mirror of
https://git.savannah.gnu.org/git/guile.git
synced 2025-04-30 11:50:28 +02:00
fa102e73c3
* libguile/numbers.c (scm_numerator, scm_denominator): Handle signed zeroes and infinities in accordance with the corresponding R6RS flonum procedures. * module/rnrs/arithmetic/flonums.scm (flnumerator, fldenominator): Remove special handling of infinities. * test-suite/tests/numbers.test (numerator, denominator): Add tests. Convert existing tests to use 'pass-if-equal'. * test-suite/tests/r6rs-arithmetic-flonums.test (flnumerator): Fix broken test of (flnumerator -0.0).
5392 lines
158 KiB
Scheme
5392 lines
158 KiB
Scheme
;;;; numbers.test --- tests guile's numbers -*- scheme -*-
|
|
;;;; 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
|
|
;;;; License as published by the Free Software Foundation; either
|
|
;;;; version 3 of the License, or (at your option) any later version.
|
|
;;;;
|
|
;;;; This library is distributed in the hope that it will be useful,
|
|
;;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
;;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
|
;;;; Lesser General Public License for more details.
|
|
;;;;
|
|
;;;; You should have received a copy of the GNU Lesser General Public
|
|
;;;; License along with this library; if not, write to the Free Software
|
|
;;;; Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
(define-module (test-suite test-numbers)
|
|
#:use-module (test-suite lib)
|
|
#:use-module (ice-9 documentation)
|
|
#:use-module (srfi srfi-1) ; list library
|
|
#:use-module (srfi srfi-11)) ; let-values
|
|
|
|
;;;
|
|
;;; miscellaneous
|
|
;;;
|
|
|
|
(define exception:numerical-overflow
|
|
(cons 'numerical-overflow "^Numerical overflow"))
|
|
|
|
(define (documented? object)
|
|
(not (not (object-documentation object))))
|
|
|
|
(define fixnum-bit
|
|
(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)
|
|
|
|
;; Divine the number of bits in the mantissa of a flonum.
|
|
;; We look for when 2.0^i+1.0 gets rounded, ie. the difference between that
|
|
;; value and 2.0^k is not 1.0.
|
|
;; Of course this assumes flonums have a fixed precision mantissa, but
|
|
;; that's the case now and probably into the forseeable future.
|
|
;; On an IEEE system, which means pretty much everywhere, the value here is
|
|
;; the usual 53.
|
|
;;
|
|
(define dbl-mant-dig
|
|
(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)
|
|
(while (> n 0)
|
|
(set! x (* 2.0 x))
|
|
(set! n (1- n)))
|
|
(while (< n 0)
|
|
(set! x (* 0.5 x))
|
|
(set! n (1+ n)))
|
|
x)
|
|
|
|
;; `quotient' but rounded towards -infinity, like `modulo' or `ash' do
|
|
;; note only positive D supported (that's all that's currently required)
|
|
(define-public (quotient-floor n d)
|
|
(if (negative? n)
|
|
(quotient (- n d -1) d) ;; neg/pos
|
|
(quotient n d))) ;; pos/pos
|
|
|
|
;; return true of X is in the range LO to HI, inclusive
|
|
(define (within-range? lo hi x)
|
|
(and (>= x (min lo hi))
|
|
(<= x (max lo hi))))
|
|
|
|
;; return true if GOT is within +/- 0.01 of GOT
|
|
;; for a complex number both real and imaginary parts must be in that range
|
|
(define (eqv-loosely? want got)
|
|
(and (within-range? (- (real-part want) 0.01)
|
|
(+ (real-part want) 0.01)
|
|
(real-part got))
|
|
(within-range? (- (imag-part want) 0.01)
|
|
(+ (imag-part want) 0.01)
|
|
(imag-part got))))
|
|
|
|
;; return true if OBJ is negative infinity
|
|
(define (negative-infinity? obj)
|
|
(and (real? obj)
|
|
(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)
|
|
|
|
|
|
;;;
|
|
;;; 1+
|
|
;;;
|
|
|
|
(with-test-prefix/c&e "1+"
|
|
|
|
(pass-if "documented?"
|
|
(documented? 1+))
|
|
|
|
(pass-if "0" (eqv? 1 (1+ 0)))
|
|
(pass-if "-1" (eqv? 0 (1+ -1)))
|
|
(pass-if "100" (eqv? 101 (1+ 100)))
|
|
(pass-if "-100" (eqv? -99 (1+ -100)))
|
|
|
|
;; The maximum fixnum on a 32-bit architecture: 2^29 - 1.
|
|
(pass-if "1+ fixnum = bignum (32-bit)"
|
|
(eqv? 536870912 (1+ 536870911)))
|
|
|
|
;; The maximum fixnum on a 64-bit architecture: 2^61 - 1.
|
|
(pass-if "1+ fixnum = bignum (64-bit)"
|
|
(eqv? 2305843009213693952 (1+ 2305843009213693951))))
|
|
|
|
;;;
|
|
;;; 1-
|
|
;;;
|
|
|
|
(with-test-prefix/c&e "1-"
|
|
|
|
(pass-if "documented?"
|
|
(documented? 1-))
|
|
|
|
(pass-if "0" (eqv? -1 (1- 0)))
|
|
(pass-if "1" (eqv? 0 (1- 1)))
|
|
(pass-if "100" (eqv? 99 (1- 100)))
|
|
(pass-if "-100" (eqv? -101 (1- -100)))
|
|
|
|
;; The minimum fixnum on a 32-bit architecture: -2^29.
|
|
(pass-if "1- fixnum = bignum (32-bit)"
|
|
(eqv? -536870913 (1- -536870912)))
|
|
|
|
;; The minimum fixnum on a 64-bit architecture: -2^61.
|
|
(pass-if "1- fixnum = bignum (64-bit)"
|
|
(eqv? -2305843009213693953 (1- -2305843009213693952))))
|
|
|
|
;;;
|
|
;;; exact?
|
|
;;;
|
|
|
|
(with-test-prefix "exact?"
|
|
|
|
(pass-if "documented?"
|
|
(documented? exact?))
|
|
|
|
(with-test-prefix "integers"
|
|
|
|
(pass-if "0"
|
|
(exact? 0))
|
|
|
|
(pass-if "fixnum-max"
|
|
(exact? fixnum-max))
|
|
|
|
(pass-if "fixnum-max + 1"
|
|
(exact? (+ fixnum-max 1)))
|
|
|
|
(pass-if "fixnum-min"
|
|
(exact? fixnum-min))
|
|
|
|
(pass-if "fixnum-min - 1"
|
|
(exact? (- fixnum-min 1))))
|
|
|
|
(with-test-prefix "reals"
|
|
|
|
;; (FIXME: need better examples.)
|
|
|
|
(pass-if "sqrt (fixnum-max^2 - 1)"
|
|
(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)))))
|
|
|
|
(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? exp))
|
|
|
|
(pass-if-exception "no args" exception:wrong-num-args
|
|
(exp))
|
|
(pass-if-exception "two args" exception:wrong-num-args
|
|
(exp 123 456))
|
|
|
|
(pass-if (eqv? 0.0 (exp -inf.0)))
|
|
(pass-if (eqv-loosely? 1.0 (exp 0)))
|
|
(pass-if (eqv-loosely? 1.0 (exp 0.0)))
|
|
(pass-if (eqv-loosely? const-e (exp 1.0)))
|
|
(pass-if (eqv-loosely? const-e^2 (exp 2.0)))
|
|
(pass-if (eqv-loosely? const-1/e (exp -1)))
|
|
|
|
(pass-if "exp(pi*i) = -1"
|
|
(eqv-loosely? -1.0 (exp 0+3.14159i)))
|
|
(pass-if "exp(-pi*i) = -1"
|
|
(eqv-loosely? -1.0 (exp 0-3.14159i)))
|
|
(pass-if "exp(2*pi*i) = +1"
|
|
(eqv-loosely? 1.0 (exp 0+6.28318i)))
|
|
|
|
(pass-if "exp(2-pi*i) = -e^2"
|
|
(eqv-loosely? (- const-e^2) (exp 2.0-3.14159i))))
|
|
|
|
;;;
|
|
;;; odd?
|
|
;;;
|
|
|
|
(with-test-prefix "odd?"
|
|
(pass-if (documented? odd?))
|
|
(pass-if (odd? 1))
|
|
(pass-if (odd? -1))
|
|
(pass-if (not (odd? 0)))
|
|
(pass-if (not (odd? 2)))
|
|
(pass-if (not (odd? -2)))
|
|
(pass-if (odd? (+ (* 2 fixnum-max) 1)))
|
|
(pass-if (not (odd? (* 2 fixnum-max))))
|
|
(pass-if (odd? (- (* 2 fixnum-min) 1)))
|
|
(pass-if (not (odd? (* 2 fixnum-min)))))
|
|
|
|
;;;
|
|
;;; even?
|
|
;;;
|
|
|
|
(with-test-prefix "even?"
|
|
(pass-if (documented? even?))
|
|
(pass-if (even? 2))
|
|
(pass-if (even? -2))
|
|
(pass-if (even? 0))
|
|
(pass-if (not (even? 1)))
|
|
(pass-if (not (even? -1)))
|
|
(pass-if (not (even? (+ (* 2 fixnum-max) 1))))
|
|
(pass-if (even? (* 2 fixnum-max)))
|
|
(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
|
|
;;;
|
|
|
|
(with-test-prefix "inf?"
|
|
(pass-if (documented? inf?))
|
|
(pass-if (inf? (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))))
|
|
(pass-if (not (inf? (- fixnum-min 1)))))
|
|
|
|
;;;
|
|
;;; nan? and nan
|
|
;;;
|
|
|
|
(with-test-prefix "nan?"
|
|
(pass-if (documented? nan?))
|
|
(pass-if (nan? (nan)))
|
|
;; FIXME: other ways we should be able to generate NaN?
