Harder Than It Looks

Problem

Read a floating point number x from input and print the number x * (x - 1).

22. Harder than it looks, Comet 64

Solution 1

Let x be a floating point number with one digit after the decimal point. Write the expression

x * (x - 1)

as

(x / 10) * [10 * (x - 1)]

The expression

10 * (x - 1) = 10*x - 10

is an integer so it can be stored in the register int. We store x / 10 in the register reg.

reg = input;      // Read the number x.
int = 10 * reg;   // 10*x
int = int - 10;   // 10*x - 10
reg = reg / 10;   // x / 10
reg = reg * int;  // (x / 10) * [10 * (x - 1)]
output = reg;     // Print the result.

Solution 2

This solution is similar to the solution in the section Easier Than It Looks. We transform the input number into an integer and apply the solution in the previous section. Let x be a floating point number with one digit after the decimal point. Write the expression

x * (x - 1)

as

[10*x * 10*(x - 1)] / 100

Store 10*x in the register reg. The expression

10 * (x - 1) = 10*x - 10

is an integer so it can be stored in the register int. Multiply the values of reg and int and store the result in reg. To recover the original expression, we must divide by 100 and use the floating point value. This solution is optimal, according to the game.

reg = 10 * input;  // 10*x
int = reg - 10;    // 10*x - 10
reg = reg * int;   // 10*x * 10*(x - 1)
reg = reg / 100;   // [10*x * 10*(x - 1)] / 100
output = reg;      // Print result.