File: [local] / OpenXM_contrib / PHC / Ada / Math_Lib / Numbers / ts_natnum.adb (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:26 2000 UTC (23 years, 8 months ago) by maekawa
Branch: PHC, MAIN
CVS Tags: v2, maekawa-ipv6, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, HEAD Changes since 1.1: +0 -0
lines
Import the second public release of PHCpack.
OKed by Jan Verschelde.
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with text_io,integer_io; use text_io,integer_io;
with Multprec_Natural_Numbers; use Multprec_Natural_Numbers;
with Multprec_Natural_Numbers_io; use Multprec_Natural_Numbers_io;
with Multprec_Random_Numbers; use Multprec_Random_Numbers;
procedure ts_natnum is
-- DESCRIPTION :
-- This procedure offers interactive and random testers for the
-- operations with multi-precision natural numbers. See the menu below.
procedure Test_Creation is
n : natural;
nn : Natural_Number;
ans : character;
begin
put_line("Testing the creation of a natural number.");
loop
put("Give a standard natural number : "); get(n);
nn := Create(n);
put("-> as natural number : "); put(nn); new_line;
Clear(nn);
put("Do you want more tests ? (y/n) "); get(ans);
exit when ans /= 'y';
end loop;
end Test_Creation;
procedure Test_io is
ans : character;
n : Natural_Number;
begin
put_line("Testing the input/output operations.");
loop
put("Give a number : "); get(n);
put("-> your number : "); put(n); new_line;
put("#decimal places : "); put(Decimal_Places(n),1); new_line;
put("Do you want more tests ? (y/n) "); get(ans);
exit when ans /= 'y';
end loop;
end Test_io;
procedure Test_Compare ( n1 : in Natural_Number; n2 : in natural ) is
begin
if Equal(n1,n2)
then put_line("The numbers are equal.");
else put_line("The numbers are different.");
end if;
if n1 < n2
then put_line("First is less than second.");
else put_line("First not less than second.");
end if;
if n1 > n2
then put_line("First is greater than second.");
else put_line("First is not greater than second.");
end if;
end Test_Compare;
procedure Test_Compare ( n1 : in natural; n2 : in Natural_Number ) is
begin
if Equal(n2,n1)
then put_line("Both numbers are equal.");
else put_line("The numbers are different.");
end if;
if n1 < n2
then put_line("First is less than second.");
else put_line("First not less than second.");
end if;
if n1 > n2
then put_line("First is greater than second.");
else put_line("First is not greater than second.");
end if;
end Test_Compare;
procedure Test_Compare ( n1,n2 : in Natural_Number ) is
begin
if Equal(n1,n2)
then put_line("Both numbers are equal.");
else put_line("The numbers are different.");
end if;
if n1 < n2
then put_line("First is less than second.");
else put_line("First not less than second.");
end if;
if n1 > n2
then put_line("First is greater than second.");
else put_line("First is not greater than second.");
end if;
end Test_Compare;
procedure Test_Comparison is
ans : character;
n1,n2 : Natural_Number;
-- n1 : natural;
begin
put_line("Testing the comparison operations.");
loop
put("Give 1st number n1 : "); get(n1);
put("-> n1 : "); put(n1); new_line;
put("Give 2nd number n2 : "); get(n2);
put("-> n2 : "); put(n2); new_line;
Test_Compare(n1,n2);
Copy(n1,n2);
put_line("Tests after copying : ");
Test_Compare(n1,n2);
Div(n1,10);
put_line("After dividing n1 by 10 :");
put(" n1 : "); put(n1); new_line;
put(" n2 : "); put(n2); new_line;
put("Do you want more tests ? (y/n) "); get(ans);
exit when ans /= 'y';
end loop;
end Test_Comparison;
procedure Test_Addition is
-- NOTE : to test n1+n2 with n2 a standard natural,
-- just change the declaration of n2.