|
|
(pass-if (not (nan? 0)))
|
|
(pass-if (not (nan? 42.0)))
|
|
(pass-if (not (nan? (+ fixnum-max 1))))
|
|
(pass-if (not (nan? (- fixnum-min 1)))))
|
|
|
|
;;;
|
|
;;; abs
|
|
;;;
|
|
|
|
(with-test-prefix "abs"
|
|
(pass-if (documented? abs))
|
|
(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"
|
|
(pass-if (documented? quotient))
|
|
|
|
(with-test-prefix "0 / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (quotient 0 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (quotient 0 -1)))
|
|
|
|
(pass-if "n = 2"
|
|
(eqv? 0 (quotient 0 2)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 0 (quotient 0 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (quotient 0 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (quotient 0 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 0 (quotient 0 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "1 / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 1 (quotient 1 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? -1 (quotient 1 -1)))
|
|
|
|
(pass-if "n = 2"
|
|
(eqv? 0 (quotient 1 2)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 0 (quotient 1 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (quotient 1 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (quotient 1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 0 (quotient 1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "-1 / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? -1 (quotient -1 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 1 (quotient -1 -1)))
|
|
|
|
(pass-if "n = 2"
|
|
(eqv? 0 (quotient -1 2)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 0 (quotient -1 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (quotient -1 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (quotient -1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 0 (quotient -1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "fixnum-max / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? fixnum-max (quotient fixnum-max 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? (- fixnum-max) (quotient fixnum-max -1)))
|
|
|
|
(pass-if "n = 2"
|
|
(eqv? fixnum-max (+ (* (quotient fixnum-max 2) 2) 1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (quotient fixnum-max fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (quotient fixnum-max (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (quotient fixnum-max fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 0 (quotient fixnum-max (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(fixnum-max + 1) / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? (+ fixnum-max 1) (quotient (+ fixnum-max 1) 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? (- (+ fixnum-max 1)) (quotient (+ fixnum-max 1) -1)))
|
|
|
|
(pass-if "n = 2"
|
|
(eqv? (+ fixnum-max 1) (* (quotient (+ fixnum-max 1) 2) 2)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (quotient (+ fixnum-max 1) fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 1 (quotient (+ fixnum-max 1) (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? -1 (quotient (+ fixnum-max 1) fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 0 (quotient (+ fixnum-max 1) (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "fixnum-min / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? fixnum-min (quotient fixnum-min 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? (- fixnum-min) (quotient fixnum-min -1)))
|
|
|
|
(pass-if "n = 2"
|
|
(eqv? fixnum-min (* (quotient fixnum-min 2) 2)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? -1 (quotient fixnum-min fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? -1 (quotient fixnum-min (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 1 (quotient fixnum-min fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 0 (quotient fixnum-min (- fixnum-min 1))))
|
|
|
|
(pass-if "n = - fixnum-min - 1"
|
|
(eqv? -1 (quotient fixnum-min (1- (- fixnum-min)))))
|
|
|
|
;; special case, normally inum/big is zero
|
|
(pass-if "n = - fixnum-min"
|
|
(eqv? -1 (quotient fixnum-min (- fixnum-min))))
|
|
|
|
(pass-if "n = - fixnum-min + 1"
|
|
(eqv? 0 (quotient fixnum-min (1+ (- fixnum-min))))))
|
|
|
|
(with-test-prefix "(fixnum-min - 1) / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? (- fixnum-min 1) (quotient (- fixnum-min 1) 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? (- (- fixnum-min 1)) (quotient (- fixnum-min 1) -1)))
|
|
|
|
(pass-if "n = 2"
|
|
(eqv? fixnum-min (* (quotient (- fixnum-min 1) 2) 2)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? -1 (quotient (- fixnum-min 1) fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? -1 (quotient (- fixnum-min 1) (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 1 (quotient (- fixnum-min 1) fixnum-min)))
|
|
|
|
(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"
|
|
(eqv? 5 (quotient 35 7)))
|
|
|
|
;; Negative dividend, positive divisor
|
|
|
|
(pass-if "-35 / 7"
|
|
(eqv? -5 (quotient -35 7)))
|
|
|
|
;; Positive dividend, negative divisor
|
|
|
|
(pass-if "35 / -7"
|
|
(eqv? -5 (quotient 35 -7)))
|
|
|
|
;; Negative dividend and divisor
|
|
|
|
(pass-if "-35 / -7"
|
|
(eqv? 5 (quotient -35 -7)))
|
|
|
|
;; Are numerical overflows detected correctly?
|
|
|
|
(with-test-prefix "division by zero"
|
|
|
|
(pass-if-exception "(quotient 1 0)"
|
|
exception:numerical-overflow
|
|
(quotient 1 0))
|
|
|
|
(pass-if-exception "(quotient bignum 0)"
|
|
exception:numerical-overflow
|
|
(quotient (+ fixnum-max 1) 0)))
|
|
|
|
;; Are wrong type arguments detected correctly?
|
|
|
|
)
|
|
|
|
;;;
|
|
;;; remainder
|
|
;;;
|
|
|
|
(with-test-prefix "remainder"
|
|
(pass-if (documented? remainder))
|
|
|
|
(with-test-prefix "0 / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (remainder 0 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (remainder 0 -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 0 (remainder 0 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (remainder 0 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (remainder 0 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 0 (remainder 0 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "1 / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (remainder 1 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (remainder 1 -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (remainder 1 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 1 (remainder 1 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 1 (remainder 1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 1 (remainder 1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "-1 / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (remainder -1 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (remainder -1 -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? -1 (remainder -1 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? -1 (remainder -1 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? -1 (remainder -1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? -1 (remainder -1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "fixnum-max / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (remainder fixnum-max 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (remainder fixnum-max -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 0 (remainder fixnum-max fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? fixnum-max (remainder fixnum-max (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? fixnum-max (remainder fixnum-max fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? fixnum-max (remainder fixnum-max (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(fixnum-max + 1) / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (remainder (+ fixnum-max 1) 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (remainder (+ fixnum-max 1) -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (remainder (+ fixnum-max 1) fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (remainder (+ fixnum-max 1) (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (remainder (+ fixnum-max 1) fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? (+ fixnum-max 1) (remainder (+ fixnum-max 1) (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "fixnum-min / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (remainder fixnum-min 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (remainder fixnum-min -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? -1 (remainder fixnum-min fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (remainder fixnum-min (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (remainder fixnum-min fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? fixnum-min (remainder fixnum-min (- fixnum-min 1))))
|
|
|
|
(pass-if "n = - fixnum-min - 1"
|
|
(eqv? -1 (remainder fixnum-min (1- (- fixnum-min)))))
|
|
|
|
;; special case, normally inum%big is the inum
|
|
(pass-if "n = - fixnum-min"
|
|
(eqv? 0 (remainder fixnum-min (- fixnum-min))))
|
|
|
|
(pass-if "n = - fixnum-min + 1"
|
|
(eqv? fixnum-min (remainder fixnum-min (1+ (- fixnum-min))))))
|
|
|
|
(with-test-prefix "(fixnum-min - 1) / n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (remainder (- fixnum-min 1) 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (remainder (- fixnum-min 1) -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? -2 (remainder (- fixnum-min 1) fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? -1 (remainder (- fixnum-min 1) (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? -1 (remainder (- fixnum-min 1) fixnum-min)))
|
|
|
|
(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"
|
|
(eqv? 0 (remainder 35 7)))
|
|
|
|
;; Negative dividend, positive divisor
|
|
|
|
(pass-if "-35 / 7"
|
|
(eqv? 0 (remainder -35 7)))
|
|
|
|
;; Positive dividend, negative divisor
|
|
|
|
(pass-if "35 / -7"
|
|
(eqv? 0 (remainder 35 -7)))
|
|
|
|
;; Negative dividend and divisor
|
|
|
|
(pass-if "-35 / -7"
|
|
(eqv? 0 (remainder -35 -7)))
|
|
|
|
;; Are numerical overflows detected correctly?
|
|
|
|
(with-test-prefix "division by zero"
|
|
|
|
(pass-if-exception "(remainder 1 0)"
|
|
exception:numerical-overflow
|
|
(remainder 1 0))
|
|
|
|
(pass-if-exception "(remainder bignum 0)"
|
|
exception:numerical-overflow
|
|
(remainder (+ fixnum-max 1) 0)))
|
|
|
|
;; Are wrong type arguments detected correctly?
|
|
|
|
)
|
|
|
|
;;;
|
|
;;; modulo
|
|
;;;
|
|
|
|
(with-test-prefix "modulo"
|
|
(pass-if (documented? modulo))
|
|
|
|
(with-test-prefix "0 % n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (modulo 0 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (modulo 0 -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 0 (modulo 0 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (modulo 0 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (modulo 0 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 0 (modulo 0 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "1 % n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (modulo 1 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (modulo 1 -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (modulo 1 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 1 (modulo 1 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? (+ fixnum-min 1) (modulo 1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? fixnum-min (modulo 1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "-1 % n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (modulo -1 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (modulo -1 -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? (- fixnum-max 1) (modulo -1 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? fixnum-max (modulo -1 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? -1 (modulo -1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? -1 (modulo -1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "fixnum-max % n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (modulo fixnum-max 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (modulo fixnum-max -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 0 (modulo fixnum-max fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? fixnum-max (modulo fixnum-max (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? -1 (modulo fixnum-max fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? -2 (modulo fixnum-max (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(fixnum-max + 1) % n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (modulo (+ fixnum-max 1) 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (modulo (+ fixnum-max 1) -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (modulo (+ fixnum-max 1) fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (modulo (+ fixnum-max 1) (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (modulo (+ fixnum-max 1) fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? -1 (modulo (+ fixnum-max 1) (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "fixnum-min % n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (modulo fixnum-min 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (modulo fixnum-min -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? (- fixnum-max 1) (modulo fixnum-min fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 0 (modulo fixnum-min (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 0 (modulo fixnum-min fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? fixnum-min (modulo fixnum-min (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(fixnum-min - 1) % n"
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 0 (modulo (- fixnum-min 1) 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 0 (modulo (- fixnum-min 1) -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? (- fixnum-max 2) (modulo (- fixnum-min 1) fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? fixnum-max (modulo (- fixnum-min 1) (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? -1 (modulo (- fixnum-min 1) fixnum-min)))
|
|
|
|
(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"
|
|
(eqv? 1 (modulo 13 4)))
|
|
|
|
(pass-if "2177452800 % 86400"
|
|
(eqv? 0 (modulo 2177452800 86400)))
|
|
|
|
;; Negative dividend, positive divisor
|
|
|
|
(pass-if "-13 % 4"
|
|
(eqv? 3 (modulo -13 4)))
|
|
|
|
(pass-if "-2177452800 % 86400"
|
|
(eqv? 0 (modulo -2177452800 86400)))
|
|
|
|
;; Positive dividend, negative divisor
|
|
|
|
(pass-if "13 % -4"
|
|
(eqv? -3 (modulo 13 -4)))
|
|
|
|
(pass-if "2177452800 % -86400"
|
|
(eqv? 0 (modulo 2177452800 -86400)))
|
|
|
|
;; Negative dividend and divisor
|
|
|
|
(pass-if "-13 % -4"
|
|
(eqv? -1 (modulo -13 -4)))
|
|
|
|
(pass-if "-2177452800 % -86400"
|
|
(eqv? 0 (modulo -2177452800 -86400)))
|
|
|
|
;; Are numerical overflows detected correctly?
|
|
|
|
(with-test-prefix "division by zero"
|
|
|
|
(pass-if-exception "(modulo 1 0)"
|
|
exception:numerical-overflow
|
|
(modulo 1 0))
|
|
|
|
(pass-if-exception "(modulo bignum 0)"
|
|
exception:numerical-overflow
|
|
(modulo (+ fixnum-max 1) 0)))
|
|
|
|
;; Are wrong type arguments detected correctly?
|
|
|
|
)
|
|
|
|
;;;
|
|
;;; modulo-expt
|
|
;;;
|
|
|
|
(with-test-prefix "modulo-expt"
|
|
(pass-if (= 1 (modulo-expt 17 23 47)))
|
|
|
|
(pass-if (= 1 (modulo-expt 17 -23 47)))
|
|
|
|
(pass-if (= 17 (modulo-expt 17 -22 47)))
|
|
|
|
(pass-if (= 36 (modulo-expt 17 22 47)))
|
|
|
|
(pass-if (= 183658794479969134816674175082294846241553725240 (modulo-expt 111122223333444455556666 111122223333444455556666 1153478690012629968439432872520758982731022934717)))
|
|
|
|
(pass-if-exception
|
|
"Proper exception with 0 modulus"
|
|
exception:numerical-overflow
|
|
(modulo-expt 17 23 0))
|
|
|
|
(pass-if-exception
|
|
"Proper exception when result not invertible"
|
|
exception:numerical-overflow
|
|
(modulo-expt 10 -1 48))
|
|
|
|
(pass-if-exception
|
|
"Proper exception with wrong type argument"
|
|
exception:wrong-type-arg
|
|
(modulo-expt "Sam" 23 10))
|
|
|
|
(pass-if-exception
|
|
"Proper exception with wrong type argument"
|
|
exception:wrong-type-arg
|
|
(modulo-expt 17 9.9 10))
|
|
|
|
(pass-if-exception
|
|
"Proper exception with wrong type argument"
|
|
exception:wrong-type-arg
|
|
(modulo-expt 17 23 'Ethel)))
|
|
|
|
;;;
|
|
;;; numerator
|
|
;;;
|
|
|
|
(with-test-prefix "numerator"
|
|
(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-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
|
|
;;;
|
|
|
|
(with-test-prefix "gcd"
|
|
|
|
(pass-if "documented?"
