Signed Arithmetic

Name:

ADD $X,$Y,$Z	ADD $X,$Y,Z
SUB $X,$Y,$Z	SUB $X,$Y,Z
MUL $X,$Y,$Z	MUL $X,$Y,Z
DIV $X,$Y,$Z	DIV $X,$Y,Z

Specification:

ADD: s($X) ← s($Y) + s($Z)

SUB: s($X) ← s($Y) - s($Z)

MUL: s($X) ← s($Y) * s($Z)

DIV:

s($X) ← ⌊s($Y) / s($Z)⌋ if $Z ≠ 0
0 if $Z = 0

the integer part of the Quotient and

s(rR) ← s($Y) mod s($Z) if $Z ≠ 0
s($Y) if $Z = 0

the remainder in special register rR.

All instructions exist in two variants. The second operand can either be a register $Z or an immediate value Z.

Timing:

ADD: 1υ
SUB: 1υ
MUL: 10υ
DIV: 60υ

Description:
These are instructions for computations with signed integers. The instructions record exceptions like overflow or division by zero in special register rA and, if enabled, cause a TRIP.

ADD: The sum $Y +$Z or $Y +Z is placed into register X using signed, two's complement arithmetic. An integer overflow exception occurs if the sum is ≥ 2⁶³ or < -2⁶³.
SUB: The difference $Y - $Z or $Y - Z is placed into register X using signed, two's complement arithmetic. An integer overflow exception occurs if the difference is ≥ 2⁶³ or < -2⁶³
MUL: The signed product of the number in register Y by either the number in $Z or the unsigned byte Z replaces the contents of register X. An integer overflow exception can occur, as with ADD or SUB, if the result is ≥ 2⁶³ or < -2⁶³.

(Consider: Immediate multiplication by powers of 2 can be done more rapidly with the SL instruction)
DIV: The signed quotient of the number in $Y divided by either the number in $Z or the unsigned byte Z replaces the contents of $X, and the signed remainder is placed in the special remainder register rR. An integer divide check exception occurs if the divisor is zero; in that case $X is set to zero and rR is set to $Y. An integer overflow exception occurs if the number -2⁶³ is divided by -1; otherwise integer overflow is impossible. The quotient of y divided by z is defined to be [y/z], and the remainder is defined to be y - [y/z]z (also written y mod z). Thus, the remainder is either zero or has the sign of the divisor.

(Consider: Dividing by z = 2^t gives exactly the same quotient as shifting right via the SR command, and exactly the same remainder as anding with z - 1 via the AND command. Division of a positive 63-bit number by a positive constant can be accomplished more quickly by computing the upper half of a suitable unsigned product and shifting it right appropriately.)

See also:

Unsigned Arithmetic.

ADD:	The sum $Y +$Z or $Y +Z is placed into register X using signed, two's complement arithmetic. An integer overflow exception occurs if the sum is ≥ 2⁶³ or < -2⁶³.
SUB:	The difference $Y - $Z or $Y - Z is placed into register X using signed, two's complement arithmetic. An integer overflow exception occurs if the difference is ≥ 2⁶³ or < -2⁶³
MUL:	The signed product of the number in register Y by either the number in $Z or the unsigned byte Z replaces the contents of register X. An integer overflow exception can occur, as with ADD or SUB, if the result is ≥ 2⁶³ or < -2⁶³. (Consider: Immediate multiplication by powers of 2 can be done more rapidly with the SL instruction)
DIV:	The signed quotient of the number in $Y divided by either the number in $Z or the unsigned byte Z replaces the contents of $X, and the signed remainder is placed in the special remainder register rR. An integer divide check exception occurs if the divisor is zero; in that case $X is set to zero and rR is set to $Y. An integer overflow exception occurs if the number -2⁶³ is divided by -1; otherwise integer overflow is impossible. The quotient of y divided by z is defined to be [y/z], and the remainder is defined to be y - [y/z]z (also written y mod z). Thus, the remainder is either zero or has the sign of the divisor. (Consider: Dividing by z = 2^t gives exactly the same quotient as shifting right via the SR command, and exactly the same remainder as anding with z - 1 via the AND command. Division of a positive 63-bit number by a positive constant can be accomplished more quickly by computing the upper half of a suitable unsigned product and shifting it right appropriately.)