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FPREM           Partial remainder                    Exceptions: I D U
FPREM1          IEEE Partial remainder (387+)        C3 C2 C1 C0: * * * *

FPREM
FPREM1

        Logic   ST . remainder (ST / ST(1))

    These instructions divide ST by ST(1), and put the remainder in ST.
    The sign of the remainder is the same as the sign of the original
    dividend in ST.
    FPREM is supported for compatibility with the 8087 and 80287 math
    coprocessors. The FPREM1 instruction is the remainder operation
    specified in IEEE Standard 754.


    An important use of FPREM/FPREM1 is to reduce the arguments of
    periodic functions. When the reduction is complete, FPREM/FPREM1
    provides the 3 least-significant bits of the quotient in flags C3,
    C1, and C0  (C0 = bit 2, C1 = bit 1, C3 = bit 0). This is important
    in argument reduction for the tangent function (using a modulus of
    PI/4), because it locates the original angle in the correct one of 8
    sectors of the unit circle.


    Note
    FPREM and FPREM1 produce an exact result; the precision (inexact)
    exception does not occur and the rounding control (RC) has no
    effect.


        Example
        ; Compute z := x MOD y
        p387
        fld   [y]
        fld   [x]
      @@again:
        fprem1          ; compute IEEE partial remainder
        fstsw ax        ; get condition bits
        test  ah, 0100b ; if C2 is set
        jnz   @@again   ;   not done yet
        fstp  [z]       ; store and pop remainder
        fstp  ST(0)     ; unstack y


    Opcode      Format
    D9 F8       FPREM
    D9 F5       FPREM1


    Timing
    Variations    8087         287        387      486     Pentium
    fprem        15-190       15-190     74-155   70-138   16-64   NP
    fprem1         -            -        95-185   72-167   20-70   NP