Prelude.Number.Float

Documentation

data Float :: *

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances

Enum Float

Eq Float

Floating Float

Fractional Float

Num Float

Ord Float

Read Float

Real Float

RealFloat Float

RealFrac Float

Show Float

data Double :: *

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances

Enum Double

Eq Double

Floating Double

Fractional Double

Num Double

Ord Double

Read Double

Real Double

RealFloat Double

RealFrac Double

Show Double

class Fractional a => Floating a where

Trigonometric and hyperbolic functions and related functions.

Minimal complete definition: pi, exp, log, sin, cos, sinh, cosh, asin, acos, atan, asinh, acosh and atanh

Minimal complete definition

pi, exp, log, sin, cos, asin, atan, acos, sinh, cosh, asinh, atanh, acosh

Methods

pi :: a

exp :: a -> a

sqrt :: a -> a

log :: a -> a

(**) :: a -> a -> a infixr 8

logBase :: a -> a -> a

sin :: a -> a

tan :: a -> a

cos :: a -> a

asin :: a -> a

atan :: a -> a

acos :: a -> a

sinh :: a -> a

tanh :: a -> a

cosh :: a -> a

asinh :: a -> a

atanh :: a -> a

acosh :: a -> a

Instances

Floating Double

Floating Float

class (RealFrac a, Floating a) => RealFloat a where

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition: all except exponent, significand, scaleFloat and atan2

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

floatRadix :: a -> Integer

a constant function, returning the radix of the representation (often 2)

floatDigits :: a -> Int

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: a -> (Int, Int)

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int)

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: Integer -> Int -> a

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: a -> a

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

scaleFloat :: Int -> a -> a

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool

True if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Instances

RealFloat Double

RealFloat Float