mpf4) (ash mpf4 3))))
-
- (pass-if (eqv? most-negative-fixnum (ash most-negative-fixnum 0)))
- (pass-if (eqv? (* 2 most-negative-fixnum) (ash most-negative-fixnum 1)))
- (pass-if (eqv? (* 4 most-negative-fixnum) (ash most-negative-fixnum 2)))
- (pass-if
- (eqv? (* most-negative-fixnum 340282366920938463463374607431768211456)
- (ash most-negative-fixnum 128)))
- (pass-if (eqv? (quotient-floor most-negative-fixnum 2)
- (ash most-negative-fixnum -1)))
- (pass-if (eqv? -1 (ash most-negative-fixnum -1000)))
-
- (let ((mnf4 (quotient-floor most-negative-fixnum 4)))
- (pass-if (eqv? (* 2 mnf4) (ash mnf4 1)))
- (pass-if (eqv? (* 4 mnf4) (ash mnf4 2)))
- (pass-if (eqv? (* 8 mnf4) (ash mnf4 3)))))
-
;;;
;;; exact?
;;;
(eq? #f (exact? (sqrt (- (expt fixnum-max 2) 1)))))
(pass-if "sqrt ((fixnum-max+1)^2 - 1)"
- (eq? #f (exact? (sqrt (- (expt (+ fixnum-max 1) 2) 1)))))))
+ (eq? #f (exact? (sqrt (- (expt (+ fixnum-max 1) 2) 1)))))
+
+ (pass-if (not (exact? +inf.0)))
+ (pass-if (not (exact? -inf.0)))
+ (pass-if (not (exact? +nan.0)))))
;;;
;;; exp
;;;
(with-test-prefix "exp"
- (pass-if "documented?"
- (documented? exp))
+ (pass-if (documented? exp))
(pass-if-exception "no args" exception:wrong-num-args
(exp))
(pass-if (not (even? (- (* 2 fixnum-min) 1))))
(pass-if (even? (* 2 fixnum-min))))
+;;;
+;;; finite?
+;;;
+
+(with-test-prefix "finite?"
+ (pass-if (documented? finite?))
+ (pass-if (not (finite? (inf))))
+ (pass-if (not (finite? +inf.0)))
+ (pass-if (not (finite? -inf.0)))
+ (pass-if-exception
+ "complex numbers not in domain of finite?"
+ exception:wrong-type-arg
+ (finite? +inf.0+1i))
+ (pass-if-exception
+ "complex numbers not in domain of finite? (2)"
+ exception:wrong-type-arg
+ (finite? +1+inf.0i))
+ (pass-if-exception
+ "complex numbers not in domain of finite? (3)"
+ exception:wrong-type-arg
+ (finite? +1+1i))
+ (pass-if (finite? 3+0i))
+ (pass-if (not (finite? (nan))))
+ (pass-if (not (finite? +nan.0)))
+ (pass-if (finite? 0))
+ (pass-if (finite? 0.0))
+ (pass-if (finite? -0.0))
+ (pass-if (finite? 42.0))
+ (pass-if (finite? 1/2))
+ (pass-if (finite? (+ fixnum-max 1)))
+ (pass-if (finite? (- fixnum-min 1))))
+
;;;
;;; inf? and inf
;;;
;; FIXME: what are the expected behaviors?
;; (pass-if (inf? (/ 1.0 0.0))
;; (pass-if (inf? (/ 1 0.0))
+ (pass-if-exception
+ "complex numbers not in domain of inf?"
+ exception:wrong-type-arg
+ (inf? +1+inf.0i))
+ (pass-if (inf? +inf.0+0i))
(pass-if (not (inf? 0)))
(pass-if (not (inf? 42.0)))
(pass-if (not (inf? (+ fixnum-max 1))))
(with-test-prefix "abs"
(pass-if (documented? abs))
- (pass-if (zero? (abs 0)))
- (pass-if (= 1 (abs 1)))
- (pass-if (= 1 (abs -1)))
- (pass-if (= (+ fixnum-max 1) (abs (+ fixnum-max 1))))
- (pass-if (= (+ (- fixnum-min) 1) (abs (- fixnum-min 1))))
- (pass-if (= 0.0 (abs 0.0)))
- (pass-if (= 1.0 (abs 1.0)))
- (pass-if (= 1.0 (abs -1.0)))
- (pass-if (nan? (abs +nan.0)))
- (pass-if (= +inf.0 (abs +inf.0)))
- (pass-if (= +inf.0 (abs -inf.0))))
+ (pass-if (eqv? 0 (abs 0)))
+ (pass-if (eqv? 1 (abs 1)))
+ (pass-if (eqv? 1 (abs -1)))
+
+ (with-test-prefix "double-negation of fixnum-min"
+ (pass-if (eqv? fixnum-min (- (abs fixnum-min)))))
+
+ (pass-if (eqv? (+ fixnum-max 1) (abs (+ fixnum-max 1))))
+ (pass-if (eqv? (+ (- fixnum-min) 1) (abs (- fixnum-min 1))))
+
+ (pass-if (eqv? 0.0 (abs 0.0)))
+ (pass-if (eqv? 0.0 (abs -0.0)))
+ (pass-if (eqv? 1.0 (abs 1.0)))
+ (pass-if (eqv? 1.0 (abs -1.0)))
+ (pass-if (real-nan? (abs +nan.0)))
+ (pass-if (eqv? +inf.0 (abs +inf.0)))
+ (pass-if (eqv? +inf.0 (abs -inf.0))))
;;;
;;; quotient
;;;
(with-test-prefix "quotient"
-
- (expect-fail "documented?"
- (documented? quotient))
+ (pass-if (documented? quotient))
(with-test-prefix "0 / n"
(pass-if "n = fixnum-min - 1"
(eqv? 1 (quotient (- fixnum-min 1) (- fixnum-min 1)))))
+ ;; Inexact integers
+
+ (pass-if (eqv? 5.0 (quotient 35.0 7.0)))
+ (pass-if (eqv? 5.0 (quotient 35 7.0)))
+ (pass-if (eqv? 5.0 (quotient 35.0 7 )))
+
;; Positive dividend and divisor
(pass-if "35 / 7"
;;;
(with-test-prefix "remainder"
-
- (expect-fail "documented?"
- (documented? remainder))
+ (pass-if (documented? remainder))
(with-test-prefix "0 / n"
(pass-if "n = fixnum-min - 1"
(eqv? 0 (remainder (- fixnum-min 1) (- fixnum-min 1)))))
+ ;; Inexact integers
+
+ (pass-if (eqv? 2.0 (remainder 37.0 7.0)))
+ (pass-if (eqv? 2.0 (remainder 37 7.0)))
+ (pass-if (eqv? 2.0 (remainder 37.0 7 )))
+
;; Positive dividend and divisor
(pass-if "35 / 7"
;;;
(with-test-prefix "modulo"
-
- (expect-fail "documented?"
- (documented? modulo))
+ (pass-if (documented? modulo))
(with-test-prefix "0 % n"
(pass-if "n = fixnum-min - 1"
(eqv? 0 (modulo (- fixnum-min 1) (- fixnum-min 1)))))
+ ;; Inexact integers
+
+ (pass-if (eqv? 1.0 (modulo 13.0 4.0)))
+ (pass-if (eqv? 1.0 (modulo 13 4.0)))
+ (pass-if (eqv? 1.0 (modulo 13.0 4 )))
+
;; Positive dividend and divisor
(pass-if "13 % 4"
;;;
(with-test-prefix "numerator"
- (pass-if "0"
- (eqv? 0 (numerator 0)))
- (pass-if "1"
- (eqv? 1 (numerator 1)))
- (pass-if "2"
- (eqv? 2 (numerator 2)))
- (pass-if "-1"
- (eqv? -1 (numerator -1)))
- (pass-if "-2"
- (eqv? -2 (numerator -2)))
-
- (pass-if "0.0"
- (eqv? 0.0 (numerator 0.0)))
- (pass-if "1.0"
- (eqv? 1.0 (numerator 1.0)))
- (pass-if "2.0"
- (eqv? 2.0 (numerator 2.0)))
- (pass-if "-1.0"
- (eqv? -1.0 (numerator -1.0)))
- (pass-if "-2.0"
- (eqv? -2.0 (numerator -2.0)))
-
- (pass-if "0.5"
- (eqv? 1.0 (numerator 0.5)))
- (pass-if "0.25"
- (eqv? 1.0 (numerator 0.25)))
- (pass-if "0.75"
- (eqv? 3.0 (numerator 0.75))))
+ (pass-if-equal "0" 0 (numerator 0))
+ (pass-if-equal "1" 1 (numerator 1))
+ (pass-if-equal "2" 2 (numerator 2))
+ (pass-if-equal "-1" -1 (numerator -1))
+ (pass-if-equal "-2" -2 (numerator -2))
+
+ (pass-if-equal "0.0" 0.0 (numerator 0.0))
+ (pass-if-equal "1.0" 1.0 (numerator 1.0))
+ (pass-if-equal "2.0" 2.0 (numerator 2.0))
+ (pass-if-equal "-0.0" -0.0 (numerator -0.0))
+ (pass-if-equal "-1.0" -1.0 (numerator -1.0))
+ (pass-if-equal "-2.0" -2.0 (numerator -2.0))
+
+ (pass-if-equal "0.5" 1.0 (numerator 0.5))
+ (pass-if-equal "0.25" 1.0 (numerator 0.25))
+ (pass-if-equal "0.75" 3.0 (numerator 0.75))
+
+ (pass-if-equal "+inf.0" +inf.0 (numerator +inf.0))
+ (pass-if-equal "-inf.0" -inf.0 (numerator -inf.0)))
;;;
;;; denominator
;;;
(with-test-prefix "denominator"
- (pass-if "0"
- (eqv? 1 (denominator 0)))
- (pass-if "1"
- (eqv? 1 (denominator 1)))
- (pass-if "2"
- (eqv? 1 (denominator 2)))
- (pass-if "-1"
- (eqv? 1 (denominator -1)))
- (pass-if "-2"
- (eqv? 1 (denominator -2)))
-
- (pass-if "0.0"
- (eqv? 1.0 (denominator 0.0)))
- (pass-if "1.0"
- (eqv? 1.0 (denominator 1.0)))
- (pass-if "2.0"
- (eqv? 1.0 (denominator 2.0)))
- (pass-if "-1.0"
- (eqv? 1.0 (denominator -1.0)))
- (pass-if "-2.0"
- (eqv? 1.0 (denominator -2.0)))
-
- (pass-if "0.5"
- (eqv? 2.0 (denominator 0.5)))
- (pass-if "0.25"
- (eqv? 4.0 (denominator 0.25)))
- (pass-if "0.75"
- (eqv? 4.0 (denominator 0.75))))
+ (pass-if-equal "0" 1 (denominator 0))
+ (pass-if-equal "1" 1 (denominator 1))
+ (pass-if-equal "2" 1 (denominator 2))
+ (pass-if-equal "-1" 1 (denominator -1))
+ (pass-if-equal "-2" 1 (denominator -2))
+
+ (pass-if-equal "0.0" 1.0 (denominator 0.0))
+ (pass-if-equal "1.0" 1.0 (denominator 1.0))
+ (pass-if-equal "2.0" 1.0 (denominator 2.0))
+ (pass-if-equal "-0.0" 1.0 (denominator -0.0))
+ (pass-if-equal "-1.0" 1.0 (denominator -1.0))
+ (pass-if-equal "-2.0" 1.0 (denominator -2.0))
+
+ (pass-if-equal "0.5" 2.0 (denominator 0.5))
+ (pass-if-equal "0.25" 4.0 (denominator 0.25))
+ (pass-if-equal "0.75" 4.0 (denominator 0.75))
+
+ (pass-if-equal "+inf.0" 1.0 (denominator +inf.0))
+ (pass-if-equal "-inf.0" 1.0 (denominator -inf.0)))
;;;
;;; gcd
(pass-if "n = fixnum-min - 1"
(eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) (- fixnum-min 1)))))
+ (with-test-prefix "flonum arguments"
+
+ (pass-if-equal "flonum"
+ 15.0
+ (gcd -15.0))
+
+ (pass-if-equal "flonum/flonum"
+ 3.0
+ (gcd 6.0 -15.0))
+
+ (pass-if-equal "flonum/fixnum"
+ 3.0
+ (gcd 6.0 -15))
+
+ (pass-if-equal "fixnum/flonum"
+ 3.0
+ (gcd -6 15.0))
+
+ (pass-if-equal "flonum/bignum"
+ 2.0
+ (gcd -6.0 (expt 2 fixnum-bit)))
+
+ (pass-if-equal "bignum/flonum"
+ 3.0
+ (gcd (- (expt 3 fixnum-bit)) 6.0)))
+
;; Are wrong type arguments detected correctly?
)
;; FIXME: more tests?
;; (some of these are already in r4rs.test)
(pass-if (documented? lcm))
- (pass-if (= (lcm) 1))
- (pass-if (= (lcm 32 -36) 288))
+ (pass-if-equal 1 (lcm))
+ (pass-if-equal 15 (lcm -15))
+ (pass-if-equal 288 (lcm 32 -36))
+
+ (with-test-prefix "flonum arguments"
+
+ (pass-if-equal "flonum"
+ 15.0
+ (lcm -15.0))
+
+ (pass-if-equal "flonum/flonum"
+ 30.0
+ (lcm 6.0 -15.0))
+
+ (pass-if-equal "flonum/fixnum"
+ 30.0
+ (lcm 6.0 -15))
+
+ (pass-if-equal "fixnum/flonum"
+ 30.0
+ (lcm -6 15.0))
+
+ (pass-if "flonum/bignum"
+ (let ((want (* 3.0 (expt 2 fixnum-bit)))
+ (got (lcm -6.0 (expt 2 fixnum-bit))))
+ (and (inexact? got)
+ (test-eqv? 1.0 (/ want got)))))
+
+ (pass-if "bignum/flonum"
+ (let ((want (* 2.0 (expt 3 fixnum-bit)))
+ (got (lcm (- (expt 3 fixnum-bit)) 6.0)))
+ (and (inexact? got)
+ (test-eqv? 1.0 (/ want got))))))
+
(let ((big-n 115792089237316195423570985008687907853269984665640564039457584007913129639936) ; 2 ^ 256
(lcm-of-big-n-and-11 1273712981610478149659280835095566986385969831322046204434033424087044426039296))
(pass-if (= lcm-of-big-n-and-11 (lcm big-n 11)))
(pass-if (= lcm-of-big-n-and-11 (lcm 11 big-n 11)))))
+;;;
+;;; rationalize
+;;;
+(with-test-prefix "rationalize"
+ (pass-if (documented? rationalize))
+ (pass-if (eqv? 2 (rationalize 4 2 )))
+ (pass-if (eqv? -2 (rationalize -4 2 )))
+ (pass-if (eqv? 2.0 (rationalize 4 2.0)))
+ (pass-if (eqv? -2.0 (rationalize -4.0 2 )))
+
+ (pass-if (eqv? 0 (rationalize 4 8 )))
+ (pass-if (eqv? 0 (rationalize -4 8 )))
+ (pass-if (eqv? 0.0 (rationalize 4 8.0)))
+ (pass-if (eqv? 0.0 (rationalize -4.0 8 )))
+
+ (pass-if (eqv? 0.0 (rationalize 3 +inf.0)))
+ (pass-if (eqv? 0.0 (rationalize -3 +inf.0)))
+
+ (pass-if (real-nan? (rationalize +inf.0 +inf.0)))
+ (pass-if (real-nan? (rationalize +nan.0 +inf.0)))
+ (pass-if (real-nan? (rationalize +nan.0 4)))
+ (pass-if (eqv? +inf.0 (rationalize +inf.0 3)))
+
+ (pass-if (eqv? 3/10 (rationalize 3/10 0)))
+ (pass-if (eqv? -3/10 (rationalize -3/10 0)))
+
+ (pass-if (eqv? 1/3 (rationalize 3/10 1/10)))
+ (pass-if (eqv? -1/3 (rationalize -3/10 1/10)))
+
+ (pass-if (eqv? 1/3 (rationalize 3/10 -1/10)))
+ (pass-if (eqv? -1/3 (rationalize -3/10 -1/10)))
+
+ ;; Prior to Guile 2.0.10, rationalize used a faulty algorithm that
+ ;; incorrectly returned 2/3 and -2/3 in the following cases.
+ (pass-if (eqv? 1/2 (rationalize #e+0.67 1/4)))
+ (pass-if (eqv? -1/2 (rationalize #e-0.67 1/4)))
+
+ (pass-if (eqv? 1 (rationalize #e+0.67 1/3)))
+ (pass-if (eqv? -1 (rationalize #e-0.67 1/3)))
+
+ (pass-if (eqv? 1/2 (rationalize #e+0.66 1/3)))
+ (pass-if (eqv? -1/2 (rationalize #e-0.66 1/3)))
+
+ (pass-if (eqv? 1 (rationalize #e+0.67 2/3)))
+ (pass-if (eqv? -1 (rationalize #e-0.67 2/3)))
+
+ (pass-if (eqv? 0 (rationalize #e+0.66 2/3)))
+ (pass-if (eqv? 0 (rationalize #e-0.66 2/3)))
+
+ ;; Prior to Guile 2.0.10, rationalize used a faulty algorithm that
+ ;; incorrectly computed the following approximations of PI.
+ (with-test-prefix "pi"
+ (define *pi* #e3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679)
+ (pass-if (eqv? 16/5 (rationalize *pi* 1/10)))
+ (pass-if (eqv? 201/64 (rationalize *pi* 1/1000)))
+ (pass-if (eqv? 75948/24175 (rationalize *pi* (expt 10 -7))))
+ (pass-if (eqv? 100798/32085 (rationalize *pi* (expt 10 -8))))
+ (pass-if (eqv? 58466453/18610450 (rationalize *pi* (expt 10 -14))))
+ (pass-if (eqv? 2307954651196778721982809475299879198775111361078/734644782339796933783743757007944508986600750685
+ (rationalize *pi* (expt 10 -95)))))
+
+ (pass-if (test-eqv? (/ 1.0 3) (rationalize 0.3 1/10)))
+ (pass-if (test-eqv? (/ -1.0 3) (rationalize -0.3 1/10)))
+ (pass-if (test-eqv? (/ 1.0 3) (rationalize 0.3 -1/10)))
+ (pass-if (test-eqv? (/ -1.0 3) (rationalize -0.3 -1/10))))
+
;;;
;;; number->string
;;;
(lambda (n radix)
(string->number (number->string n radix) radix))))
+ (define (test num)
+ (pass-if-equal (list num 'pos)
+ num
+ (num->str->num num 10))
+ (pass-if-equal (list num 'neg)
+ (- num)
+ (num->str->num (- num) 10)))
+
(pass-if (documented? number->string))
(pass-if (string=? (number->string 0) "0"))
(pass-if (string=? (number->string 171) "171"))
(pass-if (= (+ fixnum-max 1) (num->str->num (+ fixnum-max 1) 10)))
(pass-if (= (- fixnum-min 1) (num->str->num (- fixnum-min 1) 10)))
- (pass-if (= (inf) (num->str->num (inf) 10)))
- (pass-if (= 1.3 (num->str->num 1.3 10)))
- ;; XXX - some results depend on whether Guile is compiled optimzed
- ;; or not. It is clearly undesirable to have number->string to be
- ;; influenced by this.
