107 lines
3.4 KiB
Perl
107 lines
3.4 KiB
Perl
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% clp(q,r) version 1.3.2 %
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% %
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% (c) Copyright 1992,1993,1994,1995 %
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% Austrian Research Institute for Artificial Intelligence (OFAI) %
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% Schottengasse 3 %
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% A-1010 Vienna, Austria %
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% %
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% File: root.pl %
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% Author: Christian Holzbaur christian@ai.univie.ac.at %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% perform N iterations of the sqrt(2) newton approx.
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%
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root( N, R) :-
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root( N, 1, R).
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root( 0, S, R) :- !, S=R.
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root( N, S, R) :-
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N1 is N-1,
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{ S1 = S/2 + 1/S },
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root( N1, S1, R).
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%
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% print e with a precision of at least N digits after 2.
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%
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e( N) :-
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e( N, E),
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print_decimal( E, N).
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e( N, E) :-
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{ Err =:= exp(10,-(N+2)), Half =:= 1/2 },
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inv_e_series( Half, Half, 3, Err, Inv_E),
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{ E =:= 1/Inv_E }.
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inv_e_series( Term, S0, _, Err, Sum) :-
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{ abs(Term) =< Err },
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!,
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S0 = Sum.
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inv_e_series( Term, S0, N, Err, Sum) :-
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N1 is N+1,
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{ Term1 =:= -Term/N, S1 =:= Term1+S0 },
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inv_e_series( Term1, S1, N1, Err, Sum).
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%
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% print Rat with a precision of N places after the decimal point
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%
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print_decimal( Rat, N) :-
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clpq:arith_eval( truncate( Rat), Int), Int=rat(I,1),
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clpq:arith_eval( Rat-Int, Rest),
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clpq:arith_eval( numer( Rest), rat(Num,1)),
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clpq:arith_eval( denom( Rest), rat(Den,1)),
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format( "~d.", [I]),
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wdig( 0, N, Num, Den),
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nl.
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wdig( N, M, _, _) :- N>=M, !.
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wdig( _, _, 0, _) :- !. % finite decimal expansion
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wdig( I, N, A, B) :-
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I1 is I+1,
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D is (10*A) // B,
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A1 is (10*A) mod B,
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( I mod 10 =:= 0 -> put(" ") ; true ),
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( I mod 70 =:= 0 -> nl, tab(2) ; true),
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write( D),
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wdig( I1, N, A1, B).
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%
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% Collect n digits of the decimal expansion of a/b
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% where a//b = 0
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%
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dig( 0, _, _, []) :- !.
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dig( _, 0, _, []) :- !. % finite decimal expansion
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dig( I, A, B, [D|Ds]) :-
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I1 is I-1,
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A10 is 10*A,
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D is A10 // B,
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A1 is A10 mod B,
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dig( I1, A1, B, Ds).
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/*
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| ?- time(expo(1000)).
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2.
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7182818284 5904523536 0287471352 6624977572 4709369995 9574966967 6277240766
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3035354759 4571382178 5251664274 2746639193 2003059921 8174135966 2904357290
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0334295260 5956307381 3232862794 3490763233 8298807531 9525101901 1573834187
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9307021540 8914993488 4167509244 7614606680 8226480016 8477411853 7423454424
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3710753907 7744992069 5517027618 3860626133 1384583000 7520449338 2656029760
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6737113200 7093287091 2744374704 7230696977 2093101416 9283681902 5515108657
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4637721112 5238978442 5056953696 7707854499 6996794686 4454905987 9316368892
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3009879312 7736178215 4249992295 7635148220 8269895193 6680331825 2886939849
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6465105820 9392398294 8879332036 2509443117 3012381970 6841614039 7019837679
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3206832823 7646480429 5311802328 7825098194 5581530175 6717361332 0698112509
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9618188159 3041690351 5988885193 4580727386 6738589422 8792284998 9208680582
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5749279610 4841984443 6346324496 8487560233 6248270419 7862320900 2160990235
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3043699418 4914631409 3431738143 6405462531 5209618369 0888707016 7683964243
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7814059271 4563549061 3031072085 1038375051 0115747704 1718986106 8739696552
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1267154688 9570350354
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%%% Timing 00:01:29.150 89.150
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*/
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