Partial Remainder
Hex  Mnemonic  Encoding  Long Mode  Legacy Mode  Description 

D9 F5  FPREM1  None  Valid  Valid  Replace ST(0) with the IEEE remainder obtained from dividing ST(0) by ST(1). 
Computes the IEEE remainder obtained from dividing the value in the ST(0) register (the dividend) by the value in the ST(1) register (the divisor or modulus), and stores the result in ST(0). The remainder represents the following value:
Remainder = ST(0)  (Q * ST(1))
Here, Q is an integer value that is obtained by rounding the floatingpoint number quotient of [ST(0) / ST(1)] toward the nearest integer value. The magnitude of the remainder is less than or equal to half the magnitude of the modulus, unless a partial remainder was computed (as described below).
This instruction produces an exact result; the precision (inexact) exception does not occur and the rounding control has no effect. The following table shows the results obtained when computing the remainder of various classes of numbers, assuming that underflow does not occur.
DEST  

SRC 

When the result is 0, its sign is the same as that of the dividend. When the modulus is ∞, the result is equal to the value in ST(0).
The FPREM1 instruction computes the remainder specified in IEEE Standard 754. This instruction operates differently from the FPREM instruction in the way that it rounds the quotient of ST(0) divided by ST(1) to an integer (see the "Operation" section below).
Like the FPREM instruction, FPREM1 computes the remainder through iterative subtraction, but can 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 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 reexecute the instruction (using the partial remainder in ST(0) as the dividend) until C2 is cleared. (Note that while executing such a remaindercomputation loop, a higherpriority interrupting routine that needs the FPU can force a context switch inbetween 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 leastsignificant 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 π/4), because it locates the original angle in the correct one of eight sectors of the unit circle.
This instruction's operation is the same in non64bit modes and 64bit mode.
D = exponent(ST(0))  exponent(ST(1)); IF D < 64 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 implementationdependent 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;
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.
Exception  Description 

#U  Result is too small for destination format. 
#D  Source operand is a denormal value. 
#IA  Source operand is an SNaN value, modulus (divisor) is 0, divi dend is ∞, or unsupported format. 
#IS  Stack underflow occurred. 
Same exceptions as in protected mode.
Same exceptions as in protected mode.
Same exceptions as in protected mode.
Same exceptions as in protected mode.
Exception  Description 

#UD  If the LOCK prefix is used. 
#MF  If there is a pending x87 FPU exception. 
#NM  CR0.EM[bit 2] or CR0.TS[bit 3] = 1. 