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