+ (test (inf))
+ (test 1.3)
+ (test (acos -1)) ; pi
+ (test (exp 1)) ; e
+ (test (/ 3.0))
+ (test (/ 7.0))
+ (test 2.2250738585072011e-308)
+ (test 2.2250738585072012e-308)
+
+ ;; Largest finite inexact
+ (test (* (- (expt 2.0 dbl-mant-dig) 1)
+ (expt 2.0 (- dbl-max-exp dbl-mant-dig))))
+
+ (pass-if (string=? "0.0" (number->string 0.0)))
+ (pass-if (or (eqv? 0.0 -0.0)
+ (string=? "-0.0" (number->string -0.0))))
(pass-if (string=? (number->string 35.25 36) "z.9"))
- (pass-if (or (string=? (number->string 0.25 2) "0.01")
- (string=? (number->string 0.25 2) "0.010")))
+ (pass-if (string=? (number->string 0.25 2) "0.01"))
(pass-if (string=? (number->string 255.0625 16) "ff.1"))
(pass-if (string=? (number->string (/ 1 3) 3) "1/10"))
(pass-if (string=? (number->string 35 36) "z"))
(pass-if (= (num->str->num 35 36) 35))
- ;; Numeric conversion from decimal is not precise, in its current
- ;; implementation, so 11.333... and 1.324... can't be expected to
- ;; reliably come out to precise values. These tests did actually work
- ;; for a while, but something in gcc changed, affecting the conversion
- ;; code.
- ;;
- ;; (pass-if (or (string=? (number->string 11.33333333333333333 12)
- ;; "B.4")
- ;; (string=? (number->string 11.33333333333333333 12)
- ;; "B.400000000000009")))
- ;; (pass-if (or (string=? (number->string 1.324e44 16)
- ;; "5.EFE0A14FAFEe24")
- ;; (string=? (number->string 1.324e44 16)
- ;; "5.EFE0A14FAFDF8e24")))
- ))
+ (pass-if (string=? (number->string 12342342340000.0) "1.234234234e13"))
+ (pass-if (string=? (number->string 1234234234000.0) "1234234234000.0"))
+ (pass-if (string=? (number->string 1240000.0) "1240000.0"))
+
+ (with-test-prefix "powers of radix"
+ (for-each
+ (lambda (radix)
+ (for-each (lambda (k)
+ (let ((val (exact->inexact (expt radix k)))
+ (str (if (<= -3 k 6)
+ (assoc-ref '((-3 . "0.001")
+ (-2 . "0.01")
+ (-1 . "0.1")
+ ( 0 . "1.0")
+ ( 1 . "10.0")
+ ( 2 . "100.0")
+ ( 3 . "1000.0")
+ ( 4 . "10000.0")
+ ( 5 . "100000.0")
+ ( 6 . "1000000.0"))
+ k)
+ (string-append "1.0e"
+ (number->string k radix)))))
+ (pass-if-equal (list radix k 'pos)
+ str
+ (number->string val radix))
+ (pass-if-equal (list radix k 'neg)
+ (string-append "-" str)
+ (number->string (- val) radix))))
+ (iota 41 -20)))
+ (iota 35 2)))
+
+ (with-test-prefix "multiples of smallest inexact"
+ (for-each (lambda (k)
+ (let ((val (* k (expt 2.0 (- dbl-min-exp dbl-mant-dig)))))
+ (test val)))
+ (iota 40 1)))
+
+ (with-test-prefix "one plus multiples of epsilon"
+ (for-each (lambda (k)
+ (let ((val (+ 1.0 (* k dbl-epsilon))))
+ (test val)))
+ (iota 40 1)))
+
+ (with-test-prefix "one minus multiples of 1/2 epsilon"
+ (for-each (lambda (k)
+ (let ((val (- 1.0 (* k 1/2 dbl-epsilon))))
+ (test val)))
+ (iota 40 1)))
+
+ ;; Before Guile 2.0.1, even in the presence of a #e forced exactness
+ ;; specifier, negative exponents were applied inexactly and then
+ ;; later coerced to exact, yielding an incorrect fraction.
+ (pass-if (eqv? (string->number "#e1e-10") 1/10000000000))
+
+ (pass-if (string=? (number->string 11.33333333333333333 12)
+ "b.4"))
+ (pass-if (string=? (number->string 1.324e44 16)
+ "5.efe0a14fafdf8e24"))))
;;;
;;; string->number
"#o.2" "3.4q" "15.16e17q" "18.19e+q" ".q" ".17#18" "10q" "#b2"
"#b3" "#b4" "#b5" "#b6" "#b7" "#b8" "#b9" "#ba" "#bb" "#bc"
"#bd" "#be" "#bf" "#q" "#b#b1" "#o#o1" "#d#d1" "#x#x1" "#e#e1"
- "#i#i1" "12@12+0i"))
+ "#i#i1" "12@12+0i" "3/0" "0/0" "4+3/0i" "4/0-3i" "2+0/0i"
+ "nan.0" "inf.0" "#e+nan.0" "#e+inf.0" "#e-inf.0"
+ "3@inf.0" "4@nan.0"))
#t)
(pass-if "valid number strings"
("1/1" 1) ("1/2" 1/2) ("-1/2" -1/2) ("1#/1" 10.0)
("10/1#" 1.0) ("1#/1#" 1.0) ("#e9/10" 9/10) ("#e10/1#" 1)
("#i6/8" 0.75) ("#i1/1" 1.0)
+ ;; Infinities and NaNs:
+ ("+inf.0" ,(inf)) ("-inf.0" ,(- (inf)))
+ ("+Inf.0" ,(inf)) ("-Inf.0" ,(- (inf)))
+ ("+InF.0" ,(inf)) ("-InF.0" ,(- (inf)))
+ ("+INF.0" ,(inf)) ("-INF.0" ,(- (inf)))
+ ("#i+InF.0" ,(inf)) ("#i-InF.0" ,(- (inf)))
+ ("+nan.0" ,(nan)) ("-nan.0" ,(nan))
+ ("#i+nan.0" ,(nan)) ("#i-nan.0" ,(nan))
;; Decimal numbers:
;; * <uinteger 10> <suffix>
("1e2" 100.0) ("1E2" 100.0) ("1s2" 100.0) ("1S2" 100.0)
("3.1#e0" 3.1)
;; * <digit 10>+ #+ . #* <suffix>
("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
- ;; Complex:
- ("1@0" 1.0) ("1@+0" 1.0) ("1@-0" 1.0)
- ("2+3i" ,(+ 2 (* 3 +i))) ("4-5i" ,(- 4 (* 5 +i)))
- ("1+i" 1+1i) ("1-i" 1-1i) ("+1i" 0+1i) ("-1i" 0-1i)
- ("+i" +1i) ("-i" -1i)
- ("1.0+.1i" 1.0+0.1i)
- ("1.0-.1i" 1.0-0.1i)
- (".1+.0i" 0.1)
- ("1.+.0i" 1.0)
- (".1+.1i" 0.1+0.1i)
- ("1e1+.1i" 10+0.1i)
+ ))
+ #t)
+
+ (pass-if "valid complex number strings"
+ (for-each (lambda (triple)
+ (apply
+ (lambda (str re im)
+ (let ((z (string->number str)))
+ (if (or (eq? z #f)
+ (not (and (eqv? (real-part z) re)
+ (eqv? (imag-part z) im))))
+ (begin
+ (pk str re im)
+ (throw 'fail)))))
+ triple))
+ `(("1@0" 1 0) ("1@+0" 1 0) ("1@-0" 1 0) ("1/2@0" 1/2 0)
+ ("1.0@0" 1.0 0) ("1.0@-0" 1.0 0)
+ ("#e1@0" 1 0) ("#e1@+0" 1 0) ("#e1@-0" 1 0) ("#e0.5@0.0" 1/2 0)
+ ("#e1.0@0" 1 0) ("#e1.0@-0" 1 0)
+ ("#i1@0" 1.0 0.0) ("#i1@+0" 1.0 0.0) ("#i1@-0" 1.0 -0.0) ("#i1/2@0" 0.5 0.0)
+ ("#i1.0@0" 1.0 0.0) ("#i1.0@-0" 1.0 -0.0)
+ ("1@+0.0" 1.0 0.0) ("1.0@-0.0" 1.0 -0.0)
+ ("2+3i" 2.0 3.0) ("4-5i" 4.0 -5.0)
+ ("1+i" 1.0 1.0) ("1-i" 1.0 -1.0) ("+1i" 0.0 1.0) ("-1i" 0.0 -1.0)
+ ("+i" 0.0 1.0) ("-i" 0.0 -1.0)
+ ("1.0+.1i" 1.0 0.1) ("1.0-.1i" 1.0 -0.1)
+ (".1+.0i" 0.1 0.0) ("1.+.0i" 1.0 0.0) (".1+.1i" 0.1 0.1)
+ ("1e1+.1i" 10.0 0.1)
+ ("0@+nan.0" 0 0) ("0@+inf.0" 0 0) ("0@-inf.0" 0 0)
+ ("0.0@+nan.0" 0.0 0.0) ("0.0@+inf.0" 0.0 0.0) ("0.0@-inf.0" 0.0 0.0)
+ ("#i0@+nan.0" 0.0 0.0) ("#i0@+inf.0" 0.0 0.0) ("#i0@-inf.0" 0.0 0.0)
+ ("0.0@1" 0.0 0.0) ("0.0@2" -0.0 0.0) ("0.0@4" -0.0 -0.0) ("0.0@5" 0.0 -0.0)
))
#t)
(pass-if (real? (+ 1 fixnum-max)))
(pass-if (real? (- 1 fixnum-min)))
(pass-if (real? 1.3))
+ (pass-if (real? +inf.0))
+ (pass-if (real? -inf.0))
+ (pass-if (real? +nan.0))
+ (pass-if (not (real? +inf.0-inf.0i)))
+ (pass-if (not (real? +nan.0+nan.0i)))
(pass-if (not (real? 3+4i)))
(pass-if (not (real? #\a)))
(pass-if (not (real? "a")))
(pass-if (not (real? (current-input-port)))))
;;;
-;;; rational? (same as real? right now)
+;;; rational?
;;;
(with-test-prefix "rational?"
(pass-if (rational? (+ 1 fixnum-max)))
(pass-if (rational? (- 1 fixnum-min)))
(pass-if (rational? 1.3))
+ (pass-if (not (rational? +inf.0)))
+ (pass-if (not (rational? -inf.0)))
+ (pass-if (not (rational? +nan.0)))
+ (pass-if (not (rational? +inf.0-inf.0i)))
+ (pass-if (not (rational? +nan.0+nan.0i)))
(pass-if (not (rational? 3+4i)))
(pass-if (not (rational? #\a)))
(pass-if (not (rational? "a")))
(pass-if (and (= 3+0i (round 3+0i)) (integer? 3+0i)))
(pass-if (and (= 1.0 (round 1.0)) (integer? 1.0)))
(pass-if (not (integer? 1.3)))
- (pass-if (integer? +inf.0))
- (pass-if (integer? -inf.0))
+ (pass-if (not (integer? +inf.0)))
+ (pass-if (not (integer? -inf.0)))
(pass-if (not (integer? +nan.0)))
+ (pass-if (not (integer? +inf.0-inf.0i)))
+ (pass-if (not (integer? +nan.0+nan.0i)))
(pass-if (not (integer? 3+4i)))
(pass-if (not (integer? #\a)))
(pass-if (not (integer? "a")))
(pass-if (not (integer? (lambda () #t))))
(pass-if (not (integer? (current-input-port)))))
+;;;
+;;; exact-integer?
+;;;
+
+(with-test-prefix "exact-integer?"
+ (pass-if (documented? exact-integer?))
+ (pass-if (exact-integer? 0))
+ (pass-if (exact-integer? 7))
+ (pass-if (exact-integer? -7))
+ (pass-if (exact-integer? (+ 1 fixnum-max)))
+ (pass-if (exact-integer? (- 1 fixnum-min)))
+ (pass-if (and (= 1.0 (round 1.0))
+ (not (exact-integer? 1.0))))
+ (pass-if (not (exact-integer? 1.3)))
+ (pass-if (not (exact-integer? +inf.0)))
+ (pass-if (not (exact-integer? -inf.0)))
+ (pass-if (not (exact-integer? +nan.0)))
+ (pass-if (not (exact-integer? +inf.0-inf.0i)))
+ (pass-if (not (exact-integer? +nan.0+nan.0i)))
+ (pass-if (not (exact-integer? 3+4i)))
+ (pass-if (not (exact-integer? #\a)))
+ (pass-if (not (exact-integer? "a")))
+ (pass-if (not (exact-integer? (make-vector 0))))
+ (pass-if (not (exact-integer? (cons 1 2))))
+ (pass-if (not (exact-integer? #t)))
+ (pass-if (not (exact-integer? (lambda () #t))))
+ (pass-if (not (exact-integer? (current-input-port)))))
+
;;;
;;; inexact?
;;;
(pass-if (not (inexact? (- 1 fixnum-min))))
(pass-if (inexact? 1.3))
(pass-if (inexact? 3.1+4.2i))
+ (pass-if (inexact? +inf.0))
+ (pass-if (inexact? -inf.0))
+ (pass-if (inexact? +nan.0))
(pass-if-exception "char"
exception:wrong-type-arg
(not (inexact? #\a)))
(with-test-prefix "equal?"
(pass-if (documented? equal?))
+
+ ;; The following test will fail on platforms
+ ;; without distinct signed zeroes 0.0 and -0.0.
+ (pass-if (not (equal? 0.0 -0.0)))
+
(pass-if (equal? 0 0))
(pass-if (equal? 7 7))
(pass-if (equal? -7 -7))
(pass-if (equal? (+ 1 fixnum-max) (+ 1 fixnum-max)))
(pass-if (equal? (- fixnum-min 1) (- fixnum-min 1)))
+ (pass-if (equal? 0.0 0.0))
+ (pass-if (equal? -0.0 -0.0))
+ (pass-if (equal? 0.0+0.0i 0.0+0.0i))
+ (pass-if (equal? 0.0-0.0i 0.0-0.0i))
+ (pass-if (equal? -0.0+0.0i -0.0+0.0i))
(pass-if (not (equal? 0 1)))
+ (pass-if (not (equal? 0 0.0)))
+ (pass-if (not (equal? 1 1.0)))
+ (pass-if (not (equal? 0.0 0)))
+ (pass-if (not (equal? 1.0 1)))
+ (pass-if (not (equal? -1.0 -1)))
+ (pass-if (not (equal? 1.0 1.0+0.0i)))
+ (pass-if (not (equal? 0.0 0.0+0.0i)))
+ (pass-if (not (equal? 0.0+0.0i 0.0-0.0i)))
+ (pass-if (not (equal? 0.0+0.0i -0.0+0.0i)))
(pass-if (not (equal? fixnum-max (+ 1 fixnum-max))))
(pass-if (not (equal? (+ 1 fixnum-max) fixnum-max)))
(pass-if (not (equal? (+ 1 fixnum-max) (+ 2 fixnum-max))))
(pass-if (not (equal? (- (ash 1 1024)) -inf.0)))
(pass-if (not (equal? -inf.0 (- (ash 1 1024)))))
- (pass-if (not (equal? +nan.0 +nan.0)))
+ (pass-if (equal? +nan.0 +nan.0))
+ (pass-if (equal? +nan.0 +nan.0))
+ (pass-if (not (equal? +nan.0 0.0+nan.0i)))
+
(pass-if (not (equal? 0 +nan.0)))
(pass-if (not (equal? +nan.0 0)))
(pass-if (not (equal? 1 +nan.0)))
(pass-if (not (equal? (ash 3 1023) +nan.0)))
(pass-if (not (equal? +nan.0 (ash 3 1023)))))
+;;;
+;;; eqv?
+;;;
+
+(with-test-prefix "eqv?"
+ (pass-if (documented? eqv?))
+
+ ;; The following test will fail on platforms
+ ;; without distinct signed zeroes 0.0 and -0.0.
