open Test;;
open Nat;;
open Big_int;;
open Ratio;;
open Int_misc;;
open Arith_status;;

set_error_when_null_denominator false;;

let infinite_failure = "infinite or undefined rational number";;

testing_function "create_ratio";;

let r = create_ratio (big_int_of_int 1) (big_int_of_int (-2)) in
test 1 eq_big_int (numerator_ratio r, big_int_of_int (-1)) && 
test 2 eq_big_int (denominator_ratio r, big_int_of_int 2);;

let r = create_ratio (big_int_of_int 2) (big_int_of_int 3) in
test 3 eq_big_int (numerator_ratio r, big_int_of_int 2) && 
test 4 eq_big_int (denominator_ratio r, big_int_of_int 3);;

set_normalize_ratio true;;

let r = create_ratio (big_int_of_int 12) (big_int_of_int (-16)) in
test 5 eq_big_int (numerator_ratio r, big_int_of_int (-3)) && 
test 6 eq_big_int (denominator_ratio r, big_int_of_int 4);;

set_normalize_ratio false;;

let r = create_ratio (big_int_of_int 0) (big_int_of_int 0) in
test 7 eq_big_int (numerator_ratio r, big_int_of_int 0) && 
test 8 eq_big_int (denominator_ratio r, big_int_of_int 0);;

testing_function "create_normalized_ratio";;

let r = create_normalized_ratio (big_int_of_int 1) (big_int_of_int (-2)) in
test 1 eq_big_int (numerator_ratio r, big_int_of_int (-1)) && 
test 2 eq_big_int (denominator_ratio r, big_int_of_int 2);;

let r = create_normalized_ratio (big_int_of_int 2) (big_int_of_int 3) in
test 3 eq_big_int (numerator_ratio r, big_int_of_int 2) && 
test 4 eq_big_int (denominator_ratio r, big_int_of_int 3);;

set_normalize_ratio true;;

let r = create_normalized_ratio (big_int_of_int 12) (big_int_of_int (-16)) in
test 5 eq_big_int (numerator_ratio r, big_int_of_int (-12)) && 
test 6 eq_big_int (denominator_ratio r, big_int_of_int 16);;

set_normalize_ratio false;;

let r = create_normalized_ratio (big_int_of_int 1) (big_int_of_int 0) in
test 7 eq_big_int (numerator_ratio r, big_int_of_int 1) && 
test 8 eq_big_int (denominator_ratio r, big_int_of_int 0);;

let r = create_normalized_ratio (big_int_of_int 0) (big_int_of_int 0) in
test 9 eq_big_int (numerator_ratio r, big_int_of_int 0) && 
test 10 eq_big_int (denominator_ratio r, big_int_of_int 0);;

testing_function "null_denominator";;

test 1
 eq (null_denominator (create_ratio (big_int_of_int 1) (big_int_of_int (-2))),
     false);;
test 2 eq
 (null_denominator (create_ratio (big_int_of_int 1) zero_big_int),true);;

(*****
testing_function "verify_null_denominator";;

test 1
 eq (verify_null_denominator (ratio_of_string "0/1"), false);;
test 2
 eq (verify_null_denominator (ratio_of_string "0/0"), true);;
*****)

testing_function "sign_ratio";;

test 1
eq_int (sign_ratio (create_ratio (big_int_of_int (-2)) (big_int_of_int (-3))), 
        1);;
test 2
eq_int (sign_ratio (create_ratio (big_int_of_int 2) (big_int_of_int (-3))), 
        (-1));;
test 3
eq_int (sign_ratio (create_ratio zero_big_int (big_int_of_int (-3))), 0);;

testing_function "normalize_ratio";;

let r = create_ratio (big_int_of_int 12) (big_int_of_int (-16)) in
normalize_ratio r;
test 1 eq_big_int (numerator_ratio r, big_int_of_int (-3)) && 
test 2 eq_big_int (denominator_ratio r, big_int_of_int 4);;

let r = create_ratio (big_int_of_int (-1)) zero_big_int in
normalize_ratio r;
test 3 eq_big_int (numerator_ratio r, big_int_of_int (-1)) && 
test 4 eq_big_int (denominator_ratio r, zero_big_int);;

testing_function "report_sign_ratio";;

