Nimber arithmetic: Difference between revisions

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<br>two test numbers.

<lang rexx>/*REXX program performs nimber arithmetic (addition and multiplication); shows a table.*/

numeric digits 40 /*use a big enough number of decimals. */

numeric digits 40; d= digits() % 8 /*use a big enough number of decimals. */

parse arg sz aa bb . /*obtain optional argument from the CL.*/

if sz=='' | sz=="," then sz= 15 /*Not specified? Then use the default.*/

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sz1= sz + 1; w1= w-1 /*define the "dash" character for table*/

do am=0 for 2 /*perform sums, then perform multiplies*/

do j=0 for sz1 /*calculate & format a row of the table*/

if j==0 then call top '║'center("("@.am')', w1) /*show title of table. */

$= '║'center(j, w1)"║" /*index for a table row.*/

do k=0 for sz1 /*build a row of table. */

if am then $= $ || right( nprod(j, k), w) /*append to a table row.*/

else $= $ || right( nsum(j, k), w) /* " " " " " */

end /*k*/

say $ '║' /*show a row of a table.*/

end /*j*/

call bot

end /*am*/

say 'nimber sum of ' comma(aa) " and " comma(bb) ' ───► ' comma( nsum(aa, bb))

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hpo2: procedure; parse arg z; return 2 ** (length( d2b(z) + 0) - 1)

lhpo2: procedure; arg z; m=hpo2(z); q=0; do while m//2==0; m= m%2; q= q+1; end; return q

nsum: procedure; parse arg x,y; d= ~~digits() % 8;~~ return c2d(bitxor(d2c(x,d), d2c(y,d)))

nsum: procedure expose d; parse arg x,y; return c2d( bitxor( d2c(x,d), d2c(y,d) ) )

shl: procedure; parse arg z,h; return z * (2**h)

shr: procedure; parse arg z,h; return z % (2**h)

/*──────────────────────────────────────────────────────────────────────────────────────*/

nprod: procedure; parse arg x,y; if x<2 | y<2 then return x * y; h= hpo2(x)

nprod: procedure expose d; parse arg x,y; if x<2 | y<2 then return x * y; h= hpo2(x)

if x>h then return nsum( nprod(h, y), nprod( nsum(x, h), y) )

if hpo2(y)<y then return nprod(y, x)

~~d= digits()%8;~~ ands= c2d( bitand( d2c( lhpo2(x), d), d2c(lhpo2(y), d) ) )

ands= c2d(bitand(d2c(lhpo2(x), d), d2c(lhpo2(y), d))); if ands==0 then return x*y

if ands~~==0~~ ~~then~~ return x * y

h= hpo2(ands); return nprod( nprod( shr(x,h), shr(y,h) ), shl(3, h-1) )</lang>

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