+ (pass-if (not (eqv? 0.0 -0.0)))
+
+ (pass-if (eqv? 0 0))
+ (pass-if (eqv? 7 7))
+ (pass-if (eqv? -7 -7))
+ (pass-if (eqv? (+ 1 fixnum-max) (+ 1 fixnum-max)))
+ (pass-if (eqv? (- fixnum-min 1) (- fixnum-min 1)))
+ (pass-if (eqv? 0.0 0.0))
+ (pass-if (eqv? -0.0 -0.0))
+ (pass-if (eqv? 0.0+0.0i 0.0+0.0i))
+ (pass-if (eqv? 0.0-0.0i 0.0-0.0i))
+ (pass-if (eqv? -0.0+0.0i -0.0+0.0i))
+ (pass-if (not (eqv? 0.0 -0.0)))
+ (pass-if (not (eqv? 0.0 0.0+0.0i)))
+ (pass-if (not (eqv? 0.0+0.0i 0.0-0.0i)))
+ (pass-if (not (eqv? 0.0+0.0i -0.0+0.0i)))
+ (pass-if (not (eqv? 0 1)))
+ (pass-if (not (eqv? 0 0.0)))
+ (pass-if (not (eqv? 1 1.0)))
+ (pass-if (not (eqv? 0.0 0)))
+ (pass-if (not (eqv? 1.0 1)))
+ (pass-if (not (eqv? -1.0 -1)))
+ (pass-if (not (eqv? 1.0 1.0+0.0i)))
+ (pass-if (not (eqv? 0.0 0.0+0.0i)))
+ (pass-if (not (eqv? fixnum-max (+ 1 fixnum-max))))
+ (pass-if (not (eqv? (+ 1 fixnum-max) fixnum-max)))
+ (pass-if (not (eqv? (+ 1 fixnum-max) (+ 2 fixnum-max))))
+ (pass-if (not (eqv? fixnum-min (- fixnum-min 1))))
+ (pass-if (not (eqv? (- fixnum-min 1) fixnum-min)))
+ (pass-if (not (eqv? (- fixnum-min 1) (- fixnum-min 2))))
+ (pass-if (not (eqv? (+ fixnum-max 1) (- fixnum-min 1))))
+
+ (pass-if (not (eqv? (ash 1 256) +inf.0)))
+ (pass-if (not (eqv? +inf.0 (ash 1 256))))
+ (pass-if (not (eqv? (ash 1 256) -inf.0)))
+ (pass-if (not (eqv? -inf.0 (ash 1 256))))
+
+ ;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
+ ;; sure we've avoided that
+ (pass-if (not (eqv? (ash 1 1024) +inf.0)))
+ (pass-if (not (eqv? +inf.0 (ash 1 1024))))
+ (pass-if (not (eqv? (- (ash 1 1024)) -inf.0)))
+ (pass-if (not (eqv? -inf.0 (- (ash 1 1024)))))
+
+ (pass-if (eqv? +nan.0 +nan.0))
+ (pass-if (not (eqv? +nan.0 0.0+nan.0i)))
+
+ (pass-if (not (eqv? 0 +nan.0)))
+ (pass-if (not (eqv? +nan.0 0)))
+ (pass-if (not (eqv? 1 +nan.0)))
+ (pass-if (not (eqv? +nan.0 1)))
+ (pass-if (not (eqv? -1 +nan.0)))
+ (pass-if (not (eqv? +nan.0 -1)))
+
+ (pass-if (not (eqv? (ash 1 256) +nan.0)))
+ (pass-if (not (eqv? +nan.0 (ash 1 256))))
+ (pass-if (not (eqv? (- (ash 1 256)) +nan.0)))
+ (pass-if (not (eqv? +nan.0 (- (ash 1 256)))))
+
+ (pass-if (not (eqv? (ash 1 8192) +nan.0)))
+ (pass-if (not (eqv? +nan.0 (ash 1 8192))))
+ (pass-if (not (eqv? (- (ash 1 8192)) +nan.0)))
+ (pass-if (not (eqv? +nan.0 (- (ash 1 8192)))))
+
+ ;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
+ ;; sure we've avoided that
+ (pass-if (not (eqv? (ash 3 1023) +nan.0)))
+ (pass-if (not (eqv? +nan.0 (ash 3 1023)))))
+
;;;
;;; =
;;;
(with-test-prefix "="
(pass-if (documented? =))
- (pass-if (= 0 0))
(pass-if (= 7 7))
(pass-if (= -7 -7))
+ (pass-if (= 1.0 1))
+ (pass-if (= 1 1.0))
+ (pass-if (= -1 -1.0))
+ (pass-if (= 0.0 0.0))
+ (pass-if (= 0.0 -0.0))
+ (pass-if (= 1 1.0+0.0i))
+
+ (pass-if (= 0 0))
+ (pass-if (= 0 0.0))
+ (pass-if (= 0 -0.0))
+ (pass-if (= 0 0.0+0.0i))
+ (pass-if (= 0 0.0-0.0i))
+ (pass-if (= 0 0.0+0.0i))
+ (pass-if (= 0 -0.0-0.0i))
+
+ (pass-if (= 0 0))
+ (pass-if (= 0.0 0))
+ (pass-if (= -0.0 0))
+ (pass-if (= 0.0+0.0i 0))
+ (pass-if (= 0.0-0.0i 0))
+ (pass-if (= 0.0+0.0i 0))
+ (pass-if (= -0.0-0.0i 0))
+
+ (pass-if (= 0.0+0.0i 0.0-0.0i))
+ (pass-if (= 0.0+0.0i -0.0+0.0i))
+
(pass-if (= (+ 1 fixnum-max) (+ 1 fixnum-max)))
(pass-if (= (- fixnum-min 1) (- fixnum-min 1)))
(pass-if (not (= 0 1)))
(pass-if (not (= (ash-flo 1.0 58) (1- (ash 1 58)))))
(pass-if (= (ash 1 58) (ash-flo 1.0 58)))
(pass-if (not (= (1+ (ash 1 58)) (ash-flo 1.0 58))))
- (pass-if (not (= (1- (ash 1 58)) (ash-flo 1.0 58)))))
+ (pass-if (not (= (1- (ash 1 58)) (ash-flo 1.0 58))))
+
+ ;; prior to guile 2.0.10, inum/complex comparisons were done just by
+ ;; converting the inum to a double, which on a 64-bit would round making
+ ;; say inexact 2^58 appear equal to exact 2^58+1
+ (pass-if (= (+ +0.0i (ash-flo 1.0 58)) (ash 1 58)))
+ (pass-if (not (= (+ +0.0i (ash-flo 1.0 58)) (1+ (ash 1 58)))))
+ (pass-if (not (= (+ +0.0i (ash-flo 1.0 58)) (1- (ash 1 58)))))
+ (pass-if (= (ash 1 58) (+ +0.0i (ash-flo 1.0 58))))
+ (pass-if (not (= (1+ (ash 1 58)) (+ +0.0i (ash-flo 1.0 58)))))
+ (pass-if (not (= (1- (ash 1 58)) (+ +0.0i (ash-flo 1.0 58)))))
+
+ ;; prior to guile 2.0.10, fraction/flonum and fraction/complex
+ ;; comparisons mishandled infinities.
+ (pass-if (not (= 1/2 +inf.0)))
+ (pass-if (not (= 1/2 -inf.0)))
+ (pass-if (not (= +inf.0 1/2)))
+ (pass-if (not (= -inf.0 1/2)))
+ (pass-if (not (= 1/2 +inf.0+0.0i)))
+ (pass-if (not (= 1/2 -inf.0+0.0i)))
+ (pass-if (not (= +inf.0+0.0i 1/2)))
+ (pass-if (not (= -inf.0+0.0i 1/2))))
;;;
;;; <
(pass-if "n = 0.0"
(not (< 0.0 0.0)))
+ (pass-if "n = -0.0"
+ (not (< 0.0 -0.0)))
+
(pass-if "n = 1"
(< 0.0 1))
(pass-if "n = fixnum-min - 1"
(not (< 0.0 (- fixnum-min 1)))))
+
+ (pass-if (not (< -0.0 0.0)))
+ (pass-if (not (< -0.0 -0.0)))
(with-test-prefix "(< 1 n)"
(pass-if (eq? #f (< x (* -4/3 x))))
(pass-if (eq? #f (< (- x) (* -4/3 x))))))
+ (with-test-prefix "inum/flonum"
+ (pass-if (< 4 4.5))
+ (pass-if (< 4.5 5))
+ (pass-if (< -5 -4.5))
+ (pass-if (< -4.5 4))
+ (pass-if (not (< 4.5 4)))
+ (pass-if (not (< 5 4.5)))
+ (pass-if (not (< -4.5 -5)))
+ (pass-if (not (< 4 -4.5)))
+
+ (pass-if (< 4 +inf.0))
+ (pass-if (< -4 +inf.0))
+ (pass-if (< -inf.0 4))
+ (pass-if (< -inf.0 -4))
+ (pass-if (not (< +inf.0 4)))
+ (pass-if (not (< +inf.0 -4)))
+ (pass-if (not (< 4 -inf.0)))
+ (pass-if (not (< -4 -inf.0)))
+
+ (pass-if (not (< +nan.0 4)))
+ (pass-if (not (< +nan.0 -4)))
+ (pass-if (not (< 4 +nan.0)))
+ (pass-if (not (< -4 +nan.0)))
+
+ (pass-if (< most-positive-fixnum (expt 2.0 fixnum-bit)))
+ (pass-if (not (< (expt 2.0 fixnum-bit) most-positive-fixnum)))
+
+ (pass-if (< (- (expt 2.0 fixnum-bit)) most-negative-fixnum))
+ (pass-if (not (< most-negative-fixnum (- (expt 2.0 fixnum-bit)))))
+
+ ;; Prior to guile 2.0.10, we would unconditionally convert the inum
+ ;; to a double, which on a 64-bit system could result in a
+ ;; significant change in its value, thus corrupting the comparison.
+ (pass-if (< most-positive-fixnum (exact->inexact (+ 1 most-positive-fixnum))))
+ (pass-if (< (exact->inexact (- (+ 1 most-positive-fixnum))) (- most-positive-fixnum))))
+
(with-test-prefix "flonum/frac"
(pass-if (< 0.75 4/3))
(pass-if (< -0.75 4/3))
;;;
(with-test-prefix "zero?"
- (expect-fail (documented? zero?))
- (pass-if (zero? 0))
- (pass-if (not (zero? 7)))
+ (pass-if (documented? zero?))
+
+ (pass-if (zero? 0))
+ (pass-if (zero? 0.0))
+ (pass-if (zero? -0.0))
+
+ (pass-if (zero? 0.0+0.0i))
+ (pass-if (zero? 0.0-0.0i))
+ (pass-if (zero? 0.0+0.0i))
+ (pass-if (zero? -0.0-0.0i))
+
+ (pass-if (not (zero? 7)))
(pass-if (not (zero? -7)))
+ (pass-if (not (zero? 1/7)))
+ (pass-if (not (zero? -inf.0)))
+ (pass-if (not (zero? +inf.0)))
+ (pass-if (not (zero? +nan.0)))
(pass-if (not (zero? (+ 1 fixnum-max))))
(pass-if (not (zero? (- 1 fixnum-min))))
(pass-if (not (zero? 1.3)))
- (pass-if (not (zero? 3.1+4.2i))))
+ (pass-if (not (zero? 3.1+4.2i)))
+ (pass-if (not (zero? 1.0+0.0i)))
+ (pass-if (not (zero? 0.0-1.0i))))
;;;
;;; positive?
;;;
(with-test-prefix "positive?"
- (expect-fail (documented? positive?))
+ (pass-if (documented? positive?))
(pass-if (positive? 1))
(pass-if (positive? (+ fixnum-max 1)))
(pass-if (positive? 1.3))
;;;
(with-test-prefix "negative?"
- (expect-fail (documented? negative?))
+ (pass-if (documented? negative?))
(pass-if (not (negative? 1)))
(pass-if (not (negative? (+ fixnum-max 1))))
(pass-if (not (negative? 1.3)))
(big*5 (* fixnum-max 5)))
(with-test-prefix "inum / frac"
- (pass-if (= 3 (max 3 5/2)))
- (pass-if (= 5/2 (max 2 5/2))))
+ (pass-if (eqv? 3 (max 3 5/2)))
+ (pass-if (eqv? 5/2 (max 2 5/2))))
(with-test-prefix "frac / inum"
- (pass-if (= 3 (max 5/2 3)))
- (pass-if (= 5/2 (max 5/2 2))))
-
- (with-test-prefix "inum / real"
- (pass-if (nan? (max 123 +nan.0))))
-
- (with-test-prefix "real / inum"
- (pass-if (nan? (max +nan.0 123))))
+ (pass-if (eqv? 3 (max 5/2 3)))
+ (pass-if (eqv? 5/2 (max 5/2 2))))
+
+ (with-test-prefix "infinities and NaNs"
+ ;; +inf.0 beats everything except NaNs
+ (pass-if (eqv? +inf.0 (max +inf.0 123 )))
+ (pass-if (eqv? +inf.0 (max 123 +inf.0 )))
+ (pass-if (eqv? +inf.0 (max +inf.0 -123.3 )))
+ (pass-if (eqv? +inf.0 (max -123.3 +inf.0 )))
+ (pass-if (eqv? +inf.0 (max +inf.0 -7/2 )))
+ (pass-if (eqv? +inf.0 (max -7/2 +inf.0 )))
+ (pass-if (eqv? +inf.0 (max +inf.0 -1e20 )))
+ (pass-if (eqv? +inf.0 (max -1e20 +inf.0 )))
+ (pass-if (eqv? +inf.0 (max +inf.0 (- big*2))))
+ (pass-if (eqv? +inf.0 (max (- big*2) +inf.0 )))
+ (pass-if (eqv? +inf.0 (max +inf.0 +inf.0 )))
+ (pass-if (eqv? +inf.0 (max +inf.0 +inf.0 )))
+ (pass-if (eqv? +inf.0 (max +inf.0 +inf.0 )))
+
+ ;; NaNs beat everything
+ (pass-if (real-nan? (max +nan.0 123 )))
+ (pass-if (real-nan? (max 123 +nan.0 )))
+ (pass-if (real-nan? (max +nan.0 123.3 )))
+ (pass-if (real-nan? (max 123.3 +nan.0 )))
+ (pass-if (real-nan? (max +nan.0 -7/2 )))
+ (pass-if (real-nan? (max -7/2 +nan.0 )))
+ (pass-if (real-nan? (max +nan.0 -1e20 )))
+ (pass-if (real-nan? (max -1e20 +nan.0 )))
+ (pass-if (real-nan? (max +nan.0 (- big*2))))
+ (pass-if (real-nan? (max (- big*2) +nan.0 )))
+ (pass-if (real-nan? (max +nan.0 -inf.0 )))
+ (pass-if (real-nan? (max -inf.0 +nan.0 )))
+ (pass-if (real-nan? (max +nan.0 +nan.0 )))
+ (pass-if (real-nan? (max +inf.0 +nan.0 )))
+ (pass-if (real-nan? (max +nan.0 +inf.0 )))
+
+ ;; -inf.0 always loses, except against itself
+ (pass-if (eqv? -inf.0 (max -inf.0 -inf.0 )))
+ (pass-if (eqv? -123.0 (max -inf.0 -123 )))
+ (pass-if (eqv? -123.0 (max -123 -inf.0 )))
+ (pass-if (eqv? -123.3 (max -inf.0 -123.3 )))
+ (pass-if (eqv? -123.3 (max -123.3 -inf.0 )))
+ (pass-if (eqv? -3.5 (max -inf.0 -7/2 )))
+ (pass-if (eqv? -3.5 (max -7/2 -inf.0 )))
+ (pass-if (eqv? -1.0e20 (max -inf.0 -1e20 )))
+ (pass-if (eqv? -1.0e20 (max -1e20 -inf.0 )))
+ (pass-if (eqv? (exact->inexact (- big*2))
+ (max -inf.0 (- big*2))))
+ (pass-if (eqv? (exact->inexact (- big*2))
+ (max (- big*2) -inf.0 ))))
+
+ (with-test-prefix "signed zeroes"
+ (pass-if (eqv? 0.0 (max 0.0 0.0)))
+ (pass-if (eqv? 0.0 (max 0.0 -0.0)))
+ (pass-if (eqv? 0.0 (max -0.0 0.0)))
+ (pass-if (eqv? -0.0 (max -0.0 -0.0)))
+ (pass-if (eqv? 0.0 (max -0.0 0 )))
+ (pass-if (eqv? 0.0 (max 0.0 0 )))
+ (pass-if (eqv? 0.0 (max 0 -0.0)))
+ (pass-if (eqv? 0.0 (max 0 0.0)))
+ (pass-if (eqv? 0 (min 0 0 ))))
(with-test-prefix "big / frac"
- (pass-if (= big*2 (max big*2 5/2)))
- (pass-if (= 5/2 (max (- big*2) 5/2))))
+ (pass-if (eqv? big*2 (max big*2 5/2)))
+ (pass-if (eqv? 5/2 (max (- big*2) 5/2))))
(with-test-prefix "frac / big"
- (pass-if (= big*2 (max 5/2 big*2)))
- (pass-if (= 5/2 (max 5/2 (- big*2)))))
+ (pass-if (eqv? big*2 (max 5/2 big*2)))
+ (pass-if (eqv? 5/2 (max 5/2 (- big*2)))))
(with-test-prefix "big / real"
- (pass-if (nan? (max big*5 +nan.0)))
+ (pass-if (real-nan? (max big*5 +nan.0)))
(pass-if (eqv? (exact->inexact big*5) (max big*5 -inf.0)))
(pass-if (eqv? (exact->inexact big*5) (max big*5 1.0)))
(pass-if (eqv? +inf.0 (max big*5 +inf.0)))
(pass-if (eqv? 1.0 (max (- big*5) 1.0))))
(with-test-prefix "real / big"
- (pass-if (nan? (max +nan.0 big*5)))
+ (pass-if (real-nan? (max +nan.0 big*5)))
(pass-if (eqv? (exact->inexact big*5) (max -inf.0 big*5)))
(pass-if (eqv? (exact->inexact big*5) (max 1.0 big*5)))
(pass-if (eqv? +inf.0 (max +inf.0 big*5)))
(pass-if (eqv? 1.0 (max 1.0 (- big*5)))))
(with-test-prefix "frac / frac"
- (pass-if (= 2/3 (max 1/2 2/3)))
- (pass-if (= 2/3 (max 2/3 1/2)))
- (pass-if (= -1/2 (max -1/2 -2/3)))
- (pass-if (= -1/2 (max -2/3 -1/2))))
+ (pass-if (eqv? 2/3 (max 1/2 2/3)))
+ (pass-if (eqv? 2/3 (max 2/3 1/2)))
+ (pass-if (eqv? -1/2 (max -1/2 -2/3)))
+ (pass-if (eqv? -1/2 (max -2/3 -1/2))))
(with-test-prefix "real / real"
- (pass-if (nan? (max 123.0 +nan.0)))
- (pass-if (nan? (max +nan.0 123.0)))
- (pass-if (nan? (max +nan.0 +nan.0)))
- (pass-if (= 456.0 (max 123.0 456.0)))
- (pass-if (= 456.0 (max 456.0 123.0)))))
+ (pass-if (real-nan? (max 123.0 +nan.0)))
+ (pass-if (real-nan? (max +nan.0 123.0)))
+ (pass-if (real-nan? (max +nan.0 +nan.0)))
