Modular arithmetic: Difference between revisions
Added an example for D
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=={{header|D}}==
<lang D>import std.stdio;
version(unittest) {
void assertEquals(T)(T actual, T expected) {
import core.exception;
import std.conv;
if (actual != expected) {
throw new AssertError("Actual [" ~ to!string(actual) ~ "]; Expected [" ~ to!string(expected) ~ "]");
}
}
}
void main() {
auto input = ModularInteger(10,13);
auto output = f(input);
writeln("f(", input, ") = ", output);
}
V f(V)(const V x) {
return x^^100 + x + 1;
}
/// Integer tests on f
unittest {
assertEquals(f(1), 3);
assertEquals(f(0), 1);
}
/// Floating tests on f
unittest {
assertEquals(f(1.0), 3.0);
assertEquals(f(0.0), 1.0);
}
struct ModularInteger {
private:
int value;
int modulus;
public:
this(int value, int modulus) {
this.modulus = modulus;
this.value = value % modulus;
}
ModularInteger opBinary(string op : "+")(ModularInteger rhs) const in {
assert(this.modulus == rhs.modulus);
} body {
return ModularInteger((this.value + rhs.value) % this.modulus, this.modulus);
}
ModularInteger opBinary(string op : "+")(int rhs) const {
return ModularInteger((this.value + rhs) % this.modulus, this.modulus);
}
ModularInteger opBinary(string op : "*")(ModularInteger rhs) const in {
assert(this.modulus == rhs.modulus);
assert(this.value < this.modulus);
assert(rhs.value < this.modulus);
} body {
return ModularInteger((this.value * rhs.value) % this.modulus, this.modulus);
}
ModularInteger opBinary(string op : "^^")(int pow) const in {
assert(pow >= 0);
} body {
auto base = ModularInteger(1, this.modulus);
while (pow-- > 0) {
base = base * this;
}
return base;
}
string toString() {
import std.format;
return format("ModularInteger(%s, %s)", value, modulus);
}
}
/// Addition with same type of int
unittest {
auto a = ModularInteger(2,5);
auto b = ModularInteger(3,5);
assertEquals(a+b, ModularInteger(0,5));
}
/// Addition with differnt int types
unittest {
auto a = ModularInteger(2,5);
assertEquals(a+0, a);
assertEquals(a+1, ModularInteger(3,5));
}
/// Muliplication
unittest {
auto a = ModularInteger(2,5);
auto b = ModularInteger(3,5);
assertEquals(a*b, ModularInteger(1,5));
}
/// Power
unittest {
const a = ModularInteger(3,13);
assertEquals(a^^2, ModularInteger(9,13));
assertEquals(a^^3, ModularInteger(1,13));
const b = ModularInteger(10,13);
assertEquals(b^^1, ModularInteger(10,13));
assertEquals(b^^2, ModularInteger(9,13));
assertEquals(b^^3, ModularInteger(12,13));
assertEquals(b^^4, ModularInteger(3,13));
assertEquals(b^^5, ModularInteger(4,13));
assertEquals(b^^6, ModularInteger(1,13));
assertEquals(b^^7, ModularInteger(10,13));
assertEquals(b^^8, ModularInteger(9,13));
assertEquals(b^^10, ModularInteger(3,13));
assertEquals(b^^20, ModularInteger(9,13));
assertEquals(b^^30, ModularInteger(1,13));
assertEquals(b^^50, ModularInteger(9,13));
assertEquals(b^^75, ModularInteger(12,13));
assertEquals(b^^90, ModularInteger(1,13));
assertEquals(b^^95, ModularInteger(4,13));
assertEquals(b^^97, ModularInteger(10,13));
assertEquals(b^^98, ModularInteger(9,13));
assertEquals(b^^99, ModularInteger(12,13));
assertEquals(b^^100, ModularInteger(3,13));
}</lang>
{{out}}
<pre>
f(ModularInteger(10, 13)) = ModularInteger(1, 13)
</pre>
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