test 1 
eq_big_int (report_sign_ratio 
            (create_ratio (big_int_of_int 2) (big_int_of_int (-3))) 
            (big_int_of_int 1),
            big_int_of_int (-1));;
test 2
eq_big_int (report_sign_ratio 
            (create_ratio (big_int_of_int 2) (big_int_of_int 3)) 
             (big_int_of_int 1),
            big_int_of_int 1);;

testing_function "is_integer_ratio";;

test 1 eq
 (is_integer_ratio (create_ratio (big_int_of_int 2) (big_int_of_int (-1))),
  true);;
test 2 eq
 (is_integer_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 3)),
  false);;

testing_function "add_ratio";;

let r = add_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 2)) 
                   (create_ratio (big_int_of_int 2) (big_int_of_int 3)) in
test 1 eq_big_int (numerator_ratio r, big_int_of_int 7) && 
test 2 eq_big_int (denominator_ratio r, big_int_of_int 6);;

let r = add_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 3)) 
                   (create_ratio (big_int_of_int 1) (big_int_of_int (-2))) in
test 3 eq_big_int (numerator_ratio r, big_int_of_int 1) && 
test 4 eq_big_int (denominator_ratio r, big_int_of_int 6);;

let r = add_ratio (create_ratio (big_int_of_int 2) zero_big_int) 
                   (create_ratio (big_int_of_int 1) (big_int_of_int (-2))) in
test 5 eq_big_int (numerator_ratio r, big_int_of_int 4) && 
test 6 eq_big_int (denominator_ratio r, zero_big_int);;

let r = add_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 3)) 
                   (create_ratio (big_int_of_int 1) zero_big_int) in
test 7 eq_big_int (numerator_ratio r, big_int_of_int 3) && 
test 8 eq_big_int (denominator_ratio r, zero_big_int);;

let r = add_ratio (create_ratio (big_int_of_int 2) zero_big_int) 
                   (create_ratio (big_int_of_int 1) zero_big_int) in
test 9 eq_big_int (numerator_ratio r, zero_big_int) && 
test 10 eq_big_int (denominator_ratio r, zero_big_int);;

let r = add_ratio (create_ratio (big_int_of_string "12724951") 
                                 (big_int_of_string "26542080")) 
                   (create_ratio (big_int_of_string "-1") 
                                 (big_int_of_string "81749606400")) in
test 11 eq_big_int (numerator_ratio r, 
                     big_int_of_string "1040259735682744320") && 
test 12 eq_big_int (denominator_ratio r, 
                     big_int_of_string "2169804593037312000");;

let r1,r2 =
 (create_ratio (big_int_of_string "12724951") 
                                 (big_int_of_string "26542080"), 
                   create_ratio (big_int_of_string "-1") 
                                 (big_int_of_string "81749606400")) in

let bi1 = mult_big_int (numerator_ratio r1) (denominator_ratio r2)
and  bi2 = mult_big_int (numerator_ratio r2) (denominator_ratio r1) 
in
test 1
eq_big_int (bi1,
            big_int_of_string "1040259735709286400")
&& 
test 2
eq_big_int (bi2,
            big_int_of_string "-26542080")
&& test 3
eq_big_int (mult_big_int (denominator_ratio r1) (denominator_ratio r2),
            big_int_of_string "2169804593037312000")
&& test 4
eq_big_int (add_big_int bi1 bi2,
            big_int_of_string "1040259735682744320")
;;

testing_function "sub_ratio";;

let r = sub_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 3)) 
                   (create_ratio (big_int_of_int 1) (big_int_of_int 2)) in
test 1  eq_big_int (numerator_ratio r, big_int_of_int 1) && 
test 2 eq_big_int (denominator_ratio r, big_int_of_int 6);;

let r = sub_ratio (create_ratio (big_int_of_int 2) zero_big_int) 
                   (create_ratio (big_int_of_int 1) (big_int_of_int (-2))) in
test 3 eq_big_int (numerator_ratio r, big_int_of_int 4) && 
test 4 eq_big_int (denominator_ratio r, zero_big_int);;

let r = sub_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 3)) 
                   (create_ratio (big_int_of_int 1) zero_big_int) in
test 5 eq_big_int (numerator_ratio r, big_int_of_int (-3)) && 
test 6 eq_big_int (denominator_ratio r, zero_big_int);;