+ (pass-if (eqv? 456.0 (max 123.0 456.0)))
+ (pass-if (eqv? 456.0 (max 456.0 123.0)))))
;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
;; sure we've avoided that
(for-each (lambda (b)
(pass-if (list b +inf.0)
- (= +inf.0 (max b +inf.0)))
+ (eqv? +inf.0 (max b +inf.0)))
(pass-if (list +inf.0 b)
- (= +inf.0 (max b +inf.0)))
+ (eqv? +inf.0 (max b +inf.0)))
(pass-if (list b -inf.0)
- (= (exact->inexact b) (max b -inf.0)))
+ (eqv? (exact->inexact b) (max b -inf.0)))
(pass-if (list -inf.0 b)
- (= (exact->inexact b) (max b -inf.0))))
+ (eqv? (exact->inexact b) (max b -inf.0))))
(list (1- (ash 1 1024))
(ash 1 1024)
(1+ (ash 1 1024))
;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
;; sure we've avoided that
- (pass-if (nan? (max (ash 1 2048) +nan.0)))
- (pass-if (nan? (max +nan.0 (ash 1 2048)))))
+ (pass-if (real-nan? (max (ash 1 2048) +nan.0)))
+ (pass-if (real-nan? (max +nan.0 (ash 1 2048)))))
;;;
;;; min
(big*5 (* fixnum-max 5)))
(pass-if (documented? min))
- (pass-if (= 1 (min 7 3 1 5)))
- (pass-if (= 1 (min 1 7 3 5)))
- (pass-if (= 1 (min 7 3 5 1)))
- (pass-if (= -7 (min 2 3 4 -2 5 -7 1 -1 4 2)))
- (pass-if (= -7 (min -7 2 3 4 -2 5 1 -1 4 2)))
- (pass-if (= -7 (min 2 3 4 -2 5 1 -1 4 2 -7)))
- (pass-if (= big*2 (min big*3 big*5 big*2 big*4)))
- (pass-if (= big*2 (min big*2 big*3 big*5 big*4)))
- (pass-if (= big*2 (min big*3 big*5 big*4 big*2)))
+ (pass-if (eqv? 1 (min 7 3 1 5)))
+ (pass-if (eqv? 1 (min 1 7 3 5)))
+ (pass-if (eqv? 1 (min 7 3 5 1)))
+ (pass-if (eqv? -7 (min 2 3 4 -2 5 -7 1 -1 4 2)))
+ (pass-if (eqv? -7 (min -7 2 3 4 -2 5 1 -1 4 2)))
+ (pass-if (eqv? -7 (min 2 3 4 -2 5 1 -1 4 2 -7)))
+ (pass-if (eqv? big*2 (min big*3 big*5 big*2 big*4)))
+ (pass-if (eqv? big*2 (min big*2 big*3 big*5 big*4)))
+ (pass-if (eqv? big*2 (min big*3 big*5 big*4 big*2)))
(pass-if
- (= (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
+ (eqv? (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
(pass-if
- (= (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
+ (eqv? (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
(pass-if
- (= (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
+ (eqv? (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
(with-test-prefix "inum / frac"
- (pass-if (= 5/2 (min 3 5/2)))
- (pass-if (= 2 (min 2 5/2))))
+ (pass-if (eqv? 5/2 (min 3 5/2)))
+ (pass-if (eqv? 2 (min 2 5/2))))
(with-test-prefix "frac / inum"
- (pass-if (= 5/2 (min 5/2 3)))
- (pass-if (= 2 (min 5/2 2))))
-
- (with-test-prefix "inum / real"
- (pass-if (nan? (min 123 +nan.0))))
-
- (with-test-prefix "real / inum"
- (pass-if (nan? (min +nan.0 123))))
+ (pass-if (eqv? 5/2 (min 5/2 3)))
+ (pass-if (eqv? 2 (min 5/2 2))))
+
+ (with-test-prefix "infinities and NaNs"
+ ;; -inf.0 beats everything except NaNs
+ (pass-if (eqv? -inf.0 (min -inf.0 123 )))
+ (pass-if (eqv? -inf.0 (min 123 -inf.0 )))
+ (pass-if (eqv? -inf.0 (min -inf.0 -123.3 )))
+ (pass-if (eqv? -inf.0 (min -123.3 -inf.0 )))
+ (pass-if (eqv? -inf.0 (min -inf.0 -7/2 )))
+ (pass-if (eqv? -inf.0 (min -7/2 -inf.0 )))
+ (pass-if (eqv? -inf.0 (min -inf.0 -1e20 )))
+ (pass-if (eqv? -inf.0 (min -1e20 -inf.0 )))
+ (pass-if (eqv? -inf.0 (min -inf.0 (- big*2))))
+ (pass-if (eqv? -inf.0 (min (- big*2) -inf.0 )))
+ (pass-if (eqv? -inf.0 (min -inf.0 +inf.0 )))
+ (pass-if (eqv? -inf.0 (min +inf.0 -inf.0 )))
+ (pass-if (eqv? -inf.0 (min -inf.0 -inf.0 )))
+
+ ;; NaNs beat everything
+ (pass-if (real-nan? (min +nan.0 123 )))
+ (pass-if (real-nan? (min 123 +nan.0 )))
+ (pass-if (real-nan? (min +nan.0 123.3 )))
+ (pass-if (real-nan? (min 123.3 +nan.0 )))
+ (pass-if (real-nan? (min +nan.0 -7/2 )))
+ (pass-if (real-nan? (min -7/2 +nan.0 )))
+ (pass-if (real-nan? (min +nan.0 -1e20 )))
+ (pass-if (real-nan? (min -1e20 +nan.0 )))
+ (pass-if (real-nan? (min +nan.0 (- big*2))))
+ (pass-if (real-nan? (min (- big*2) +nan.0 )))
+ (pass-if (real-nan? (min +nan.0 +inf.0 )))
+ (pass-if (real-nan? (min +inf.0 +nan.0 )))
+ (pass-if (real-nan? (min +nan.0 +nan.0 )))
+ (pass-if (real-nan? (min -inf.0 +nan.0 )))
+ (pass-if (real-nan? (min +nan.0 -inf.0 )))
+
+ ;; +inf.0 always loses, except against itself
+ (pass-if (eqv? +inf.0 (min +inf.0 +inf.0 )))
+ (pass-if (eqv? -123.0 (min +inf.0 -123 )))
+ (pass-if (eqv? -123.0 (min -123 +inf.0 )))
+ (pass-if (eqv? -123.3 (min +inf.0 -123.3 )))
+ (pass-if (eqv? -123.3 (min -123.3 +inf.0 )))
+ (pass-if (eqv? -3.5 (min +inf.0 -7/2 )))
+ (pass-if (eqv? -3.5 (min -7/2 +inf.0 )))
+ (pass-if (eqv? -1.0e20 (min +inf.0 -1e20 )))
+ (pass-if (eqv? -1.0e20 (min -1e20 +inf.0 )))
+ (pass-if (eqv? (exact->inexact (- big*2))
+ (min +inf.0 (- big*2))))
+ (pass-if (eqv? (exact->inexact (- big*2))
+ (min (- big*2) +inf.0 ))))
+
+ (with-test-prefix "signed zeroes"
+ (pass-if (eqv? 0.0 (min 0.0 0.0)))
+ (pass-if (eqv? -0.0 (min 0.0 -0.0)))
+ (pass-if (eqv? -0.0 (min -0.0 0.0)))
+ (pass-if (eqv? -0.0 (min -0.0 -0.0)))
+ (pass-if (eqv? -0.0 (min -0.0 0 )))
+ (pass-if (eqv? 0.0 (min 0.0 0 )))
+ (pass-if (eqv? -0.0 (min 0 -0.0)))
+ (pass-if (eqv? 0.0 (min 0 0.0)))
+ (pass-if (eqv? 0 (min 0 0 ))))
(with-test-prefix "big / frac"
- (pass-if (= 5/2 (min big*2 5/2)))
- (pass-if (= (- big*2) (min (- big*2) 5/2))))
+ (pass-if (eqv? 5/2 (min big*2 5/2)))
+ (pass-if (eqv? (- big*2) (min (- big*2) 5/2))))
(with-test-prefix "frac / big"
- (pass-if (= 5/2 (min 5/2 big*2)))
- (pass-if (= (- big*2) (min 5/2 (- big*2)))))
+ (pass-if (eqv? 5/2 (min 5/2 big*2)))
+ (pass-if (eqv? (- big*2) (min 5/2 (- big*2)))))
(with-test-prefix "big / real"
- (pass-if (nan? (min big*5 +nan.0)))
+ (pass-if (real-nan? (min big*5 +nan.0)))
(pass-if (eqv? (exact->inexact big*5) (min big*5 +inf.0)))
(pass-if (eqv? -inf.0 (min big*5 -inf.0)))
(pass-if (eqv? 1.0 (min big*5 1.0)))
(pass-if (eqv? (exact->inexact (- big*5)) (min (- big*5) 1.0))))
(with-test-prefix "real / big"
- (pass-if (nan? (min +nan.0 big*5)))
+ (pass-if (real-nan? (min +nan.0 big*5)))
(pass-if (eqv? (exact->inexact big*5) (min +inf.0 big*5)))
(pass-if (eqv? -inf.0 (min -inf.0 big*5)))
(pass-if (eqv? 1.0 (min 1.0 big*5)))
(pass-if (eqv? (exact->inexact (- big*5)) (min 1.0 (- big*5)))))
(with-test-prefix "frac / frac"
- (pass-if (= 1/2 (min 1/2 2/3)))
- (pass-if (= 1/2 (min 2/3 1/2)))
- (pass-if (= -2/3 (min -1/2 -2/3)))
- (pass-if (= -2/3 (min -2/3 -1/2))))
+ (pass-if (eqv? 1/2 (min 1/2 2/3)))
+ (pass-if (eqv? 1/2 (min 2/3 1/2)))
+ (pass-if (eqv? -2/3 (min -1/2 -2/3)))
+ (pass-if (eqv? -2/3 (min -2/3 -1/2))))
(with-test-prefix "real / real"
- (pass-if (nan? (min 123.0 +nan.0)))
- (pass-if (nan? (min +nan.0 123.0)))
- (pass-if (nan? (min +nan.0 +nan.0)))
- (pass-if (= 123.0 (min 123.0 456.0)))
- (pass-if (= 123.0 (min 456.0 123.0)))))
+ (pass-if (real-nan? (min 123.0 +nan.0)))
+ (pass-if (real-nan? (min +nan.0 123.0)))
+ (pass-if (real-nan? (min +nan.0 +nan.0)))
+ (pass-if (eqv? 123.0 (min 123.0 456.0)))
+ (pass-if (eqv? 123.0 (min 456.0 123.0)))))
;; in gmp prior to 4.2, mpz_cmp_d ended up treating Inf as 2^1024, make
;; sure we've avoided that
(for-each (lambda (b)
(pass-if (list b +inf.0)
- (= (exact->inexact b) (min b +inf.0)))
+ (eqv? (exact->inexact b) (min b +inf.0)))
(pass-if (list +inf.0 b)
- (= (exact->inexact b) (min b +inf.0)))
+ (eqv? (exact->inexact b) (min b +inf.0)))
(pass-if (list b -inf.0)
- (= -inf.0 (min b -inf.0)))
+ (eqv? -inf.0 (min b -inf.0)))
(pass-if (list -inf.0 b)
- (= -inf.0 (min b -inf.0))))
+ (eqv? -inf.0 (min b -inf.0))))
(list (1- (ash 1 1024))
(ash 1 1024)
(1+ (ash 1 1024))
;; in gmp prior to 4.2, mpz_cmp_d ended up treating NaN as 3*2^1023, make
;; sure we've avoided that
- (pass-if (nan? (min (- (ash 1 2048)) (- +nan.0))))
- (pass-if (nan? (min (- +nan.0) (- (ash 1 2048))))))
+ (pass-if (real-nan? (min (- (ash 1 2048)) (- +nan.0))))
+ (pass-if (real-nan? (min (- +nan.0) (- (ash 1 2048))))))
;;;
;;; +
;;;
-(with-test-prefix "+"
+(with-test-prefix/c&e "+"
(pass-if "documented?"
- (documented? +)))
+ (documented? +))
+
+ (pass-if "simple"
+ (and (eqv? 7 (+ 3 4))
+ (eqv? 3 (+ 3))
+ (eqv? 0 (+))))
+
+ (pass-if "exactness propagation"
+ (and (eqv? 8 (+ 3 5))
+ (eqv? 8.0 (+ 3 5.0))
+ (eqv? 8.0 (+ 3.0 5))
+ (eqv? 8.0 (+ 3.0 5.0))
+
+ (eqv? 5/6 (+ 1/2 1/3))
+ (eqv? 5.5 (+ 1/2 5.0))
+ (eqv? 3.25 (+ 3.0 1/4))))
+
+ (pass-if "signed zeroes"
+ (and (eqv? 0.0 (+ 0.0))
+ (eqv? -0.0 (+ -0.0))
+ (eqv? 0.0 (+ 0.0 0.0))
+ (eqv? 0.0 (+ 0.0 -0.0))
+ (eqv? 0.0 (+ -0.0 0.0))
+ (eqv? -0.0 (+ -0.0 -0.0))))
+
+ (pass-if "NaNs"
+ (and (real-nan? (+ +nan.0 +nan.0))
+ (real-nan? (+ 0 +nan.0))
+ (real-nan? (+ +nan.0 0))
+ (real-nan? (+ 1 +nan.0))
+ (real-nan? (+ +nan.0 1))
+ (real-nan? (+ -1 +nan.0))
+ (real-nan? (+ +nan.0 -1))
+ (real-nan? (+ -7/2 +nan.0))
+ (real-nan? (+ +nan.0 -7/2))
+ (real-nan? (+ 1e20 +nan.0))
+ (real-nan? (+ +nan.0 1e20))
+ (real-nan? (+ +inf.0 +nan.0))
+ (real-nan? (+ +nan.0 +inf.0))
+ (real-nan? (+ -inf.0 +nan.0))
+ (real-nan? (+ +nan.0 -inf.0))
+ (real-nan? (+ (* fixnum-max 2) +nan.0))
+ (real-nan? (+ +nan.0 (* fixnum-max 2)))))
+
+ (pass-if "infinities"
+ (and (eqv? +inf.0 (+ +inf.0 +inf.0))
+ (eqv? -inf.0 (+ -inf.0 -inf.0))
+ (real-nan? (+ +inf.0 -inf.0))
+ (real-nan? (+ -inf.0 +inf.0))))
+
+ ;; The maximum fixnum on a 32-bit architecture: 2^29 - 1.
+ (pass-if "fixnum + fixnum = bignum (32-bit)"
+ (eqv? 536870912 (+ 536870910 2)))
+
+ ;; The maximum fixnum on a 64-bit architecture: 2^61 - 1.
+ (pass-if "fixnum + fixnum = bignum (64-bit)"
+ (eqv? 2305843009213693952 (+ 2305843009213693950 2)))
+
+ (pass-if "bignum + fixnum = fixnum"
+ (eqv? 0 (+ (1+ most-positive-fixnum) most-negative-fixnum))))
;;;
;;; -
;;;
-(with-test-prefix "-"
+(with-test-prefix/c&e "-"
+
+ (pass-if "double-negation of fixnum-min: ="
+ (= fixnum-min (- (- fixnum-min))))
+ (pass-if "double-negation of fixnum-min: eqv?"
+ (eqv? fixnum-min (- (- fixnum-min))))
+ (pass-if "double-negation of fixnum-min: equal?"
+ (equal? fixnum-min (- (- fixnum-min))))
+
+ (pass-if "binary double-negation of fixnum-min: ="
+ (= fixnum-min (- 0 (- 0 fixnum-min))))
+ (pass-if "binary double-negation of fixnum-min: eqv?"
+ (eqv? fixnum-min (- 0 (- 0 fixnum-min))))
+ (pass-if "binary double-negation of fixnum-min: equal?"
+ (equal? fixnum-min (- 0 (- 0 fixnum-min))))
+
+ (pass-if "signed zeroes"
+ (and (eqv? +0.0 (- -0.0))
+ (eqv? -0.0 (- +0.0))
+ (eqv? 0.0 (- 0.0 0.0))
+ (eqv? 0.0 (- 0.0 -0.0))
+ (eqv? 0.0 (- -0.0 -0.0))
+ (eqv? -0.0 (- -0.0 0.0))))
+
+ (pass-if "exactness propagation"
+ (and (eqv? 3 (- 8 5))
+ (eqv? 3.0 (- 8 5.0))
+ (eqv? 3.0 (- 8.0 5))
+ (eqv? 3.0 (- 8.0 5.0))
+ (eqv? -1/6 (- 1/3 1/2))
+ (eqv? -4.5 (- 1/2 5.0))
+ (eqv? 2.75 (- 3.0 1/4))))
+
+ (pass-if "infinities"
+ (and (eqv? +inf.0 (- +inf.0 -inf.0))
+ (eqv? -inf.0 (- -inf.0 +inf.0))
+ (real-nan? (- +inf.0 +inf.0))
+ (real-nan? (- -inf.0 -inf.0))))
+
+ (pass-if "NaNs"
+ (and (real-nan? (- +nan.0 +nan.0))
+ (real-nan? (- 0 +nan.0))
+ (real-nan? (- +nan.0 0))
+ (real-nan? (- 1 +nan.0))
+ (real-nan? (- +nan.0 1))
+ (real-nan? (- -1 +nan.0))
+ (real-nan? (- +nan.0 -1))
+ (real-nan? (- -7/2 +nan.0))
+ (real-nan? (- +nan.0 -7/2))
+ (real-nan? (- 1e20 +nan.0))
+ (real-nan? (- +nan.0 1e20))
+ (real-nan? (- +inf.0 +nan.0))
+ (real-nan? (- +nan.0 +inf.0))
+ (real-nan? (- -inf.0 +nan.0))
+ (real-nan? (- +nan.0 -inf.0))
+ (real-nan? (- (* fixnum-max 2) +nan.0))
+ (real-nan? (- +nan.0 (* fixnum-max 2)))))
+
+ (pass-if "(eqv? fixnum-min (- (- fixnum-min)))"
+ (eqv? fixnum-min (- (- fixnum-min))))
+ (pass-if "(eqv? fixnum-min (- 0 (- 0 fixnum-min)))"
+ (eqv? fixnum-min (- 0 (- 0 fixnum-min))))
+ (pass-if "(eqv? fixnum-num (apply - (list (apply - (list fixnum-min)))))"
+ (eqv? fixnum-min (apply - (list (apply - (list fixnum-min))))))
(pass-if "-inum - +bignum"
(= #x-100000000000000000000000000000001
(pass-if "big - -inum"
(= #x100000000000000000000000000000001
- (- #x100000000000000000000000000000000 -1))))
+ (- #x100000000000000000000000000000000 -1)))
+
+ ;; The mininum fixnum on a 32-bit architecture: -2^29.
+ (pass-if "fixnum - fixnum = bignum (32-bit)"
+ (eqv? -536870912 (- -536870910 2)))
+
+ ;; The minimum fixnum on a 64-bit architecture: -2^61.
