[haskell] 数值的类型

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 `Integer`s.
`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 6.3. 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
Source 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

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