let r = sub_ratio (create_ratio (big_int_of_int 2) zero_big_int) 
                   (create_ratio (big_int_of_int 1) zero_big_int) in
test 7 eq_big_int (numerator_ratio r, zero_big_int) && 
test 8 eq_big_int (denominator_ratio r, zero_big_int);;

testing_function "mult_ratio";;

let r = mult_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 3)) 
                    (create_ratio (big_int_of_int 7) (big_int_of_int 5)) in
test 1 eq_big_int (numerator_ratio r, big_int_of_int 14) && 
test 2 eq_big_int (denominator_ratio r, big_int_of_int 15);;

let r = mult_ratio (create_ratio (big_int_of_int 2) zero_big_int) 
                    (create_ratio (big_int_of_int 1) (big_int_of_int (-2))) in
test 3 eq_big_int (numerator_ratio r, big_int_of_int (-2)) &&
test 4 eq_big_int (denominator_ratio r, zero_big_int);;

let r = mult_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 3)) 
                   (create_ratio (big_int_of_int 1) zero_big_int) in
test 5 eq_big_int (numerator_ratio r, big_int_of_int 2) && 
test 6 eq_big_int (denominator_ratio r, zero_big_int);;

let r = mult_ratio (create_ratio (big_int_of_int 2) zero_big_int) 
                   (create_ratio (big_int_of_int 1) zero_big_int) in
test 7 eq_big_int (numerator_ratio r, big_int_of_int 2) && 
test 8 eq_big_int (denominator_ratio r, zero_big_int);;

testing_function "div_ratio";;

let r = div_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 3)) 
                   (create_ratio (big_int_of_int 5) (big_int_of_int 7)) in
test 1 eq_big_int (numerator_ratio r, big_int_of_int 14) && 
test 2 eq_big_int (denominator_ratio r, big_int_of_int 15);;

let r = div_ratio (create_ratio (big_int_of_int 2) zero_big_int) 
                   (create_ratio (big_int_of_int 1) (big_int_of_int (-2))) in
test 3 eq_big_int (numerator_ratio r, big_int_of_int (-4)) && 
test 4 eq_big_int (denominator_ratio r, zero_big_int);;

let r = div_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 3)) 
                   (create_ratio (big_int_of_int 1) zero_big_int) in
test 5 eq_big_int (numerator_ratio r, zero_big_int) && 
test 6 eq_big_int (denominator_ratio r, big_int_of_int 3);;

let r = div_ratio (create_ratio (big_int_of_int 2) zero_big_int) 
                   (create_ratio (big_int_of_int 1) zero_big_int) in
test 7 eq_big_int (numerator_ratio r, zero_big_int) && 
test 8 eq_big_int (denominator_ratio r, zero_big_int);;

testing_function "integer_ratio";;

test 1 
eq_big_int (integer_ratio 
            (create_ratio (big_int_of_int 5) (big_int_of_int 3)), 
            big_int_of_int 1);;
test 2
eq_big_int (integer_ratio 
            (create_ratio (big_int_of_int 5) (big_int_of_int (-3))), 
            big_int_of_int (-1));;
test 3
eq_big_int (integer_ratio 
            (create_ratio (big_int_of_int 3) (big_int_of_int 2)), 
            big_int_of_int 1);;
test 4
eq_big_int (integer_ratio 
            (create_ratio (big_int_of_int 3) (big_int_of_int (-2))), 
            big_int_of_int (-1));;

failwith_test 5
integer_ratio (create_ratio (big_int_of_int 3) zero_big_int)
(Failure("integer_ratio "^infinite_failure));;

testing_function "floor_ratio";;

test 1
eq_big_int (floor_ratio 
            (create_ratio (big_int_of_int 5) (big_int_of_int 3)), 
            big_int_of_int 1);;
test 2
eq_big_int (floor_ratio 
            (create_ratio (big_int_of_int 5) (big_int_of_int (-3))), 
            big_int_of_int (-2));;
test 3
eq_big_int (floor_ratio 
            (create_ratio (big_int_of_int 3) (big_int_of_int 2)), 
            big_int_of_int 1);;
test 4
eq_big_int (floor_ratio 
            (create_ratio (big_int_of_int 3) (big_int_of_int (-2))), 
            big_int_of_int (-2));;

failwith_test 5 floor_ratio (create_ratio (big_int_of_int 3) zero_big_int)
Division_by_zero;;


testing_function "round_ratio";;

