The construction of arbitrary translation tables can be error-prone, and when it is it is better done procedurally. I use the HLASM macro language, which is entirely adequate to such tasks; mais à chacun son goût.
Here, however, we have for a TROO only the 256 permutations taken two at a time of the sixteen hexadecimal digits, viz., 0==>0, 1==>8, 2==>4, 3==>c, 4==>2, 5==>a, 6==>6, 7==>e, 8==>1, 9==>9, a==>5, b==>d, c==>3, d==>b, e==>7, f==>f and they can be enumerated readily, by program or manually (and certainly without resort to cut-and-paste from a dump). Symmetries can also be exploited, and the whole thing can be arithmetized, but to do either would put mathematics dropouts at a disadvantage. The problem CAN be addressed with left circular shifts/left rotations, but they must be nested (and iterated for long bit strings). The TROO turns out to be faster, particularly for those long bit strings. The problem of bit-string reversal has its own interest, but if its purpose is in effect to simulate a FROGR using a FLOGR, then other approaches are possible. Specifically, a TRTRE, Translate and Test Reverse Extended, can be used. It proceeds from right to left, high to low storage address, in a byte string only until it finds a non-zero value in its table that corresponds to the current byte's rank. Permutations taken two at a time of the hexadecimal digit-codes 0000==>0000, 0 0001==>0001, 1 0010==>0010, 2 0011==>0001, 1 0100==>0011, 3 0101==>0001, 1 0110==>0010, 2 0111==>0001, 1 1000==>0100, 4 1001==>0001, 1 1010==>0010, 2 1011==>0001, 1 1100==>0011, 3 1101==>0001, 1 1110==>0010, 2 1111==>0001, 1 in which zero indicates the absence of a one bit and a non-zero value indicates both the presence of a one bit and its one-origin offset from the rightmost bit position. The permutations/code points x'N0', N = 1, 2, . . . , f need 'special' treatment, 8 must be added to the values shown above for them. Unsurprisingly, this turns out to be faster than reversal followed by FLOG. John Gilmore, Ashland, MA 01721 - USA ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN
