(define-library (chibi numeric-test)
(export run-tests)
(import (scheme base) (scheme inexact) (chibi test))
(begin
(define (integer-neighborhoods x)
(list x (+ 1 x) (+ -1 x) (- x) (- 1 x) (- -1 x)))
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
(define (atanh z) (/ (- (log (+ 1 z)) (log (- 1 z))) 2))
(define (integer-arithmetic-combinations a b)
(list (+ a b) (- a b) (* a b) (quotient a b) (remainder a b)))
(define (sign-combinations a b)
(list (integer-arithmetic-combinations a b)
(integer-arithmetic-combinations (- a) b)
(integer-arithmetic-combinations a (- b))
(integer-arithmetic-combinations (- a) (- b))))
(define (run-tests)
(test-begin "numbers")
(test 0 (expt 0 1))
(test 1 (expt 3 0))
(test 3 (expt 3 1))
(test 1/3 (expt 3 -1))
(test 1/300000000000000000000 (expt 300000000000000000000 -1))
(test '(536870912 536870913 536870911 -536870912 -536870911 -536870913)
(integer-neighborhoods (expt 2 29)))
(test '(1073741824 1073741825 1073741823
-1073741824 -1073741823 -1073741825)
(integer-neighborhoods (expt 2 30)))
(test '(2147483648 2147483649 2147483647
-2147483648 -2147483647 -2147483649)
(integer-neighborhoods (expt 2 31)))
(test '(4294967296 4294967297 4294967295
-4294967296 -4294967295 -4294967297)
(integer-neighborhoods (expt 2 32)))
(test '(4611686018427387904 4611686018427387905 4611686018427387903
-4611686018427387904 -4611686018427387903 -4611686018427387905)
(integer-neighborhoods (expt 2 62)))
(test '(9223372036854775808 9223372036854775809 9223372036854775807
-9223372036854775808 -9223372036854775807 -9223372036854775809)
(integer-neighborhoods (expt 2 63)))
(test '(18446744073709551616 18446744073709551617 18446744073709551615
-18446744073709551616 -18446744073709551615 -18446744073709551617)
(integer-neighborhoods (expt 2 64)))
(test '(85070591730234615865843651857942052864
85070591730234615865843651857942052865
85070591730234615865843651857942052863
-85070591730234615865843651857942052864
-85070591730234615865843651857942052863
-85070591730234615865843651857942052865)
(integer-neighborhoods (expt 2 126)))
(test '(170141183460469231731687303715884105728
170141183460469231731687303715884105729
170141183460469231731687303715884105727
-170141183460469231731687303715884105728
-170141183460469231731687303715884105727
-170141183460469231731687303715884105729)
(integer-neighborhoods (expt 2 127)))
(test '(340282366920938463463374607431768211456
340282366920938463463374607431768211457
340282366920938463463374607431768211455
-340282366920938463463374607431768211456
-340282366920938463463374607431768211455
-340282366920938463463374607431768211457)
(integer-neighborhoods (expt 2 128)))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; fix x fix
(test '((1 -1 0 0 0) (1 -1 0 0 0) (-1 1 0 0 0) (-1 1 0 0 0))
(sign-combinations 0 1))
(test '((2 0 1 1 0) (0 -2 -1 -1 0) (0 2 -1 -1 0) (-2 0 1 1 0))
(sign-combinations 1 1))
(test '((59 25 714 2 8) (-25 -59 -714 -2 -8)
(25 59 -714 -2 8) (-59 -25 714 2 -8))
(sign-combinations 42 17))
;; fix x big
(test '((4294967338 -4294967254 180388626432 0 42)
(4294967254 -4294967338 -180388626432 0 -42)
(-4294967254 4294967338 -180388626432 0 42)
(-4294967338 4294967254 180388626432 0 -42))
(sign-combinations 42 (expt 2 32)))
;; big x fix
(test '((4294967338 4294967254 180388626432 102261126 4)
(-4294967254 -4294967338 -180388626432 -102261126 -4)
(4294967254 4294967338 -180388626432 -102261126 4)
(-4294967338 -4294967254 180388626432 102261126 -4))
(sign-combinations (expt 2 32) 42))
;; big x bigger
(test '((12884901889 -4294967297 36893488151714070528 0 4294967296)
(4294967297 -12884901889 -36893488151714070528 0 -4294967296)
(-4294967297 12884901889 -36893488151714070528 0 4294967296)
(-12884901889 4294967297 36893488151714070528 0 -4294967296))
(sign-combinations (expt 2 32) (+ 1 (expt 2 33))))
(test '((18446744078004518913 -18446744069414584321
79228162514264337597838917632
0 4294967296)
(18446744069414584321 -18446744078004518913
-79228162514264337597838917632
0 -4294967296)
(-18446744069414584321 18446744078004518913
-79228162514264337597838917632
0 4294967296)
(-18446744078004518913 18446744069414584321
