SM/REM

( d1 n1 -- n2 n3 )

Divide d1 by n1, giving the symmetric quotient n3 and the remainder n2. Input and output stack arguments are signed. An ambiguous condition exists if n1 is zero or if the quotient lies outside the range of a single-cell signed integer.

See:

Rationale:

See the previous discussion of division under FM/MOD. SM/REM is the symmetric-division primitive, which allows programs to define the following symmetric-division operators:

: /-REM ( n1 n2 -- n3 n4 ) >R S>D R> SM/REM ;

: /- ( n1 n2 -- n3 ) /-REM SWAP DROP ;

: -REM ( n1 n2 -- n3 ) /-REM DROP ;

: */-REM ( n1 n2 n3 -- n4 n5 ) >R M* R> SM/REM ;

: */- ( n1 n2 n3 -- n4 ) */-REM SWAP DROP ;

Testing:

T{       0 S>D              1 SM/REM ->  0       0 }T
T{       1 S>D              1 SM/REM ->  0       1 }T
T{       2 S>D              1 SM/REM ->  0       2 }T
T{      -1 S>D              1 SM/REM ->  0      -1 }T
T{      -2 S>D              1 SM/REM ->  0      -2 }T
T{       0 S>D             -1 SM/REM ->  0       0 }T
T{       1 S>D             -1 SM/REM ->  0      -1 }T
T{       2 S>D             -1 SM/REM ->  0      -2 }T
T{      -1 S>D             -1 SM/REM ->  0       1 }T
T{      -2 S>D             -1 SM/REM ->  0       2 }T
T{       2 S>D              2 SM/REM ->  0       1 }T
T{      -1 S>D             -1 SM/REM ->  0       1 }T
T{      -2 S>D             -2 SM/REM ->  0       1 }T
T{       7 S>D              3 SM/REM ->  1       2 }T
T{       7 S>D             -3 SM/REM ->  1      -2 }T
T{      -7 S>D              3 SM/REM ->  1      -2 }T
T{      -7 S>D             -3 SM/REM -> -1       2 }T
T{ MAX-INT S>D              1 SM/REM ->  0 MAX-INT }T
T{ MIN-INT S>D              1 SM/REM ->  0 MIN-INT }T
T{ MAX-INT S>D        MAX-INT SM/REM ->  0       1 }T
T{ MIN-INT S>D        MIN-INT SM/REM ->  0       1 }T
T{      1S 1                4 SM/REM ->  3 MAX-INT }T
T{       2 MIN-INT M*       2 SM/REM ->  0 MIN-INT }T
T{       2 MIN-INT M* MIN-INT SM/REM ->  0       2 }T
T{       2 MAX-INT M*       2 SM/REM ->  0 MAX-INT }T
T{       2 MAX-INT M* MAX-INT SM/REM ->  0       2 }T
T{ MIN-INT MIN-INT M* MIN-INT SM/REM ->  0 MIN-INT }T
T{ MIN-INT MAX-INT M* MIN-INT SM/REM ->  0 MAX-INT }T
T{ MIN-INT MAX-INT M* MAX-INT SM/REM ->  0 MIN-INT }T
T{ MAX-INT MAX-INT M* MAX-INT SM/REM ->  0 MAX-INT }T

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