test 1
eq_big_int (round_ratio 
            (create_ratio (big_int_of_int 5) (big_int_of_int 3)), 
            big_int_of_int 2);;
test 2
eq_big_int (round_ratio 
            (create_ratio (big_int_of_int 5) (big_int_of_int (-3))), 
            big_int_of_int (-2));;
test 3
eq_big_int (round_ratio 
            (create_ratio (big_int_of_int 3) (big_int_of_int 2)), 
            big_int_of_int 2);;
test 4
eq_big_int (round_ratio 
            (create_ratio (big_int_of_int 3) (big_int_of_int (-2))), 
            big_int_of_int (-2));;

failwith_test 5
round_ratio (create_ratio (big_int_of_int 3) zero_big_int)
Division_by_zero;;


testing_function "ceiling_ratio";;

test 1
eq_big_int (ceiling_ratio 
            (create_ratio (big_int_of_int 5) (big_int_of_int 3)), 
            big_int_of_int 2);;
test 2
eq_big_int (ceiling_ratio 
            (create_ratio (big_int_of_int 5) (big_int_of_int (-3))), 
            big_int_of_int (-1));;
test 3
eq_big_int (ceiling_ratio 
            (create_ratio (big_int_of_int 3) (big_int_of_int 2)), 
            big_int_of_int 2);;
test 4
eq_big_int (ceiling_ratio 
            (create_ratio (big_int_of_int 3) (big_int_of_int (-2))), 
            big_int_of_int (-1));;
test 5
eq_big_int (ceiling_ratio 
            (create_ratio (big_int_of_int 4) (big_int_of_int 2)), 
            big_int_of_int 2);;
failwith_test 6
ceiling_ratio (create_ratio (big_int_of_int 3) zero_big_int)
Division_by_zero;;

testing_function "eq_ratio";;

test 1
eq_ratio (create_ratio (big_int_of_int 5) (big_int_of_int 3),
          create_ratio (big_int_of_int (-20)) (big_int_of_int (-12)));;
test 2
eq_ratio (create_ratio (big_int_of_int 1) zero_big_int, 
          create_ratio (big_int_of_int 2) zero_big_int);;

let neq_ratio x y = not (eq_ratio x y);;

test 3
neq_ratio (create_ratio (big_int_of_int 1) zero_big_int,
           create_ratio (big_int_of_int (-1)) zero_big_int);;
test 4
neq_ratio (create_ratio (big_int_of_int 1) zero_big_int, 
           create_ratio zero_big_int zero_big_int);;
test 5
eq_ratio (create_ratio zero_big_int zero_big_int, 
          create_ratio zero_big_int zero_big_int);;

testing_function "compare_ratio";;