|
|
(documented? gcd))
|
|
|
|
(with-test-prefix "(n)"
|
|
|
|
(pass-if "n = -2"
|
|
(eqv? 2 (gcd -2))))
|
|
|
|
(with-test-prefix "(0 n)"
|
|
|
|
(pass-if "n = 0"
|
|
(eqv? 0 (gcd 0 0)))
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 1 (gcd 0 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 1 (gcd 0 -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? fixnum-max (gcd 0 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? (+ fixnum-max 1) (gcd 0 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? (- fixnum-min) (gcd 0 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? (- (- fixnum-min 1)) (gcd 0 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(n 0)"
|
|
|
|
(pass-if "n = 2^128 * fixnum-max"
|
|
(eqv? (ash fixnum-max 128) (gcd (ash fixnum-max 128) 0))))
|
|
|
|
(with-test-prefix "(1 n)"
|
|
|
|
(pass-if "n = 0"
|
|
(eqv? 1 (gcd 1 0)))
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 1 (gcd 1 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 1 (gcd 1 -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (gcd 1 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 1 (gcd 1 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 1 (gcd 1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 1 (gcd 1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(-1 n)"
|
|
|
|
(pass-if "n = 0"
|
|
(eqv? 1 (gcd -1 0)))
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 1 (gcd -1 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 1 (gcd -1 -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (gcd -1 fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 1 (gcd -1 (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 1 (gcd -1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 1 (gcd -1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(fixnum-max n)"
|
|
|
|
(pass-if "n = 0"
|
|
(eqv? fixnum-max (gcd fixnum-max 0)))
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 1 (gcd fixnum-max 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 1 (gcd fixnum-max -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? fixnum-max (gcd fixnum-max fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 1 (gcd fixnum-max (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 1 (gcd fixnum-max fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 1 (gcd fixnum-max (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "((+ fixnum-max 1) n)"
|
|
|
|
(pass-if "n = 0"
|
|
(eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) 0)))
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 1 (gcd (+ fixnum-max 1) 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 1 (gcd (+ fixnum-max 1) -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (gcd (+ fixnum-max 1) fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 1 (gcd (+ fixnum-max 1) (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(fixnum-min n)"
|
|
|
|
(pass-if "n = 0"
|
|
(eqv? (- fixnum-min) (gcd fixnum-min 0)))
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 1 (gcd fixnum-min 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 1 (gcd fixnum-min -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (gcd fixnum-min fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? (+ fixnum-max 1) (gcd fixnum-min (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? (- fixnum-min) (gcd fixnum-min fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(eqv? 1 (gcd fixnum-min (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "((- fixnum-min 1) n)"
|
|
|
|
(pass-if "n = 0"
|
|
(eqv? (- (- fixnum-min 1)) (gcd (- fixnum-min 1) 0)))
|
|
|
|
(pass-if "n = 1"
|
|
(eqv? 1 (gcd (- fixnum-min 1) 1)))
|
|
|
|
(pass-if "n = -1"
|
|
(eqv? 1 (gcd (- fixnum-min 1) -1)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(eqv? 1 (gcd (- fixnum-min 1) fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(eqv? 1 (gcd (- fixnum-min 1) (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(eqv? 1 (gcd (- fixnum-min 1) fixnum-min)))
|
|
|
|
(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?
|
|
|
|
)
|
|
|
|
;;;
|
|
;;; lcm
|
|
;;;
|
|
|
|
(with-test-prefix "lcm"
|
|
;; FIXME: more tests?
|
|
;; (some of these are already in r4rs.test)
|
|
(pass-if (documented? lcm))
|
|
(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
|
|
;;;
|
|
|
|
(with-test-prefix "number->string"
|
|
(let ((num->str->num
|
|
(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)))
|
|
|
|
(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 (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 10) "10"))
|
|
(pass-if (string=? (number->string 10 11) "a"))
|
|
(pass-if (string=? (number->string 36 36) "10"))
|
|
(pass-if (= (num->str->num 36 36) 36))
|
|
(pass-if (= (string->number "z" 36) 35))
|
|
(pass-if (= (string->number "Z" 36) 35))
|
|
(pass-if (not (string->number "Z" 35)))
|
|
(pass-if (string=? (number->string 35 36) "z"))
|
|
(pass-if (= (num->str->num 35 36) 35))
|
|
|
|
(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
|
|
;;;
|
|
|
|
(with-test-prefix "string->number"
|
|
|
|
(pass-if "documented?"
|
|
(documented? string->number))
|
|
|
|
(pass-if "non number strings"
|
|
(for-each (lambda (x) (if (string->number x) (throw 'fail)))
|
|
'("" "q" "1q" "6+7iq" "8+9q" "10+11" "13+" "18@19q" "20@q" "23@"
|
|
"+25iq" "26i" "-q" "-iq" "i" "5#.0" "8/" "10#11" ".#" "."
|
|
"#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" "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"
|
|
(for-each (lambda (couple)
|
|
(apply
|
|
(lambda (x y)
|
|
(let ((xx (string->number x)))
|
|
(if (or (eq? xx #f) (not (eqv? xx y)))
|
|
(begin
|
|
(pk x y)
|
|
(throw 'fail)))))
|
|
couple))
|
|
`(;; Radix:
|
|
("#b0" 0) ("#B0" 0) ("#b1" 1) ("#B1" 1) ("#o0" 0) ("#O0" 0)
|
|
("#o1" 1) ("#O1" 1) ("#o2" 2) ("#O2" 2) ("#o3" 3) ("#O3" 3)
|
|
("#o4" 4) ("#O4" 4) ("#o5" 5) ("#O5" 5) ("#o6" 6) ("#O6" 6)
|
|
("#o7" 7) ("#O7" 7) ("#d0" 0) ("#D0" 0) ("#d1" 1) ("#D1" 1)
|
|
("#d2" 2) ("#D2" 2) ("#d3" 3) ("#D3" 3) ("#d4" 4) ("#D4" 4)
|
|
("#d5" 5) ("#D5" 5) ("#d6" 6) ("#D6" 6) ("#d7" 7) ("#D7" 7)
|
|
("#d8" 8) ("#D8" 8) ("#d9" 9) ("#D9" 9)
|
|
("#xa" 10) ("#Xa" 10) ("#xb" 11) ("#Xb" 11)
|
|
("#xc" 12) ("#Xc" 12) ("#xd" 13) ("#Xd" 13)
|
|
("#xe" 14) ("#Xe" 14) ("#xf" 15) ("#Xf" 15)
|
|
("#b1010" 10)
|
|
("#o12345670" 2739128)
|
|
("#d1234567890" 1234567890)
|
|
("#x1234567890abcdef" 1311768467294899695)
|
|
;; Exactness:
|
|
("#e1" 1) ("#e1.2" 12/10)
|
|
("#i1.1" 1.1) ("#i1" 1.0)
|
|
;; Integers:
|
|
("1" ,(1+ 0)) ("23" ,(+ 9 9 5)) ("-1" ,(- 0 1))
|
|
("-45" ,(- 0 45)) ("2#" 20.0) ("2##" 200.0) ("12##" 1200.0)
|
|
("#b#i100" 4.0)
|
|
;; Fractions:
|
|
("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)
|
|
("1f2" 100.0) ("1F2" 100.0) ("1d2" 100.0) ("1D2" 100.0)
|
|
("1l2" 100.0) ("1L2" 100.0) ("1e+2" 100.0) ("1e-2" 0.01)
|
|
;; * . <digit 10>+ #* <suffix>
|
|
(".1" .1) (".0123456789" 123456789e-10) (".16#" 0.16)
|
|
(".0123456789e10" 123456789.0) (".16#e3" 160.0) ("#d.3" 0.3)
|
|
;; * <digit 10>+ . <digit 10>* #* <suffix>
|
|
("3." ,(exact->inexact 3)) ("3.e0" ,(exact->inexact 3))
|
|
("3.1" ,(exact->inexact 31/10)) ("3.1e0" 3.1) ("3.1#" 3.1)
|
|
("3.1#e0" 3.1)
|
|
;; * <digit 10>+ #+ . #* <suffix>
|
|
("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
|
|
))
|
|
#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-exception "exponent too big"
|
|
exception:out-of-range
|
|
(string->number "12.13e141414"))
|
|
|
|
;; in guile 1.6.7 and earlier, bad polar forms (where the conversion of
|
|
;; the angle gave #f) caused a segv
|
|
(pass-if "1@a"
|
|
(eq? #f (string->number "1@a"))))
|
|
|
|
;;;
|
|
;;; number?
|
|
;;;
|
|
|
|
(with-test-prefix "number?"
|
|
(pass-if (documented? number?))
|
|
(pass-if (number? 0))
|
|
(pass-if (number? 7))
|
|
(pass-if (number? -7))
|
|
(pass-if (number? 1.3))
|
|
(pass-if (number? (+ 1 fixnum-max)))
|
|
(pass-if (number? (- 1 fixnum-min)))
|
|
(pass-if (number? 3+4i))
|
|
(pass-if (not (number? #\a)))
|
|
(pass-if (not (number? "a")))
|
|
(pass-if (not (number? (make-vector 0))))
|
|
(pass-if (not (number? (cons 1 2))))
|
|
(pass-if (not (number? #t)))
|
|
(pass-if (not (number? (lambda () #t))))
|
|
(pass-if (not (number? (current-input-port)))))
|
|
|
|
;;;
|
|
;;; complex?
|
|
;;;
|
|
|
|
(with-test-prefix "complex?"
|
|
(pass-if (documented? complex?))
|
|
(pass-if (complex? 0))
|
|
(pass-if (complex? 7))
|
|
(pass-if (complex? -7))
|
|
(pass-if (complex? (+ 1 fixnum-max)))
|
|
(pass-if (complex? (- 1 fixnum-min)))
|
|
(pass-if (complex? 1.3))
|
|
(pass-if (complex? 3+4i))
|
|
(pass-if (not (complex? #\a)))
|
|
(pass-if (not (complex? "a")))
|
|
(pass-if (not (complex? (make-vector 0))))
|
|
(pass-if (not (complex? (cons 1 2))))
|
|
(pass-if (not (complex? #t)))
|
|
(pass-if (not (complex? (lambda () #t))))
|
|
(pass-if (not (complex? (current-input-port)))))
|
|
|
|
;;;
|
|
;;; real?
|
|
;;;
|
|
|
|
(with-test-prefix "real?"
|
|
(pass-if (documented? real?))
