factor/extra/math/derivatives/derivatives.factor

! Copyright (C) 2009 Jason W. Merrill.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.functions math.derivatives.syntax 
    math.order math.parser summary accessors make combinators ;
IN: math.derivatives

ERROR: undefined-derivative point word ;
M: undefined-derivative summary
    [ dup "Derivative of " % word>> name>> % 
    " is undefined at " % point>> # "." % ]
    "" make ;

DERIVATIVE: + [ 2drop ] [ 2drop ]
DERIVATIVE: - [ 2drop ] [ 2drop neg ]
DERIVATIVE: * [ nip * ] [ drop * ]
DERIVATIVE: / [ nip / ] [ sq / neg * ]
! Conditional checks if the epsilon-part of the exponent is 
! 0 to avoid getting float answers for integer powers.
DERIVATIVE: ^ [ [ 1 - ^ ] keep * * ] 
    [ [ dup zero? ] 2dip [ 3drop 0 ] [ [ ^ ] keep log * * ] if ]

DERIVATIVE: abs 
    [ 0 <=> 
        { 
            { +lt+ [ neg ] } 
            { +eq+ [ 0 \ abs undefined-derivative ] } 
            { +gt+ [ ] } 
        } case
    ]

DERIVATIVE: sqrt [ sqrt 2 * / ]

DERIVATIVE: e^ [ e^ * ]
DERIVATIVE: log [ / ]

DERIVATIVE: sin [ cos * ]
DERIVATIVE: cos [ sin neg * ]
DERIVATIVE: tan [ sec sq * ]

DERIVATIVE: sinh [ cosh * ]
DERIVATIVE: cosh [ sinh * ]
DERIVATIVE: tanh [ sech sq * ]

DERIVATIVE: asin [ sq neg 1 + sqrt / ]
DERIVATIVE: acos [ sq neg 1 + sqrt neg / ]
DERIVATIVE: atan [ sq 1 + / ]

DERIVATIVE: asinh [ sq 1 + sqrt / ]
DERIVATIVE: acosh [ [ 1 + sqrt ] [ 1 - sqrt ] bi * / ]
DERIVATIVE: atanh [ sq neg 1 + / ]

DERIVATIVE: neg [ drop neg ]
DERIVATIVE: recip [ sq recip neg * ]