test 1
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 0)),
        0);;
test 2
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 1) (big_int_of_int 0)),
        0);;
test 3
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)),
        0);;
test 4
eq_int (compare_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 0)),
        0);;
test 5
eq_int (compare_ratio (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 0)),
        0);;
test 6
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 5) (big_int_of_int 3)),
        0);;
test 7
eq_int (compare_ratio (create_ratio (big_int_of_int 5) (big_int_of_int 3)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 0)),
        0);;
test 8
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int (-5)) (big_int_of_int 3)),
        0);;
test 9
eq_int (compare_ratio (create_ratio (big_int_of_int (-5)) (big_int_of_int 3)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 0)),
        0);;
test 10
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 1)),
        0);;
test 11
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 1)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 0)),
        0);;
test 12
eq_int (compare_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 1) (big_int_of_int 0)),
        0);;
test 13
eq_int (compare_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 2) (big_int_of_int 0)),
        0);;
test 14
eq_int (compare_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)),
        1);;
test 15
eq_int (compare_ratio (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 1) (big_int_of_int 0)),
        (-1));;
test 16
eq_int (compare_ratio (create_ratio (big_int_of_int 5) (big_int_of_int 3)) 
                       (create_ratio (big_int_of_int 1) (big_int_of_int 0)), 
        (-1));;
test 17
eq_int (compare_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 5) (big_int_of_int 3)),
        1);;
test 18
eq_int (compare_ratio (create_ratio (big_int_of_int (-5)) (big_int_of_int 3)) 
                       (create_ratio (big_int_of_int 1) (big_int_of_int 0)), 
        (-1));;
test 19
eq_int (compare_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int (-5)) (big_int_of_int 3)),
        1);;
test 20
eq_int (compare_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 3)),
        1);;
test 21
eq_int (compare_ratio (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)),
        0);;
test 22
eq_int (compare_ratio (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int (-2)) (big_int_of_int 0)),
        0);;
test 23
eq_int (compare_ratio (create_ratio (big_int_of_int 5) (big_int_of_int 3)) 
                       (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)), 
        1);;
test 24
eq_int (compare_ratio (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 5) (big_int_of_int 3)),
        (-1));;
test 25
eq_int (compare_ratio (create_ratio (big_int_of_int (-5)) (big_int_of_int 3)) 
                       (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)), 
        1);;
test 26
eq_int (compare_ratio (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int (-5)) (big_int_of_int 3)),
        (-1));;
test 27
eq_int (compare_ratio (create_ratio (big_int_of_int (-1)) (big_int_of_int 0)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 3)),
        (-1));;
test 28
eq_int (compare_ratio (create_ratio (big_int_of_int 5) (big_int_of_int 3)) 
                       (create_ratio (big_int_of_int 3) (big_int_of_int 2)), 
        1);;
test 29
eq_int (compare_ratio (create_ratio (big_int_of_int 3) (big_int_of_int 2)) 
                       (create_ratio (big_int_of_int 5) (big_int_of_int 3)), 
        (-1));;
test 30
eq_int (compare_ratio (create_ratio (big_int_of_int 5) (big_int_of_int 3)) 
                       (create_ratio (big_int_of_int (-3)) (big_int_of_int 2)), 
        1);;
test 31
eq_int (compare_ratio (create_ratio (big_int_of_int (-3)) (big_int_of_int 2)) 
                       (create_ratio (big_int_of_int 5) (big_int_of_int 3)), 
        (-1));;
test 32
eq_int (compare_ratio (create_ratio (big_int_of_int 3) (big_int_of_int 2)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 3)), 
        1);;
test 33
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 2)) 
                       (create_ratio (big_int_of_int 5) (big_int_of_int 3)), 
        (-1));;
test 34
eq_int (compare_ratio (create_ratio (big_int_of_int (-3)) (big_int_of_int 2)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 3)), 
        (-1));;
test 35
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 2)) 
                       (create_ratio (big_int_of_int (-5)) (big_int_of_int 3)), 
        1);;
test 36
eq_int (compare_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 2)) 
                       (create_ratio (big_int_of_int 0) (big_int_of_int 3)), 
        0);;

testing_function "eq_big_int_ratio";;

test 1
eq_big_int_ratio (big_int_of_int 3,  
                  (create_ratio (big_int_of_int 3) (big_int_of_int 1)));;
test 2
eq
(not (eq_big_int_ratio (big_int_of_int 1) 
                       (create_ratio (big_int_of_int 3) (big_int_of_int 1))),
true);;

test 3
eq
(not (eq_big_int_ratio (big_int_of_int 1) 
                       (create_ratio (big_int_of_int 3) (big_int_of_int 2))),
 true);;

test 4
eq
(not (eq_big_int_ratio (big_int_of_int 1) 
                       (create_ratio (big_int_of_int 3) (big_int_of_int 0))),
 true);;

test 5
eq
(not (eq_big_int_ratio (big_int_of_int 1) 
                       (create_ratio (big_int_of_int (-3)) (big_int_of_int 2))),
 true);;

testing_function "compare_big_int_ratio";;

test 1
eq_int (compare_big_int_ratio 
           (big_int_of_int 1) 
            (create_ratio (big_int_of_int 3) (big_int_of_int 0)), (-1));;
test 2
eq_int (compare_big_int_ratio 
           (big_int_of_int 1) 
            (create_ratio (big_int_of_int 0) (big_int_of_int 0)), 0);;
test 3
eq_int (compare_big_int_ratio 
           (big_int_of_int 1) 
            (create_ratio (big_int_of_int (-3)) (big_int_of_int 0)), 1);;
test 4
eq_int (compare_big_int_ratio 
           (big_int_of_int (-1)) 
            (create_ratio (big_int_of_int 3) (big_int_of_int 0)), (-1));;
test 5
eq_int (compare_big_int_ratio 
           (big_int_of_int (-1)) 
            (create_ratio (big_int_of_int 0) (big_int_of_int 0)), 0);;
test 6
eq_int (compare_big_int_ratio 
           (big_int_of_int (-1)) 
            (create_ratio (big_int_of_int (-3)) (big_int_of_int 0)), 1);;
test 7
eq_int (compare_big_int_ratio 
           (big_int_of_int 1) 
            (create_ratio (big_int_of_int 1) (big_int_of_int 1)), 0);;
test 8
eq_int (compare_big_int_ratio 
           (big_int_of_int 1) 
            (create_ratio (big_int_of_int 3) (big_int_of_int 2)), (-1));;
test 9
eq_int (compare_big_int_ratio 
           (big_int_of_int 1) 
            (create_ratio (big_int_of_int 2) (big_int_of_int 3)), 1);;