+ (pass-if "fixnum - fixnum = bignum (64-bit)"
+ (eqv? -2305843009213693952 (- -2305843009213693950 2)))
+
+ (pass-if "bignum - fixnum = fixnum"
+ (eqv? most-positive-fixnum (- (1+ most-positive-fixnum) 1))))
;;;
;;; *
(with-test-prefix "*"
+ (with-test-prefix "double-negation of fixnum-min"
+ (pass-if (= fixnum-min (* -1 (* -1 fixnum-min))))
+ (pass-if (eqv? fixnum-min (* -1 (* -1 fixnum-min))))
+ (pass-if (equal? fixnum-min (* -1 (* -1 fixnum-min))))
+ (pass-if (= fixnum-min (* (* fixnum-min -1) -1)))
+ (pass-if (eqv? fixnum-min (* (* fixnum-min -1) -1)))
+ (pass-if (equal? fixnum-min (* (* fixnum-min -1) -1))))
+
+ (with-test-prefix "signed fixnum overflow"
+ (pass-if (eqv? (* 65536 65536) 4294967296))
+ (pass-if (eqv? (* -65536 65536) -4294967296))
+ (pass-if (eqv? (* 65536 -65536) -4294967296))
+ (pass-if (eqv? (* -65536 -65536) 4294967296))
+ (pass-if (eqv? (* 4294967296 4294967296) 18446744073709551616))
+ (pass-if (eqv? (* -4294967296 4294967296) -18446744073709551616))
+ (pass-if (eqv? (* 4294967296 -4294967296) -18446744073709551616))
+ (pass-if (eqv? (* -4294967296 -4294967296) 18446744073709551616)))
+
+ (with-test-prefix "signed zeroes"
+ (pass-if (eqv? +0.0 (* +0.0 +0.0)))
+ (pass-if (eqv? -0.0 (* -0.0 +0.0)))
+ (pass-if (eqv? +0.0 (* -0.0 -0.0)))
+ (pass-if (eqv? -0.0 (* +0.0 -0.0)))
+ (pass-if (eqv? +0.0+0.0i (* +i +0.0)))
+ (pass-if (eqv? +0.0-0.0i (* -i +0.0)))
+ (pass-if (eqv? -0.0-0.0i (* +i -0.0)))
+ (pass-if (eqv? -0.0+0.0i (* -i -0.0))))
+
+ (with-test-prefix "exactness propagation"
+ (pass-if (eqv? -0.0 (* 0 -1.0 )))
+ (pass-if (eqv? 0.0 (* 0 1.0 )))
+ (pass-if (eqv? -0.0 (* -1.0 0 )))
+ (pass-if (eqv? 0.0 (* 1.0 0 )))
+ (pass-if (eqv? 0 (* 0 1/2 )))
+ (pass-if (eqv? 0 (* 1/2 0 )))
+ (pass-if (eqv? 0.0+0.0i (* 0 1+i )))
+ (pass-if (eqv? 0.0+0.0i (* 1+i 0 )))
+ (pass-if (eqv? -1.0 (* 1 -1.0 )))
+ (pass-if (eqv? 1.0 (* 1 1.0 )))
+ (pass-if (eqv? -1.0 (* -1.0 1 )))
+ (pass-if (eqv? 1.0 (* 1.0 1 )))
+ (pass-if (eqv? 1/2 (* 1 1/2 )))
+ (pass-if (eqv? 1/2 (* 1/2 1 )))
+ (pass-if (eqv? 1+i (* 1 1+i )))
+ (pass-if (eqv? 1+i (* 1+i 1 ))))
+
+ (with-test-prefix "propagation of NaNs"
+ (pass-if (real-nan? (* +nan.0 +nan.0)))
+ (pass-if (real-nan? (* +nan.0 1 )))
+ (pass-if (real-nan? (* +nan.0 -1 )))
+ (pass-if (real-nan? (* +nan.0 -7/2 )))
+ (pass-if (real-nan? (* +nan.0 1e20 )))
+ (pass-if (real-nan? (* 1 +nan.0)))
+ (pass-if (real-nan? (* -1 +nan.0)))
+ (pass-if (real-nan? (* -7/2 +nan.0)))
+ (pass-if (real-nan? (* 1e20 +nan.0)))
+ (pass-if (real-nan? (* +inf.0 +nan.0)))
+ (pass-if (real-nan? (* +nan.0 +inf.0)))
+ (pass-if (real-nan? (* -inf.0 +nan.0)))
+ (pass-if (real-nan? (* +nan.0 -inf.0)))
+ (pass-if (real-nan? (* (* fixnum-max 2) +nan.0)))
+ (pass-if (real-nan? (* +nan.0 (* fixnum-max 2))))
+
+ (pass-if (real-nan? (* 0 +nan.0 )))
+ (pass-if (real-nan? (* +nan.0 0 )))
+ (pass-if (almost-real-nan? (* 0 +nan.0+i)))
+ (pass-if (almost-real-nan? (* +nan.0+i 0 )))
+
+ (pass-if (imaginary-nan? (* 0 +nan.0i )))
+ (pass-if (imaginary-nan? (* +nan.0i 0 )))
+ (pass-if (imaginary-nan? (* 0 1+nan.0i )))
+ (pass-if (imaginary-nan? (* 1+nan.0i 0 )))
+
+ (pass-if (complex-nan? (* 0 +nan.0+nan.0i )))
+ (pass-if (complex-nan? (* +nan.0+nan.0i 0 ))))
+
+ (with-test-prefix "infinities"
+ (pass-if (eqv? +inf.0 (* +inf.0 5 )))
+ (pass-if (eqv? -inf.0 (* +inf.0 -5 )))
+ (pass-if (eqv? +inf.0 (* +inf.0 73.1)))
+ (pass-if (eqv? -inf.0 (* +inf.0 -9.2)))
+ (pass-if (eqv? +inf.0 (* +inf.0 5/2)))
+ (pass-if (eqv? -inf.0 (* +inf.0 -5/2)))
+ (pass-if (eqv? -inf.0 (* -5 +inf.0)))
+ (pass-if (eqv? +inf.0 (* 73.1 +inf.0)))
+ (pass-if (eqv? -inf.0 (* -9.2 +inf.0)))
+ (pass-if (eqv? +inf.0 (* 5/2 +inf.0)))
+ (pass-if (eqv? -inf.0 (* -5/2 +inf.0)))
+
+ (pass-if (eqv? -inf.0 (* -inf.0 5 )))
+ (pass-if (eqv? +inf.0 (* -inf.0 -5 )))
+ (pass-if (eqv? -inf.0 (* -inf.0 73.1)))
+ (pass-if (eqv? +inf.0 (* -inf.0 -9.2)))
+ (pass-if (eqv? -inf.0 (* -inf.0 5/2)))
+ (pass-if (eqv? +inf.0 (* -inf.0 -5/2)))
+ (pass-if (eqv? +inf.0 (* -5 -inf.0)))
+ (pass-if (eqv? -inf.0 (* 73.1 -inf.0)))
+ (pass-if (eqv? +inf.0 (* -9.2 -inf.0)))
+ (pass-if (eqv? -inf.0 (* 5/2 -inf.0)))
+ (pass-if (eqv? +inf.0 (* -5/2 -inf.0)))
+
+ (pass-if (real-nan? (* 0.0 +inf.0)))
+ (pass-if (real-nan? (* -0.0 +inf.0)))
+ (pass-if (real-nan? (* +inf.0 0.0)))
+ (pass-if (real-nan? (* +inf.0 -0.0)))
+
+ (pass-if (real-nan? (* 0.0 -inf.0)))
+ (pass-if (real-nan? (* -0.0 -inf.0)))
+ (pass-if (real-nan? (* -inf.0 0.0)))
+ (pass-if (real-nan? (* -inf.0 -0.0)))
+
+ (pass-if (real-nan? (* 0 +inf.0 )))
+ (pass-if (real-nan? (* +inf.0 0 )))
+ (pass-if (real-nan? (* 0 -inf.0 )))
+ (pass-if (real-nan? (* -inf.0 0 )))
+
+ (pass-if (almost-real-nan? (* 0 +inf.0+i)))
+ (pass-if (almost-real-nan? (* +inf.0+i 0 )))
+ (pass-if (almost-real-nan? (* 0 -inf.0+i)))
+ (pass-if (almost-real-nan? (* -inf.0+i 0 )))
+
+ (pass-if (imaginary-nan? (* 0 +inf.0i )))
+ (pass-if (imaginary-nan? (* +inf.0i 0 )))
+ (pass-if (imaginary-nan? (* 0 1+inf.0i )))
+ (pass-if (imaginary-nan? (* 1+inf.0i 0 )))
+
+ (pass-if (imaginary-nan? (* 0 -inf.0i )))
+ (pass-if (imaginary-nan? (* -inf.0i 0 )))
+ (pass-if (imaginary-nan? (* 0 1-inf.0i )))
+ (pass-if (imaginary-nan? (* 1-inf.0i 0 )))
+
+ (pass-if (complex-nan? (* 0 +inf.0+inf.0i )))
+ (pass-if (complex-nan? (* +inf.0+inf.0i 0 )))
+
+ (pass-if (complex-nan? (* 0 +inf.0-inf.0i )))
+ (pass-if (complex-nan? (* -inf.0+inf.0i 0 ))))
+
(with-test-prefix "inum * bignum"
(pass-if "0 * 2^256 = 0"
(with-test-prefix "inum * flonum"
- (pass-if "0 * 1.0 = 0"
- (eqv? 0 (* 0 1.0))))
+ (pass-if "0 * 1.0 = 0.0"
+ (eqv? 0.0 (* 0 1.0))))
(with-test-prefix "inum * complex"
- (pass-if "0 * 1+1i = 0"
- (eqv? 0 (* 0 1+1i))))
+ (pass-if "0 * 1+1i = 0.0+0.0i"
+ (eqv? 0.0+0.0i (* 0 1+1i))))
(with-test-prefix "inum * frac"
(eqv? 0 (* (ash 1 256) 0))))
(with-test-prefix "flonum * inum"
-
- ;; in guile 1.6.8 and 1.8.1 and earlier this returned inexact 0.0
- (pass-if "1.0 * 0 = 0"
- (eqv? 0 (* 1.0 0))))
+ (pass-if "1.0 * 0 = 0.0"
+ (eqv? 0.0 (* 1.0 0))))
(with-test-prefix "complex * inum"
-
- ;; in guile 1.6.8 and 1.8.1 and earlier this returned inexact 0.0
- (pass-if "1+1i * 0 = 0"
- (eqv? 0 (* 1+1i 0))))
+ (pass-if "1+1i * 0 = 0.0+0.0i"
+ (eqv? 0.0+0.0i (* 1+1i 0))))
(pass-if "complex * bignum"
(let ((big (ash 1 90)))
(with-test-prefix "/"
+ (with-test-prefix "double-negation of fixnum-min"
+ (pass-if (= fixnum-min (/ (/ fixnum-min -1) -1)))
+ (pass-if (eqv? fixnum-min (/ (/ fixnum-min -1) -1)))
+ (pass-if (equal? fixnum-min (/ (/ fixnum-min -1) -1))))
+
(pass-if "documented?"
(documented? /))
(pass-if "(/ 25+125i 4+3i)"
(= (/ 25+125i 4+3i) 19.0+17.0i))))
+;;;
+;;; floor
+;;;
+
+(with-test-prefix "floor"
+ (pass-if (= 1 (floor 1.75)))
+ (pass-if (= 1 (floor 1.5)))
+ (pass-if (= 1 (floor 1.25)))
+ (pass-if (= 0 (floor 0.75)))
+ (pass-if (= 0 (floor 0.5)))
+ (pass-if (= 0 (floor 0.0)))
+ (pass-if (= -1 (floor -0.5)))
+ (pass-if (= -2 (floor -1.25)))
+ (pass-if (= -2 (floor -1.5)))
+
+ (with-test-prefix "inum"
+ (pass-if "0"
+ (and (= 0 (floor 0))
+ (exact? (floor 0))))
+
+ (pass-if "1"
+ (and (= 1 (floor 1))
+ (exact? (floor 1))))
+
+ (pass-if "-1"
+ (and (= -1 (floor -1))
+ (exact? (floor -1)))))
+
+ (with-test-prefix "bignum"
+ (let ((x (1+ most-positive-fixnum)))
+ (pass-if "(1+ most-positive-fixnum)"
+ (and (= x (floor x))
+ (exact? (floor x)))))
+
+ (let ((x (1- most-negative-fixnum)))
+ (pass-if "(1- most-negative-fixnum)"
+ (and (= x (floor x))
+ (exact? (floor x))))))
+
+ (with-test-prefix "frac"
+ (define (=exact x y)
+ (and (= x y)
+ (exact? y)))
+
+ (pass-if (=exact -3 (floor -7/3)))
+ (pass-if (=exact -2 (floor -5/3)))
+ (pass-if (=exact -2 (floor -4/3)))
+ (pass-if (=exact -1 (floor -2/3)))
+ (pass-if (=exact -1 (floor -1/3)))
+ (pass-if (=exact 0 (floor 1/3)))
+ (pass-if (=exact 0 (floor 2/3)))
+ (pass-if (=exact 1 (floor 4/3)))
+ (pass-if (=exact 1 (floor 5/3)))
+ (pass-if (=exact 2 (floor 7/3)))
+
+ (pass-if (=exact -3 (floor -17/6)))
+ (pass-if (=exact -3 (floor -16/6)))
+ (pass-if (=exact -3 (floor -15/6)))
+ (pass-if (=exact -3 (floor -14/6)))
+ (pass-if (=exact -3 (floor -13/6)))
+ (pass-if (=exact -2 (floor -11/6)))
+ (pass-if (=exact -2 (floor -10/6)))
+ (pass-if (=exact -2 (floor -9/6)))
+ (pass-if (=exact -2 (floor -8/6)))
+ (pass-if (=exact -2 (floor -7/6)))
+ (pass-if (=exact -1 (floor -5/6)))
+ (pass-if (=exact -1 (floor -4/6)))
+ (pass-if (=exact -1 (floor -3/6)))
+ (pass-if (=exact -1 (floor -2/6)))
+ (pass-if (=exact -1 (floor -1/6)))
+ (pass-if (=exact 0 (floor 1/6)))
+ (pass-if (=exact 0 (floor 2/6)))
+ (pass-if (=exact 0 (floor 3/6)))
+ (pass-if (=exact 0 (floor 4/6)))
+ (pass-if (=exact 0 (floor 5/6)))
+ (pass-if (=exact 1 (floor 7/6)))
+ (pass-if (=exact 1 (floor 8/6)))
+ (pass-if (=exact 1 (floor 9/6)))
+ (pass-if (=exact 1 (floor 10/6)))
+ (pass-if (=exact 1 (floor 11/6)))
+ (pass-if (=exact 2 (floor 13/6)))
+ (pass-if (=exact 2 (floor 14/6)))
+ (pass-if (=exact 2 (floor 15/6)))
+ (pass-if (=exact 2 (floor 16/6)))
+ (pass-if (=exact 2 (floor 17/6))))
+
+ (with-test-prefix "real"
+ (pass-if "0.0"
+ (and (= 0.0 (floor 0.0))
+ (inexact? (floor 0.0))))
+
+ (pass-if "1.0"
+ (and (= 1.0 (floor 1.0))
+ (inexact? (floor 1.0))))
+
+ (pass-if "-1.0"
+ (and (= -1.0 (floor -1.0))
+ (inexact? (floor -1.0))))
+
+ (pass-if "-3.1"
+ (and (= -4.0 (floor -3.1))
+ (inexact? (floor -3.1))))
+
+ (pass-if "3.1"
+ (and (= 3.0 (floor 3.1))
+ (inexact? (floor 3.1))))
+
+ (pass-if "3.9"
+ (and (= 3.0 (floor 3.9))
+ (inexact? (floor 3.9))))
+
+ (pass-if "-3.9"
+ (and (= -4.0 (floor -3.9))
+ (inexact? (floor -3.9))))
+
+ (pass-if "1.5"
+ (and (= 1.0 (floor 1.5))
+ (inexact? (floor 1.5))))
+
+ (pass-if "2.5"
+ (and (= 2.0 (floor 2.5))
+ (inexact? (floor 2.5))))
+
+ (pass-if "3.5"
+ (and (= 3.0 (floor 3.5))
+ (inexact? (floor 3.5))))
+
+ (pass-if "-1.5"
+ (and (= -2.0 (floor -1.5))
+ (inexact? (floor -1.5))))
+
+ (pass-if "-2.5"
+ (and (= -3.0 (floor -2.5))
+ (inexact? (floor -2.5))))
+
+ (pass-if "-3.5"
+ (and (= -4.0 (floor -3.5))
+ (inexact? (floor -3.5))))))
+
+;;;
+;;; ceiling
+;;;
+
+(with-test-prefix "ceiling"
+ (pass-if (= 2 (ceiling 1.75)))
+ (pass-if (= 2 (ceiling 1.5)))
+ (pass-if (= 2 (ceiling 1.25)))
+ (pass-if (= 1 (ceiling 0.75)))
+ (pass-if (= 1 (ceiling 0.5)))
+ (pass-if (= 0 (ceiling 0.0)))
+ (pass-if (= 0 (ceiling -0.5)))
+ (pass-if (= -1 (ceiling -1.25)))
+ (pass-if (= -1 (ceiling -1.5)))
+
+ (with-test-prefix "inum"
+ (pass-if "0"
+ (and (= 0 (ceiling 0))
+ (exact? (ceiling 0))))
+
+ (pass-if "1"
+ (and (= 1 (ceiling 1))
+ (exact? (ceiling 1))))
+
+ (pass-if "-1"
+ (and (= -1 (ceiling -1))
+ (exact? (ceiling -1)))))
+
+ (with-test-prefix "bignum"
+ (let ((x (1+ most-positive-fixnum)))
+ (pass-if "(1+ most-positive-fixnum)"
+ (and (= x (ceiling x))
+ (exact? (ceiling x)))))
+
+ (let ((x (1- most-negative-fixnum)))
+ (pass-if "(1- most-negative-fixnum)"
+ (and (= x (ceiling x))
+ (exact? (ceiling x))))))
+
+ (with-test-prefix "frac"
+ (define (=exact x y)
+ (and (= x y)
+ (exact? y)))
+
+ (pass-if (=exact -2 (ceiling -7/3)))
+ (pass-if (=exact -1 (ceiling -5/3)))
+ (pass-if (=exact -1 (ceiling -4/3)))
+ (pass-if (=exact 0 (ceiling -2/3)))
+ (pass-if (=exact 0 (ceiling -1/3)))
+ (pass-if (=exact 1 (ceiling 1/3)))
+ (pass-if (=exact 1 (ceiling 2/3)))
+ (pass-if (=exact 2 (ceiling 4/3)))
+ (pass-if (=exact 2 (ceiling 5/3)))
+ (pass-if (=exact 3 (ceiling 7/3)))
+
+ (pass-if (=exact -2 (ceiling -17/6)))
+ (pass-if (=exact -2 (ceiling -16/6)))
+ (pass-if (=exact -2 (ceiling -15/6)))
+ (pass-if (=exact -2 (ceiling -14/6)))
+ (pass-if (=exact -2 (ceiling -13/6)))
+ (pass-if (=exact -1 (ceiling -11/6)))
+ (pass-if (=exact -1 (ceiling -10/6)))
+ (pass-if (=exact -1 (ceiling -9/6)))
+ (pass-if (=exact -1 (ceiling -8/6)))
+ (pass-if (=exact -1 (ceiling -7/6)))
+ (pass-if (=exact 0 (ceiling -5/6)))
+ (pass-if (=exact 0 (ceiling -4/6)))
+ (pass-if (=exact 0 (ceiling -3/6)))
+ (pass-if (=exact 0 (ceiling -2/6)))
+ (pass-if (=exact 0 (ceiling -1/6)))
+ (pass-if (=exact 1 (ceiling 1/6)))
+ (pass-if (=exact 1 (ceiling 2/6)))
+ (pass-if (=exact 1 (ceiling 3/6)))
+ (pass-if (=exact 1 (ceiling 4/6)))
+ (pass-if (=exact 1 (ceiling 5/6)))
+ (pass-if (=exact 2 (ceiling 7/6)))
+ (pass-if (=exact 2 (ceiling 8/6)))
+ (pass-if (=exact 2 (ceiling 9/6)))
+ (pass-if (=exact 2 (ceiling 10/6)))