79228162514264337597838917632
0 -4294967296))
(sign-combinations (expt 2 32) (+ 1 (expt 2 64))))
;; bigger x big
(test '((12884901889 4294967297 36893488151714070528 2 1)
(-4294967297 -12884901889 -36893488151714070528 -2 -1)
(4294967297 12884901889 -36893488151714070528 -2 1)
(-12884901889 -4294967297 36893488151714070528 2 -1))
(sign-combinations (+ 1 (expt 2 33)) (expt 2 32)))
(test '((18446744078004518913 18446744069414584321
79228162514264337597838917632
4294967296 1)
(-18446744069414584321 -18446744078004518913
-79228162514264337597838917632
-4294967296 -1)
(18446744069414584321 18446744078004518913
-79228162514264337597838917632
-4294967296 1)
(-18446744078004518913 -18446744069414584321
79228162514264337597838917632
4294967296 -1))
(sign-combinations (+ 1 (expt 2 64)) (expt 2 32)))
(test '((170141183460469231750134047789593657344
170141183460469231713240559642174554110
3138550867693340382088035895064302439764418281874191810559
9223372036854775807
9223372036854775808)
(-170141183460469231713240559642174554110
-170141183460469231750134047789593657344
-3138550867693340382088035895064302439764418281874191810559
-9223372036854775807
-9223372036854775808)
(170141183460469231713240559642174554110
170141183460469231750134047789593657344
-3138550867693340382088035895064302439764418281874191810559
-9223372036854775807
9223372036854775808)
(-170141183460469231750134047789593657344
-170141183460469231713240559642174554110
3138550867693340382088035895064302439764418281874191810559
9223372036854775807
-9223372036854775808))
(sign-combinations (- (expt 2 127) 1) (+ 1 (expt 2 64))))
;; fixnum-bignum boundaries (machine word - 1 bit for sign - 2
;; bits for tag)
(test 8191 (- -8191))
(test 8192 (- -8192))
(test 8193 (- -8193))
(test 536870911 (- -536870911))
(test 536870912 (- -536870912))
(test 536870913 (- -536870913))
(test 2305843009213693951 (- -2305843009213693951))
(test 2305843009213693952 (- -2305843009213693952))
(test 2305843009213693953 (- -2305843009213693953))
(test 42535295865117307932921825928971026431
(- -42535295865117307932921825928971026431))
(test 42535295865117307932921825928971026432
(- -42535295865117307932921825928971026432))
(test 42535295865117307932921825928971026433
(- -42535295865117307932921825928971026433))
(test '((536879104 -536862720 4398046511104 0 8192)
(536862720 -536879104 -4398046511104 0 -8192)
(-536862720 536879104 -4398046511104 0 8192)
(-536879104 536862720 4398046511104 0 -8192))
(sign-combinations (expt 2 13) (expt 2 29)))
(test '((536879104 536862720 4398046511104 65536 0)
(-536862720 -536879104 -4398046511104 -65536 0)
(536862720 536879104 -4398046511104 -65536 0)
(-536879104 -536862720 4398046511104 65536 0))
(sign-combinations (expt 2 29) (expt 2 13)))
(test '((2305843009750564864 -2305843008676823040
1237940039285380274899124224 0 536870912)
(2305843008676823040 -2305843009750564864
-1237940039285380274899124224 0 -536870912)
(-2305843008676823040 2305843009750564864
-1237940039285380274899124224 0 536870912)
(-2305843009750564864 2305843008676823040
1237940039285380274899124224 0 -536870912))
(sign-combinations (expt 2 29) (expt 2 61)))
(test '((2305843009750564864 2305843008676823040
1237940039285380274899124224 4294967296 0)
(-2305843008676823040 -2305843009750564864
-1237940039285380274899124224 -4294967296 0)
(2305843008676823040 2305843009750564864
-1237940039285380274899124224 -4294967296 0)
(-2305843009750564864 -2305843008676823040
1237940039285380274899124224 4294967296 0))
(sign-combinations (expt 2 61) (expt 2 29)))
(test '((42535295865117307935227668938184720384
-42535295865117307930615982919757332480
98079714615416886934934209737619787751599303819750539264
0
2305843009213693952)
(42535295865117307930615982919757332480
-42535295865117307935227668938184720384
-98079714615416886934934209737619787751599303819750539264
0
-2305843009213693952)
(-42535295865117307930615982919757332480
42535295865117307935227668938184720384
-98079714615416886934934209737619787751599303819750539264
0
2305843009213693952)
(-42535295865117307935227668938184720384
42535295865117307930615982919757332480