testing_function "int_of_ratio";;

test 1
eq_int (int_of_ratio (create_ratio (big_int_of_int 4) (big_int_of_int 2)), 
        2);;

test 2
eq_int (int_of_ratio 
        (create_ratio (big_int_of_int biggest_int) (big_int_of_int 1)), 
        biggest_int);;

failwith_test 3
int_of_ratio (create_ratio (big_int_of_int 4) (big_int_of_int 0))
(Failure "integer argument required");;

failwith_test 4
int_of_ratio (create_ratio (succ_big_int (big_int_of_int biggest_int)) 
                             (big_int_of_int 1))
(Failure "integer argument required");;

failwith_test 5
int_of_ratio (create_ratio (big_int_of_int 4) (big_int_of_int 3))
(Failure "integer argument required");;

testing_function "ratio_of_int";;

test 1
eq_ratio (ratio_of_int 3, 
          create_ratio (big_int_of_int 3) (big_int_of_int 1));;
 
test 2
eq_ratio (ratio_of_nat (nat_of_int 2), 
          create_ratio (big_int_of_int 2) (big_int_of_int 1));;

testing_function "nat_of_ratio";;

let nat1 = nat_of_ratio (create_ratio (big_int_of_int 3) (big_int_of_int 1))
and nat2 = nat_of_int 3 in
test 1
eq (eq_nat nat1 0 (length_nat nat1) nat2 0 (length_nat nat2), true)
;;

failwith_test 2
nat_of_ratio (create_ratio (big_int_of_int 3) (big_int_of_int 0))
(Failure "nat_of_ratio");;

failwith_test 3
nat_of_ratio (create_ratio (big_int_of_int (-3)) (big_int_of_int 1))
(Failure "nat_of_ratio");;

failwith_test 4
nat_of_ratio (create_ratio (big_int_of_int 3) (big_int_of_int 2))
(Failure "nat_of_ratio");;

testing_function "ratio_of_big_int";;

test 1
eq_ratio (ratio_of_big_int (big_int_of_int 3), 
          create_ratio (big_int_of_int 3) (big_int_of_int 1));;

testing_function "big_int_of_ratio";;

test 1
eq_big_int (big_int_of_ratio 
                (create_ratio (big_int_of_int 3) (big_int_of_int 1)), 
            big_int_of_int 3);;
test 2
eq_big_int (big_int_of_ratio 
                (create_ratio (big_int_of_int (-3)) (big_int_of_int 1)),
            big_int_of_int (-3));;

failwith_test 3
big_int_of_ratio (create_ratio (big_int_of_int 3) (big_int_of_int 0))
(Failure "big_int_of_ratio");;

testing_function "string_of_ratio";;

test 1
eq_string (string_of_ratio 
              (create_ratio (big_int_of_int 43) (big_int_of_int 35)), 
           "43/35");;
test 2
eq_string (string_of_ratio 
              (create_ratio (big_int_of_int 42) (big_int_of_int 0)), 
           "1/0");;

set_normalize_ratio_when_printing false;;

test 3
eq_string (string_of_ratio 
              (create_ratio (big_int_of_int 42) (big_int_of_int 35)), 
           "42/35");;

set_normalize_ratio_when_printing true;;

test 4
eq_string (string_of_ratio
              (create_ratio (big_int_of_int 42) (big_int_of_int 35)), 
           "6/5");;

testing_function "ratio_of_string";;

test 1
eq_ratio (ratio_of_string ("123/3456"), 
          create_ratio (big_int_of_int 123) (big_int_of_int 3456));;