ans : character;
n1,n2,sum1,sum2 : Natural_Number;
begin
put_line("Testing the addition operations.");
loop
put("Give 1st number : "); get(n1);
put("-> your 1st number n1 : "); put(n1); new_line;
put("Give 2nd number : "); get(n2);
put("-> your 2nd number n2 : "); put(n2); new_line;
sum1 := n1+n2;
put("n1+n2 : "); put(sum1); new_line;
sum2 := n2+n1;
put("n2+n1 : "); put(sum2); new_line;
if Equal(sum1,sum2)
then put_line("Test on commutativity is successful.");
else put_line("Failure, sum not commutative: bug!");
end if;
put("Do you want more tests ? (y/n) "); get(ans);
exit when ans /= 'y';
end loop;
end Test_Addition;
function Mult_by_Add ( n1 : Natural_Number; n2 : natural )
return Natural_Number is
-- DESCRIPTION :
-- Does the multiplication by adding up n1 to itself as many times
-- as the number n2. Only to be used as test of course.
res : Natural_Number;
begin
if n2 = 0
then return res;
else Copy(n1,res);
for i in 1..n2-1 loop
Add(res,n1);
end loop;
return res;
end if;
end Mult_by_Add;
function Mult_by_Add ( n1,n2 : Natural_Number ) return Natural_Number is
-- DESCRIPTION :
-- Does the multiplication by adding up n1 to itself as many times
-- as the number n2. Only to be used as test of course.
-- This can be quite time consuming as n2 gets large.
res,cnt : Natural_Number;
begin
if Equal(n2,0)
then return res;
else Copy(n1,res);
cnt := Create(1);
while not Equal(cnt,n2) loop
Add(res,n1);
Add(cnt,1);
end loop;
Clear(cnt);
return res;
end if;
end Mult_by_Add;
procedure Test_Multiplication is
-- NOTE : to test n1*n2 with n2 : natural, change the declaration of n2.
ans : character;
n1,prod1,prod2,prod3 : Natural_Number;
n2 : natural;
begin
put_line("Testing the multiplication operations.");
loop
put("Give 1st number : "); get(n1);
put("-> your 1st number : "); put(n1); new_line;
put("Give 2nd number : "); get(n2);
put("-> your 2nd number : "); put(n2); new_line;
prod1 := n1*n2;
put("Product n1*n2 : "); put(prod1); new_line;
prod2 := n2*n1;
put("Product n2*n1 : "); put(prod2); new_line;
if Equal(prod1,prod2)
then put_line("Test on commutativity is successful.");
else put_line("Failure, product not commutative: bug!");
end if;
put("Do you want multiplication by addition ? (y/n) "); get(ans);
if ans = 'y'
then put_line("Testing the multiplication by addition. Be patient...");
prod3 := Mult_by_Add(n1,n2);
put("After adding "); put(n2); put(" times : "); put(prod3);
new_line;
if Equal(prod1,prod3)
then put_line("Test of multiplication is successful.");
else put_line("Failure, bug detected.");
end if;
end if;
put("Do you want more tests ? (y/n) "); get(ans);
exit when ans /= 'y';
end loop;
end Test_Multiplication;
procedure Test_Exponentiation is
ans : character;
n,e1,e2,exp1,exp2,prod,expo : Natural_Number;
begin
put_line("Testing the exponentiation operations.");
loop
put("Give a number : "); get(n);
put("-> your number n : "); put(n); new_line;
put("Give 1st exponent : "); get(e1);
put("-> your 1st exponent e1 : "); put(e1); new_line;
exp1 := n**e1;
put("n**e1 : "); put(exp1); new_line;
put("Give 2nd exponent : "); get(e2);
put("-> your 2nd exponent e2 : "); put(e2); new_line;
exp2 := n**e2;
put("n**e2 : "); put(exp2); new_line;
prod := exp1*exp2;
put("(n**e1)*(n**e2) : "); put(prod); new_line;
expo := n**(e1+e2);
put("n**(e1+e2) : "); put(expo); new_line;
if Equal(prod,expo)
then put_line("Test of exponentiation is successful.");
else put_line("Failure, bug detected.");
end if;
put("Do you want more tests ? (y/n) "); get(ans);
exit when ans /= 'y';
end loop;
end Test_Exponentiation;
procedure Test_Subtraction is
ans : character;
n1,n2,diff : Natural_Number;
begin
put_line("Testing the subtraction operations.");
loop
put("Give 1st number : "); get(n1);
put("-> your 1st number n1 : "); put(n1); new_line;
put("Give 2nd number : "); get(n2);
put("-> your 2nd number n2 : "); put(n2); new_line;
diff := n1-n2;
put("n1 - n2 : "); put(diff); new_line;
Add(diff,n2);
put("(n1-n2)+n2 : "); put(diff); new_line;
if Equal(diff,n1)
then put_line("Test of subtraction is successful.");
else put_line("Failure, bug detected.");
end if;
put("Do you want more tests ? (y/n) "); get(ans);
exit when ans /= 'y';
end loop;
end Test_Subtraction;
procedure Divide10 ( n : in Natural_Number ) is
-- DESCRIPTION :
-- Checks whether the number n is divisible by 1..10.
