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/*
Implement some basic math functions.
*/
/* basic arithmetic and algebra */
int factorial(int n) {
int prod := 1;
repeat
prod := prod * n;
n := n - 1;
until n <= 1
return prod;
}
float pow(float x, int y) {
if x = 0 then return 0; end
if x = 1 || y = 0 then return 1; end
/* handle negative powers */
negative_pow := sgn(y) < 0;
y := abs(y);
float result := 1;
repeat
result := result * x;
y := y - 1;
until y = 0
if negative_pow then result := 1 / result; end
return result;
}
float abs(float a) {
if a < 0 then return -a; end
return a;
}
int sgn(float x) {
if x > 0 then return 1; end
if x < 0 then return -1; end
return 0;
}
float round(float a, int n) {
int mag := 1;
if n > 0 then
repeat
mag := mag * 10;
n := n - 1;
until n = 0
end
int trunc := a * mag + 0.5;
return trunc / mag;
}
int div(int a, int b) {
int quo := a / b;
return quo;
}
int mod(int a, int b) {
int quo := a / b;
int ret := a - quo * b;
if ret < 0 then ret := ret + b; end
return ret;
}
float sqrt(float a) {
float eps := 0.00000000001;
float y := a / 2.0;
repeat
if abs(y * y - a) < eps then return y; end
y := (y + a / y) / 2;
until 0
}
float hypot(float x, float y) {
return sqrt(x * x + y * y);
}
/* Some trig functions */
float pi() { return 3.14159265358979323846; }
float rad(float deg) { return deg * pi() / 180.0; }
float deg(float rad) { return rad * 180.0 / pi(); }
float sin(float rad_) {
/* Taylor series expansion of sin(x) */
float x := rad_;
int mult := 1;
float sum := x;
int n := 1;
int exponent := 1;
repeat
n := n + 1;
mult := -mult;
exponent := exponent + 2;
sum := sum + mult * (pow(x, exponent) / factorial(exponent));
until n >= 12
return sum;
}
float cos(float rad_) {
/* Taylor series expansion of cos(x) */
float sum := 1;
int n := 1;
int exponent := 0;
int mult := 1;
repeat
n := n + 1;
mult := -mult;
exponent := exponent + 2;
sum := sum + mult * pow(rad_, exponent) / factorial(exponent);
until n >= 12
return sum;
}
float tan(float rad_) {
min_cos := 1e-18;
float num := sin(rad_);
float den := cos(rad_);
/* Avoid division by zero */
if abs(den) < min_cos then den := sgn(den) * min_cos; end
return num / den;
}
float exp(float x) {
/* Taylor series expansion of eˣ */
float sum := 1.0;
int n := 0;
if x > 0 then
repeat
n := n + 1;
sum := sum + pow(x, n) / factorial(n);
until n >= 12
end
return sum;
}
int main() {
int i := 1;
repeat
write "sqrt("; write i; write ") = =";
write round(sqrt(i), 4);
write endl;
i := i + 1;
until i > 10
int a:= 0;
int b;
repeat
a := a + 1;
b := a - 1;
repeat
b := b + 1;
write "hypot("; write a; write ", "; write b; write ") = ";
write round(hypot(a, b), 3);
write endl;
until b >= 10
until a = 10
write "rad(180) = "; write rad(180); write endl;
write "deg(pi()) = "; write deg(pi()); write endl;
write "sin(rad(30)) = "; write sin(rad(30)); write endl;
write "sin(rad(90)) = "; write sin(rad(90)); write endl;
write "cos(rad(60)) = "; write cos(rad(60)); write endl;
write "cos(rad(90)) = "; write cos(rad(90)); write endl;
write "cos(rad(180)) = "; write cos(rad(180)); write endl;
write "tan(rad(45)) = "; write tan(rad(45)); write endl;
write "tan(0) = "; write tan(0); write endl;
write "tan(pi() / 2) = "; write tan(pi() / 2); write endl;
write "pow(10, 0) = "; write pow(10, 0); write endl;
write "pow(10, 1) = "; write pow(10, 1); write endl;
write "pow(10, 2) = "; write pow(10, 2); write endl;
write "exp(0) = "; write exp(0); write endl;
write "exp(1) = "; write exp(1); write endl;
i := -5;
repeat
write "mod("; write i; write ", 3) = ";
write mod(i, 3); write endl;
i := i + 1;
until i > 5
return 0;
}
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