simple_fraction

default_create

create f.default_create

Creates zero (0/1).

Postconditions: is_zero, denominator = 1

make

create f.make (a_numerator, a_denominator: INTEGER_64)

Creates fraction from numerator and denominator. Automatically reduces to lowest terms.

Precondition: a_denominator /= 0

Postconditions: is_reduced, denominator > 0

Example:

create f.make (2, 4)   -- Automatically reduces to 1/2

make_integer

create f.make_integer (a_value: INTEGER_64)

Creates fraction from integer (value/1).

Postconditions: numerator = a_value, denominator = 1

make_mixed

create f.make_mixed (a_whole, a_numerator, a_denominator: INTEGER_64)

Creates from mixed number: whole + numerator/denominator.

Preconditions: a_denominator /= 0, a_numerator >= 0, a_denominator > 0

Example:

create f.make_mixed (2, 3, 4)  -- 2 3/4 = 11/4

make_from_string

create f.make_from_string (a_str: READABLE_STRING_GENERAL)

Creates from string. Accepts: "3/4", "-1/2", "5", "2 3/4", "0.5"

Precondition: a_str /= Void and then not a_str.is_empty

make_zero

create f.make_zero

Creates zero (0/1).

make_one

create f.make_one

Creates one (1/1).

numerator

numerator: INTEGER_64

The numerator (top number). May be negative.

denominator

denominator: INTEGER_64

The denominator (bottom number). Always positive.

Invariant: denominator > 0

is_zero

is_zero: BOOLEAN

True if numerator = 0.

is_negative

is_negative: BOOLEAN

True if numerator < 0.

is_positive

is_positive: BOOLEAN

True if numerator > 0 (not zero, not negative).

is_integer

is_integer: BOOLEAN

True if denominator = 1 (whole number).

is_proper

is_proper: BOOLEAN

True if |numerator| < denominator. Example: 3/4 is proper.

is_improper

is_improper: BOOLEAN

True if |numerator| >= denominator. Example: 5/4 is improper.

is_reduced

is_reduced: BOOLEAN

True if fraction is in lowest terms. Always true due to automatic reduction.

is_unit_fraction

is_unit_fraction: BOOLEAN

True if numerator = 1. Examples: 1/2, 1/3, 1/4.

is_less alias "<"

is_less alias "<" (other: like Current): BOOLEAN

True if current fraction is less than other.

is_equal

is_equal (other: like Current): BOOLEAN

True if fractions are mathematically equal.

to_double

to_double: DOUBLE

Converts to double (may lose precision for fractions like 1/3).

to_integer

to_integer: INTEGER_64

Converts to integer (truncates toward zero).

whole_part

whole_part: INTEGER_64

The whole number portion. Example: 11/4 returns 2.

fractional_part

fractional_part: SIMPLE_FRACTION

The fractional remainder. Example: 11/4 returns 3/4.

Postconditions: Result.is_proper or Result.is_zero, not Result.is_negative

out

out: STRING

String as "numerator/denominator" or just "integer" if denominator = 1.

to_string

to_string: STRING

Same as out.

to_mixed_string

to_mixed_string: STRING

String as mixed number "whole num/den". Examples: 11/4 returns "2 3/4", 3/4 returns "3/4".

to_decimal_string

to_decimal_string (a_places: INTEGER): STRING

Decimal representation to specified places.

Precondition: a_places >= 0

add alias "+"

add alias "+" (other: like Current): SIMPLE_FRACTION

Sum of current and other.

subtract alias "-"

subtract alias "-" (other: like Current): SIMPLE_FRACTION

Difference of current and other.

multiply alias "*"

multiply alias "*" (other: like Current): SIMPLE_FRACTION

Product of current and other.

divide alias "/"

divide alias "/" (other: like Current): SIMPLE_FRACTION

Quotient of current divided by other.

Precondition: not other.is_zero

negate

negate: SIMPLE_FRACTION

Negated value (flips sign).

absolute

absolute: SIMPLE_FRACTION

Absolute value.

Postcondition: not Result.is_negative

reciprocal

reciprocal: SIMPLE_FRACTION

Reciprocal (1/this = denominator/numerator).

Precondition: not is_zero

Postcondition: (Current * Result).is_equal (one)

power

power (n: INTEGER): SIMPLE_FRACTION

Current raised to integer power n. Negative powers use reciprocal.

Example: (2/3).power(2) = 4/9, (2/3).power(-1) = 3/2

scale

scale (a_factor: INTEGER_64): SIMPLE_FRACTION

Multiply by integer factor.

Example: (1/4).scale(3) = 3/4

scale_down

scale_down (a_factor: INTEGER_64): SIMPLE_FRACTION

Divide by integer factor.

Precondition: a_factor /= 0

Example: (3/4).scale_down(2) = 3/8

zero

zero: SIMPLE_FRACTION

Returns new zero fraction.

one

one: SIMPLE_FRACTION

Returns new fraction equal to 1.

half

half: SIMPLE_FRACTION

Returns 1/2.

third

third: SIMPLE_FRACTION

Returns 1/3.

quarter

quarter: SIMPLE_FRACTION

Returns 1/4.

halves

halves (n: INTEGER_64): SIMPLE_FRACTION

Returns n/2.

thirds

thirds (n: INTEGER_64): SIMPLE_FRACTION

Returns n/3.

quarters

quarters (n: INTEGER_64): SIMPLE_FRACTION

Returns n/4.

eighths

eighths (n: INTEGER_64): SIMPLE_FRACTION

Returns n/8.

sixteenths

sixteenths (n: INTEGER_64): SIMPLE_FRACTION

Returns n/16.