# Paste: math.dual

Author: Jason Merrill factor Thu, 12 Feb 2009 00:49:26
Plain Text |
```USING: kernel math math.functions math.derivatives accessors words
generalizations sequences generic.parser fry locals compiler.units
continuations quotations combinators macros make ;

IN: math.dual

TUPLE: dual ordinary-part epsilon-part ;

C: <dual> dual

! Ordinary numbers implement the dual protocol by returning themselves as the
! ordinary part, and 0 as the epsilon part.
M: number ordinary-part>> ;

M: number epsilon-part>> drop 0 ;

: unpack-dual ( dual -- ordinary-part epsilon-part )
[ ordinary-part>> ] [ epsilon-part>> ] bi ;

<PRIVATE

MACRO: ordinary-op ( word n -- )
swap '[ [ ordinary-part>> ] _ napply _ execute ] ;

MACRO:: chain-rule ( derivative-list n -- x )
n n n n derivative-list n 1+ n
'[ [ [ epsilon-part>> ] _ napply ] _ nkeep [ ordinary-part>> ] _ napply
_ nweave
_ nsum ] ;

PRIVATE>

! dual-op is similar to execute, but promotes the word to operate on duals.
! Uses the "derivative" word-prop, which holds a list of quotations giving the
! partial derivative of the word with respect to each of its argumets.
:: [dual-op] ( word -- quot )
word "derivative" word-prop :> derivative-list
derivative-list length :> n
word n '[ _ _ ordinary-op ]
n
derivative-list n '[ _ _ chain-rule ]
'[ _ _ nkeep @ <dual> ] ;

MACRO: dual-op ( word -- ) [dual-op] ;

: define-dual-method ( word -- )
[ \ dual swap create-method-in ] keep [dual-op] define ;

! Specialize math functions to operate on dual numbers.
<< { sqrt exp log sin cos tan sinh cosh tanh atan }
[ define-dual-method ] each >>

! Inverse methods { asin, acos, asinh, acosh, atanh } are not generic,
! so there is no way to specialize them for dual numbers.

! Arithmetic methods are not generic (yet?), so we have to define special
! versions of them to operate on dual numbers.
: d+ ( x y -- x+y ) \ + dual-op ;
: d- ( x y -- x+y ) \ - dual-op ;
: d* ( x y -- x*y ) \ * dual-op ;
: d/ ( x y -- x/y ) \ / dual-op ;
: d^ ( x y -- x^y ) \ ^ dual-op ;```

## Annotation: math.duals

Author: Jason Merrill factor Thu, 12 Feb 2009 03:09:39
Plain Text |
```USING: kernel math math.functions math.derivatives accessors
words generalizations sequences generic fry locals
compiler.units continuations quotations combinators
combinators.smart macros effects ;

IN: math.dual

TUPLE: dual ordinary-part epsilon-part ;

C: <dual> dual

! Ordinary numbers implement the dual protocol by returning
! themselves as the ordinary part, and 0 as the epsilon part.
M: number ordinary-part>> ;

M: number epsilon-part>> drop 0 ;

: unpack-dual ( dual -- ordinary-part epsilon-part )
[ ordinary-part>> ] [ epsilon-part>> ] bi ;

<PRIVATE

: input-length ( word -- n ) stack-effect in>> length ;

MACRO: ordinary-op ( word -- )
[ input-length ] keep
'[ [ ordinary-part>> ] _ napply _ execute ] ;

! Takes n dual numbers o1 e1 o2 e2 ... on en and weaves their
! ordinary and epsilon parts to produce
! e1 o1 o2 ... on e2 o1 o2 ... on ... en o1 o2 ... on
! This allows a set of partial derivatives each to be evaluated
! at the same point.
MACRO: duals>weave ( n -- )
dup dup dup '[
[ [ epsilon-part>> ] _ napply ]
_ nkeep
[ ordinary-part>> ] _ napply
_ nweave
] ;

MACRO: chain-rule ( word -- x )
[ input-length ]
[ "derivative" word-prop ]
[ input-length 1+ ]
tri
'[ [ _ duals>weave _ _ nspread ] sum-outputs ] ;

PRIVATE>

! dual-op is similar to execute, but promotes the word to
! operate on duals. Uses the "derivative" word-prop, which
! holds a list of quotations giving the partial derivative of
! the word with respect to each of its argumets.
MACRO: dual-op ( word -- )
[ ] [ input-length ] [ ] tri
'[ [ _ ordinary-op ] _ nkeep _ chain-rule <dual> ] ;

: define-dual-method ( word -- )
[ \ dual swap create-method ] keep '[ _ dual-op ] define ;

! Specialize math functions to operate on dual numbers.
[ { sqrt exp log sin cos tan sinh cosh tanh atan }
[ define-dual-method ] each ] with-compilation-unit

! Inverse methods { asin, acos, asinh, acosh, atanh } are not
! generic, so there is no way to specialize them for dual
! numbers.

! Arithmetic methods are not generic (yet?), so we have to
! define special versions of them to operate on dual numbers.
: d+ ( x y -- x+y ) \ + dual-op ;
: d- ( x y -- x+y ) \ - dual-op ;
: d* ( x y -- x*y ) \ * dual-op ;
: d/ ( x y -- x/y ) \ / dual-op ;
: d^ ( x y -- x^y ) \ ^ dual-op ;```