Currency Conversion

This exercise builds on the integer arithmetic from Leah's Luscious Lasagna. Here you will work with floating- point numbers and pick the right division word for the job.

Integers and floats

Factor distinguishes integers (1, 42, 1_000_000) from floating- point numbers (1.0, 3.14, 6.02e23). If you mix an integer and a float in one calculation, the result comes out as a float:

2 3 + .      ! => 5
2 3.0 + .    ! => 5.0

You can put underscores inside a number to group the digits — 1_000_000 — and Factor just ignores them.

Division words

Factor has separate division words. They all live in the math vocabulary.

/    ( x y -- x/y )    ! exact: ratio for two integers, float if either is a float
/f   ( x y -- f   )    ! always a float
/i   ( x y -- q   )    ! integer division (truncates toward zero)
mod  ( x y -- r   )    ! remainder
/mod ( x y -- q r )    ! quotient and remainder together

1 2 / .        ! => 1/2     (a proper ratio)
16 3 / .       ! => 5+1/3   (an improper ratio, printed as a mixed numeral)
16 3 /f .      ! => 5.333333333333333
16 3 /i .      ! => 5      (truncated)
16 3 mod .     ! => 1
16 3 /mod .s   ! quotient and remainder in one pass
! => 5
! => 1
16.0 3 / .     ! => 5.333333333333333

/ produces a ratio (Factor's exact rational type) for two integers, or a float if either input is a float. /f forces a float result even for two integers. /i always truncates toward zero.

Checking

Number predicates from math, math.functions, and math.primes:

zero?    ( x       -- ? )
even?    ( x       -- ? )
odd?     ( x       -- ? )
prime?   ( x       -- ? )
divisor? ( m n     -- ? )    ! true when n divides m
integer? ( x       -- ? )    ! true for ints (fixnum or bignum)
float?   ( x       -- ? )    ! true for floats
number?  ( x       -- ? )    ! true for any numeric kind

0 zero? .            ! => t
0.0 zero? .          ! => t
3 zero? .            ! => f

4 even? .            ! => t
7 even? .            ! => f
7 odd? .             ! => t

7 prime? .           ! => t
9 prime? .           ! => f

15 5 divisor? .      ! => t   (5 divides 15)
15 4 divisor? .      ! => f

Float to integer

floor, ceiling, and round from the math.functions vocabulary all return a float (3.0, not 3). To get a true integer, chain >integer:

3.7 floor >integer .       ! => 3
3.2 ceiling >integer .     ! => 4

Powers and absolute value

sq, ^, and abs (in math.functions) compute squares, arbitrary powers, and absolute values:

sq  ( x   -- x*x )
^   ( x y -- x^y )
abs ( x   -- |x| )

5 sq .          ! => 25
2 10 ^ .        ! => 1024
2 0.5 ^ .       ! => 1.4142135623730951
-7 abs .        ! => 7
3 abs .         ! => 3

Min and max

min ( x y -- z ) and max ( x y -- z ) (in math.order) return the lesser or greater of two numbers:

3 7 min .       ! => 3
3 7 max .       ! => 7

The most common use is clamping — pinning a value to a floor with max (e.g., 0 max keeps a value non-negative) or to a ceiling with min.

Ordering predicates

math.order also provides before?, after?, before=?, after=? for comparison predicates that work on any orderable type — numbers, strings, characters:

before?  ( obj1 obj2 -- ? )   ! obj1 <  obj2
before=? ( obj1 obj2 -- ? )   ! obj1 <= obj2
after?   ( obj1 obj2 -- ? )   ! obj1 >  obj2
after=?  ( obj1 obj2 -- ? )   ! obj1 >= obj2

Use these instead of </<= when the values might be strings — the arithmetic operators don't dispatch on strings.