StdInt¶
This module can be imported directly or as a part of the StdEnv module.
It provides definition for many critical operations and functions on integers.
Visit StdInt on Cloogle for source code of this module.
Units¶
The integer units follow their definitions in mathematics.
Zero¶
Implementation
// CLEAN
zero :: Int
zero :== 0
Definition
Represents the additive identity of integers.
One¶
Implementation
// CLEAN
one :: Int
one :== 1
Definition
Represents the multiplicative identity of integers.
Math operations¶
The definition and behavior of these operators follow their mathematic counterpart. It is worth noting that, natively, these operations only work with integer operands, but the programmer can define additional behaviors and functionalities.
Addition¶
Signature
// CLEAN
(+) infixl 6 :: Int Int -> Int
(+) a b => ...
Behavior
Adds a and b.
Usage
// CLEAN
1 + 1 // 2
1 + (-1) // 0
(-1) + 1 // 0
(-1) + (-1) // -2
Subtraction¶
Signature
// CLEAN
(-) infixl 6 :: Int Int -> Int
(-) a b => ...
Behavior
Subtracts b from a.
Usage
// CLEAN
1 - 1 // 0
1 - (-1) // 2
(-1) - 1 // -2
(-1) - (-1) // 0
Multiplication¶
Signature
// CLEAN
(*) infixl 7 :: Int Int -> Int
(*) a b => ...
Behavior
Multiplies a and b.
Usage
// CLEAN
1 * 1 // 1
1 * (-1) // -1
(-1) * 1 // -1
(-1) * (-1) // 1
Floor Division¶
Signature
// CLEAN
(/) infixl 7 :: Int Int -> Int
(/) a b => ...
Behavior
Divides a by b rounds the result down to the nearest integer..
Results in a silent run-time crash if b is zero.
Usage
// CLEAN
1 / 1 // 1
1 / (-1) // -1
(-1) / 1 // -1
(-1) / (-1) // 1
7 / 0 // silently crashes
Reminder Division¶
Signature
// CLEAN
(rem) infix 7 :: Int Int -> Int
(rem) a b => ...
and
// CLEAN
(mod) infix 7 :: Int Int -> Int
(mod) a b => ...
Behavior
Returns the reminder after dividing a by b.
Usage
// CLEAN
3 mod (-2) // 1
(-3) mod (-2) // -1
(-3) mod 2 // -1
3 mod 2 // 1
Exponentiation¶
Signature
// CLEAN
(^) infixr 8 :: Int Int -> Int
(^) a b => ...
Behavior
Raises a to the power of b.
Results in a run-time error if b is negative.
$ ^ (Int) called with negative power argument
Usage
// CLEAN
1 ^ 1 // 1
1 ^ (-1) // Run-time error
(-1) ^ 1 // -1
(-1) ^ (-1) // Run-time error
Math functions¶
Some of these "functions" are unary operators, but there is no such thing as a unary operator in CLEAN, so to keep things tidy, I have decided to place them here.
Negation¶
Signature
// CLEAN
~ :: Int -> Int
~ a => ...
Behavior
Inverts the sign a.
Usage
// CLEAN
~ 0 // 0
~ 1 // -1
~(-1) // 1
sign¶
Signature
// CLEAN
sign :: Int -> Int
sign a => ...
Behavior
Returns the sign of a.
Usage
// CLEAN
sign 1 // 1
sign 0 // 0
sign (-1) // -1
abs¶
Signature
// CLEAN
abs :: Int -> Int
abs a => ...
Behavior
Returns the absolute value of a.
Usage
// CLEAN
abs 1 // 1
abs 0 // 0
abs (-1) // 1
gcd¶
Signature
// CLEAN
gcd :: Int Int -> Int
gcd a b => ...
Behavior
Returns the greatest common divisor of a and b.
Usage
// CLEAN
gcd 3 2 // 1
gcd (-3) 2 // 1
gcd 3 (-2) // 1
gcd (-3) (-2) // 1
lcm¶
Signature
// CLEAN
lcm :: Int Int -> Int
lcm a b => ...