98079714615416886934934209737619787751599303819750539264
0
-2305843009213693952))
(sign-combinations (expt 2 61) (expt 2 125)))
(test '((42535295865117307935227668938184720384
42535295865117307930615982919757332480
98079714615416886934934209737619787751599303819750539264
18446744073709551616
0)
(-42535295865117307930615982919757332480
-42535295865117307935227668938184720384
-98079714615416886934934209737619787751599303819750539264
-18446744073709551616
0)
(42535295865117307930615982919757332480
42535295865117307935227668938184720384
-98079714615416886934934209737619787751599303819750539264
-18446744073709551616
0)
(-42535295865117307935227668938184720384
-42535295865117307930615982919757332480
98079714615416886934934209737619787751599303819750539264
18446744073709551616
0))
(sign-combinations (expt 2 125) (expt 2 61)))
;; Regression tests for an overflow in bignum addition
(test 8589869056
(+ 4294934528 4294934528))
(test 36893488143124135936
(+ 18446744071562067968 18446744071562067968))
(test 680564733841876926908302470789826871296
(+ 340282366920938463454151235394913435648
340282366920938463454151235394913435648))
(test 231584178474632390847141970017375815706199686964360189615451793408394491068416
(+ 115792089237316195423570985008687907853099843482180094807725896704197245534208
115792089237316195423570985008687907853099843482180094807725896704197245534208))
(test #f (< +nan.0 +nan.0))
(test #f (<= +nan.0 +nan.0))
(test #f (= +nan.0 +nan.0))
(test #f (>= +nan.0 +nan.0))
(test #f (> +nan.0 +nan.0))
(test #f (< +inf.0 +inf.0))
(test #t (<= +inf.0 +inf.0))
(test #t (= +inf.0 +inf.0))
(test #t (>= +inf.0 +inf.0))
(test #f (> +inf.0 +inf.0))
(test #f (< -inf.0 -inf.0))
(test #t (<= -inf.0 -inf.0))
(test #t (= -inf.0 -inf.0))
(test #t (>= -inf.0 -inf.0))
(test #f (> -inf.0 -inf.0))
(test #t (< -inf.0 +inf.0))
(test #t (<= -inf.0 +inf.0))
(test #f (= -inf.0 +inf.0))
(test #f (>= -inf.0 +inf.0))
(test #f (> -inf.0 +inf.0))
(test 88962710306127702866241727433142015
(string->number "#x00112233445566778899aabbccddeeff"))
(test (expt 10 154) (sqrt (expt 10 308)))
(test 36893488147419103231
(- 340282366920938463463374607431768211456
340282366920938463426481119284349108225))
(test '(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0)
(call-with-values (lambda () (exact-integer-sqrt (expt 10 308)))
list))
(test '(31622776601683793319988935444327185337195551393252168268575048527925944386392382213442481083793002951873472841528400551485488560304538800146905195967001539 2115514206302273599980766398157920200790560418205865231071804946360990550570367022991069288361418688781500755061112588417520206827470474760717813571631479)
(call-with-values (lambda () (exact-integer-sqrt (expt 10 309)))
list))
;; Steele's three-part test.
(test #t #t)
(test 100 (/ (factorial 100) (factorial 99)))
(test -0.549306144334055+1.5707963267949i (atanh -2))
;; ... and variants
(test -9900 (/ (- (factorial 100)) (factorial 98)))
(test -10100 (/ (factorial 101) (- (factorial 99))))
(test 100 (/ (- (factorial 100)) (- (factorial 98)) 99))
(test 100000000000000000000000
(string->number "100000000000000000000e3"))
(test 1/100+8i
(string->number "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-102+8i"))
(test #t (< 1/2 1.0))
(test #t (< 1.0 3/2))
(test #t (< 1/2 1.5))
(test #t (< 1/2 2.0))
(test 1.0 (max 1/2 1.0))
(test 18446744073709551617 (numerator (/ 18446744073709551617 2)))
(test "18446744073709551617/2" (number->string (/ 18446744073709551617 2)))
(let ((a 1000000000000000000000000000000000000000)
(b 31622776601683794000))
(test 31622776601683792639 (quotient a b))
(test 30922992657207634000 (remainder a b)))
(let ((g 18446744073709551616/6148914691236517205))
(test 36893488147419103231/113427455640312821148309287786019553280
(- g (/ 9 g))))
(let ((r (/ (expt 2 61) 3)))
(test 0 (- r r))
(test 2305843009213693952/3 r))
(let ((x (+ (expt 2 32) +2))
(y (+ (expt 2 32) -1)))
(test 0(remainder (* x y) y))
(test 0(remainder (* x y) x)))
(let ((x (+ (expt 2 64) +2))
(y (+ (expt 2 64) -1)))
(test 0(remainder (* x y) y))
(test 0(remainder (* x y) x)))
(test-end))))