|
|
(pass-if (real? 0))
|
|
(pass-if (real? 7))
|
|
(pass-if (real? -7))
|
|
(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? (make-vector 0))))
|
|
(pass-if (not (real? (cons 1 2))))
|
|
(pass-if (not (real? #t)))
|
|
(pass-if (not (real? (lambda () #t))))
|
|
(pass-if (not (real? (current-input-port)))))
|
|
|
|
;;;
|
|
;;; rational?
|
|
;;;
|
|
|
|
(with-test-prefix "rational?"
|
|
(pass-if (documented? rational?))
|
|
(pass-if (rational? 0))
|
|
(pass-if (rational? 7))
|
|
(pass-if (rational? -7))
|
|
(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 (not (rational? (make-vector 0))))
|
|
(pass-if (not (rational? (cons 1 2))))
|
|
(pass-if (not (rational? #t)))
|
|
(pass-if (not (rational? (lambda () #t))))
|
|
(pass-if (not (rational? (current-input-port)))))
|
|
|
|
;;;
|
|
;;; integer?
|
|
;;;
|
|
|
|
(with-test-prefix "integer?"
|
|
(pass-if (documented? integer?))
|
|
(pass-if (integer? 0))
|
|
(pass-if (integer? 7))
|
|
(pass-if (integer? -7))
|
|
(pass-if (integer? (+ 1 fixnum-max)))
|
|
(pass-if (integer? (- 1 fixnum-min)))
|
|
(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 (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? (make-vector 0))))
|
|
(pass-if (not (integer? (cons 1 2))))
|
|
(pass-if (not (integer? #t)))
|
|
(pass-if (not (integer? (lambda () #t))))
|
|
(pass-if (not (integer? (current-input-port)))))
|
|
|
|
;;;
|
|
;;; inexact?
|
|
;;;
|
|
|
|
(with-test-prefix "inexact?"
|
|
(pass-if (documented? inexact?))
|
|
(pass-if (not (inexact? 0)))
|
|
(pass-if (not (inexact? 7)))
|
|
(pass-if (not (inexact? -7)))
|
|
(pass-if (not (inexact? (+ 1 fixnum-max))))
|
|
(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)))
|
|
(pass-if-exception "string"
|
|
exception:wrong-type-arg
|
|
(not (inexact? "a")))
|
|
(pass-if-exception "vector"
|
|
exception:wrong-type-arg
|
|
(not (inexact? (make-vector 0))))
|
|
(pass-if-exception "cons"
|
|
exception:wrong-type-arg
|
|
(not (inexact? (cons 1 2))))
|
|
(pass-if-exception "bool"
|
|
exception:wrong-type-arg
|
|
(not (inexact? #t)))
|
|
(pass-if-exception "procedure"
|
|
exception:wrong-type-arg
|
|
(not (inexact? (lambda () #t))))
|
|
(pass-if-exception "port"
|
|
exception:wrong-type-arg
|
|
(not (inexact? (current-input-port)))))
|
|
|
|
;;;
|
|
;;; equal?
|
|
;;;
|
|
|
|
(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? fixnum-min (- fixnum-min 1))))
|
|
(pass-if (not (equal? (- fixnum-min 1) fixnum-min)))
|
|
(pass-if (not (equal? (- fixnum-min 1) (- fixnum-min 2))))
|
|
(pass-if (not (equal? (+ fixnum-max 1) (- fixnum-min 1))))
|
|
|
|
(pass-if (not (equal? (ash 1 256) +inf.0)))
|
|
(pass-if (not (equal? +inf.0 (ash 1 256))))
|
|
(pass-if (not (equal? (ash 1 256) -inf.0)))
|
|
(pass-if (not (equal? -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 (equal? (ash 1 1024) +inf.0)))
|
|
(pass-if (not (equal? +inf.0 (ash 1 1024))))
|
|
(pass-if (not (equal? (- (ash 1 1024)) -inf.0)))
|
|
(pass-if (not (equal? -inf.0 (- (ash 1 1024)))))
|
|
|
|
(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? +nan.0 1)))
|
|
(pass-if (not (equal? -1 +nan.0)))
|
|
(pass-if (not (equal? +nan.0 -1)))
|
|
|
|
(pass-if (not (equal? (ash 1 256) +nan.0)))
|
|
(pass-if (not (equal? +nan.0 (ash 1 256))))
|
|
(pass-if (not (equal? (- (ash 1 256)) +nan.0)))
|
|
(pass-if (not (equal? +nan.0 (- (ash 1 256)))))
|
|
|
|
(pass-if (not (equal? (ash 1 8192) +nan.0)))
|
|
(pass-if (not (equal? +nan.0 (ash 1 8192))))
|
|
(pass-if (not (equal? (- (ash 1 8192)) +nan.0)))
|
|
(pass-if (not (equal? +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 (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 (= 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 (= fixnum-max (+ 1 fixnum-max))))
|
|
(pass-if (not (= (+ 1 fixnum-max) fixnum-max)))
|
|
(pass-if (not (= (+ 1 fixnum-max) (+ 2 fixnum-max))))
|
|
(pass-if (not (= fixnum-min (- fixnum-min 1))))
|
|
(pass-if (not (= (- fixnum-min 1) fixnum-min)))
|
|
(pass-if (not (= (- fixnum-min 1) (- fixnum-min 2))))
|
|
(pass-if (not (= (+ fixnum-max 1) (- fixnum-min 1))))
|
|
|
|
(pass-if (not (= (ash 1 256) +inf.0)))
|
|
(pass-if (not (= +inf.0 (ash 1 256))))
|
|
(pass-if (not (= (ash 1 256) -inf.0)))
|
|
(pass-if (not (= -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 (= (ash 1 1024) +inf.0)))
|
|
(pass-if (not (= +inf.0 (ash 1 1024))))
|
|
(pass-if (not (= (- (ash 1 1024)) -inf.0)))
|
|
(pass-if (not (= -inf.0 (- (ash 1 1024)))))
|
|
|
|
(pass-if (not (= +nan.0 +nan.0)))
|
|
(pass-if (not (= 0 +nan.0)))
|
|
(pass-if (not (= +nan.0 0)))
|
|
(pass-if (not (= 1 +nan.0)))
|
|
(pass-if (not (= +nan.0 1)))
|
|
(pass-if (not (= -1 +nan.0)))
|
|
(pass-if (not (= +nan.0 -1)))
|
|
|
|
(pass-if (not (= (ash 1 256) +nan.0)))
|
|
(pass-if (not (= +nan.0 (ash 1 256))))
|
|
(pass-if (not (= (- (ash 1 256)) +nan.0)))
|
|
(pass-if (not (= +nan.0 (- (ash 1 256)))))
|
|
|
|
(pass-if (not (= (ash 1 8192) +nan.0)))
|
|
(pass-if (not (= +nan.0 (ash 1 8192))))
|
|
(pass-if (not (= (- (ash 1 8192)) +nan.0)))
|
|
(pass-if (not (= +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 (= (ash 3 1023) +nan.0)))
|
|
(pass-if (not (= +nan.0 (ash 3 1023))))
|
|
|
|
(pass-if (= 1/2 0.5))
|
|
(pass-if (not (= 1/3 0.333333333333333333333333333333333)))
|
|
(pass-if (not (= 2/3 0.5)))
|
|
(pass-if (not (= 0.5 (+ 1/2 (/ 1 (ash 1 1000))))))
|
|
|
|
(pass-if (= 1/2 0.5+0i))
|
|
(pass-if (not (= 0.333333333333333333333333333333333 1/3)))
|
|
(pass-if (not (= 2/3 0.5+0i)))
|
|
(pass-if (not (= 1/2 0+0.5i)))
|
|
|
|
(pass-if (= 0.5 1/2))
|
|
(pass-if (not (= 0.5 2/3)))
|
|
(pass-if (not (= (+ 1/2 (/ 1 (ash 1 1000))) 0.5)))
|
|
|
|
(pass-if (= 0.5+0i 1/2))
|
|
(pass-if (not (= 0.5+0i 2/3)))
|
|
(pass-if (not (= 0+0.5i 1/2)))
|
|
|
|
;; prior to guile 1.8, inum/flonum 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 (= (ash-flo 1.0 58) (ash 1 58)))
|
|
(pass-if (not (= (ash-flo 1.0 58) (1+ (ash 1 58)))))
|
|
(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))))
|
|
|
|
;; 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))))
|
|
|
|
;;;
|
|
;;; <
|
|
;;;
|
|
|
|
(with-test-prefix "<"
|
|
|
|
(pass-if "documented?"
