June 2018 Update
This commit is contained in:
Ingy döt Net
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commit
22f33d4004
5278 changed files with 84726 additions and 14379 deletions
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@ -1,11 +1,7 @@
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function vdc{T<:Integer}(n::T, b::T)
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sum([d*float(b)^-i for (i, d) in enumerate(digits(n, b))])
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end
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vandercorput(num::Integer, base::Integer) = sum(d * Float64(base) ^ -ex for (ex, d) in enumerate(digits(num, base)))
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for i in 2:9
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print(" Base ", i)
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for j in 0:9
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print(@sprintf(" %8.6f", vdc(j, i)))
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end
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println()
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for base in 2:9
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@printf("%10s %i:", "Base", base)
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for num in 0:9 @printf("%7.3f", vandercorput(num, base)) end
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println(" [...]")
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end
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@ -0,0 +1,50 @@
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MODULE Sequence;
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FROM FormatString IMPORT FormatString;
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FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
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PROCEDURE vc(n,base : INTEGER; VAR num,denom : INTEGER);
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VAR p,q : INTEGER;
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BEGIN
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p := 0;
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q := 1;
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WHILE n#0 DO
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p := p * base + (n MOD base);
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q := q * base;
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n := n DIV base
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END;
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num := p;
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denom := q;
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WHILE p#0 DO
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n := p;
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p := q MOD p;
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q := n
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END;
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num := num DIV q;
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denom := denom DIV q
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END vc;
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VAR
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buf : ARRAY[0..31] OF CHAR;
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d,n,i,b : INTEGER;
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BEGIN
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FOR b:=2 TO 5 DO
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FormatString("base %i:", buf, b);
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WriteString(buf);
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FOR i:=0 TO 9 DO
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vc(i,b,n,d);
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IF n#0 THEN
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FormatString(" %i/%i", buf, n, d);
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WriteString(buf)
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ELSE
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WriteString(" 0")
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END
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END;
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WriteLn
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END;
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ReadChar
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END Sequence.
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@ -6,47 +6,48 @@ if a=='' | a=="," then parse value 0 10 with a b /*Not specified? Then use the
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if b=='' | b=="," then b=a /* " " " " " " */
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if r=='' | r=="," then r=2 /* " " " " " " */
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z= /*a placeholder for a list of numbers. */
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do j=a to b /*traipse through the range of integers*/
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_=VdC( abs(j), abs(r) ) /*convert the ABSolute value of integer*/
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_=substr('-', 2+sign(j) )_ /*if needed, keep the leading - sign.*/
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if r>0 then say _ /*if positive base, then just show it. */
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else z=z _ /* ··· else append (build) a list. */
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end /*j*/
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do j=a to b /*traipse through the range of integers*/
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_=VdC( abs(j), abs(r) ) /*convert the ABSolute value of integer*/
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_=substr('-', 2 + sign(j) )_ /*if needed, keep the leading - sign.*/
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if r>0 then say _ /*if positive base, then just show it. */
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else z=z _ /* ··· else append (build) a list. */
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end /*j*/
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if z\=='' then say strip(z) /*if a list is wanted, then display it.*/
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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base: procedure; parse arg x, toB, inB /*get a number, toBase, and inBase. */
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/*┌───────────────────────────────────────────────────────────────────┐
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┌─┘ Input to this function: x (is required & must be an integer).└─┐
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│ toBase the base to convert X to. │
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│ inBase the base X is expressed in. │
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│ │
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│ toBase or inBase can be omitted which causes the default of 10 │
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└─┐ to be used. Both have a limit of: 2 ──► 90.┌─┘
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└───────────────────────────────────────────────────────────────────┘*/
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@abc= 'abcdefghijklmnopqrstuvwxyz' /*the Latin lowercase alphabet chars. */
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@abcU=@abc; upper @abcU /*go whole hog and extend characters. */
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@@@= 0123456789 || @abc || @abcU /*prefix them with some numeric digits.*/
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/*╔══════════════════════════════════════════════════════════════════════════════════╗
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║ Input to this function: x (X is required and it must be an integer). ║
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║ toBase the base to convert X to (default=10). ║
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║ inBase the base X is expressed in (default=10). ║
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║ ║
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║ toBase & inBase have a limit of: 2 ──► 90 ║
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╚══════════════════════════════════════════════════════════════════════════════════╝*/
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@abc= 'abcdefghijklmnopqrstuvwxyz' /*the lowercase Latin alphabet letters.*/
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@abcU=@abc; upper @abcU /*go whole hog & extend with uppercase.*/
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@@@= 0123456789 || @abc || @abcU /*prefix them with the decimal digits. */
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@@@= @@@'<>[]{}()?~!@#$%^&*_+-=|\/;:`' /*add some special characters as well, */
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/*special characters should be viewable*/
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numeric digits 1000 /*what the hey, support biggy numbers.*/
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/*──those chars should all be viewable.*/
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numeric digits 1000 /*what the hey, support bigun' numbers.*/
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maxB=length(@@@) /*maximum base (radix) supported here. */
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if toB=='' then toB=10 /*if skipped, then assume default (10)*/
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if toB=='' then toB=10 /*if omitted, then assume default (10)*/
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if inB=='' then inB=10 /* " " " " " " */
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#=0 /* [↓] convert base inB X ──► base 10*/
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do j=1 for length(x)
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do j=1 for length(x) /*process each "numeral" in the string.*/
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_=substr(x, j, 1) /*pick off a "digit" (numeral) from X.*/
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v=pos(_, @@@) /*get the value of this "digit"/numeral*/
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if v==0|v>inB then call erd x,j,inB /*is it an illegal "digit" (numeral) ? */
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#=#*inB + v - 1 /*construct new number, digit by digit.*/
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if v==0 | v>inB then call erd /*is it an illegal "digit" (numeral) ? */
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#=# * inB + v - 1 /*construct new number, digit by digit.*/
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end /*j*/
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y= /* [↓] convert base 10 # ──► base toB.*/
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do while #>=toB /*deconstruct the new number (#). */
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y=substr(@@@, #//toB + 1, 1)y /* construct the output number, ··· */
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do while #>=toB /*deconstruct the new number (#). */
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y=substr(@@@, # // toB + 1, 1)y /* construct the output number, ··· */
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#=# % toB /* ··· and also whittle down #. */
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end /*while*/
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return substr(@@@, #+1, 1)y
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return substr(@@@, # + 1, 1)y /*return a constructed "numeric" string*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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erd: say 'the character ' v " isn't a legal numeral for base " inB'.'; exit 13
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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VdC: return '.'reverse(base(arg(1), arg(2))) /*convert the #, reverse the #, append.*/
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@ -10,4 +10,6 @@ st_store(k,2,0.5*runiform(2500,1))
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st_store(k,3,0.5:+0.5*halton(2500,1))
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end
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twoway scatter y x, msize(tiny) color(blue) ///
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|| scatter z x, msize(tiny) color(green)
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|| scatter z x, msize(tiny) color(green) legend(off) xtitle("") ///
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title(Distribution: Van der Corput (top) vs pseudorandom) ///
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ylabel(, angle(0) format(%3.1f))
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