Haskell Numeric Types

From http://book.realworldhaskell.org/read/using-typeclasses.html

Table 6.1. Selected Numeric Types

Type	Description
Double	Double-precision floating point. A common choice for floating-point data.
Float	Single-precision floating point. Often used when interfacing with C.
Int	Fixed-precision signed integer; minimum range [-2^29..2^29-1]. Commonly used.
Int8	8-bit signed integer
Int16	16-bit signed integer
Int32	32-bit signed integer
Int64	64-bit signed integer
Integer	Arbitrary-precision signed integer; range limited only by machine resources. Commonly used.
Rational	Arbitrary-precision rational numbers. Stored as a ratio of two Integers.
Word	Fixed-precision unsigned integer; storage size same as Int
Word8	8-bit unsigned integer
Word16	16-bit unsigned integer
Word32	32-bit unsigned integer
Word64	64-bit unsigned integer

Table 6.2. Selected Numeric Functions and Constants

Item	Type	Module	Description
(+)	Num a => a -> a -> a	Prelude	Addition
(-)	Num a => a -> a -> a	Prelude	Subtraction
(*)	Num a => a -> a -> a	Prelude	Multiplication
(/)	Fractional a => a -> a -> a	Prelude	Fractional division
(**)	Floating a => a -> a -> a	Prelude	Raise to the power of
(^)	(Num a, Integral b) => a -> b -> a	Prelude	Raise a number to a non-negative, integral power
(^^)	(Fractional a, Integral b) => a -> b -> a	Prelude	Raise a fractional number to any integral power
(%)	Integral a => a -> a -> Ratio a	Data.Ratio	Ratio composition
(.&.)	Bits a => a -> a -> a	Data.Bits	Bitwise and
(.|.)	Bits a => a -> a -> a	Data.Bits	Bitwise or
abs	Num a => a -> a	Prelude	Absolute value
approxRational	RealFrac a => a -> a -> Rational	Data.Ratio	Approximate rational composition based on fractional numerators and denominators
cos	Floating a => a -> a	Prelude	Cosine. Also provided are acos, cosh, and acosh, with the same type.
div	Integral a => a -> a -> a	Prelude	Integer division always truncated down; see also quot
fromInteger	Num a => Integer -> a	Prelude	Conversion from an Integer to any numeric type
fromIntegral	(Integral a, Num b) => a -> b	Prelude	More general conversion from any Integral to any numeric type
fromRational	Fractional a => Rational -> a	Prelude	Conversion from a Rational. May be lossy.
log	Floating a => a -> a	Prelude	Natural logarithm
logBase	Floating a => a -> a -> a	Prelude	Log with explicit base
maxBound	Bounded a => a	Prelude	The maximum value of a bounded type
minBound	Bounded a => a	Prelude	The minimum value of a bounded type
mod	Integral a => a -> a -> a	Prelude	Integer modulus
pi	Floating a => a	Prelude	Mathematical constant pi
quot	Integral a => a -> a -> a	Prelude	Integer division; fractional part of quotient truncated towards zero
recip	Fractional a => a -> a	Prelude	Reciprocal
rem	Integral a => a -> a -> a	Prelude	Remainder of integer division
round	(RealFrac a, Integral b) => a -> b	Prelude	Rounds to nearest integer
shift	Bits a => a -> Int -> a	Bits	Shift left by the specified number of bits, which may be negative for a right shift.
sin	Floating a => a -> a	Prelude	Sine. Also provided are asin, sinh, and asinh, with the same type.
sqrt	Floating a => a -> a	Prelude	Square root
tan	Floating a => a -> a	Prelude	Tangent. Also provided are atan, tanh, and atanh, with the same type.
toInteger	Integral a => a -> Integer	Prelude	Convert any Integral to an Integer
toRational	Real a => a -> Rational	Prelude	Convert losslessly to Rational
truncate	(RealFrac a, Integral b) => a -> b	Prelude	Truncates number towards zero
xor	Bits a => a -> a -> a	Data.Bits	Bitwise exclusive or

Table 6.3. Typeclass Instances for Numeric Types

Type	Bits	Bounded	Floating	Fractional	Integral	Num	Real	RealFrac
Double			X	X		X	X	X
Float			X	X		X	X	X
Int	X	X			X	X	X
Int16	X	X			X	X	X
Int32	X	X			X	X	X
Int64	X	X			X	X	X
Integer	X				X	X	X
Rational or any Ratio				X		X	X	X
Word	X	X			X	X	X
Word16	X	X			X	X	X
Word32	X	X			X	X	X
Word64	X	X			X	X	X

Table 6.4. Conversion Between Numeric Types

Source Type	Destination Type
	Double, Float	Int, Word	Integer	Rational
Double, Float	fromRational . toRational	truncate *	truncate *	toRational
Int, Word	fromIntegral	fromIntegral	fromIntegral	fromIntegral
Integer	fromIntegral	fromIntegral	N/A	fromIntegral
Rational	fromRational	truncate *	truncate *	N/A