|
|
(documented? <))
|
|
|
|
(with-test-prefix "(< 0 n)"
|
|
|
|
(pass-if "n = 0"
|
|
(not (< 0 0)))
|
|
|
|
(pass-if "n = 0.0"
|
|
(not (< 0 0.0)))
|
|
|
|
(pass-if "n = 1"
|
|
(< 0 1))
|
|
|
|
(pass-if "n = 1.0"
|
|
(< 0 1.0))
|
|
|
|
(pass-if "n = -1"
|
|
(not (< 0 -1)))
|
|
|
|
(pass-if "n = -1.0"
|
|
(not (< 0 -1.0)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(< 0 fixnum-max))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(< 0 (+ fixnum-max 1)))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(not (< 0 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(not (< 0 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(< 0.0 n)"
|
|
|
|
(pass-if "n = 0"
|
|
(not (< 0.0 0)))
|
|
|
|
(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 = 1.0"
|
|
(< 0.0 1.0))
|
|
|
|
(pass-if "n = -1"
|
|
(not (< 0.0 -1)))
|
|
|
|
(pass-if "n = -1.0"
|
|
(not (< 0.0 -1.0)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(< 0.0 fixnum-max))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(< 0.0 (+ fixnum-max 1)))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(not (< 0.0 fixnum-min)))
|
|
|
|
(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 "n = 0"
|
|
(not (< 1 0)))
|
|
|
|
(pass-if "n = 0.0"
|
|
(not (< 1 0.0)))
|
|
|
|
(pass-if "n = 1"
|
|
(not (< 1 1)))
|
|
|
|
(pass-if "n = 1.0"
|
|
(not (< 1 1.0)))
|
|
|
|
(pass-if "n = -1"
|
|
(not (< 1 -1)))
|
|
|
|
(pass-if "n = -1.0"
|
|
(not (< 1 -1.0)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(< 1 fixnum-max))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(< 1 (+ fixnum-max 1)))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(not (< 1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(not (< 1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(< 1.0 n)"
|
|
|
|
(pass-if "n = 0"
|
|
(not (< 1.0 0)))
|
|
|
|
(pass-if "n = 0.0"
|
|
(not (< 1.0 0.0)))
|
|
|
|
(pass-if "n = 1"
|
|
(not (< 1.0 1)))
|
|
|
|
(pass-if "n = 1.0"
|
|
(not (< 1.0 1.0)))
|
|
|
|
(pass-if "n = -1"
|
|
(not (< 1.0 -1)))
|
|
|
|
(pass-if "n = -1.0"
|
|
(not (< 1.0 -1.0)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(< 1.0 fixnum-max))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(< 1.0 (+ fixnum-max 1)))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(not (< 1.0 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(not (< 1.0 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(< -1 n)"
|
|
|
|
(pass-if "n = 0"
|
|
(< -1 0))
|
|
|
|
(pass-if "n = 0.0"
|
|
(< -1 0.0))
|
|
|
|
(pass-if "n = 1"
|
|
(< -1 1))
|
|
|
|
(pass-if "n = 1.0"
|
|
(< -1 1.0))
|
|
|
|
(pass-if "n = -1"
|
|
(not (< -1 -1)))
|
|
|
|
(pass-if "n = -1.0"
|
|
(not (< -1 -1.0)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(< -1 fixnum-max))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(< -1 (+ fixnum-max 1)))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(not (< -1 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(not (< -1 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(< -1.0 n)"
|
|
|
|
(pass-if "n = 0"
|
|
(< -1.0 0))
|
|
|
|
(pass-if "n = 0.0"
|
|
(< -1.0 0.0))
|
|
|
|
(pass-if "n = 1"
|
|
(< -1.0 1))
|
|
|
|
(pass-if "n = 1.0"
|
|
(< -1.0 1.0))
|
|
|
|
(pass-if "n = -1"
|
|
(not (< -1.0 -1)))
|
|
|
|
(pass-if "n = -1.0"
|
|
(not (< -1.0 -1.0)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(< -1.0 fixnum-max))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(< -1.0 (+ fixnum-max 1)))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(not (< -1.0 fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(not (< -1.0 (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(< fixnum-max n)"
|
|
|
|
(pass-if "n = 0"
|
|
(not (< fixnum-max 0)))
|
|
|
|
(pass-if "n = 0.0"
|
|
(not (< fixnum-max 0.0)))
|
|
|
|
(pass-if "n = 1"
|
|
(not (< fixnum-max 1)))
|
|
|
|
(pass-if "n = 1.0"
|
|
(not (< fixnum-max 1.0)))
|
|
|
|
(pass-if "n = -1"
|
|
(not (< fixnum-max -1)))
|
|
|
|
(pass-if "n = -1.0"
|
|
(not (< fixnum-max -1.0)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(not (< fixnum-max fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(< fixnum-max (+ fixnum-max 1)))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(not (< fixnum-max fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(not (< fixnum-max (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(< (+ fixnum-max 1) n)"
|
|
|
|
(pass-if "n = 0"
|
|
(not (< (+ fixnum-max 1) 0)))
|
|
|
|
(pass-if "n = 0.0"
|
|
(not (< (+ fixnum-max 1) 0.0)))
|
|
|
|
(pass-if "n = 1"
|
|
(not (< (+ fixnum-max 1) 1)))
|
|
|
|
(pass-if "n = 1.0"
|
|
(not (< (+ fixnum-max 1) 1.0)))
|
|
|
|
(pass-if "n = -1"
|
|
(not (< (+ fixnum-max 1) -1)))
|
|
|
|
(pass-if "n = -1.0"
|
|
(not (< (+ fixnum-max 1) -1.0)))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(not (< (+ fixnum-max 1) fixnum-max)))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(not (< (+ fixnum-max 1) (+ fixnum-max 1))))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(not (< (+ fixnum-max 1) fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(not (< (+ fixnum-max 1) (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(< fixnum-min n)"
|
|
|
|
(pass-if "n = 0"
|
|
(< fixnum-min 0))
|
|
|
|
(pass-if "n = 0.0"
|
|
(< fixnum-min 0.0))
|
|
|
|
(pass-if "n = 1"
|
|
(< fixnum-min 1))
|
|
|
|
(pass-if "n = 1.0"
|
|
(< fixnum-min 1.0))
|
|
|
|
(pass-if "n = -1"
|
|
(< fixnum-min -1))
|
|
|
|
(pass-if "n = -1.0"
|
|
(< fixnum-min -1.0))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(< fixnum-min fixnum-max))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(< fixnum-min (+ fixnum-max 1)))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(not (< fixnum-min fixnum-min)))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(not (< fixnum-min (- fixnum-min 1)))))
|
|
|
|
(with-test-prefix "(< (- fixnum-min 1) n)"
|
|
|
|
(pass-if "n = 0"
|
|
(< (- fixnum-min 1) 0))
|
|
|
|
(pass-if "n = 0.0"
|
|
(< (- fixnum-min 1) 0.0))
|
|
|
|
(pass-if "n = 1"
|
|
(< (- fixnum-min 1) 1))
|
|
|
|
(pass-if "n = 1.0"
|
|
(< (- fixnum-min 1) 1.0))
|
|
|
|
(pass-if "n = -1"
|
|
(< (- fixnum-min 1) -1))
|
|
|
|
(pass-if "n = -1.0"
|
|
(< (- fixnum-min 1) -1.0))
|
|
|
|
(pass-if "n = fixnum-max"
|
|
(< (- fixnum-min 1) fixnum-max))
|
|
|
|
(pass-if "n = fixnum-max + 1"
|
|
(< (- fixnum-min 1) (+ fixnum-max 1)))
|
|
|
|
(pass-if "n = fixnum-min"
|
|
(< (- fixnum-min 1) fixnum-min))
|
|
|
|
(pass-if "n = fixnum-min - 1"
|
|
(not (< (- fixnum-min 1) (- fixnum-min 1)))))
|
|
|
|
(pass-if (< (ash 1 256) +inf.0))
|
|
(pass-if (not (< +inf.0 (ash 1 256))))
|
|
(pass-if (not (< (ash 1 256) -inf.0)))
|
|
(pass-if (< -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 (< (1- (ash 1 1024)) +inf.0))
|
|
(pass-if (< (ash 1 1024) +inf.0))
|
|
(pass-if (< (1+ (ash 1 1024)) +inf.0))
|
|
(pass-if (not (< +inf.0 (1- (ash 1 1024)))))
|
|
(pass-if (not (< +inf.0 (ash 1 1024))))
|
|
(pass-if (not (< +inf.0 (1+ (ash 1 1024)))))
|
|
(pass-if (< -inf.0 (- (1- (ash 1 1024)))))
|
|
(pass-if (< -inf.0 (- (ash 1 1024))))
|
|
(pass-if (< -inf.0 (- (1+ (ash 1 1024)))))
|
|
(pass-if (not (< (- (1- (ash 1 1024))) -inf.0)))
|
|
(pass-if (not (< (- (ash 1 1024)) -inf.0)))
|
|
(pass-if (not (< (- (1+ (ash 1 1024))) -inf.0)))
|
|
|
|
(pass-if (not (< +nan.0 +nan.0)))
|
|
(pass-if (not (< 0 +nan.0)))
|
|
(pass-if (not (< +nan.0 0)))
|
|
(pass-if (not (< 1 +nan.0)))
|
|
(pass-if (not (< +nan.0 1)))
|
|
(pass-if (not (< -1 +nan.0)))
|
|
(pass-if (not (< +nan.0 -1)))
|
|
|
|
(pass-if (not (< (ash 1 256) +nan.0)))
|
|
(pass-if (not (< +nan.0 (ash 1 256))))
|
|
(pass-if (not (< (- (ash 1 256)) +nan.0)))
|
|
(pass-if (not (< +nan.0 (- (ash 1 256)))))
|
|
|
|
(pass-if (not (< (ash 1 8192) +nan.0)))
|
|
(pass-if (not (< +nan.0 (ash 1 8192))))
|
|
(pass-if (not (< (- (ash 1 8192)) +nan.0)))
|
|
(pass-if (not (< +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 (< (ash 3 1023) +nan.0)))
|
|
(pass-if (not (< (1+ (ash 3 1023)) +nan.0)))
|
|
(pass-if (not (< (1- (ash 3 1023)) +nan.0)))
|
|
(pass-if (not (< +nan.0 (ash 3 1023))))
|
|
(pass-if (not (< +nan.0 (1+ (ash 3 1023)))))
|
|
(pass-if (not (< +nan.0 (1- (ash 3 1023)))))
|
|
|
|
(with-test-prefix "inum/frac"
|
|
(pass-if (< 2 9/4))
|
|
(pass-if (< -2 9/4))
|
|
(pass-if (< -2 7/4))
|
|
(pass-if (< -2 -7/4))
|
|
(pass-if (eq? #f (< 2 7/4)))
|
|
(pass-if (eq? #f (< 2 -7/4)))
|
|
(pass-if (eq? #f (< 2 -9/4)))
|
|
(pass-if (eq? #f (< -2 -9/4))))
|
|
|
|
(with-test-prefix "bignum/frac"
|
|
(let ((x (ash 1 2048)))
|
|
(pass-if (< x (* 4/3 x)))
|
|
(pass-if (< (- x) (* 4/3 x)))
|
|
(pass-if (< (- x) (* 2/3 x)))
|
|
(pass-if (< (- x) (* -2/3 x)))
|
|
(pass-if (eq? #f (< x (* 2/3 x))))
|
|
(pass-if (eq? #f (< x (* -2/3 x))))
|
|
(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))
|
|
(pass-if (< -0.75 2/3))
|
|
(pass-if (< -0.75 -2/3))
|
|
(pass-if (eq? #f (< 0.75 2/3)))
|
|
(pass-if (eq? #f (< 0.75 -2/3)))
|
|
(pass-if (eq? #f (< 0.75 -4/3)))
|
|
(pass-if (eq? #f (< -0.75 -4/3)))
|
|
|
|
(pass-if (< -inf.0 4/3))
|
|
(pass-if (< -inf.0 -4/3))
|
|
(pass-if (eq? #f (< +inf.0 4/3)))
|
|
(pass-if (eq? #f (< +inf.0 -4/3)))
|
|
|
|
(pass-if (eq? #f (< +nan.0 4/3)))
|
|
(pass-if (eq? #f (< +nan.0 -4/3))))
|
|
|
|
(with-test-prefix "frac/inum"
|
|
(pass-if (< 7/4 2))
|
|
(pass-if (< -7/4 2))
|
|
(pass-if (< -9/4 2))
|
|
(pass-if (< -9/4 -2))
|
|
(pass-if (eq? #f (< 9/4 2)))
|
|
(pass-if (eq? #f (< 9/4 -2)))
|
|
(pass-if (eq? #f (< 7/4 -2)))
|
|
(pass-if (eq? #f (< -7/4 -2))))
|
|
|
|
(with-test-prefix "frac/bignum"
|
|
(let ((x (ash 1 2048)))
|
|
(pass-if (< (* 2/3 x) x))
|
|
(pass-if (< (* -2/3 x) x))
|
|
(pass-if (< (* -4/3 x) x))
|
|
(pass-if (< (* -4/3 x) (- x)))
|
|
(pass-if (eq? #f (< (* 4/3 x) x)))
|
|
(pass-if (eq? #f (< (* 4/3 x) (- x))))
|
|
(pass-if (eq? #f (< (* 2/3 x) (- x))))
|
|
(pass-if (eq? #f (< (* -2/3 x) (- x))))))
|
|
|
|
(with-test-prefix "frac/flonum"
|
|
(pass-if (< 2/3 0.75))
|
|
(pass-if (< -2/3 0.75))
|
|
(pass-if (< -4/3 0.75))
|
|
(pass-if (< -4/3 -0.75))
|
|
(pass-if (eq? #f (< 4/3 0.75)))
|
|
(pass-if (eq? #f (< 4/3 -0.75)))
|
|
(pass-if (eq? #f (< 2/3 -0.75)))
|
|
(pass-if (eq? #f (< -2/3 -0.75)))
|
|
|
|
(pass-if (< 4/3 +inf.0))
|
|
(pass-if (< -4/3 +inf.0))
|
|
(pass-if (eq? #f (< 4/3 -inf.0)))
|
|
(pass-if (eq? #f (< -4/3 -inf.0)))
|
|
|
|
(pass-if (eq? #f (< 4/3 +nan.0)))
|
|
(pass-if (eq? #f (< -4/3 +nan.0))))
|
|
|
|
(with-test-prefix "frac/frac"
|
|
(pass-if (< 2/3 6/7))
|
|
(pass-if (< -2/3 6/7))
|
|
(pass-if (< -4/3 6/7))
|
|
(pass-if (< -4/3 -6/7))
|
|
(pass-if (eq? #f (< 4/3 6/7)))
|
|
(pass-if (eq? #f (< 4/3 -6/7)))
|
|
(pass-if (eq? #f (< 2/3 -6/7)))
|
|
(pass-if (eq? #f (< -2/3 -6/7)))))
|
|
|
|
;;;
|
|
;;; >
|
|
;;;
|
|
|
|
;; currently not tested -- implementation is trivial
|
|
;; (> x y) is implemented as (< y x)
|
|
;; FIXME: tests should probably be added in case we change implementation.