Behavior
Returns the least common multiple of a and b.
Usage
// CLEAN
lcm 3 2 // 6
lcm (-3) 2 // 6
lcm 3 (-2) // 6
lcm (-3) (-2) // 6
Relational operations¶
These relations behave in the exact same way as their math counterpart.
Equal to¶
Signature
// CLEAN
(==) infix 4 :: Int Int -> Bool
(==) a b => ...
Behavior
Returns true if a is equal to b.
Otherwise, returns false.
Usage
// CLEAN
5 == 2 // False
(-5) == 2 // False
5 == (-2) // False
(-5) == (-2) // False
(-2) == (-2) // True
Not equal to¶
Signature
// CLEAN
(<>) infix 4 :: Int Int -> Bool
(<>) a b => ...
Behavior
Returns true if a is not equal to b.
Otherwise, returns false.
Usage
// CLEAN
5 <> 2 // True
(-5) <> 2 // True
5 <> (-2) // True
(-5) <> (-2) // True
(-2) <> (-2) // False
Less Than¶
Signature
// CLEAN
(<) infix 4 :: Int Int -> Bool
(<) a b => ...
Behavior
Returns true if a is strictly less than b.
Otherwise, returns false.
Usage
// CLEAN
5 < 2 // False
(-5) < 2 // True
5 < (-2) // False
(-5) < (-2) // True
(-2) < (-2) // False
Less than or equal to¶
Signature
// CLEAN
(<=) infix 4 :: Int Int -> Bool
(<=) a b => ...
Behavior
Returns true if a is less than or equal to b.
Otherwise, returns false.
Usage
// CLEAN
5 <= 2 // False
(-5) <= 2 // True
5 <= (-2) // False
(-5) <= (-2) // True
(-2) <= (-2) // True
Greater than¶
Signature
// CLEAN
(>) infix 4 :: Int Int -> Bool
(>) a b => ...
Behavior
Returns true if a is strictly greater than b.
Otherwise, returns false.
Usage
// CLEAN
5 > 2 // True
(-5) > 2 // False
5 > (-2) // True
(-5) > (-2) // False
(-2) > (-2) // False
Greater than or equal to¶
Signature
// CLEAN
(>=) infix 4 :: Int Int -> Bool
(>=) a b => ...
Behavior
Returns true if a is greater than or equal to b.
Otherwise, returns false.
Usage
// CLEAN
5 >= 2 // True
(-5) >= 2 // False
5 >= (-2) // True
(-5) >= (-2) // False
(-2) >= (-2) // True
Bitwise operations¶
These operators and functions provide a method to interact with the bits of integers.
A quick web search should provide more details about the formal definition of each bitwise operator.
Bitwise and¶
Signature
// CLEAN
(bitand) infixl 6 :: Int Int -> Int
(bitand) a b => ...
Behavior
Returns bitwise AND of a and b.
Usage
// CLEAN
5 bitand 2 // 0
(-5) bitand 2 // 2
5 bitand (-2) // 4
(-5) bitand (-2) // -6
Bitwise or¶
Signature
// CLEAN
(bitor) infixl 6 :: Int Int -> Int
(bitor) a b => ...
Behavior
Returns bitwise OR of a and b.
Usage
// CLEAN
5 bitor 2 // 7
(-5) bitor 2 // -5
5 bitor (-2) // -1
(-5) bitor (-2) // -1
Bitwise exclusive or¶
Signature
// CLEAN
(bitxor) infixl 6 :: Int Int -> Int
(bitxor) a b => ...
Behavior
Returns bitwise XOR of a and b.
Usage
// CLEAN
5 bitxor 2 // 7
(-5) bitxor 2 // -7
5 bitxor (-2) // -5
(-5) bitxor (-2) // 5
Bitwise left shift¶
Signature
// CLEAN
(<<) infix 7 :: Int Int -> Int
(<<) a b => ...
Behavior
Shifts a to the left by b bits.