quot,prod : Natural_Number;
rest : natural;
begin
put("n : "); put(n); new_line;
for i in 1..10 loop
rest := Rmd(n,i);
quot := n/i;
if rest = 0
then put("Divisible by "); put(i,1);
else put("Not divisible by "); put(i,1);
end if;
put(" rest : "); put(rest,1); new_line;
put("quotient : "); put(quot); new_line;
prod := quot*i + rest;
if Equal(prod,n)
then put_line("Test on Remainder/Division is successful.");
else put_line("Failure, bug detected.");
end if;
end loop;
end Divide10;
procedure Test_Division is
ans : character;
n1,n2,quot,prod,rest : Natural_Number;
-- n2,rest : natural;
begin
put_line("Testing the division operations.");
loop
put("Give 1st number : "); get(n1);
put("-> your 1st number n1 : "); put(n1); new_line;
put("Give 2nd number : "); get(n2);
put("-> your 2nd number n2 : "); put(n2); new_line;
prod := n1*n2;
put("n1*n2 : "); put(prod); new_line;
quot := prod/n2; rest := Rmd(prod,n2);
put("(n1*n2)/n2 : "); put(quot); new_line;
put("Remainder : "); put(rest); new_line;
if Equal(quot,n1) and Equal(rest,0)
then put_line("Test of division is successful.");
else put_line("Failure, bug detected.");
end if;
Div(n1,n2,quot,rest);
put("n1/n2 : "); put(quot); new_line;
put("rest : "); put(rest); new_line;
prod := quot*n2 + rest;
if Equal(prod,n1)
then put_line("Test of division/remainder computation is successful.");
else put_line("Failure, bug detected.");
end if;
-- if n2 <= 10
-- then Divide10(n1);
-- end if;
put("Do you want more tests ? (y/n) "); get(ans);
exit when ans /= 'y';
end loop;
end Test_Division;
procedure Random_Addition_and_Subtraction ( sz1,sz2 : in natural ) is
-- DESCRIPTION :
-- Three tests are performed:
-- 1) n1+n2-n2 = n1, with "+" and "-".
-- 2) Add(n1,n2) is the same as n1 := n1+n2?
-- 3) Sub(n1+n2,n1) leads to n2?
n1,n2,sum1,sum2 : Natural_Number;
procedure Report_Bug is
begin
new_line;
put(" n1 : "); put(n1); new_line;
put(" n2 : "); put(n2); new_line;
end Report_Bug;
begin
n1 := Random(sz1);
n2 := Random(sz2);
sum1 := n1+n2;
sum2 := sum1-n2;
if Equal(sum2,n1)
then put("n1+n2-n2 okay");
else put("n1+n2-n2 Bug!"); Report_Bug;
end if;
Add(sum2,n2);
if Equal(sum2,sum1)
then put(" Add okay");
else put(" Add Bug!"); Report_Bug;
end if;
Sub(sum2,n1);
if Equal(sum2,n2)
then put(" Sub okay"); new_line;
else put(" Sub Bug!"); Report_Bug;
end if;
Clear(n1); Clear(n2);
Clear(sum1); Clear(sum2);
end Random_Addition_and_Subtraction;
procedure Additions_and_Subtractions_on_Randoms is
-- DESCRIPTION :
-- Generates a number of random naturals and performs repeated
-- additions and subtractions with checks on consistencies.
nb,sz1,sz2 : natural;
begin
put("Give the number of tests : "); get(nb);
put("Give the size of the 1st number : "); get(sz1);
put("Give the size of the 2nd number : "); get(sz2);
for i in 1..nb loop
Random_Addition_and_Subtraction(sz1,sz2);
end loop;
end Additions_and_Subtractions_on_Randoms;
procedure Random_Multiplication_and_Division ( sz1,sz2 : in natural ) is
-- DESCRIPTION :
-- Four tests are performed :
-- 1) n1*n2/n2 = n1, with "*" and "/".