+ (pass-if (=exact 2 (ceiling 11/6)))
+ (pass-if (=exact 3 (ceiling 13/6)))
+ (pass-if (=exact 3 (ceiling 14/6)))
+ (pass-if (=exact 3 (ceiling 15/6)))
+ (pass-if (=exact 3 (ceiling 16/6)))
+ (pass-if (=exact 3 (ceiling 17/6))))
+
+ (with-test-prefix "real"
+ (pass-if "0.0"
+ (and (= 0.0 (ceiling 0.0))
+ (inexact? (ceiling 0.0))))
+
+ (pass-if "1.0"
+ (and (= 1.0 (ceiling 1.0))
+ (inexact? (ceiling 1.0))))
+
+ (pass-if "-1.0"
+ (and (= -1.0 (ceiling -1.0))
+ (inexact? (ceiling -1.0))))
+
+ (pass-if "-3.1"
+ (and (= -3.0 (ceiling -3.1))
+ (inexact? (ceiling -3.1))))
+
+ (pass-if "3.1"
+ (and (= 4.0 (ceiling 3.1))
+ (inexact? (ceiling 3.1))))
+
+ (pass-if "3.9"
+ (and (= 4.0 (ceiling 3.9))
+ (inexact? (ceiling 3.9))))
+
+ (pass-if "-3.9"
+ (and (= -3.0 (ceiling -3.9))
+ (inexact? (ceiling -3.9))))
+
+ (pass-if "1.5"
+ (and (= 2.0 (ceiling 1.5))
+ (inexact? (ceiling 1.5))))
+
+ (pass-if "2.5"
+ (and (= 3.0 (ceiling 2.5))
+ (inexact? (ceiling 2.5))))
+
+ (pass-if "3.5"
+ (and (= 4.0 (ceiling 3.5))
+ (inexact? (ceiling 3.5))))
+
+ (pass-if "-1.5"
+ (and (= -1.0 (ceiling -1.5))
+ (inexact? (ceiling -1.5))))
+
+ (pass-if "-2.5"
+ (and (= -2.0 (ceiling -2.5))
+ (inexact? (ceiling -2.5))))
+
+ (pass-if "-3.5"
+ (and (= -3.0 (ceiling -3.5))
+ (inexact? (ceiling -3.5))))))
+
;;;
;;; truncate
;;;
(pass-if (= 0 (truncate 0.0)))
(pass-if (= 0 (truncate -0.5)))
(pass-if (= -1 (truncate -1.25)))
- (pass-if (= -1 (truncate -1.5))))
+ (pass-if (= -1 (truncate -1.5)))
+
+ (with-test-prefix "inum"
+ (pass-if "0"
+ (and (= 0 (truncate 0))
+ (exact? (truncate 0))))
+
+ (pass-if "1"
+ (and (= 1 (truncate 1))
+ (exact? (truncate 1))))
+
+ (pass-if "-1"
+ (and (= -1 (truncate -1))
+ (exact? (truncate -1)))))
+
+ (with-test-prefix "bignum"
+ (let ((x (1+ most-positive-fixnum)))
+ (pass-if "(1+ most-positive-fixnum)"
+ (and (= x (truncate x))
+ (exact? (truncate x)))))
+
+ (let ((x (1- most-negative-fixnum)))
+ (pass-if "(1- most-negative-fixnum)"
+ (and (= x (truncate x))
+ (exact? (truncate x))))))
+
+ (with-test-prefix "frac"
+ (define (=exact x y)
+ (and (= x y)
+ (exact? y)))
+
+ (pass-if (=exact -2 (truncate -7/3)))
+ (pass-if (=exact -1 (truncate -5/3)))
+ (pass-if (=exact -1 (truncate -4/3)))
+ (pass-if (=exact 0 (truncate -2/3)))
+ (pass-if (=exact 0 (truncate -1/3)))
+ (pass-if (=exact 0 (truncate 1/3)))
+ (pass-if (=exact 0 (truncate 2/3)))
+ (pass-if (=exact 1 (truncate 4/3)))
+ (pass-if (=exact 1 (truncate 5/3)))
+ (pass-if (=exact 2 (truncate 7/3)))
+
+ (pass-if (=exact -2 (truncate -17/6)))
+ (pass-if (=exact -2 (truncate -16/6)))
+ (pass-if (=exact -2 (truncate -15/6)))
+ (pass-if (=exact -2 (truncate -14/6)))
+ (pass-if (=exact -2 (truncate -13/6)))
+ (pass-if (=exact -1 (truncate -11/6)))
+ (pass-if (=exact -1 (truncate -10/6)))
+ (pass-if (=exact -1 (truncate -9/6)))
+ (pass-if (=exact -1 (truncate -8/6)))
+ (pass-if (=exact -1 (truncate -7/6)))
+ (pass-if (=exact 0 (truncate -5/6)))
+ (pass-if (=exact 0 (truncate -4/6)))
+ (pass-if (=exact 0 (truncate -3/6)))
+ (pass-if (=exact 0 (truncate -2/6)))
+ (pass-if (=exact 0 (truncate -1/6)))
+ (pass-if (=exact 0 (truncate 1/6)))
+ (pass-if (=exact 0 (truncate 2/6)))
+ (pass-if (=exact 0 (truncate 3/6)))
+ (pass-if (=exact 0 (truncate 4/6)))
+ (pass-if (=exact 0 (truncate 5/6)))
+ (pass-if (=exact 1 (truncate 7/6)))
+ (pass-if (=exact 1 (truncate 8/6)))
+ (pass-if (=exact 1 (truncate 9/6)))
+ (pass-if (=exact 1 (truncate 10/6)))
+ (pass-if (=exact 1 (truncate 11/6)))
+ (pass-if (=exact 2 (truncate 13/6)))
+ (pass-if (=exact 2 (truncate 14/6)))
+ (pass-if (=exact 2 (truncate 15/6)))
+ (pass-if (=exact 2 (truncate 16/6)))
+ (pass-if (=exact 2 (truncate 17/6))))
+
+ (with-test-prefix "real"
+ (pass-if "0.0"
+ (and (= 0.0 (truncate 0.0))
+ (inexact? (truncate 0.0))))
+
+ (pass-if "1.0"
+ (and (= 1.0 (truncate 1.0))
+ (inexact? (truncate 1.0))))
+
+ (pass-if "-1.0"
+ (and (= -1.0 (truncate -1.0))
+ (inexact? (truncate -1.0))))
+
+ (pass-if "-3.1"
+ (and (= -3.0 (truncate -3.1))
+ (inexact? (truncate -3.1))))
+
+ (pass-if "3.1"
+ (and (= 3.0 (truncate 3.1))
+ (inexact? (truncate 3.1))))
+
+ (pass-if "3.9"
+ (and (= 3.0 (truncate 3.9))
+ (inexact? (truncate 3.9))))
+
+ (pass-if "-3.9"
+ (and (= -3.0 (truncate -3.9))
+ (inexact? (truncate -3.9))))
+
+ (pass-if "1.5"
+ (and (= 1.0 (truncate 1.5))
+ (inexact? (truncate 1.5))))
+
+ (pass-if "2.5"
+ (and (= 2.0 (truncate 2.5))
+ (inexact? (truncate 2.5))))
+
+ (pass-if "3.5"
+ (and (= 3.0 (truncate 3.5))
+ (inexact? (truncate 3.5))))
+
+ (pass-if "-1.5"
+ (and (= -1.0 (truncate -1.5))
+ (inexact? (truncate -1.5))))
+
+ (pass-if "-2.5"
+ (and (= -2.0 (truncate -2.5))
+ (inexact? (truncate -2.5))))
+
+ (pass-if "-3.5"
+ (and (= -3.0 (truncate -3.5))
+ (inexact? (truncate -3.5))))))
;;;
;;; round
;;;
(with-test-prefix "exact->inexact"
-
+
+ ;; Test "(exact->inexact n)", expect "want".
+ (define (test name n want)
+ (with-test-prefix name
+ (pass-if-equal "pos" want (exact->inexact n))
+ (pass-if-equal "neg" (- want) (exact->inexact (- n)))))
+
;; Test "(exact->inexact n)", expect "want".
;; "i" is a index, for diagnostic purposes.
(define (try-i i n want)
- (with-test-prefix (list i n want)
- (with-test-prefix "pos"
- (let ((got (exact->inexact n)))
- (pass-if "inexact?" (inexact? got))
- (pass-if (list "=" got) (= want got))))
- (set! n (- n))
- (set! want (- want))
- (with-test-prefix "neg"
- (let ((got (exact->inexact n)))
- (pass-if "inexact?" (inexact? got))
- (pass-if (list "=" got) (= want got))))))
+ (test (list i n want) n want))
(with-test-prefix "2^i, no round"
(do ((i 0 (1+ i))
;; convert the num and den to doubles, resulting in infs.
(pass-if "frac big/big, exceeding double"
(let ((big (ash 1 4096)))
- (= 1.0 (exact->inexact (/ (1+ big) big))))))
+ (= 1.0 (exact->inexact (/ (1+ big) big)))))
+
+ ;; In guile 2.0.9, 'exact->inexact' guaranteed proper rounding when
+ ;; applied to non-negative fractions, but on 64-bit systems would
+ ;; sometimes double-round when applied to negative fractions,
+ ;; specifically when the numerator was a fixnum not exactly
+ ;; representable as a double.
+ (with-test-prefix "frac inum/inum, numerator not exactly representable as a double"
+ (let ((n (+ 1 (expt 2 dbl-mant-dig))))
+ (for-each (lambda (d)
+ (test (/ n d)
+ (/ n d)
+ (exact->inexact (/ n d))))
+ '(3 5 6 7 9 11 13 17 19 23 0.0 -0.0 +nan.0 +inf.0 -inf.0))))
+
+ (test "round up to odd"
+ ;; =====================================================
+ ;; 11111111111111111111111111111111111111111111111111000101 ->
+ ;; 11111111111111111111111111111111111111111111111111001000
+ (+ (expt 2 (+ dbl-mant-dig 3)) -64 #b000101)
+ (+ (expt 2.0 (+ dbl-mant-dig 3)) -64 #b001000))
+
+ (test "round down to odd"
+ ;; =====================================================
+ ;; 11111111111111111111111111111111111111111111111111001011 ->
+ ;; 11111111111111111111111111111111111111111111111111001000
+ (+ (expt 2 (+ dbl-mant-dig 3)) -64 #b001011)
+ (+ (expt 2.0 (+ dbl-mant-dig 3)) -64 #b001000))
+
+ (test "round tie up to even"
+ ;; =====================================================
+ ;; 11111111111111111111111111111111111111111111111111011100 ->
+ ;; 11111111111111111111111111111111111111111111111111100000
+ (+ (expt 2 (+ dbl-mant-dig 3)) -64 #b011100)
+ (+ (expt 2.0 (+ dbl-mant-dig 3)) -64 #b100000))
+
+ (test "round tie down to even"
+ ;; =====================================================
+ ;; 11111111111111111111111111111111111111111111111111000100 ->
+ ;; 11111111111111111111111111111111111111111111111111000000
+ (+ (expt 2 (+ dbl-mant-dig 3)) -64 #b000100)
+ (+ (expt 2.0 (+ dbl-mant-dig 3)) -64 #b000000))
+
+ (test "round tie up to next power of two"
+ ;; =====================================================
+ ;; 11111111111111111111111111111111111111111111111111111100 ->
+ ;; 100000000000000000000000000000000000000000000000000000000
+ (+ (expt 2 (+ dbl-mant-dig 3)) -64 #b111100)
+ (expt 2.0 (+ dbl-mant-dig 3)))
+
+ (test "miniscule value rounds to zero of appropriate sign"
+ (expt 17 (- dbl-min-exp dbl-mant-dig))
+ 0.0)
+
+ (test "smallest inexact"
+ (expt 2 (- dbl-min-exp dbl-mant-dig))
+ (expt 2.0 (- dbl-min-exp dbl-mant-dig)))
+
+ (test "1/2 smallest inexact rounds down to zero"
+ (* 1/2 (expt 2 (- dbl-min-exp dbl-mant-dig)))
+ 0.0)
+
+ (test "just over 1/2 smallest inexact rounds up"
+ (+ (* 1/2 (expt 2 (- dbl-min-exp dbl-mant-dig)))
+ (expt 7 (- dbl-min-exp dbl-mant-dig)))
+ (expt 2.0 (- dbl-min-exp dbl-mant-dig)))
+
+ (test "3/2 smallest inexact rounds up to twice smallest inexact"
+ (* 3/2 (expt 2 (- dbl-min-exp dbl-mant-dig)))
+ (* 2.0 (expt 2.0 (- dbl-min-exp dbl-mant-dig))))
+
+ (test "just under 3/2 smallest inexact rounds down"
+ (- (* 3/2 (expt 2 (- dbl-min-exp dbl-mant-dig)))
+ (expt 11 (- dbl-min-exp dbl-mant-dig)))
+ (expt 2.0 (- dbl-min-exp dbl-mant-dig)))
+
+ (test "5/2 smallest inexact rounds down to twice smallest inexact"
+ (* 5/2 (expt 2 (- dbl-min-exp dbl-mant-dig)))
+ (* 2.0 (expt 2.0 (- dbl-min-exp dbl-mant-dig))))
+
+ (test "just over 5/2 smallest inexact rounds up"
+ (+ (* 5/2 (expt 2 (- dbl-min-exp dbl-mant-dig)))
+ (expt 13 (- dbl-min-exp dbl-mant-dig)))
+ (* 3.0 (expt 2.0 (- dbl-min-exp dbl-mant-dig))))
+
+ (test "one plus dbl-epsilon"
+ (+ 1 dbl-epsilon-exact)
+ (+ 1.0 dbl-epsilon))
+
+ (test "one plus 1/2 dbl-epsilon rounds down to 1.0"
+ (+ 1 (* 1/2 dbl-epsilon-exact))
+ 1.0)
+
+ (test "just over one plus 1/2 dbl-epsilon rounds up"
+ (+ 1
+ (* 1/2 dbl-epsilon-exact)
+ (expt 13 (- dbl-min-exp dbl-mant-dig)))
+ (+ 1.0 dbl-epsilon))
+
+ (test "one plus 3/2 dbl-epsilon rounds up"
+ (+ 1 (* 3/2 dbl-epsilon-exact))
+ (+ 1.0 (* 2.0 dbl-epsilon)))
+
+ (test "just under one plus 3/2 dbl-epsilon rounds down"
+ (+ 1
+ (* 3/2 dbl-epsilon-exact)
+ (- (expt 17 (- dbl-min-exp dbl-mant-dig))))
+ (+ 1.0 dbl-epsilon))
+
+ (test "one plus 5/2 dbl-epsilon rounds down"
+ (+ 1 (* 5/2 dbl-epsilon-exact))
+ (+ 1.0 (* 2.0 dbl-epsilon)))
+
+ (test "just over one plus 5/2 dbl-epsilon rounds up"
+ (+ 1
+ (* 5/2 dbl-epsilon-exact)
+ (expt 13 (- dbl-min-exp dbl-mant-dig)))
+ (+ 1.0 (* 3.0 dbl-epsilon)))
+
+ (test "largest finite inexact"
+ (* (- (expt 2 dbl-mant-dig) 1)
+ (expt 2 (- dbl-max-exp dbl-mant-dig)))
+ (* (- (expt 2.0 dbl-mant-dig) 1)
+ (expt 2.0 (- dbl-max-exp dbl-mant-dig))))
+
+ (test "largest finite inexact plus 1/2 epsilon rounds up to infinity"
+ (* (+ (expt 2 dbl-mant-dig) -1 1/2)
+ (expt 2 (- dbl-max-exp dbl-mant-dig)))
+ (inf))
+
+ (test "largest finite inexact plus just under 1/2 epsilon rounds down"
+ (* (+ (expt 2 dbl-mant-dig) -1 1/2
+ (- (expt 13 (- dbl-min-exp dbl-mant-dig))))
+ (expt 2 (- dbl-max-exp dbl-mant-dig)))
+ (* (- (expt 2.0 dbl-mant-dig) 1)
+ (expt 2.0 (- dbl-max-exp dbl-mant-dig))))
+
+ (test "1/2 largest finite inexact"
+ (* (- (expt 2 dbl-mant-dig) 1)
+ (expt 2 (- dbl-max-exp dbl-mant-dig 1)))
+ (* (- (expt 2.0 dbl-mant-dig) 1)
+ (expt 2.0 (- dbl-max-exp dbl-mant-dig 1))))
+
+ (test "1/2 largest finite inexact plus 1/2 epsilon rounds up to next power of two"
+ (* (+ (expt 2 dbl-mant-dig) -1 1/2)
+ (expt 2 (- dbl-max-exp dbl-mant-dig 1)))
+ (expt 2.0 (- dbl-max-exp 1)))
+
+ (test "1/2 largest finite inexact plus just over 1/2 epsilon rounds up to next power of two"
+ (* (+ (expt 2 dbl-mant-dig) -1 1/2
+ (expt 13 (- dbl-min-exp dbl-mant-dig)))
+ (expt 2 (- dbl-max-exp dbl-mant-dig 1)))
+ (expt 2.0 (- dbl-max-exp 1)))
+
+ (test "1/2 largest finite inexact plus just under 1/2 epsilon rounds down"
+ (* (+ (expt 2 dbl-mant-dig) -1 1/2
+ (- (expt 13 (- dbl-min-exp dbl-mant-dig))))
+ (expt 2 (- dbl-max-exp dbl-mant-dig 1)))
+ (* (- (expt 2.0 dbl-mant-dig) 1)
+ (expt 2.0 (- dbl-max-exp dbl-mant-dig 1))))
+
+ )
;;;
-;;; floor
+;;; expt
;;;
+(with-test-prefix "expt"
+ (pass-if (documented? expt))
+
+ ;;
+ ;; expt no longer requires its first argument to be a scheme number,
+ ;; for the sake of extensibility, and expt calls integer-expt for
+ ;; integer powers. To raise to a positive power, all that is required
+ ;; is that it can be multiplied using `*'. For negative powers we
+ ;; must also be able to find the reciprocal. If we try to raise #t to
+ ;; any power other than 0 or 1 it may throw an exception, depending on
+ ;; whether * has been defined for #t. However, when raising to the 0
+ ;; or 1 power, the first argument is not manipulated at all.