|
|
|
|
;;;
|
|
;;; <=
|
|
;;;
|
|
|
|
;; currently not tested -- implementation is trivial
|
|
;; (<= x y) is implemented as (not (< y x))
|
|
;; FIXME: tests should probably be added in case we change implementation.
|
|
|
|
;;;
|
|
;;; >=
|
|
;;;
|
|
|
|
;; currently not tested -- implementation is trivial
|
|
;; (>= x y) is implemented as (not (< x y))
|
|
;; FIXME: tests should probably be added in case we change implementation.
|
|
|
|
;;;
|
|
;;; zero?
|
|
;;;
|
|
|
|
(with-test-prefix "zero?"
|
|
(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? 1.0+0.0i)))
|
|
(pass-if (not (zero? 0.0-1.0i))))
|
|
|
|
;;;
|
|
;;; positive?
|
|
;;;
|
|
|
|
(with-test-prefix "positive?"
|
|
(pass-if (documented? positive?))
|
|
(pass-if (positive? 1))
|
|
(pass-if (positive? (+ fixnum-max 1)))
|
|
(pass-if (positive? 1.3))
|
|
(pass-if (not (positive? 0)))
|
|
(pass-if (not (positive? -1)))
|
|
(pass-if (not (positive? (- fixnum-min 1))))
|
|
(pass-if (not (positive? -1.3))))
|
|
|
|
;;;
|
|
;;; negative?
|
|
;;;
|
|
|
|
(with-test-prefix "negative?"
|
|
(pass-if (documented? negative?))
|
|
(pass-if (not (negative? 1)))
|
|
(pass-if (not (negative? (+ fixnum-max 1))))
|
|
(pass-if (not (negative? 1.3)))
|
|
(pass-if (not (negative? 0)))
|
|
(pass-if (negative? -1))
|
|
(pass-if (negative? (- fixnum-min 1)))
|
|
(pass-if (negative? -1.3)))
|
|
|
|
;;;
|
|
;;; max
|
|
;;;
|
|
|
|
(with-test-prefix "max"
|
|
(pass-if-exception "no args" exception:wrong-num-args
|
|
(max))
|
|
|
|
(pass-if-exception "one complex" exception:wrong-type-arg
|
|
(max 1+i))
|
|
|
|
(pass-if-exception "inum/complex" exception:wrong-type-arg
|
|
(max 123 1+i))
|
|
(pass-if-exception "big/complex" exception:wrong-type-arg
|
|
(max 9999999999999999999999999999999999999999 1+i))
|
|
(pass-if-exception "real/complex" exception:wrong-type-arg
|
|
(max 123.0 1+i))
|
|
(pass-if-exception "frac/complex" exception:wrong-type-arg
|
|
(max 123/456 1+i))
|
|
|
|
(pass-if-exception "complex/inum" exception:wrong-type-arg
|
|
(max 1+i 123))
|
|
(pass-if-exception "complex/big" exception:wrong-type-arg
|
|
(max 1+i 9999999999999999999999999999999999999999))
|
|
(pass-if-exception "complex/real" exception:wrong-type-arg
|
|
(max 1+i 123.0))
|
|
(pass-if-exception "complex/frac" exception:wrong-type-arg
|
|
(max 1+i 123/456))
|
|
|
|
(let ((big*2 (* fixnum-max 2))
|
|
(big*3 (* fixnum-max 3))
|
|
(big*4 (* fixnum-max 4))
|
|
(big*5 (* fixnum-max 5)))
|
|
|
|
(with-test-prefix "inum / frac"
|
|
(pass-if (eqv? 3 (max 3 5/2)))
|
|
(pass-if (eqv? 5/2 (max 2 5/2))))
|
|
|
|
(with-test-prefix "frac / inum"
|
|
(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 (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 (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 (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 (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 (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 (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)
|
|
(eqv? +inf.0 (max b +inf.0)))
|
|
(pass-if (list +inf.0 b)
|
|
(eqv? +inf.0 (max b +inf.0)))
|
|
(pass-if (list b -inf.0)
|
|
(eqv? (exact->inexact b) (max b -inf.0)))
|
|
(pass-if (list -inf.0 b)
|
|
(eqv? (exact->inexact b) (max b -inf.0))))
|
|
(list (1- (ash 1 1024))
|
|
(ash 1 1024)
|
|
(1+ (ash 1 1024))
|
|
(- (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 (real-nan? (max (ash 1 2048) +nan.0)))
|
|
(pass-if (real-nan? (max +nan.0 (ash 1 2048)))))
|
|
|
|
;;;
|
|
;;; min
|
|
;;;
|
|
|
|
;; FIXME: unfinished...
|
|
|
|
(with-test-prefix "min"
|
|
(pass-if-exception "no args" exception:wrong-num-args
|
|
(min))
|
|
|
|
(pass-if-exception "one complex" exception:wrong-type-arg
|
|
(min 1+i))
|
|
|
|
(pass-if-exception "inum/complex" exception:wrong-type-arg
|
|
(min 123 1+i))
|
|
(pass-if-exception "big/complex" exception:wrong-type-arg
|
|
(min 9999999999999999999999999999999999999999 1+i))
|
|
(pass-if-exception "real/complex" exception:wrong-type-arg
|
|
(min 123.0 1+i))
|
|
(pass-if-exception "frac/complex" exception:wrong-type-arg
|
|
(min 123/456 1+i))
|
|
|
|
(pass-if-exception "complex/inum" exception:wrong-type-arg
|
|
(min 1+i 123))
|
|
(pass-if-exception "complex/big" exception:wrong-type-arg
|
|
(min 1+i 9999999999999999999999999999999999999999))
|
|
(pass-if-exception "complex/real" exception:wrong-type-arg
|
|
(min 1+i 123.0))
|
|
(pass-if-exception "complex/frac" exception:wrong-type-arg
|
|
(min 1+i 123/456))
|
|
|
|
(let ((big*2 (* fixnum-max 2))
|
|
(big*3 (* fixnum-max 3))
|
|
(big*4 (* fixnum-max 4))
|
|
(big*5 (* fixnum-max 5)))
|
|
|
|
(pass-if (documented? min))
|
|
(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
|
|
(eqv? (- fixnum-min 1) (min 2 4 (- fixnum-min 1) 3 (* 2 fixnum-max))))
|
|
(pass-if
|
|
(eqv? (- fixnum-min 1) (min (- fixnum-min 1) 2 4 3 (* 2 fixnum-max))))
|
|
(pass-if
|
|
(eqv? (- fixnum-min 1) (min 2 4 3 (* 2 fixnum-max) (- fixnum-min 1))))
|
|
|
|
(with-test-prefix "inum / frac"
|
|
(pass-if (eqv? 5/2 (min 3 5/2)))
|
|
(pass-if (eqv? 2 (min 2 5/2))))
|
|
|
|
(with-test-prefix "frac / inum"
|
|
(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 (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 (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 (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 (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 (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 (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)
|
|
(eqv? (exact->inexact b) (min b +inf.0)))
|
|
(pass-if (list +inf.0 b)
|
|
(eqv? (exact->inexact b) (min b +inf.0)))
|
|
(pass-if (list b -inf.0)
|
|
(eqv? -inf.0 (min b -inf.0)))
|
|
(pass-if (list -inf.0 b)
|
|
(eqv? -inf.0 (min b -inf.0))))
|
|
(list (1- (ash 1 1024))
|
|
(ash 1 1024)
|
|
(1+ (ash 1 1024))
|
|
(- (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 (real-nan? (min (- (ash 1 2048)) (- +nan.0))))
|
|
(pass-if (real-nan? (min (- +nan.0) (- (ash 1 2048))))))
|
|
|
|
;;;
|
|
;;; +
|
|
;;;
|
|
|
|
(with-test-prefix/c&e "+"
|
|
|
|
(pass-if "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/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
|
|
(- -1 #x100000000000000000000000000000000)))
|
|
|
|
(pass-if "big - inum"
|
|
(= #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
|
|
(- #x100000000000000000000000000000000 1)))
|
|
|
|
(pass-if "big - -inum"
|
|
(= #x100000000000000000000000000000001
|
|
(- #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"
|
|
(eqv? 0 (* 0 (ash 1 256)))))
|
|
|
|
(with-test-prefix "inum * flonum"
|
|
|
|
(pass-if "0 * 1.0 = 0.0"
|
|
(eqv? 0.0 (* 0 1.0))))
|
|
|
|
(with-test-prefix "inum * complex"
|
|
|
|
(pass-if "0 * 1+1i = 0.0+0.0i"
|
|
(eqv? 0.0+0.0i (* 0 1+1i))))
|
|
|
|
(with-test-prefix "inum * frac"
|
|
|
|
(pass-if "0 * 2/3 = 0"
|
|
(eqv? 0 (* 0 2/3))))
|
|
|
|
(with-test-prefix "bignum * inum"
|
|
|
|
(pass-if "2^256 * 0 = 0"
|
|
(eqv? 0 (* (ash 1 256) 0))))
|
|
|
|
(with-test-prefix "flonum * inum"
|
|
(pass-if "1.0 * 0 = 0.0"
|
|
(eqv? 0.0 (* 1.0 0))))
|
|
|
|
(with-test-prefix "complex * inum"
|
|
(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)))
|
|
(= (make-rectangular big big)
|
|
(* 1+1i big))))
|
|
|
|
(with-test-prefix "frac * inum"
|
|
|
|
(pass-if "2/3 * 0 = 0"
|
|
(eqv? 0 (* 2/3 0)))))
|
|
|
|
;;;
|
|
;;; /
|
|
;;;
|
|
|
|
(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? /))
|
|
|
|
(with-test-prefix "division by zero"
