3-224
INSTRUCTION SET REFERENCE
FPREMPartial Remainder (Continued)
The FPREM instruction gets its name partial remainder because of the way it computes the
remainder. This instructions arrives at a remainder through iterative subtraction. It can, however,
reduce the exponent of ST(0) by no more than 63 in one execution of the instruction. If the
instruction succeeds in producing a remainder that is less than the modulus, the operation is
complete and the C2 flag in the FPU status word is cleared. Otherwise, C2 is set, and the result
in ST(0) is called the partial remainder. The exponent of the partial remainder will be less than
the exponent of the original dividend by at least 32. Software can re-execute the instruction
(using the partial remainder in ST(0) as the dividend) until C2 is cleared. (Note that while
executing such a remainder-computation loop, a higher-priority interrupting routine that needs
the FPU can force a context switch in-between the instructions in the loop.)
An important use of the FPREM instruction is to reduce the arguments of periodic functions.
When reduction is complete, the instruction stores the three least-significant bits of the quotient
in the C3, C1, and C0 flags of the FPU status word. This information is important in argument
reduction for the tangent function (using a modulus of
?
/4), because it locates the original angle
in the correct one of eight sectors of the unit circle.
Operation
D
<
exponent(ST(0)) exponent(ST(1));
IF D < 64
THEN
Q
<
Integer(TruncateTowardZero(ST(0)
/
ST(1)));
ST(0)
<
ST(0) (ST(1)
?
Q);
C2
<
0;
C0, C3, C1
<
LeastSignificantBits(Q); (* Q2, Q1, Q0 *)
ELSE
C2
<
1;
N
<
an implementation-dependent number between 32 and 63;
QQ
<
Integer(TruncateTowardZero((ST(0)
/
ST(1)) / 2
(D
?
N)
));
ST(0)
<
ST(0) (ST(1)
?
QQ
?
2
(D
?
N)
);
FI;
FPU Flags Affected
C0
Set to bit 2 (Q2) of the quotient.
C1
Set to 0 if stack underflow occurred; otherwise, set to least significant bit
of quotient (Q0).
C2
Set to 0 if reduction complete; set to 1 if incomplete.
C3
Set to bit 1 (Q1) of the quotient.
