A-M baby
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Ingy döt Net
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19005 changed files with 197040 additions and 7 deletions
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: pow ( f n -- f' )
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dup 0 < [ abs pow recip ]
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[ [ 1 ] 2dip swap [ * ] curry times ] if ;
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: pow ( f n -- f' )
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{
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{ [ dup 0 < ] [ abs pow recip ] }
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{ [ dup 0 = ] [ 2drop 1 ] }
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[ [ 2 mod 1 = swap 1 ? ] [ [ sq ] [ 2 /i ] bi* pow ] 2bi * ]
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} cond ;
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USING: combinators kernel math ;
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IN: test
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: (pow) ( f n -- f' )
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[ dup even? ] [ [ sq ] [ 2 /i ] bi* ] while
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dup 1 = [ drop ] [ dupd 1 - (pow) * ] if ;
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: pow ( f n -- f' )
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{
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{ [ dup 0 < ] [ abs (pow) recip ] }
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{ [ dup 0 = ] [ 2drop 1 ] }
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[ (pow) ]
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} cond ;
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: (pow) ( f n -- f' )
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[ 1 ] 2dip
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[ dup 1 = ] [
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dup even? [ [ sq ] [ 2 /i ] bi* ] [ [ [ * ] keep ] dip 1 - ] if
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] until
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drop * ;
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20
Task/Exponentiation-operator/GAP/exponentiation-operator.gap
Normal file
20
Task/Exponentiation-operator/GAP/exponentiation-operator.gap
Normal file
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expon := function(a, n, one, mul)
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local p;
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p := one;
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while n > 0 do
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if IsOddInt(n) then
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p := mul(a, p);
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fi;
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a := mul(a, a);
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n := QuoInt(n, 2);
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od;
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return p;
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end;
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expon(2, 10, 1, \*);
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# 1024
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# a more creative use of exponentiation
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List([0 .. 31], n -> (1 - expon(0, n, 1, \-))/2);
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# [ 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,
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# 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1 ]
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WRITE(Clipboard) pow(5, 3) ! 125
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WRITE(ClipBoard) pow(5.5, 7) ! 152243.5234
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FUNCTION pow(x, n)
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pow = 1
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DO i = 1, n
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pow = pow * x
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ENDDO
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END
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procedure main()
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bases := [5,5.]
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numbers := [0,2,2.,-1,3]
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every write("expon(",b := !bases,", ",x := !numbers,")=",(expon(b,x) | "failed") \ 1)
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end
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procedure expon(base,power)
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local op,res
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base := numeric(base) | runerror(102,base)
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power := power = integer(power) | runerr(101,power)
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if power = 0 then return 1
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else op := if power < 1 then
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(base := real(base)) & "/" # force real base
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else "*"
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res := 1
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every 1 to abs(power) do
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res := op(res,base)
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return res
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end
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exp =: */@:#~
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10 exp 3
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1000
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10 exp 0
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1
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exp =: *@:] %: */@:(#~|)
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10 exp _3
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0.001
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exp =: dyad def 'x *^:y 1'
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10 exp 3
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1000
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10 exp _3
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0.001
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exp =: ^.^:_1
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81 exp 0.5
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9
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exp =: %:^:_1~
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81 exp 0.5
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9
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pi =: 3.14159265358979323846
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e =: 2.71828182845904523536
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i =: 2 %: _1 NB. Square root of -1
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e^(pi*i)
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_1
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exp =: %:^:_1~
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e exp (pi*i)
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_1
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print " 11^5 = ", floatPow( 11, 5 )
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print " (-11)^5 = ", floatPow( -11, 5 )
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print " 11^( -5) = ", floatPow( 11, -5 )
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print " 3.1416^3 = ", floatPow( 3.1416, 3 )
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print " 0^2 = ", floatPow( 0, 2 )
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print " 2^0 = ", floatPow( 2, 0 )
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print " -2^0 = ", floatPow( -2, 0 )
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end
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function floatPow( a, b)
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if a <>0 then
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m =1
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if b =abs( b) then
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for n =1 to b
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m =m *a
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next n
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else
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m =1 /floatPow( a, 0 - b) ' LB has no unitary minus operator.
