53 lines
1.4 KiB
Text
53 lines
1.4 KiB
Text
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\ Cube root of real number by Newton's method
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\ ANS compatible version V1.2 10/6/1994
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\ Forth Scientific Library Algorithm #5
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\ This code conforms with ANS requiring:
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\ The FLOAT and FLOAT EXT word sets
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\ Non STANDARD words
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\ : FTUCK ( F: x y -- y x y) FSWAP FOVER ;
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\ : F2* ( F: x -- 2x ) FDUP F+ ;
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\ : F**2 FDUP F* ;
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\ (c) Copyright 1994 Julian V. Noble. Permission is granted
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\ by the author to use this software for any application provided
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\ the copyright notice is preserved.
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3 S>D D>F FCONSTANT F=3
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: X' ( F: N x -- x')
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FTUCK F**2 F/ FSWAP F2* F+ F=3 F/ ;
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\ The magic number 1E-8 needs no change, even when extended (80-bit) precision
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\ is needed.
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: CONVERGED? ( F: x' x x' --) ( -- f)
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F- FOVER F/ FABS 1.0E-8 F< ;
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: FCBRT ( F: N -- N^1/3)
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FDUP F0< FABS ( F: -- |N|) ( -- f)
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FDUP FSQRT ( F: -- N x0 )
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BEGIN FOVER FOVER X' FTUCK CONVERGED? UNTIL
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X' IF FNEGATE THEN ;
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~~~
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:x' (f:nx-X)
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f:tuck f:dup f:* f:/ f:swap f:dup f:+ f:+ .3 f:/ ;
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:converged? (f:XxX-) (-f)
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f:- f:over f:/ f:abs .1.0e-8 f:lt? ;
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:fcbrt (f:n-[n^1/3])
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f:dup .0 f:lt? f:abs
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f:dup f:sqrt
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[ f:over f:over x' f:tuck converged? ] until
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x' n:-zero? [ f:negate ] if ;
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~~~
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~~~
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.9 fcbrt f:put nl
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~~~
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