|
|
|
|
(pass-if-exception "(/ 0)"
|
|
exception:numerical-overflow
|
|
(/ 0))
|
|
|
|
(pass-if "(/ 0.0)"
|
|
(= +inf.0 (/ 0.0)))
|
|
|
|
(pass-if-exception "(/ 1 0)"
|
|
exception:numerical-overflow
|
|
(/ 1 0))
|
|
|
|
(pass-if "(/ 1 0.0)"
|
|
(= +inf.0 (/ 1 0.0)))
|
|
|
|
(pass-if-exception "(/ bignum 0)"
|
|
exception:numerical-overflow
|
|
(/ (+ fixnum-max 1) 0))
|
|
|
|
(pass-if "(/ bignum 0.0)"
|
|
(= +inf.0 (/ (+ fixnum-max 1) 0.0)))
|
|
|
|
(pass-if-exception "(/ 1.0 0)"
|
|
exception:numerical-overflow
|
|
(/ 1.0 0))
|
|
|
|
(pass-if "(/ 1.0 0.0)"
|
|
(= +inf.0 (/ 1.0 0.0)))
|
|
|
|
(pass-if-exception "(/ +i 0)"
|
|
exception:numerical-overflow
|
|
(/ +i 0))
|
|
|
|
(pass-if "(/ +i 0.0)"
|
|
(= +inf.0 (imag-part (/ +i 0.0)))))
|
|
|
|
(with-test-prefix "1/complex"
|
|
|
|
(pass-if "0+1i"
|
|
(eqv? 0-1i (/ 0+1i)))
|
|
|
|
;; in guile 1.6 through 1.6.7 this incorrectly resulted in nans
|
|
(pass-if "0-1i"
|
|
(eqv? 0+1i (/ 0-1i)))
|
|
|
|
(pass-if "1+1i"
|
|
(eqv? 0.5-0.5i (/ 1+1i)))
|
|
|
|
(pass-if "1-1i"
|
|
(eqv? 0.5+0.5i (/ 1-1i)))
|
|
|
|
(pass-if "-1+1i"
|
|
(eqv? -0.5-0.5i (/ -1+1i)))
|
|
|
|
(pass-if "-1-1i"
|
|
(eqv? -0.5+0.5i (/ -1-1i)))
|
|
|
|
(pass-if "(/ 3+4i)"
|
|
(= (/ 3+4i) 0.12-0.16i))
|
|
|
|
(pass-if "(/ 4+3i)"
|
|
(= (/ 4+3i) 0.16-0.12i))
|
|
|
|
(pass-if "(/ 1e200+1e200i)"
|
|
(= (/ 1e200+1e200i) 5.0e-201-5.0e-201i)))
|
|
|
|
(with-test-prefix "inum/complex"
|
|
|
|
(pass-if "(/ 25 3+4i)"
|
|
(= (/ 25 3+4i) 3.0-4.0i))
|
|
|
|
(pass-if "(/ 25 4+3i)"
|
|
(= (/ 25 4+3i) 4.0-3.0i)))
|
|
|
|
(with-test-prefix "complex/complex"
|
|
|
|
(pass-if "(/ 25+125i 3+4i)"
|
|
(= (/ 25+125i 3+4i) 23.0+11.0i))
|
|
|
|
(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
|
|
;;;
|
|
|
|
(with-test-prefix "truncate"
|
|
(pass-if (= 1 (truncate 1.75)))
|
|
(pass-if (= 1 (truncate 1.5)))
|
|
(pass-if (= 1 (truncate 1.25)))
|
|
(pass-if (= 0 (truncate 0.75)))
|
|
(pass-if (= 0 (truncate 0.5)))
|
|
(pass-if (= 0 (truncate 0.0)))
|
|
(pass-if (= 0 (truncate -0.5)))
|
|
(pass-if (= -1 (truncate -1.25)))
|
|
(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 "round"
|
|
(pass-if (= 2 (round 1.75)))
|
|
(pass-if (= 2 (round 1.5)))
|
|
(pass-if (= 1 (round 1.25)))
|
|
(pass-if (= 1 (round 0.75)))
|
|
(pass-if (= 0 (round 0.5)))
|
|
(pass-if (= 0 (round 0.0)))
|
|
(pass-if (= 0 (round -0.5)))
|
|
(pass-if (= -1 (round -1.25)))
|
|
(pass-if (= -2 (round -1.5)))
|
|
|
|
(with-test-prefix "inum"
|
|
(pass-if "0"
|
|
(and (= 0 (round 0))
|
|
(exact? (round 0))))
|
|
|
|
(pass-if "1"
|
|
(and (= 1 (round 1))
|
|
(exact? (round 1))))
|
|
|
|
(pass-if "-1"
|
|
(and (= -1 (round -1))
|
|
(exact? (round -1)))))
|
|
|
|
(with-test-prefix "bignum"
|
|
(let ((x (1+ most-positive-fixnum)))
|
|
(pass-if "(1+ most-positive-fixnum)"
|
|
(and (= x (round x))
|
|
(exact? (round x)))))
|
|
|
|
(let ((x (1- most-negative-fixnum)))
|
|
(pass-if "(1- most-negative-fixnum)"
|
|
(and (= x (round x))
|
|
(exact? (round x))))))
|
|
|
|
(with-test-prefix "frac"
|
|
(define (=exact x y)
|
|
(and (= x y)
|
|
(exact? y)))
|
|
|
|
(pass-if (=exact -2 (round -7/3)))
|
|
(pass-if (=exact -2 (round -5/3)))
|
|
(pass-if (=exact -1 (round -4/3)))
|
|
(pass-if (=exact -1 (round -2/3)))
|
|
(pass-if (=exact 0 (round -1/3)))
|
|
(pass-if (=exact 0 (round 1/3)))
|
|
(pass-if (=exact 1 (round 2/3)))
|
|
(pass-if (=exact 1 (round 4/3)))
|
|
(pass-if (=exact 2 (round 5/3)))
|
|
(pass-if (=exact 2 (round 7/3)))
|
|
|
|
(pass-if (=exact -3 (round -17/6)))
|
|
(pass-if (=exact -3 (round -16/6)))
|
|
(pass-if (=exact -2 (round -15/6)))
|
|
(pass-if (=exact -2 (round -14/6)))
|
|
(pass-if (=exact -2 (round -13/6)))
|
|
(pass-if (=exact -2 (round -11/6)))
|
|
(pass-if (=exact -2 (round -10/6)))
|
|
(pass-if (=exact -2 (round -9/6)))
|
|
(pass-if (=exact -1 (round -8/6)))
|
|
(pass-if (=exact -1 (round -7/6)))
|
|
(pass-if (=exact -1 (round -5/6)))
|
|
(pass-if (=exact -1 (round -4/6)))
|
|
(pass-if (=exact 0 (round -3/6)))
|
|
(pass-if (=exact 0 (round -2/6)))
|
|
(pass-if (=exact 0 (round -1/6)))
|
|
(pass-if (=exact 0 (round 1/6)))
|
|
(pass-if (=exact 0 (round 2/6)))
|
|
(pass-if (=exact 0 (round 3/6)))
|
|
(pass-if (=exact 1 (round 4/6)))
|
|
(pass-if (=exact 1 (round 5/6)))
|
|
(pass-if (=exact 1 (round 7/6)))
|
|
(pass-if (=exact 1 (round 8/6)))
|
|
(pass-if (=exact 2 (round 9/6)))
|
|
(pass-if (=exact 2 (round 10/6)))
|
|
(pass-if (=exact 2 (round 11/6)))
|
|
(pass-if (=exact 2 (round 13/6)))
|
|
(pass-if (=exact 2 (round 14/6)))
|
|
(pass-if (=exact 2 (round 15/6)))
|
|
(pass-if (=exact 3 (round 16/6)))
|
|
(pass-if (=exact 3 (round 17/6))))
|
|
|
|
(with-test-prefix "real"
|
|
(pass-if "0.0"
|
|
(and (= 0.0 (round 0.0))
|
|
(inexact? (round 0.0))))
|
|
|
|
(pass-if "1.0"
|
|
(and (= 1.0 (round 1.0))
|
|
(inexact? (round 1.0))))
|
|
|
|
(pass-if "-1.0"
|
|
(and (= -1.0 (round -1.0))
|
|
(inexact? (round -1.0))))
|
|
|
|
(pass-if "-3.1"
|
|
(and (= -3.0 (round -3.1))
|
|
(inexact? (round -3.1))))
|
|
|
|
(pass-if "3.1"
|
|
(and (= 3.0 (round 3.1))
|
|
(inexact? (round 3.1))))
|
|
|
|
(pass-if "3.9"
|
|
(and (= 4.0 (round 3.9))
|
|
(inexact? (round 3.9))))
|
|
|
|
(pass-if "-3.9"
|
|
(and (= -4.0 (round -3.9))
|
|
(inexact? (round -3.9))))
|
|
|
|
(pass-if "1.5"
|
|
(and (= 2.0 (round 1.5))
|
|
(inexact? (round 1.5))))
|
|
|
|
(pass-if "2.5"
|
|
(and (= 2.0 (round 2.5))
|
|
(inexact? (round 2.5))))
|
|
|
|
(pass-if "3.5"
|
|
(and (= 4.0 (round 3.5))
|
|
(inexact? (round 3.5))))
|
|
|
|
(pass-if "-1.5"
|
|
(and (= -2.0 (round -1.5))
|
|
(inexact? (round -1.5))))
|
|
|
|
(pass-if "-2.5"
|
|
(and (= -2.0 (round -2.5))
|
|
(inexact? (round -2.5))))
|
|
|
|
(pass-if "-3.5"
|
|
(and (= -4.0 (round -3.5))
|
|
(inexact? (round -3.5))))
|
|
|
|
;; prior to guile 1.6.5, on an IEEE system an inexact 2^53-1 (ie. a
|
|
;; float with mantissa all ones) came out as 2^53 from `round' (except
|
|
;; on i386 and m68k systems using the coprocessor and optimizing, where
|
|
;; extra precision hid the problem)
|
|
(pass-if "2^53-1"
|
|
(let ((x (exact->inexact (1- (ash 1 53)))))
|
|
(and (= x (round x))
|
|
(inexact? (round x)))))
|
|
(pass-if "-(2^53-1)"
|
|
(let ((x (exact->inexact (- (1- (ash 1 53))))))
|
|
(and (= x (round x))
|
|
(inexact? (round x)))))))
|
|
|
|
;;;
|
|
;;; exact->inexact
|
|
;;;
|
|
|
|
(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)
|
|
(test (list i n want) n want))
|
|
|
|
(with-test-prefix "2^i, no round"
|
|
(do ((i 0 (1+ i))
|
|
(n 1 (* 2 n))
|
|
(want 1.0 (* 2.0 want)))
|
|
((> i 100))
|
|
(try-i i n want)))
|
|
|
|
(with-test-prefix "2^i+1, no round"
|
|
(do ((i 1 (1+ i))
|
|
(n 3 (1- (* 2 n)))
|
|
(want 3.0 (- (* 2.0 want) 1.0)))
|
|
((>= i dbl-mant-dig))
|
|
(try-i i n want)))
|
|
|
|
(with-test-prefix "(2^i+1)*2^100, no round"
|
|
(do ((i 1 (1+ i))
|
|
(n 3 (1- (* 2 n)))
|
|
(want 3.0 (- (* 2.0 want) 1.0)))
|
|
((>= i dbl-mant-dig))
|
|
(try-i i (ash n 100) (ash-flo want 100))))
|
|
|
|
;; bit pattern: 1111....11100.00
|
|
;; <-mantdig-><-i->
|
|
;;
|
|
(with-test-prefix "mantdig ones then zeros, no rounding"
|
|
(do ((i 0 (1+ i))
|
|
(n (- (ash 1 dbl-mant-dig) 1) (* 2 n))
|
|
(want (- (ash-flo 1.0 dbl-mant-dig) 1.0) (* 2.0 want)))
|
|
((> i 100))
|
|
(try-i i n want)))
|
|
|
|
;; bit pattern: 1111....111011..1
|
|
;; <-mantdig-> <-i->
|
|
;; This sort of value was incorrectly rounded upwards in Guile 1.6.4 when
|
|
;; i >= 11 (that's when the total is 65 or more bits).
