When you (a coder
) don't have a FPU
to do all the dirty work of decimal arithmetic
for you, and you want your program to be able to perform decimal arithmetic operations, you must use fixed-point
arithmetic. (Or you can use someone else's subroutines
to do it, but they also use fixed-point arithmetic. Back to square one
Lacking an FPU, your (probably old) CPU only has opcodes which will handle integer arithmetic. Therefore you must figure out a way to use the integer functions to perform floating-point operations on your numbers. But how?
Let's say you want to add 10.5 to 5.5.
- Figure out how many powers of 10 you will have to multiply these numbers by to make them integers. In this case, we only need to multiply them by 10^1. (In other words, 10.)
- Perform the multiplication:
10.5 * 10 = 105
5.5 * 10 = 55
- Now add the numbers:
105 + 55 = 160
- Since we are adding, the rule is to divide the result by what we multiplied the originals by. This gives us the decimal result - in this case, 10:
160 / 10 = 16
Subtraction is done the same way. 105 - 55 = 50. 50 / 10 = 5.
Multiplication is done in a similar, but not identical, way:
105 * 55 = 5775. 5775 / 100 = 57.75. (Because the integers were 10 times greater than the real numbers, their multiplied result was 100 (or 10 * 10) times greater than the real result.)
Division is rather an unruly beast, and from what I remember from the ASM class I took in 1996, it is basically done by performing a reciprocal multiplication:
10 / 2 =
100 / 20 =
100 * (1/20) =
You are saved from having to divide the result, since your fraction, being based on the powers of 10, is already reduced. 100/1000 = 10/100 = 1/10.