-- 2) Mul(n1,n2) is the same as n1 := n1*n2 ?
-- 3) Div(n1*n2,n1) leads to n2 ?
-- 4) n1 = (n1/n2)*n2 + Rmd(n1,n2) ?
-- 5) Div(n1,n2,q,r) satisfies n1 = q*n2 + r ?
n1,n2,prod1,prod2,quot1,quot2,quot3,rest1,rest2 : Natural_Number;
procedure Report_Bug is
begin
new_line;
put(" n1 : "); put(n1); new_line;
put(" n2 : "); put(n2); new_line;
end Report_Bug;
begin
n1 := Random(sz1);
n2 := Random(sz2);
prod1 := n1*n2;
quot1 := prod1/n2;
if Equal(quot1,n1)
then put("n1*n2/n2 okay");
else put("n1*n2/n2 Bug!"); Report_Bug;
end if;
Mul(quot1,n2);
if Equal(prod1,quot1)
then put(" Mul okay");
else put(" Mul Bug!"); Report_Bug;
end if;
Div(prod1,n1);
if Equal(prod1,n2)
then put(" Div okay");
else put(" Div Bug!"); Report_Bug;
end if;
rest1 := Rmd(n1,n2);
quot2 := n1/n2;
prod2 := quot2*n2;
Add(prod2,rest1);
if Equal(prod2,n1)
then put(" Rmd okay");
else put(" Rmd Bug!"); Report_Bug;
end if;
Div(n1,n2,quot3,rest2);
Mul(quot3,n2);
Add(quot3,rest2);
if Equal(quot3,n1)
then put(" Div/Rmd okay"); new_line;
else put(" Div/Rmd Bug!"); Report_Bug;
end if;
Clear(n1); Clear(n2);
Clear(prod1); Clear(quot1);
Clear(prod2); Clear(quot2);
Clear(quot3); Clear(rest1); Clear(rest2);
end Random_Multiplication_and_Division;
procedure Multiplications_and_Divisions_on_Randoms is
-- DESCRIPTION :
-- Generates a number of random naturals and performs repeated
-- multiplications and divisions with checks on consistencies.
nb,sz1,sz2 : natural;
begin
put("Give the number of tests : "); get(nb);
put("Give the size of the 1st number : "); get(sz1);
put("Give the size of the 2nd number : "); get(sz2);
for i in 1..nb loop
Random_Multiplication_and_Division(sz1,sz2);
end loop;
end Multiplications_and_Divisions_on_Randoms;
procedure Main is
ans : character;
begin
new_line;
put_line("Interactive testing of multi-precision natural numbers.");
loop
new_line;
put_line("Choose one of the following : ");
put_line(" 0. exit program 1. Input/Output 2. Creation ");
put_line(" 3. Comparison/Copy 4. Addition 5. Subtraction ");
put_line(" 6. Multiplication 7. Exponentiation 8. Division ");
put_line(" 9. Addition/subtraction on randomly generated numbers. ");
put_line(" A. Multiplication/division/remainder on random numbers. ");
put("Type in your choice (0,1,2,3,4,5,6,7,8,9 or A) : "); get(ans);
exit when (ans = '0');
new_line;
case ans is
when '1' => Test_io;
when '2' => Test_Creation;
when '3' => Test_Comparison;
when '4' => Test_Addition;
when '5' => Test_Subtraction;
when '6' => Test_Multiplication;
when '7' => Test_Exponentiation;
when '8' => Test_Division;
when '9' => Additions_and_Subtractions_on_Randoms;
when 'A' => Multiplications_and_Divisions_on_Randoms;
when others => null;
end case;
end loop;
end Main;
begin
Main;
end ts_natnum;