|
|
;;
|
|
(with-test-prefix "mantdig ones then 011..11, round down"
|
|
(do ((i 0 (1+ i))
|
|
(n (- (ash 1 (+ 1 dbl-mant-dig)) 2) (+ 1 (* 2 n)))
|
|
(want (- (ash-flo 1.0 (+ 1 dbl-mant-dig)) 2.0) (* 2.0 want)))
|
|
((> i 100))
|
|
(try-i i n want)))
|
|
|
|
;; bit pattern: 1111....111100..001
|
|
;; <-mantdig-> <--i->
|
|
;;
|
|
(with-test-prefix "mantdig ones then 100..001, round up"
|
|
(do ((i 0 (1+ i))
|
|
(n (- (ash 1 (+ 2 dbl-mant-dig)) 1) (1- (* 2 n)))
|
|
(want (ash-flo 1.0 (+ 2 dbl-mant-dig)) (* 2.0 want)))
|
|
((> i 100))
|
|
(try-i i n want)))
|
|
|
|
;; bit pattern: 1000....000100..001
|
|
;; <-mantdig-> <--i->
|
|
;;
|
|
(with-test-prefix "2^mantdig then 100..001, round up"
|
|
(do ((i 0 (1+ i))
|
|
(n (- (ash 1 (+ 2 dbl-mant-dig)) 1) (1- (* 2 n)))
|
|
(want (+ (ash-flo 1.0 (+ 2 dbl-mant-dig)) 4.0) (* 2.0 want)))
|
|
((> i 100))
|
|
(try-i i n want)))
|
|
|
|
(pass-if "frac big/big"
|
|
(let ((big (ash 1 256)))
|
|
(= 1.0 (exact->inexact (/ (1+ big) big)))))
|
|
|
|
;; In guile 1.8.0 this failed, giving back "nan" because it tried to
|
|
;; 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)))))
|
|
|
|
;; 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))))
|
|
|
|
)
|
|
|
|
;;;
|
|
;;; 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))))
|
|
|
|
|
|
;;;
|
|
;;; 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))))
|
|
|
|
;;;
|
|
;;; cos
|
|
;;;
|
|
|
|
(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 (= 0.0 (asinh 0.0))))
|
|
|
|
;;;
|
|
;;; acosh
|
|
;;;
|
|
|
|
(with-test-prefix "acosh"
|
|
(pass-if (= 0 (acosh 1)))
|
|
(pass-if (= 0.0 (acosh 1.0))))
|
|
|
|
;;;
|
|
;;; atanh
|
|
;;;
|
|
|
|
(with-test-prefix "atanh"
|
|
(pass-if (= 0 (atanh 0)))
|
|
(pass-if (= 0.0 (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
|
|
;;;
|
|
|
|
(with-test-prefix "make-polar"
|
|
(define pi 3.14159265358979323846)
|
|
(define (almost= x y)
|
|
(> 0.01 (magnitude (- x y))))
|
|
|
|
(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))))
|
|
(pass-if (almost= 0-i (make-polar 1 (* 1.5 pi))))
|
|
(pass-if (almost= 1 (make-polar 1 (* 2.0 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)))
|
|
(pass-if (= 1 (magnitude 0+i)))
|
|
(pass-if (= 1 (magnitude 0-i)))
|
|
(pass-if (= 5 (magnitude 3+4i)))
|
|
(pass-if (= 5 (magnitude 3-4i)))
|
|
(pass-if (= 5 (magnitude -3+4i)))
|
|
(pass-if (= 5 (magnitude -3-4i))))
|
|
|
|
;;;
|
|
;;; angle
|
|
;;;
|
|
|
|
(with-test-prefix "angle"
|
|
(define pi 3.14159265358979323846)
|
|
(define (almost= 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" (= 0 (angle (1+ fixnum-max))))
|
|
(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 "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 "-inf" exception:out-of-range
|
|
(inexact->exact -inf.0))
|
|
|
|
(pass-if-exception "nan" exception:out-of-range
|
|
(inexact->exact +nan.0))
|
|
|
|
(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 (* 2 n))
|
|
(f 1.0 (* 2.0 f)))
|
|
((> i 100))
|
|
(test (list i n) f n))))
|
|
|
|
;;;
|
|
;;; integer-expt
|
|
;;;
|
|
|
|
(with-test-prefix "integer-expt"
|
|
(pass-if (documented? integer-expt))
|
|
|
|
(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))
|
|
|
|
(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))
|
|
(i 0 (1+ i)))
|
|
((> i 256))
|
|
(pass-if (list n "expect" i)
|
|
(= i (integer-length n)))))
|
|
|
|
(with-test-prefix "-2^i+1 ...11100..01"
|
|
(do ((n -3 (logxor 3 (ash n 1)))
|
|
(i 2 (1+ i)))
|
|
((> i 256))
|
|
(pass-if n
|
|
(= i (integer-length n)))))
|
|
|
|
(with-test-prefix "-2^i-1 ...111011..11"
|
|
(do ((n -2 (1+ (ash n 1)))
|
|
(i 1 (1+ i)))
|
|
((> i 256))
|
|
(pass-if n
|
|
(= i (integer-length n))))))
|
|
|
|
;;;
|
|
;;; log
|
|
;;;
|
|
|
|
(with-test-prefix "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-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)))
|
|
|
|
(pass-if (eqv-loosely? 0.0+3.14159i (log -1.0)))
|
|
(pass-if (eqv-loosely? 1.0+3.14159i (log -2.71828)))
|
|
(pass-if (eqv-loosely? 2.0+3.14159i (log (* -2.71828 2.71828)))))
|
|
|
|
;;;
|
|
;;; log10
|
|
;;;
|
|
|
|
(with-test-prefix "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-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? 2.0+1.36437i (log10 -100))))
|
|
|
|
;;;
|
|
;;; logbit?
|
|
;;;
|
|
|
|
(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)))
|
|
(pass-if (eq? #f (logbit? 32 0)))
|
|
(pass-if (eq? #f (logbit? 33 0)))
|
|
(pass-if (eq? #f (logbit? 63 0)))
|
|
(pass-if (eq? #f (logbit? 64 0)))
|
|
(pass-if (eq? #f (logbit? 65 0)))
|
|
|
|
;; prior to guile 1.6.5, testing bit 32, 64 etc of value 1 would wrap
|
|
;; around and return #t where it ought to be #f
|
|
(pass-if (eq? #t (logbit? 0 1)))
|
|
(pass-if (eq? #f (logbit? 1 1)))
|
|
(pass-if (eq? #f (logbit? 31 1)))
|
|
(pass-if (eq? #f (logbit? 32 1)))
|
|
(pass-if (eq? #f (logbit? 33 1)))
|
|
(pass-if (eq? #f (logbit? 63 1)))
|
|
(pass-if (eq? #f (logbit? 64 1)))
|
|
(pass-if (eq? #f (logbit? 65 1)))
|
|
(pass-if (eq? #f (logbit? 128 1)))
|
|
|
|
(pass-if (eq? #t (logbit? 0 -1)))
|
|
(pass-if (eq? #t (logbit? 1 -1)))
|
|
(pass-if (eq? #t (logbit? 31 -1)))
|
|
(pass-if (eq? #t (logbit? 32 -1)))
|
|
(pass-if (eq? #t (logbit? 33 -1)))
|
|
(pass-if (eq? #t (logbit? 63 -1)))
|
|
(pass-if (eq? #t (logbit? 64 -1)))
|
|
(pass-if (eq? #t (logbit? 65 -1))))
|
|
|
|
;;;
|
|
;;; logcount
|
|
;;;
|
|
|
|
(with-test-prefix "logcount"
|
|
(pass-if (documented? logcount))
|
|
|
|
(with-test-prefix "-2^i, meaning ...11100..00"
|
|
(do ((n -1 (ash n 1))
|
|
(i 0 (1+ i)))
|
|
((> i 256))
|
|
(pass-if n
|
|
(= i (logcount n)))))
|
|
|
|
(with-test-prefix "2^i"
|
|
(do ((n 1 (ash n 1))
|
|
(i 0 (1+ i)))
|
|
((> i 256))
|
|
(pass-if n
|
|
(= 1 (logcount n)))))
|
|
|
|
(with-test-prefix "2^i-1"
|
|
(do ((n 0 (1+ (ash n 1)))
|
|
(i 0 (1+ i)))
|
|
((> i 256))
|
|
(pass-if n
|
|
(= i (logcount n))))))
|
|
|
|
;;;
|
|
;;; logior
|
|
;;;
|
|
|
|
(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
|
|
(let ()
|
|
(define (test x y)
|
|
(pass-if (list x y '=> -1)
|
|
(eqv? -1 (logior x y)))
|
|
(pass-if (list y x '=> -1)
|
|
(eqv? -1 (logior y x))))
|
|
(test (ash -1 8) #xFF)
|
|
(test (ash -1 28) #x0FFFFFFF)
|
|
(test (ash -1 29) #x1FFFFFFF)
|
|
(test (ash -1 30) #x3FFFFFFF)
|
|
(test (ash -1 31) #x7FFFFFFF)
|
|
(test (ash -1 32) #xFFFFFFFF)
|
|
(test (ash -1 33) #x1FFFFFFFF)
|
|
(test (ash -1 60) #x0FFFFFFFFFFFFFFF)
|
|
(test (ash -1 61) #x1FFFFFFFFFFFFFFF)
|
|
(test (ash -1 62) #x3FFFFFFFFFFFFFFF)
|
|
(test (ash -1 63) #x7FFFFFFFFFFFFFFF)
|
|
(test (ash -1 64) #xFFFFFFFFFFFFFFFF)
|
|
(test (ash -1 65) #x1FFFFFFFFFFFFFFFF)
|
|
(test (ash -1 128) #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
|
|
|
|
;;;
|
|
;;; lognot
|
|
;;;
|
|
|
|
(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 (= 1 (lognot -2)))
|
|
|
|
(pass-if (= #x-100000000000000000000000000000000
|
|
(lognot #xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)))
|
|
(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? 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 (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)))
|
|
(pass-if (eqv-loosely? 31.62 (sqrt 1000.0)))
|
|
|
|
(pass-if (eqv? +1.0i (sqrt -1.0)))
|
|
(pass-if (eqv-loosely? +2.0i (sqrt -4.0)))
|
|
(pass-if (eqv-loosely? +31.62i (sqrt -1000.0)))
|
|
|
|
(pass-if "+i swings back to 45deg angle"
|
|
(eqv-loosely? +0.7071+0.7071i (sqrt +1.0i)))
|
|
|
|
;; Note: glibc 2.3 csqrt() had a bug affecting this test case, so if it
|
|
;; fails check whether that's the cause (there's a configure test to
|
|
;; reject it, but when cross-compiling we assume the C library is ok).
|
|
(pass-if "-100i swings back to 45deg down"
|
|
(eqv-loosely? +7.071-7.071i (sqrt -100.0i))))
|
|
|
|
|
|
;;;
|
|
;;; 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?)))
|
|
|
|
;;;
|
|
;;; 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 -3 -2 -1 0 1 2 3 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))
|