Usage
// CLEAN
5 << 2 // 20
(-5) << 2 // -20
5 << (-2) // 4611686018427387904
(-5) << (-2) // -4611686018427387904
Bitwise right shift¶
Signature
// CLEAN
(>>) infix 7 :: Int Int -> Int
(>>) a b => ...
Behavior
Shifts a to the right by b bits.
Usage
// CLEAN
5 >> 2 // 1
(-5) >> 2 // -2
5 >> (-2) // 0
(-5) >> (-2) // -1
Bitwise functions¶
There is only one function which classifies under this section, its behavior is not well-documented.
bitnot¶
Signature
// CLEAN
bitnot :: Int -> Int
bitnot a => ...
Behavior
Returns bitwise one-complement of a.
Usage
// CLEAN
bitnot (-5) // -4
bitnot (-2) // 1
bitnot 2 // -3
bitnot 5 // -6
Validator functions¶
These function takes an integer as an argument and check whether it has a certain property or not.
isEven¶
Signature
// CLEAN
isEven :: Int -> Bool
isEven a => ...
Behavior
Returns true if a is an even integer.
Otherwise, returns false.
Usage
// CLEAN
isEven 2 // False
isEven 1 // True
isEven 0 // True
isEven -1 // True
isEven -2 // False
isOdd¶
Signature
// CLEAN
isOdd :: Int -> Bool
isOdd a => ...
Behavior
Returns true if a is an odd integer.
Otherwise, returns false.
Usage
// CLEAN
isOdd 2 // True
isOdd 1 // False
isOdd 0 // False
isOdd -1 // False
isOdd -2 // True
Conversions to integer¶
Natively, three types can convert to integer, namely, real numbers, characters, and strings.
From real number¶
Signature
// CLEAN
toInt :: Real -> Int
toInt a => ...
Behavior
Rounds a up or down to its nearest integer.
Usage
// CLEAN
toInt 1.5 // 2
toInt 1.4 // 1
toInt 0.0 // 0
toInt (-1.4) // -1
toInt (-1.5) // -2
From character¶
Signature
// CLEAN
toInt :: Char -> Int
toInt a => ...
Behavior
Returns the ASCII encoding of a.
Usage
// CLEAN
toInt '1' // 49
toInt '9' // 59
toInt 'A' // 65
toInt 'Z' // 90
toInt 'a' // 97
toInt 'z' // 122
From string¶
Signature
// CLEAN
toInt :: {#Char} -> Int
toInt a => ...
Behavior
Parses a as an integer.
Returns zero if when the parsing is unsuccessful.
The string should only contain decimal digits and the minus sign. The parsing step will be unsuccessful if it contains any other character.
Usage
// CLEAN
toInt "1.0" // 0
toInt "1" // 1
toInt "0" // 0
toInt "-1" // -1
toInt "-1.0" // 0
Conversions from integer¶
The function responsible for type conversion is overloaded, it has the same parameter but different return type, so to use it, the desired type must be unambiguous.
To real number¶
Signature
// CLEAN
fromInt :: Int -> Real
fromInt a => ...
Behavior
Sets the decimal places of a to zeroes.
Usage
// CLEAN
expr :: Real
expr = fromInt 1 // 1.0
expr = fromInt 19 // 19.0
expr = fromInt 0 // 0.0
To character¶
Signature
// CLEAN
fromInt :: Int -> Char
fromInt a => ...
Behavior
Returns the character whose ASCII encoding is a.
Usage
// CLEAN
expr :: Char
expr = fromInt 49 // '1'
expr = fromInt 59 // '9'
expr = fromInt 65 // 'A'
expr = fromInt 90 // 'Z'
expr = fromInt 97 // 'a'
expr = fromInt 122 // 'z'
To string¶
Signature
// CLEAN
fromInt :: Int -> {#Char}
fromInt a => ...
Behavior
Returns the string representation of a.
Usage
// CLEAN
expr :: {#Char}
expr = fromInt 1 // "1"
expr = fromInt 19 // "19"
expr = fromInt 0 // "0"