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end if
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else
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m =0
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end if
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floatPow =m
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end function
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to int_power :n :m
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if equal? 0 :m [output 1]
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if equal? 0 modulo :m 2 [output int_power :n*:n :m/2]
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output :n * int_power :n :m-1
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end
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pow(n,x)
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k = n fby k div 2;
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p = x fby p*p;
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y =1 fby if even(k) then y else y*p;
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result y asa k eq 0;
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end
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define(`power',`ifelse($2,0,1,`eval($1*$0($1,decr($2)))')')
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power(2,10)
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exponentiation[x_,y_Integer]:=Which[y>0,Times@@ConstantArray[x,y],y==0,1,y<0,1/exponentiation[x,-y]]
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CirclePlus[x_,y_Integer]:=exponentiation[x,y]
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exponentiation[1.23,3]
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exponentiation[4,0]
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exponentiation[2.5,-2]
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1.23\[CirclePlus]3
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4\[CirclePlus]0
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2.5\[CirclePlus]-2
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1.86087
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1
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0.16
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1.86087
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1
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0.16
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"^^^"(a, n) := block(
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[p: 1],
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while n > 0 do (
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if oddp(n) then p: p * a,
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a: a * a,
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n: quotient(n, 2)
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),
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p
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)$
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infix("^^^")$
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2 ^^^ 10;
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1024
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2.5 ^^^ 10;
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9536.7431640625
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(* Library Interface *)
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DEFINITION MODULE Exponentiation;
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PROCEDURE IntExp(base, exp : INTEGER) : INTEGER;
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(* Raises base to the power of exp and returns the result
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both base and exp must be of type INTEGER *)
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PROCEDURE RealExp(base : REAL; exp : INTEGER) : REAL;
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(* Raises base to the power of exp and returns the result
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base must be of type REAL, exp of type INTEGER *)
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END Exponentiation.
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(* Library Implementation *)
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IMPLEMENTATION MODULE Exponentiation;
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PROCEDURE IntExp(base, exp : INTEGER) : INTEGER;
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VAR
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i, res : INTEGER;
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BEGIN
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res := 1;
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FOR i := 1 TO exp DO
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res := res * base;
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END;
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RETURN res;
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END IntExp;
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PROCEDURE RealExp(base: REAL; exp: INTEGER) : REAL;
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VAR
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i : INTEGER;
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res : REAL;
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BEGIN
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res := 1.0;
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IF exp < 0 THEN
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FOR i := exp TO -1 DO
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res := res / base;
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END;
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ELSE (* exp >= 0 *)
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FOR i := 1 TO exp DO
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res := res * base;
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END;
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END;
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RETURN res;
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END RealExp;
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END Exponentiation.
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MODULE Expt EXPORTS Main;
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IMPORT IO, Fmt;
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PROCEDURE IntExpt(arg, exp: INTEGER): INTEGER =
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VAR result := 1;
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BEGIN
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FOR i := 1 TO exp DO
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result := result * arg;
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END;
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RETURN result;
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END IntExpt;
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PROCEDURE RealExpt(arg: REAL; exp: INTEGER): REAL =
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VAR result := 1.0;
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BEGIN
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IF exp < 0 THEN
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FOR i := exp TO -1 DO
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result := result / arg;
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END;
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ELSE
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FOR i := 1 TO exp DO
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result := result * arg;
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END;
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END;
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RETURN result;
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END RealExpt;
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BEGIN
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IO.Put("2 ^ 4 = " & Fmt.Int(IntExpt(2, 4)) & "\n");
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IO.Put("2.5 ^ 4 = " & Fmt.Real(RealExpt(2.5, 4)) & "\n");
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END Expt.
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