Portability | BangPatterns |
---|---|

Stability | unstable |

Maintainer | claude@mathr.co.uk |

Safe Haskell | Safe-Inferred |

Implementations of various floating point algorithms. Accuracy has not been extensively verified, and termination has not been proven.

Everything assumes that `floatRadix`

is 2. This is *not* checked.

Functions taking an `accuracy`

parameter may fail to terminate if
`accuracy`

is too small. Accuracy is measured in least significant
bits, similarly to '(=~=)'.

In this documentation, *basic functionality* denotes that methods used
are from classes:

Further, *basic RealFloat functionality* denotes *basic functionality*
with the addition of:

The intention behind the used functionality documentation is to help users decide when it is appropriate to use these generic implementations to implement instances.

- recodeFloat :: (RealFloat a, RealFloat b) => a -> b
- viaDouble :: (RealFloat a, RealFloat b) => (Double -> Double) -> a -> b
- (=~=) :: RealFloat a => a -> a -> Int -> Bool
- genericRecip :: RealFloat a => Int -> a -> a
- genericSqrt :: RealFloat a => Int -> a -> a
- genericExp :: RealFloat a => Int -> a -> a
- genericLog :: RealFloat a => Int -> a -> a
- genericLog' :: RealFloat a => Int -> a -> a -> a
- genericLog2 :: RealFloat a => Int -> a
- genericLog'' :: RealFloat a => Int -> a -> a
- genericPi :: RealFloat a => Int -> a
- genericSin :: RealFloat a => Int -> a -> a -> a
- genericPositiveZero :: RealFloat a => a
- genericNegativeZero :: RealFloat a => a
- genericPositiveInfinity :: RealFloat a => a
- genericNegativeInfinity :: RealFloat a => a
- genericNotANumber :: RealFloat a => a
- sameSign :: (Ord a, Num a) => a -> a -> Bool

# Documentation

recodeFloat :: (RealFloat a, RealFloat b) => a -> bSource

Convert between generic `RealFloat`

types more efficiently than
`realToFrac`

. Tries hard to preserve special values like
infinities and negative zero, but any NaN payload is lost.

Uses only basic RealFloat functionality.

viaDouble :: (RealFloat a, RealFloat b) => (Double -> Double) -> a -> bSource

Lift a function from Double to generic `RealFloat`

types.

(=~=) :: RealFloat a => a -> a -> Int -> BoolSource

Approximate equality.
`(a =~= b) c`

when adding the difference to the larger in magnitude
changes at most `c`

least significant mantissa bits.

Uses only basic RealFloat functionality.

Compute a reciprocal using the Newton-Raphson division algorithm, as described in http://en.wikipedia.org/wiki/Division_%28digital%29#Newton.E2.80.93Raphson_division.

Uses only basic RealFloat functionality.

Compute a square root using Newton's method.

Uses basic RealFloat functionality and '(/)'.

Compute an exponential using power series.

Uses basic RealFloat functionality, '(/)' and `recip`

.

Compute a logarithm.

See `genericLog''`

for algorithmic references.

Compute a logarithm using decomposition and a value for `log 2`

.

See `genericLog''`

for algorithmic references.

Compute log 2.

See `genericLog''`

for algorithmic references.

Compute a logarithm for a value in [0.5,1) using the AGM method
as described in section 7 of
*The Logarithmic Constant: log 2*
Xavier Gourdon and Pascal Sebah, May 18, 2010,
http://numbers.computation.free.fr/Constants/Log2/log2.ps.

The precondition is not checked.

Compute pi using the method described in section 8 of
*Multiple-precision zero-finding methods and the complexity of elementary function evaluation*
Richard P Brent, 1975 (revised May 30, 2010),
http://arxiv.org/abs/1004.3412.

Uses basic RealFloat functionality, '(/)', and `sqrt`

.

Compute `sin`

using the method described in section 3 of
*Efficient multiple-precision evaluation of elementary functions*
David M Smith, 1989,
http://digitalcommons.lmu.edu/math_fac/1/

Requires a value for pi.

Uses basic RealFloat functionality, '(/)', and sqrt.

genericPositiveZero :: RealFloat a => aSource

Special values implemented using basic RealFloat functionality.

genericNegativeZero :: RealFloat a => aSource

Special values implemented using basic RealFloat functionality.

genericPositiveInfinity :: RealFloat a => aSource

Special values implemented using basic RealFloat functionality.

genericNegativeInfinity :: RealFloat a => aSource

Special values implemented using basic RealFloat functionality.

genericNotANumber :: RealFloat a => aSource

Special values implemented using basic RealFloat functionality.