Intel 80287, 80286 manual Fprem

PROGRAMMING NUMERIC APPLICATIONS

Note that FSCALE assumes the scale factor in ST(l) is an integral value in the range -215 :sX<21' .If the value is not integral, but is in-range and is greater in magnitude than 1, FSCALE uses the nearest integer smaller in magnitude; i.e., it chops the value toward O. If the value is out of range, or 0

<I X I < 1, the instruction will produce an undefined result and will not signal an exception, ,The recommended practice is to load the scale factor from a word integer to ensure correct operation.

FPREM

FPREM (partial remainder) performs modulo division of the top stack element by the next stack element, i.e., ST(l) is the modulus. FPREM produces an exact result; the precision exception does not occur. The sign of the remainder is the same as the sign of the original dividend.

FPREM operates by performing successive scaled subtractions; obtaining the exact remainder when the operands differ greatly in magnitude can consume large amounts of execution time. Because the 80287 can only be preempted between instructions, the remainder function could seriously increase interrupt latency in these cases. Accordingly, the instruction is designed to be executed iteratively in a software-controlled loop.

FPREM can reduce a magnitude difference of up to 264 in one execution. If FPREM produces a remainder that is less than the modulus, the function is complete and bit C2 of the status word condi- tion code is cleared. If the function is incomplete, C2 is set to 1; the result in ST is then called the partial remainder. Software can inspect C2 by storing the status word following execution of FPREM and re-execute the instruction (using the partial remainder in ST as the dividend), until C2 is cleared. Alternatively, a program can determine when the function is complete by comparing ST to ST(1). If ST>ST(1),then FPREM must be executed again; if ST=ST(1), then the remainder is 0; if ST<ST(I), then the remainder is ST. A higher priority interrupting routine that needs the 80287 can force a context switch between the instructions in the remainder loop.

An important use for FPREM is to reduce arguments (operands) of periodic transcendental functions to the range permitted by these instructions. For example, the FPTAN (tangent) instruction requires its argument to be less than 7r/4. Using 7r /4 as a modulus, FPREM will reduce an argument so that it is in range of FPTAN. Because FPREM produces an exact result, the argument reduction does not introduce roundoff error into the calculation, even if several iterations are required to bring the argument into range. (The rounding of 7r does not create the effect of a rounded argument, but of a rounded period.)

FPREM also provides the least-significant three bits of the quotient generated by FPREM (in C3, C h Co). This is also important for transcendental argument reduction, because it locates the original angle in the correct one of eight 7r/4 segments of the unit circle (see table 2-4). If the quotient is less than 4, then CO will be the value of C3 before FPREM was executed. If the quotient is less than 2, then C3 ~,:m be the \'~!!.!e of ('! hpfoTP FPREM was executed.

FRNDINT

FRNDINT (round to integer) rounds the top stack element to an integer. For example, assume that ST contains the 80287 real number encoding of the decimal value 155.625. FRNDINT will change the value to 155 if the RC field of the control word is set to down or chop, or to 156 if it is set to up or nearest.

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