(***********
test 2
eq_ratio (ratio_of_string ("12.3/34.56"), 
          create_ratio (big_int_of_int 1230) (big_int_of_int 3456));;
test 3
eq_ratio (ratio_of_string ("1.23/325.6"), 
          create_ratio (big_int_of_int 123) (big_int_of_int 32560));;
test 4
eq_ratio (ratio_of_string ("12.3/345.6"), 
          create_ratio (big_int_of_int 123) (big_int_of_int 3456));;
test 5
eq_ratio (ratio_of_string ("12.3/0.0"), 
          create_ratio (big_int_of_int 123) (big_int_of_int 0));;
***********)
test 6
eq_ratio (ratio_of_string ("0/0"), 
          create_ratio (big_int_of_int 0) (big_int_of_int 0));;

test 7
eq_ratio (ratio_of_string "1234567890", 
          create_ratio (big_int_of_string "1234567890") unit_big_int);;
failwith_test 8
ratio_of_string "frlshjkurty" (Failure "invalid digit");;

(***********
testing_function "msd_ratio";;

test 1
eq_int (msd_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 1)),
        0);;
test 2
eq_int (msd_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 12)),
        (-2));;
test 3
eq_int (msd_ratio (create_ratio (big_int_of_int 12) (big_int_of_int 1)),
        1);;
test 4
eq_int (msd_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 2)),
        (-1));;
test 5
eq_int (msd_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 1)),
        0);;
test 6
eq_int (msd_ratio (create_ratio (big_int_of_int 25) (big_int_of_int 21)),
        0);;
test 7
eq_int (msd_ratio (create_ratio (big_int_of_int 35) (big_int_of_int 21)),
        0);;
test 8
eq_int (msd_ratio (create_ratio (big_int_of_int 215) (big_int_of_int 31)),
        0);;
test 9
eq_int (msd_ratio (create_ratio (big_int_of_int 2) (big_int_of_int 30)),
        (-2));;
test 10
eq_int (msd_ratio (create_ratio (big_int_of_int 2345) 
                                     (big_int_of_int 23456)),
        (-2));;
test 11
eq_int (msd_ratio (create_ratio (big_int_of_int 2345) 
                                     (big_int_of_int 2346)),
        (-1));;
test 12
eq_int (msd_ratio (create_ratio (big_int_of_int 2345) 
                                     (big_int_of_int 2344)),
        0);;
test 13
eq_int (msd_ratio (create_ratio (big_int_of_int 23456) 
                                     (big_int_of_int 2345)),
        1);;
test 14
eq_int (msd_ratio (create_ratio (big_int_of_int 23467) 
                                     (big_int_of_int 2345)),
        1);;
failwith_test 15
msd_ratio (create_ratio (big_int_of_int 1) (big_int_of_int 0))
("msd_ratio "^infinite_failure);;
failwith_test 16
msd_ratio (create_ratio (big_int_of_int (-1)) (big_int_of_int 0))
("msd_ratio "^infinite_failure);;
failwith_test 17
msd_ratio (create_ratio (big_int_of_int 0) (big_int_of_int 0))
("msd_ratio "^infinite_failure);;
*************************)

testing_function "round_futur_last_digit";;

let s = "+123456" in
test 1 eq (round_futur_last_digit s 1 (pred (String.length s)), 
            false) &&
test 2 eq_string (s, "+123466");;

let s = "123456" in
test 3 eq (round_futur_last_digit s 0 (String.length s), false) &&
test 4 eq_string (s, "123466");;

let s = "-123456" in
test 5 eq (round_futur_last_digit s 1 (pred (String.length s)),
            false) &&
test 6 eq_string (s, "-123466");;

let s = "+123496" in
test 7 eq (round_futur_last_digit s 1 (pred (String.length s)),
            false) &&
test 8 eq_string (s, "+123506");;

let s = "123496" in
test 9 eq (round_futur_last_digit s 0 (String.length s), false) &&
test 10 eq_string (s, "123506");;

let s = "-123496" in
test 11 eq (round_futur_last_digit s 1 (pred (String.length s)),
            false) &&
test 12 eq_string (s, "-123506");;

let s = "+996" in
test 13 eq (round_futur_last_digit s 1 (pred (String.length s)), 
            true) &&
test 14 eq_string (s, "+006");;

let s = "996" in
test 15 eq (round_futur_last_digit s 0 (String.length s), true) &&
test 16 eq_string (s, "006");;

let s = "-996" in
test 17 eq (round_futur_last_digit s 1 (pred (String.length s)), 
             true) &&
test 18 eq_string (s, "-006");;