+ ;;
+ ;; (pass-if-exception "non-numeric base" exception:wrong-type-arg
+ ;; (expt #t 0))
+ ;;
+
+ (pass-if (eqv? 1 (expt 0 0)))
+ (pass-if (eqv? 1 (expt 0.0 0)))
+ (pass-if (eqv? 1.0 (expt 0 0.0)))
+ (pass-if (eqv? 1.0 (expt 0.0 0.0)))
+ (pass-if (real-nan? (expt 0 -1)))
+ (pass-if (real-nan? (expt 0 -1.0)))
+ (pass-if (real-nan? (expt 0.0 -1)))
+ (pass-if (real-nan? (expt 0.0 -1.0)))
+ (pass-if (eqv? 0 (expt 0 3)))
+ (pass-if (= 0 (expt 0 4.0)))
+ (pass-if (eqv? 0.0 (expt 0.0 5)))
+ (pass-if (eqv? 0.0 (expt 0.0 6.0)))
+ (pass-if (eqv? -2742638075.5 (expt -2742638075.5 1)))
+ (pass-if (eqv? (* -2742638075.5 -2742638075.5)
+ (expt -2742638075.5 2)))
+ (pass-if (eqv? 4.0 (expt -2.0 2.0)))
+ (pass-if (eqv? -1/8 (expt -2 -3)))
+ (pass-if (eqv? -0.125 (expt -2.0 -3)))
+ (pass-if (eqv? -0.125 (expt -2 -3.0)))
+ (pass-if (eqv? -0.125 (expt -2.0 -3.0)))
+ (pass-if (eqv? 0.25 (expt 2.0 -2.0)))
+ (pass-if (eqv? 32/243 (expt 2/3 5)))
+ (pass-if (eqv? 243/32 (expt 2/3 -5)))
+ (pass-if (eqv? 32 (expt 1/2 -5)))
+ (pass-if (test-eqv? (* -1.0+0.0i 12398 12398) (expt +12398i 2.0)))
+ (pass-if (eqv-loosely? +i (expt -1 0.5)))
+ (pass-if (eqv-loosely? +i (expt -1 1/2)))
+ (pass-if (eqv-loosely? 1.0+1.7320508075688i (expt -8 1/3)))
+ (pass-if (eqv? +inf.0 (expt 2 +inf.0)))
+ (pass-if (eqv? +inf.0 (expt 2.0 +inf.0)))
+ (pass-if (eqv? 0.0 (expt 2 -inf.0)))
+ (pass-if (eqv? 0.0 (expt 2.0 -inf.0))))
+
+
;;;
-;;; ceiling
+;;; sin
;;;
+(with-test-prefix "sin"
+ (pass-if (eqv? 0 (sin 0)))
+ (pass-if (eqv? 0.0 (sin 0.0)))
+ (pass-if (eqv-loosely? 1.0 (sin 1.57)))
+ (pass-if (eqv-loosely? +1.175i (sin +i)))
+ (pass-if (real-nan? (sin +nan.0)))
+ (pass-if (real-nan? (sin +inf.0)))
+ (pass-if (real-nan? (sin -inf.0))))
+
;;;
-;;; expt
+;;; cos
;;;
-(with-test-prefix "expt"
- (pass-if-exception "non-numeric base" exception:wrong-type-arg
- (expt #t 0))
- (pass-if "(= 1 (expt 0 0))" (= 1 (expt 0 0)))
- (pass-if "(= 1 (expt 0 0.0))" (= 1 (expt 0 0.0)))
- (pass-if "(= 1 (expt 0.0 0))" (= 1 (expt 0.0 0)))
- (pass-if "(= 1 (expt 0.0 0.0))" (= 1 (expt 0.0 0.0))))
+(with-test-prefix "cos"
+ (pass-if (eqv? 1 (cos 0)))
+ (pass-if (eqv? 1.0 (cos 0.0)))
+ (pass-if (eqv-loosely? 0.0 (cos 1.57)))
+ (pass-if (eqv-loosely? 1.543 (cos +i)))
+ (pass-if (real-nan? (cos +nan.0)))
+ (pass-if (real-nan? (cos +inf.0)))
+ (pass-if (real-nan? (cos -inf.0))))
+
+;;;
+;;; tan
+;;;
+
+(with-test-prefix "tan"
+ (pass-if (eqv? 0 (tan 0)))
+ (pass-if (eqv? 0.0 (tan 0.0)))
+ (pass-if (eqv-loosely? 1.0 (tan 0.785)))
+ (pass-if (eqv-loosely? +0.76i (tan +i)))
+ (pass-if (real-nan? (tan +nan.0)))
+ (pass-if (real-nan? (tan +inf.0)))
+ (pass-if (real-nan? (tan -inf.0))))
+
+;;;
+;;; asin
+;;;
+
+(with-test-prefix "asin"
+ (pass-if (complex-nan? (asin +nan.0)))
+ (pass-if (eqv? 0 (asin 0)))
+ (pass-if (eqv? 0.0 (asin 0.0))))
+
+;;;
+;;; acos
+;;;
+
+(with-test-prefix "acos"
+ (pass-if (complex-nan? (acos +nan.0)))
+ (pass-if (eqv? 0 (acos 1)))
+ (pass-if (eqv? 0.0 (acos 1.0))))
+
+;;;
+;;; atan
+;;;
+;;; FIXME: add tests for two-argument atan
+;;;
+(with-test-prefix "atan"
+ (pass-if (real-nan? (atan +nan.0)))
+ (pass-if (eqv? 0 (atan 0)))
+ (pass-if (eqv? 0.0 (atan 0.0)))
+ (pass-if (eqv-loosely? 1.57 (atan +inf.0)))
+ (pass-if (eqv-loosely? -1.57 (atan -inf.0))))
+
+;;;
+;;; sinh
+;;;
+
+(with-test-prefix "sinh"
+ (pass-if (= 0 (sinh 0)))
+ (pass-if (= 0.0 (sinh 0.0))))
+
+;;;
+;;; cosh
+;;;
+
+(with-test-prefix "cosh"
+ (pass-if (= 1 (cosh 0)))
+ (pass-if (= 1.0 (cosh 0.0))))
+
+;;;
+;;; tanh
+;;;
+
+(with-test-prefix "tanh"
+ (pass-if (= 0 (tanh 0)))
+ (pass-if (= 0.0 (tanh 0.0))))
;;;
;;; asinh
;;;
(with-test-prefix "asinh"
- (pass-if (= 0 (asinh 0))))
+ (pass-if (= 0 (asinh 0)))
+ (pass-if (= 0.0 (asinh 0.0))))
;;;
;;; acosh
;;;
(with-test-prefix "acosh"
- (pass-if (= 0 (acosh 1))))
+ (pass-if (= 0 (acosh 1)))
+ (pass-if (= 0.0 (acosh 1.0))))
;;;
;;; atanh
;;;
(with-test-prefix "atanh"
- (pass-if (= 0 (atanh 0))))
+ (pass-if (= 0 (atanh 0)))
+ (pass-if (= 0.0 (atanh 0.0))))
;;;
;;; make-rectangular
;;;
+
+(with-test-prefix "make-rectangular"
+ (pass-if (real? (make-rectangular 5.0 0 )))
+ (pass-if (not (real? (make-rectangular 5.0 0.0))))
+ (pass-if (not (real? (make-rectangular 5.0 -0.0)))))
;;;
;;; make-polar
(define (almost= x y)
(> 0.01 (magnitude (- x y))))
- (pass-if (= 0 (make-polar 0 0)))
- (pass-if (= 0 (make-polar 0 123.456)))
- (pass-if (= 1 (make-polar 1 0)))
- (pass-if (= -1 (make-polar -1 0)))
+ (pass-if (real? (make-polar 0 1.0)))
+ (pass-if (real? (make-polar 5.0 0 )))
+ (pass-if (not (real? (make-polar 5.0 0.0))))
+ (pass-if (not (real? (make-polar 5.0 -0.0))))
+
+ (pass-if (eqv? 0 (make-polar 0 0)))
+ (pass-if (eqv? 0 (make-polar 0 123.456)))
+ (pass-if (eqv? 1 (make-polar 1 0)))
+ (pass-if (eqv? -1 (make-polar -1 0)))
(pass-if (almost= 0+i (make-polar 1 (* 0.5 pi))))
(pass-if (almost= -1 (make-polar 1 (* 1.0 pi))))
;;; real-part
;;;
+(with-test-prefix "real-part"
+ (pass-if (documented? real-part))
+ (pass-if (eqv? 5.0 (real-part 5.0)))
+ (pass-if (eqv? 0.0 (real-part +5.0i)))
+ (pass-if (eqv? 5 (real-part 5)))
+ (pass-if (eqv? 1/5 (real-part 1/5)))
+ (pass-if (eqv? (1+ fixnum-max) (real-part (1+ fixnum-max)))))
+
;;;
;;; imag-part
;;;
+(with-test-prefix "imag-part"
+ (pass-if (documented? imag-part))
+ (pass-if (eqv? 0 (imag-part 5.0)))
+ (pass-if (eqv? 5.0 (imag-part +5.0i)))
+ (pass-if (eqv? 0 (imag-part 5)))
+ (pass-if (eqv? 0 (imag-part 1/5)))
+ (pass-if (eqv? 0 (imag-part (1+ fixnum-max)))))
+
;;;
;;; magnitude
;;;
(with-test-prefix "magnitude"
+ (pass-if (documented? magnitude))
(pass-if (= 0 (magnitude 0)))
(pass-if (= 1 (magnitude 1)))
(pass-if (= 1 (magnitude -1)))
(with-test-prefix "angle"
(define pi 3.14159265358979323846)
(define (almost= x y)
- (> 0.01 (magnitude (- x y))))
+ (> 0.000001 (magnitude (- x y))))
+ (pass-if (documented? angle))
+
(pass-if "inum +ve" (= 0 (angle 1)))
(pass-if "inum -ve" (almost= pi (angle -1)))
(pass-if "bignum -ve" (almost= pi (angle (1- fixnum-min))))
(pass-if "flonum +ve" (= 0 (angle 1.5)))
- (pass-if "flonum -ve" (almost= pi (angle -1.5))))
+ (pass-if "flonum -ve" (almost= pi (angle -1.5)))
+
+ (pass-if "signed zero +ve" (= 0 (angle 0.0)))
+ (pass-if "signed zero -ve" (almost= pi (angle -0.0))))
;;;
;;; inexact->exact
;;;
(with-test-prefix "inexact->exact"
-
+
+ ;; Test "(inexact->exact f)", expect "want".
+ (define (test name f want)
+ (with-test-prefix name
+ (pass-if-equal "pos" want (inexact->exact f))
+ (pass-if-equal "neg" (- want) (inexact->exact (- f)))))
+
+ (pass-if (documented? inexact->exact))
+
(pass-if-exception "+inf" exception:out-of-range
(inexact->exact +inf.0))
(pass-if-exception "nan" exception:out-of-range
(inexact->exact +nan.0))
-
- (with-test-prefix "2.0**i to exact and back"
+
+ (test "0.0" 0.0 0)
+ (test "small even integer" 72.0 72)
+ (test "small odd integer" 73.0 73)
+
+ (test "largest inexact odd integer"
+ (- (expt 2.0 dbl-mant-dig) 1)
+ (- (expt 2 dbl-mant-dig) 1))
+
+ (test "largest inexact odd integer - 1"
+ (- (expt 2.0 dbl-mant-dig) 2)
+ (- (expt 2 dbl-mant-dig) 2))
+
+ (test "largest inexact odd integer + 3"
+ (+ (expt 2.0 dbl-mant-dig) 2)
+ (+ (expt 2 dbl-mant-dig) 2))
+
+ (test "largest inexact odd integer * 2^48"
+ (* (expt 2.0 48) (- (expt 2.0 dbl-mant-dig) 1))
+ (* (expt 2 48) (- (expt 2 dbl-mant-dig) 1)))
+
+ (test "largest inexact odd integer / 2^48"
+ (* (expt 0.5 48) (- (expt 2.0 dbl-mant-dig) 1))
+ (* (expt 1/2 48) (- (expt 2 dbl-mant-dig) 1)))
+
+ (test "largest finite inexact"
+ (* (- (expt 2.0 dbl-mant-dig) 1)
+ (expt 2.0 (- dbl-max-exp dbl-mant-dig)))
+ (* (- (expt 2 dbl-mant-dig) 1)
+ (expt 2 (- dbl-max-exp dbl-mant-dig))))
+
+ (test "smallest inexact"
+ (expt 2.0 (- dbl-min-exp dbl-mant-dig))
+ (expt 2 (- dbl-min-exp dbl-mant-dig)))
+
+ (test "smallest inexact * 2"
+ (* 2.0 (expt 2.0 (- dbl-min-exp dbl-mant-dig)))
+ (* 2 (expt 2 (- dbl-min-exp dbl-mant-dig))))
+
+ (test "smallest inexact * 3"
+ (* 3.0 (expt 2.0 (- dbl-min-exp dbl-mant-dig)))
+ (* 3 (expt 2 (- dbl-min-exp dbl-mant-dig))))
+
+ (with-test-prefix "2.0**i to exact"
(do ((i 0 (1+ i))
- (n 1.0 (* 2.0 n)))
+ (n 1 (* 2 n))
+ (f 1.0 (* 2.0 f)))
((> i 100))
- (pass-if (list i n)
- (= n (inexact->exact (exact->inexact n)))))))
+ (test (list i n) f n))))
;;;
;;; integer-expt
;;;
(with-test-prefix "integer-expt"
+ (pass-if (documented? integer-expt))
- (pass-if-exception "non-numeric base" exception:wrong-type-arg
- (integer-expt #t 0))
(pass-if-exception "2^+inf" exception:wrong-type-arg
(integer-expt 2 +inf.0))
(pass-if-exception "2^-inf" exception:wrong-type-arg
(integer-expt 2 -inf.0))
(pass-if-exception "2^nan" exception:wrong-type-arg
- (integer-expt 2 +nan.0)))
+ (integer-expt 2 +nan.0))
+
+ (pass-if (eqv? 1 (integer-expt 0 0)))
+ (pass-if (eqv? 1 (integer-expt 0.0 0)))
+ (pass-if (real-nan? (integer-expt 0 -1)))
+ (pass-if (real-nan? (integer-expt 0.0 -1)))
+ (pass-if (eqv? 0 (integer-expt 0 3)))
+ (pass-if (eqv? 0.0 (integer-expt 0.0 5)))
+ (pass-if (eqv? -2742638075.5 (integer-expt -2742638075.5 1)))
+ (pass-if (eqv? (* -2742638075.5 -2742638075.5)
+ (integer-expt -2742638075.5 2)))
+ (pass-if (eqv? 4.0 (integer-expt -2.0 2)))
+ (pass-if (eqv? -1/8 (integer-expt -2 -3)))
+ (pass-if (eqv? -0.125 (integer-expt -2.0 -3)))
+ (pass-if (eqv? 0.25 (integer-expt 2.0 -2)))
+ (pass-if (eqv? 32/243 (integer-expt 2/3 5)))
+ (pass-if (eqv? 243/32 (integer-expt 2/3 -5)))
+ (pass-if (eqv? 32 (integer-expt 1/2 -5)))
+ (pass-if (test-eqv? (* -1.0+0.0i 12398 12398) (integer-expt +12398.0i 2))))
+
;;;
;;; integer-length
;;;
(with-test-prefix "integer-length"
+ (pass-if (documented? integer-length))
(with-test-prefix "-2^i, ...11100..00"
(do ((n -1 (ash n 1))
;;;
(with-test-prefix "log"
- (pass-if "documented?"
- (documented? log))
+ (pass-if (documented? log))
(pass-if-exception "no args" exception:wrong-num-args
(log))
(pass-if-exception "two args" exception:wrong-num-args
(log 123 456))
-
- (pass-if (negative-infinity? (log 0)))
- (pass-if (negative-infinity? (log 0.0)))
- (pass-if (eqv? 0.0 (log 1)))
- (pass-if (eqv? 0.0 (log 1.0)))
- (pass-if (eqv-loosely? 1.0 (log const-e)))
- (pass-if (eqv-loosely? 2.0 (log const-e^2)))
- (pass-if (eqv-loosely? -1.0 (log const-1/e)))
+ (pass-if-exception "(log 0)" exception:numerical-overflow
+ (log 0))
+
+ (pass-if (test-eqv? -inf.0 (log 0.0)))
+ (pass-if (test-eqv? +inf.0 (log +inf.0)))
+ (pass-if (test-eqv? -inf.0+3.14159265358979i (log -0.0)))
+ (pass-if (test-eqv? +inf.0+3.14159265358979i (log -inf.0)))
+ (pass-if (test-eqv? 0.0 (log 1 )))
+ (pass-if (test-eqv? 0.0 (log 1.0)))
+ (pass-if (test-eqv? 1.0 (log const-e)))
+ (pass-if (test-eqv? 2.0 (log const-e^2)))
+ (pass-if (test-eqv? -1.0 (log const-1/e)))
+ (pass-if (test-eqv? -1.0+3.14159265358979i (log (- const-1/e))))
+ (pass-if (test-eqv? 2.30258509299405 (log 10)))
+ (pass-if (test-eqv? 2.30258509299405+3.14159265358979i (log -10)))
+
+ (pass-if (test-eqv? 1.0+0.0i (log (+ const-e +0.0i))))
+ (pass-if (test-eqv? 1.0-0.0i (log (+ const-e -0.0i))))
+
+ (pass-if (eqv-loosely? 230258.509299405 (log (expt 10 100000))))
+ (pass-if (eqv-loosely? -230258.509299405 (log (expt 10 -100000))))
+ (pass-if (eqv-loosely? 230257.410687116 (log (/ (expt 10 100000) 3))))
+ (pass-if (eqv-loosely? 230258.509299405+3.14159265358979i
+ (log (- (expt 10 100000)))))
+ (pass-if (eqv-loosely? -230258.509299405+3.14159265358979i
+ (log (- (expt 10 -100000)))))
+ (pass-if (eqv-loosely? 230257.410687116+3.14159265358979i
+ (log (- (/ (expt 10 100000) 3)))))
+ (pass-if (test-eqv? 3.05493636349961e-151
+ (log (/ (1+ (expt 2 500)) (expt 2 500)))))
(pass-if (eqv-loosely? 1.0+1.57079i (log 0+2.71828i)))
(pass-if (eqv-loosely? 1.0-1.57079i (log 0-2.71828i)))
;;;
(with-test-prefix "log10"
- (pass-if "documented?"
- (documented? log10))
+ (pass-if (documented? log10))
(pass-if-exception "no args" exception:wrong-num-args
(log10))
(pass-if-exception "two args" exception:wrong-num-args
(log10 123 456))
-
- (pass-if (negative-infinity? (log10 0)))
- (pass-if (negative-infinity? (log10 0.0)))
- (pass-if (eqv? 0.0 (log10 1)))
- (pass-if (eqv? 0.0 (log10 1.0)))
- (pass-if (eqv-loosely? 1.0 (log10 10.0)))
- (pass-if (eqv-loosely? 2.0 (log10 100.0)))
- (pass-if (eqv-loosely? -1.0 (log10 0.1)))
+ (pass-if-exception "(log10 0)" exception:numerical-overflow
+ (log10 0))
+
+ (pass-if (test-eqv? -inf.0 (log10 0.0)))
+ (pass-if (test-eqv? +inf.0 (log10 +inf.0)))
+ (pass-if (test-eqv? -inf.0+1.36437635384184i (log10 -0.0)))
+ (pass-if (test-eqv? +inf.0+1.36437635384184i (log10 -inf.0)))
+ (pass-if (test-eqv? 0.0 (log10 1 )))
+ (pass-if (test-eqv? 0.0 (log10 1.0)))
+ (pass-if (test-eqv? 1.0 (log10 10 )))
+ (pass-if (test-eqv? 1.0 (log10 10.0)))
+ (pass-if (test-eqv? 2.0 (log10 100.0)))
+ (pass-if (test-eqv? -1.0 (log10 0.1)))
+ (pass-if (test-eqv? -1.0+1.36437635384184i (log10 -0.1)))
+ (pass-if (test-eqv? 1.0+1.36437635384184i (log10 -10 )))
+
+ (pass-if (test-eqv? 1.0+0.0i (log10 10.0+0.0i)))
+ (pass-if (test-eqv? 1.0-0.0i (log10 10.0-0.0i)))
+
+ (pass-if (eqv-loosely? 100000.0 (log10 (expt 10 100000))))
+ (pass-if (eqv-loosely? -100000.0 (log10 (expt 10 -100000))))
+ (pass-if (eqv-loosely? 99999.5228787453 (log10 (/ (expt 10 100000) 3))))
+ (pass-if (eqv-loosely? 100000.0+1.36437635384184i
+ (log10 (- (expt 10 100000)))))
+ (pass-if (eqv-loosely? -100000.0+1.36437635384184i
+ (log10 (- (expt 10 -100000)))))
+ (pass-if (eqv-loosely? 99999.5228787453+1.36437635384184i
+ (log10 (- (/ (expt 10 100000) 3)))))
+ (pass-if (test-eqv? 1.32674200523347e-151
+ (log10 (/ (1+ (expt 2 500)) (expt 2 500)))))
(pass-if (eqv-loosely? 1.0+0.68218i (log10 0+10.0i)))
(pass-if (eqv-loosely? 1.0-0.68218i (log10 0-10.0i)))
- (pass-if (eqv-loosely? 0.0+1.36437i (log10 -1)))
- (pass-if (eqv-loosely? 1.0+1.36437i (log10 -10)))
+ (pass-if (eqv-loosely? 0.0+1.36437i (log10 -1)))
+ (pass-if (eqv-loosely? 1.0+1.36437i (log10 -10)))
(pass-if (eqv-loosely? 2.0+1.36437i (log10 -100))))
;;;
;;;
(with-test-prefix "logbit?"
