factor/library/math/complex.factor

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Factor

! Copyright (C) 2004, 2005 Slava Pestov.
! See http://factor.sf.net/license.txt for BSD license.
IN: math-internals
USING: errors generic kernel kernel-internals math ;
: (rect>) ( xr xi -- x )
#! Does not perform a check that the arguments are reals.
#! Do not use in your own code.
dup 0 number= [ drop ] [ <complex> ] ifte ;
IN: math
BUILTIN: complex 6 [ 0 "real" f ] [ 1 "imaginary" f ] ;
UNION: number real complex ;
M: real real ;
M: real imaginary drop 0 ;
M: number = ( n n -- ? ) number= ;
: rect> ( xr xi -- x )
over real? over real? and [
(rect>)
] [
"Complex number must have real components" throw drop
] ifte ;
: >rect ( x -- xr xi ) dup real swap imaginary ;
: conjugate ( z -- z* )
>rect neg rect> ;
: arg ( z -- arg )
#! Compute the complex argument.
>rect swap fatan2 ;
: >polar ( z -- abs arg )
dup abs swap >rect swap fatan2 ;
: cis ( theta -- cis )
dup fcos swap fsin rect> ;
: polar> ( abs arg -- z )
cis * ;
: absq >rect swap sq swap sq + ;
: dot ( #{ x1 x2 }# #{ y1 y2 }# -- x1*y1+x2*y2 )
over real over real * >r
swap imaginary swap imaginary * r> + ;
: proj ( u v -- w )
#! Orthogonal projection of u onto v.
[ [ dot ] keep absq /f ] keep * ;
IN: math-internals
: 2>rect ( x y -- xr yr xi yi )
[ swap real swap real ] 2keep
swap imaginary swap imaginary ;
M: complex number= ( x y -- ? )
2>rect number= [ number= ] [ 2drop f ] ifte ;
: *re ( x y -- xr*yr xi*ri ) 2>rect * >r * r> ;
: *im ( x y -- xi*yr xr*yi ) 2>rect >r * swap r> * ;
M: complex + 2>rect + >r + r> (rect>) ;
M: complex - 2>rect - >r - r> (rect>) ;
M: complex * ( x y -- x*y ) 2dup *re - -rot *im + (rect>) ;
: complex/ ( x y -- r i m )
#! r = xr*yr+xi*yi, i = xi*yr-xr*yi, m = yr*yr+yi*yi
dup absq >r 2dup *re + -rot *im - r> ;
M: complex / ( x y -- x/y ) complex/ tuck / >r / r> (rect>) ;
M: complex /f ( x y -- x/y ) complex/ tuck /f >r /f r> (rect>) ;
M: complex abs ( z -- |z| ) absq fsqrt ;
M: complex hashcode ( n -- n )
>rect >fixnum swap >fixnum bitxor ;