[Haskell] numeric type

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 twoIntegerS.
Word	Fixed-precision unsigned integer; storage size sameInt
Word8	8-bit unsigned integer
Word16	16-bit unsigned integer
Word32	32-bit unsigned integer
Word64	64-bit unsigned integer

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
RationalOr anyRatio				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/	Fromintegral
Rational	Fromrational	Truncate*	Truncate*	N/

Table 6.2. Selected numeric functions and constants

Item	Type	Module	Description
(+)	Num A => A->	Prelude	Addition
(-)	Num A => A->	Prelude	Subtraction
(*)	Num A => A->	Prelude	Multiplication
(/)	Fractional A => A->	Prelude	Fractional Division
(**)	Floating A => A->	Prelude	Raise to the power
(^)	(Num A, integral B) => A-> B->	Prelude	Raise a number to a non-negative, integral power
(^)	(Fractional A, integral B) => A-> B->	Prelude	Raise a fractional number to any integral power
(%)	Integral A => A-> Ratio	Data. Ratio	Ratio Composition
(.&.)	Bits A => A->	Data. Bits	Bitwise AND
(. | .)	Bits A => A->	Data. Bits	Bitwise OR
ABS	Num A => A->	Prelude	Absolute Value
Approxrational	Realfrac A => A-> rational	Data. Ratio	Approximate rational composition based on Fractional numerators and denominators
Cos	Floating A => A->	Prelude	Cosine. Also provided areACOs,Cosh, AndAcossh, With the same type.
Div	Integral A => A->	Prelude	Integer Division always truncated down; see alsoQuot
Frominteger	Num A => integer->	Prelude	Conversion fromIntegerTo any numeric type
Fromintegral	(Integral A, num B) => A-> B	Prelude	More general conversion from anyIntegralTo any numeric type
Fromrational	Fractional A => rational->	Prelude	Conversion fromRational. May be lossy.
Log	Floating A => A->	Prelude	Natural logarithm
Logbase	Floating A => A->	Prelude	Log with explicit Base
Maxbound	Bounded A =>	Prelude	The maximum value of a bounded type
Minbound	Bounded A =>	Prelude	The minimum value of a bounded type
MoD	Integral A => A->	Prelude	Integer Modulus
Pi	Floating A =>	Prelude	Mathematical constant pi
Quot	Integral A => A->	Prelude	Integer Division; fractional part of quotient truncated towards zero
Recip	Fractional A => A->	Prelude	Reciprocal
Rem	Integral A => A->	Prelude	Remainder of Integer Division
Round	(Realfrac A, integral B) => A-> B	Prelude	Rounds to nearest integer
Shift	Bits A => A-> int->	Bits	Shift left by the specified number of BITs, which may be negative for a right shift.
Sin	Floating A => A->	Prelude	SINE. Also provided areAsin,Sinh, AndAsinh, With the same type.
SQRT	Floating A => A->	Prelude	Square Root
Tan	Floating A => A->	Prelude	Tangent. Also provided areAtan,Tanh, AndAtanh, With the same type.
Tointeger	Integral A => A-> integer	Prelude	Convert anyIntegralToInteger
Torational	Real A => A-> rational	Prelude	Convert losslesslyRational
Truncate	(Realfrac A, integral B) => A-> B	Prelude	Truncates number towards zero
XOR	Bits A => A->	Data. Bits	Bitwise exclusive or