8 The optional Double-Number word set

8.6.1.1820 M*/ m-star-slash DOUBLE

( d1 n1 +n2 -- d2 )

Multiply d1 by n1 producing the triple-cell intermediate result t. Divide t by +n2 giving the double-cell quotient d2. An ambiguous condition exists if +n2 is zero or negative, or the quotient lies outside of the range of a double-precision signed integer.

See:

Rationale:

M*/ was once described by Chuck Moore as the most useful arithmetic operator in Forth. It is the main workhorse in most computations involving double-cell numbers. Note that some systems allow signed divisors. This can cost a lot in performance on some CPUs. The requirement for a positive divisor has not proven to be a problem.

Testing:

To correct the result if the division is floored, only used when necessary, i.e., negative quotient and remainder <>= 0.

: ?floored [ -3 2 / -2 = ] LITERAL IF 1. D- THEN ;

T{       5.       7             11 M*/ ->  3. }T
T{       5.      -7             11 M*/ -> -3. ?floored }T
T{      -5.       7             11 M*/ -> -3. ?floored }T
T{      -5.      -7             11 M*/ ->  3. }T
T{ MAX-2INT       8             16 M*/ -> HI-2INT }T
T{ MAX-2INT      -8             16 M*/ -> HI-2INT DNEGATE ?floored }T
T{ MIN-2INT       8             16 M*/ -> LO-2INT }T
T{ MIN-2INT      -8             16 M*/ -> LO-2INT DNEGATE }T

T{ MAX-2INT MAX-INT        MAX-INT M*/ -> MAX-2INT }T
T{ MAX-2INT MAX-INT 2/     MAX-INT M*/ -> MAX-INT 1- HI-2INT NIP }T
T{ MIN-2INT LO-2INT NIP DUP NEGATE M*/ -> MIN-2INT }T
T{ MIN-2INT LO-2INT NIP 1- MAX-INT M*/ -> MIN-INT 3 + HI-2INT NIP 2 + }T
T{ MAX-2INT LO-2INT NIP DUP NEGATE M*/ -> MAX-2INT DNEGATE }T
T{ MIN-2INT MAX-INT            DUP M*/ -> MIN-2INT }T

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