let s = "+6666666" in
test 19 eq (round_futur_last_digit s 1 (pred (String.length s)), 
             false) &&
test 20 eq_string (s, "+6666676") ;; 

let s = "6666666" in
test 21 eq (round_futur_last_digit s 0 (String.length s), false) &&
test 22 eq_string (s, "6666676") ;; 

let s = "-6666666" in
test 23 eq (round_futur_last_digit s 1 (pred (String.length s)), 
             false) &&
test 24 eq_string (s, "-6666676") ;; 

testing_function "approx_ratio_fix";;

let s = approx_ratio_fix 5 
                          (create_ratio (big_int_of_int 2) 
                                        (big_int_of_int 3)) in
test 1
eq_string (s, "+0.66667");;

test 2
eq_string (approx_ratio_fix 5 
                             (create_ratio (big_int_of_int 20) 
                                           (big_int_of_int 3)), 
           "+6.66667");;
test 3
eq_string (approx_ratio_fix 5 
                             (create_ratio (big_int_of_int 2) 
                                           (big_int_of_int 30)),
           "+0.06667");;
test 4
eq_string (approx_ratio_fix 5 
                             (create_ratio (big_int_of_string "999996") 
                                           (big_int_of_string "1000000")), 
           "+1.00000");;
test 5
eq_string (approx_ratio_fix 5 
                             (create_ratio (big_int_of_string "299996") 
                                           (big_int_of_string "100000")), 
           "+2.99996");;
test 6
eq_string (approx_ratio_fix 5 
                             (create_ratio (big_int_of_string "2999996") 
                                           (big_int_of_string "1000000")), 
           "+3.00000");;
test 7
eq_string (approx_ratio_fix 4 
                             (create_ratio (big_int_of_string "299996") 
                                           (big_int_of_string "100000")), 
           "+3.0000");;
test 8
eq_string (approx_ratio_fix 5 
                             (create_ratio (big_int_of_int 29996) 
                                           (big_int_of_string "100000")), 
           "+0.29996");;
test 9
eq_string (approx_ratio_fix 5 
                             (create_ratio (big_int_of_int 0) 
                                           (big_int_of_int 1)), 
           "+0");;
failwith_test 10
(approx_ratio_fix 5) (create_ratio (big_int_of_int 1) (big_int_of_int 0))
(Failure "approx_ratio_fix infinite or undefined rational number");;
failwith_test 11
(approx_ratio_fix 5) (create_ratio (big_int_of_int 0) (big_int_of_int 0))
(Failure "approx_ratio_fix infinite or undefined rational number");;

testing_function "approx_ratio_exp";;

test 1
eq_string (approx_ratio_exp 5 
                             (create_ratio (big_int_of_int 2) 
                                           (big_int_of_int 3)), 
           "+0.66667e0");;
test 2
eq_string (approx_ratio_exp 5 
                             (create_ratio (big_int_of_int 20) 
                                           (big_int_of_int 3)), 
           "+0.66667e1");;
test 3
eq_string (approx_ratio_exp 5 
                             (create_ratio (big_int_of_int 2) 
                                           (big_int_of_int 30)), 
           "+0.66667e-1");;
test 4
eq_string (approx_ratio_exp 5 
                             (create_ratio (big_int_of_string "999996") 
                                           (big_int_of_string "1000000")), 
           "+1.00000e0");;
test 5
eq_string (approx_ratio_exp 5 
                             (create_ratio (big_int_of_string "299996") 
                                           (big_int_of_string "100000")), 
           "+0.30000e1");;
test 6
eq_string (approx_ratio_exp 5 
                             (create_ratio (big_int_of_int 29996) 
                                           (big_int_of_string "100000")), 
           "+0.29996e0");;
test 7
eq_string (approx_ratio_exp 5 
                             (create_ratio (big_int_of_int 0) 
                                           (big_int_of_int 1)), 
           "+0.00000e0");;
failwith_test 8
(approx_ratio_exp 5) (create_ratio (big_int_of_int 1) (big_int_of_int 0))
(Failure "approx_ratio_exp infinite or undefined rational number");;
failwith_test 9
(approx_ratio_exp 5) (create_ratio (big_int_of_int 0) (big_int_of_int 0))
(Failure "approx_ratio_exp infinite or undefined rational number");;