3-227
INSTRUCTION SET REFERENCE
FPREM1Partial Remainder (Continued)
Like the FPREM instruction, the FPREM1 computes the remainder through iterative subtrac-
tion, but can reduce the exponent of ST(0) by no more than 63 in one execution of the instruc-
tion. If the instruction succeeds in producing a remainder that is less than one half 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 FPREM1 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(RoundTowardNearestInteger(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.