+ (pass-if (documented? logbit?))
+
(pass-if (eq? #f (logbit? 0 0)))
(pass-if (eq? #f (logbit? 1 0)))
(pass-if (eq? #f (logbit? 31 0)))
;;;
(with-test-prefix "logcount"
+ (pass-if (documented? logcount))
(with-test-prefix "-2^i, meaning ...11100..00"
(do ((n -1 (ash n 1))
;;;
(with-test-prefix "logior"
+ (pass-if (documented? logior))
+
(pass-if (eqv? -1 (logior (ash -1 1) 1)))
;; check that bignum or bignum+inum args will reduce to an inum
;;;
(with-test-prefix "lognot"
+ (pass-if (documented? lognot))
+
(pass-if (= -1 (lognot 0)))
(pass-if (= 0 (lognot -1)))
(pass-if (= -2 (lognot 1)))
(pass-if (= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
(lognot #x-100000000000000000000000000000000))))
+;;;
+;;; exact-integer-sqrt
+;;;
+
+(with-test-prefix "exact-integer-sqrt"
+ (define (non-negative-exact-integer? k)
+ (and (integer? k) (exact? k) (>= k 0)))
+
+ (define (test k)
+ (pass-if k (let-values (((s r) (exact-integer-sqrt k)))
+ (and (non-negative-exact-integer? s)
+ (non-negative-exact-integer? r)
+ (= k (+ r (* s s)))
+ (< k (* (1+ s) (1+ s)))))))
+
+ (define (test-wrong-type-arg k)
+ (pass-if-exception k exception:wrong-type-arg
+ (let-values (((s r) (exact-integer-sqrt k)))
+ #t)))
+
+ (pass-if (documented? exact-integer-sqrt))
+
+ (pass-if-exception "no args" exception:wrong-num-args
+ (exact-integer-sqrt))
+ (pass-if-exception "two args" exception:wrong-num-args
+ (exact-integer-sqrt 123 456))
+
+ (test 0)
+ (test 1)
+ (test 9)
+ (test 10)
+ (test fixnum-max)
+ (test (1+ fixnum-max))
+ (test (* fixnum-max fixnum-max))
+ (test (+ 1 (* fixnum-max fixnum-max)))
+ (test (expt 10 100))
+ (test (+ 3 (expt 10 100)))
+
+ (test-wrong-type-arg -1)
+ (test-wrong-type-arg 1/9)
+ (test-wrong-type-arg fixnum-min)
+ (test-wrong-type-arg (1- fixnum-min))
+ (test-wrong-type-arg 1.0)
+ (test-wrong-type-arg 1.5)
+ (test-wrong-type-arg "foo")
+ (test-wrong-type-arg 'foo))
+
+
;;;
;;; sqrt
;;;
(with-test-prefix "sqrt"
- (pass-if "documented?"
- (documented? sqrt))
+ (pass-if (documented? sqrt))
(pass-if-exception "no args" exception:wrong-num-args
(sqrt))
(pass-if-exception "two args" exception:wrong-num-args
(sqrt 123 456))
- (pass-if (eqv? 0.0 (sqrt 0)))
+ (pass-if (eqv? 0 (sqrt 0)))
+ (pass-if (eqv? 1 (sqrt 1)))
+ (pass-if (eqv? 2 (sqrt 4)))
+ (pass-if (eqv? 3 (sqrt 9)))
+ (pass-if (eqv? 4 (sqrt 16)))
+ (pass-if (eqv? fixnum-max (sqrt (expt fixnum-max 2))))
+ (pass-if (eqv? (+ 1 fixnum-max) (sqrt (expt (+ 1 fixnum-max) 2))))
+ (pass-if (eqv? (expt 10 400) (sqrt (expt 10 800))))
+ (pass-if (eqv? (/ (expt 10 1000)
+ (expt 13 1000))
+ (sqrt (/ (expt 10 2000)
+ (expt 13 2000)))))
+
+ (with-test-prefix "exact sqrt"
+
+ (define (test root)
+ (pass-if (list root 'exact)
+ (eqv? root (sqrt (expt root 2))))
+ (pass-if (list root '*2)
+ (let ((r (sqrt (* 2 (expt root 2)))))
+ (and (inexact? r)
+ (eqv-loosely? (* (sqrt 2) root) r))))
+ (pass-if (list root '-1)
+ (let ((r (sqrt (- (expt root 2) 1))))
+ (and (inexact? r)
+ (eqv-loosely? root r))))
+ (pass-if (list root '+1)
+ (let ((r (sqrt (+ (expt root 2) 1))))
+ (and (inexact? r)
+ (eqv-loosely? root r))))
+ (pass-if (list root 'negative)
+ (eqv-loosely? (* +i root) (sqrt (- (expt root 2))))))
+
+ (test (exact-integer-sqrt (+ -1 (expt 2 (+ 2 dbl-mant-dig)))))
+ (test (exact-integer-sqrt (+ -1 (expt 2 (+ 1 dbl-mant-dig)))))
+ (test (exact-integer-sqrt (+ -1 (expt 2 (+ 0 dbl-mant-dig)))))
+ (test (exact-integer-sqrt (+ -1 (expt 2 (+ -1 dbl-mant-dig)))))
+ (test (exact-integer-sqrt (+ -1 (expt 2 (+ -2 dbl-mant-dig)))))
+
+ ;; largest finite inexact
+ (test (* (- (expt 2 dbl-mant-dig) 1)
+ (expt 2 (- dbl-max-exp dbl-mant-dig)))))
+
+ (pass-if-equal "smallest inexact"
+ (expt 2.0 (- dbl-min-exp dbl-mant-dig))
+ (sqrt (/ (+ -1 (expt 2 (* 2 (- dbl-mant-dig dbl-min-exp)))))))
+
+ (with-test-prefix "extreme ratios"
+ (define-syntax-rule (test want x)
+ (pass-if 'x
+ (let ((got (sqrt x)))
+ (and (inexact? got)
+ (test-eqv? 1.0 (/ want got))))))
+ (test 1.511139943175573e176 (/ (expt 3 2001) (expt 2 2001)))
+ (test 2.1370746022826034e176 (/ (expt 3 2001) (expt 2 2000)))
+ (test 8.724570529756128e175 (/ (expt 3 2000) (expt 2 2001)))
+ (test 6.6175207962444435e-177 (/ (expt 2 2001) (expt 3 2001)))
+ (test 1.1461882239239027e-176 (/ (expt 2 2001) (expt 3 2000)))
+ (test 4.679293829667447e-177 (/ (expt 2 2000) (expt 3 2001))))
+
+ (pass-if (eqv? (/ (expt 2 1000)
+ (expt 3 1000))
+ (sqrt (/ (expt 2 2000)
+ (expt 3 2000)))))
+
+ (pass-if (eqv? (/ (expt 3 1000)
+ (expt 2 1000))
+ (sqrt (/ (expt 3 2000)
+ (expt 2 2000)))))
+
+ (pass-if (eqv? +4i (sqrt -16)))
+ (pass-if (eqv-loosely? +1.0e150i (sqrt #e-1e300)))
+ (pass-if (eqv-loosely? +0.7071i (sqrt -1/2)))
+
(pass-if (eqv? 0.0 (sqrt 0.0)))
(pass-if (eqv? 1.0 (sqrt 1.0)))
(pass-if (eqv-loosely? 2.0 (sqrt 4.0)))
(eqv-loosely? +7.071-7.071i (sqrt -100.0i))))
-;;
-;; equal?
-;;
-
-
-(with-test-prefix "equal?"
- (pass-if
+;;;
+;;; Tests for number-theoretic division operators:
+;;;
+;;; euclidean/
+;;; euclidean-quotient
+;;; euclidean-remainder
+;;; floor/
+;;; floor-quotient
+;;; floor-remainder
+;;; ceiling/
+;;; ceiling-quotient
+;;; ceiling-remainder
+;;; truncate/
+;;; truncate-quotient
+;;; truncate-remainder
+;;; centered/
+;;; centered-quotient
+;;; centered-remainder
+;;; round/
+;;; round-quotient
+;;; round-remainder
+;;;
+
+(with-test-prefix "Number-theoretic division"
+
+ ;; Tests that (lo <1 x <2 hi),
+ ;; but allowing for imprecision
+ ;; if x is inexact.
+ (define (test-within-range? lo <1 x <2 hi)
+ (if (exact? x)
+ (and (<1 lo x) (<2 x hi))
+ (let ((lo (- lo test-epsilon))
+ (hi (+ hi test-epsilon)))
+ (<= lo x hi))))
+
+ (define (valid-euclidean-answer? x y q r)
+ (and (eq? (exact? q)
+ (exact? r)
+ (and (exact? x) (exact? y)))
+ (test-eqv? r (- x (* q y)))
+ (if (and (finite? x) (finite? y))
+ (and (integer? q)
+ (test-within-range? 0 <= r < (abs y)))
+ (test-eqv? q (/ x y)))))
+
+ (define (valid-floor-answer? x y q r)
+ (and (eq? (exact? q)
+ (exact? r)
+ (and (exact? x) (exact? y)))
+ (test-eqv? r (- x (* q y)))
+ (if (and (finite? x) (finite? y))
+ (and (integer? q)
+ (if (> y 0)
+ (test-within-range? 0 <= r < y)
+ (test-within-range? y < r <= 0)))
+ (test-eqv? q (/ x y)))))
+
+ (define (valid-ceiling-answer? x y q r)
+ (and (eq? (exact? q)
+ (exact? r)
+ (and (exact? x) (exact? y)))
+ (test-eqv? r (- x (* q y)))
+ (if (and (finite? x) (finite? y))
+ (and (integer? q)
+ (if (> y 0)
+ (test-within-range? (- y) < r <= 0)
+ (test-within-range? 0 <= r < (- y))))
+ (test-eqv? q (/ x y)))))
+
+ (define (valid-truncate-answer? x y q r)
+ (and (eq? (exact? q)
+ (exact? r)
+ (and (exact? x) (exact? y)))
+ (test-eqv? r (- x (* q y)))
+ (if (and (finite? x) (finite? y))
+ (and (integer? q)
+ (if (> x 0)
+ (test-within-range? 0 <= r < (abs y))
+ (test-within-range? (- (abs y)) < r <= 0)))
+ (test-eqv? q (/ x y)))))
+
+ (define (valid-centered-answer? x y q r)
+ (and (eq? (exact? q)
+ (exact? r)
+ (and (exact? x) (exact? y)))
+ (test-eqv? r (- x (* q y)))
+ (if (and (finite? x) (finite? y))
+ (and (integer? q)
+ (test-within-range?
+ (* -1/2 (abs y)) <= r < (* +1/2 (abs y))))
+ (test-eqv? q (/ x y)))))
+
+ (define (valid-round-answer? x y q r)
+ (and (eq? (exact? q)
+ (exact? r)
+ (and (exact? x) (exact? y)))
+ (test-eqv? r (- x (* q y)))
+ (if (and (finite? x) (finite? y))
+ (and (integer? q)
+ (let ((ay/2 (/ (abs y) 2)))
+ (if (even? q)
+ (test-within-range? (- ay/2) <= r <= ay/2)
+ (test-within-range? (- ay/2) < r < ay/2))))
+ (test-eqv? q (/ x y)))))
+
+ (define (for lsts f) (apply for-each f lsts))
+
+ (define big (expt 10 (1+ (inexact->exact (ceiling (log10 fixnum-max))))))
+
+ (define (run-division-tests quo+rem quo rem valid-answer?)
+ (define (test n d)
+ (run-test (list n d) #t
+ (lambda ()
+ (let-values (((q r) (quo+rem n d)))
+ (and (test-eqv? q (quo n d))
+ (test-eqv? r (rem n d))
+ (valid-answer? n d q r))))))
+ (define (test+/- n d)
+ (test n d )
+ (test n (- d))
+ (cond ((not (zero? n))
+ (test (- n) d )
+ (test (- n) (- d)))))
+
+ (define (test-for-exception n d exception)
+ (let ((name (list n d)))
+ (pass-if-exception name exception (quo+rem n d))
+ (pass-if-exception name exception (quo n d))
+ (pass-if-exception name exception (rem n d))))
+
+ (run-test "documented?" #t
+ (lambda ()
+ (and (documented? quo+rem)
+ (documented? quo)
+ (documented? rem))))
+
+ (with-test-prefix "inum / inum"
+ (with-test-prefix "fixnum-min / -1"
+ (test fixnum-min -1))
+ (for '((1 2 5 10)) ;; denominators
+ (lambda (d)
+ (for '((0 1 2 5 10)) ;; multiples
+ (lambda (m)
+ (for '((-2 -1 0 1 2 3 4 5 7 10
+ 12 15 16 19 20)) ;; offsets
+ (lambda (b)
+ (test+/- (+ b (* m d))
+ d))))))))
+
+ (with-test-prefix "inum / big"
+ (with-test-prefix "fixnum-min / -fixnum-min"
+ (test fixnum-min (- fixnum-min)))
+ (with-test-prefix "fixnum-max / (2*fixnum-max)"
+ (test+/- fixnum-max (* 2 fixnum-max)))
+ (for `((0 1 2 10 ,(1- fixnum-max) ,fixnum-max))
+ (lambda (n)
+ (test n (1+ fixnum-max))
+ (test (- n) (1+ fixnum-max))
+ (test n (1- fixnum-min))
+ (test (- n) (1- fixnum-min)))))
+
+ (with-test-prefix "big / inum"
+ (with-test-prefix "-fixnum-min / fixnum-min"
+ (test (- fixnum-min) fixnum-min))
+ (for '((1 4 5 10)) ;; denominators
+ (lambda (d)
+ (for `((1 2 5 ,@(if (even? d)
+ '(1/2 3/2 5/2)
+ '()))) ;; multiples
+ (lambda (m)
+ (for '((-2 -1 0 1 2)) ;; offsets
+ (lambda (b)
+ (test+/- (+ b (* m d big))
+ d))))))))
+
+ (with-test-prefix "big / big"
+ (for `((,big ,(1+ big))) ;; denominators
+ (lambda (d)
+ (for `((1 2 5 ,@(if (even? d)
+ '(1/2 3/2 5/2)
+ '()))) ;; multiples
+ (lambda (m)
+ (for '((-2 -1 0 1 2)) ;; offsets
+ (lambda (b)
+ (test+/- (+ b (* m d))
+ d))))))))
+
+ (with-test-prefix "inexact"
+ (for '((0.5 1.5 2.25 5.75)) ;; denominators
+ (lambda (d)
+ (for '((0 1 2 5 1/2 3/2 5/2)) ;; multiples
+ (lambda (m)
+ (for '((-2 -1 0 1 2)) ;; offsets
+ (lambda (b)
+ (test+/- (+ b (* m d))
+ d))))))))
+
+ (with-test-prefix "fractions"
+ (for '((1/10 16/3 10/7)) ;; denominators
+ (lambda (d)
+ (for '((0 1 2 5 1/2 3/2 5/2)) ;; multiples
+ (lambda (m)
+ (for '((-2/9 -1/11 0 1/3 2/3)) ;; offsets
+ (lambda (b)
+ (test+/- (+ b (* m d))
+ d))))))))
+
+ (with-test-prefix "mixed types"
+ (for `((10 ,big 12.0 10/7 +inf.0 -inf.0 +nan.0)) ;; denominators
+ (lambda (d)
+ (for `((25 ,(* 3/2 big) 130.0 15/7
+ 0 0.0 -0.0 +inf.0 -inf.0 +nan.0)) ;; numerators
+ (lambda (n)
+ (test+/- n d))))))
+
+ (with-test-prefix "divide by zero"
+ (for `((0 0.0 -0.0)) ;; denominators
+ (lambda (d)
+ (for `((15 ,(* 3/2 big) 18.0 33/7
+ 0 0.0 -0.0 +inf.0 -inf.0 +nan.0)) ;; numerators
+ (lambda (n)
+ (test-for-exception
+ n d exception:numerical-overflow)))))))
+
+ (with-test-prefix "euclidean/"
+ (run-division-tests euclidean/
+ euclidean-quotient
+ euclidean-remainder
+ valid-euclidean-answer?))
+
+ (with-test-prefix "floor/"
+ (run-division-tests floor/
+ floor-quotient
+ floor-remainder
+ valid-floor-answer?))
+
+ (with-test-prefix "ceiling/"
+ (run-division-tests ceiling/
+ ceiling-quotient
+ ceiling-remainder
+ valid-ceiling-answer?))
+
+ (with-test-prefix "truncate/"
+ (run-division-tests truncate/
+ truncate-quotient
+ truncate-remainder
+ valid-truncate-answer?))
+
+ (with-test-prefix "centered/"
+ (run-division-tests centered/
+ centered-quotient
+ centered-remainder
+ valid-centered-answer?))
+
+ (with-test-prefix "round/"
+ (run-division-tests round/
+ round-quotient
+ round-remainder
+ valid-round-answer?)))
- ;; lazy reduction bit for rationals should not affect equal?
- (equal? 1/2 ((lambda (x) (denominator x) x) 1/2))))
-
+;;;
+;;; ash
+;;; round-ash
+;;;
+
+(let ()
+ (define (test-ash-variant name ash-variant round-variant)
+ (with-test-prefix name
+ (define (test n count)
+ (pass-if (list n count)
+ (eqv? (ash-variant n count)
+ (round-variant (* n (expt 2 count))))))
+
+ (pass-if "documented?"
+ (documented? ash-variant))
+
+ (for-each (lambda (n)
+ (for-each (lambda (count) (test n count))
+ `(-1000
+ ,(- fixnum-bit)
+ ,(- (- fixnum-bit 1))
+ -3 -2 -1 0 1 2 3
+ ,(- fixnum-bit 1)
+ ,fixnum-bit
+ 1000)))
+ (list 0 1 3 23 -1 -3 -23
+ fixnum-max
+ (1+ fixnum-max)
+ (1- fixnum-max)
+ (* fixnum-max 4)
+ (quotient fixnum-max 4)
+ fixnum-min
+ (1+ fixnum-min)
+ (1- fixnum-min)
+ (* fixnum-min 4)
+ (quotient fixnum-min 4)))
+
+ (do ((count -2 (1- count))
+ (vals '(1 3 5 7 9 11)
+ (map (lambda (n) (* 2 n)) vals)))
+ ((> (car vals) (* 2 fixnum-max)) 'done)
+ (for-each (lambda (n)
+ (test n count)
+ (test (- n) count))
+ vals))
+
+ ;; Test rounding
+ (for-each (lambda (base)
+ (for-each (lambda (offset) (test (+ base offset) -3))
+ '(#b11001 #b11100 #b11101 #b10001 #b10100 #b10101)))
+ (list 0 64 -64 (* 64 fixnum-max) (* 64 fixnum-min)))))
+
+ (test-ash-variant 'ash ash floor)
+ (test-ash-variant 'round-ash round-ash round))
HCoop / bpt / guile.git / blobdiff