## ALP Programming Guide and Reference

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### Notes

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

The FPREM1 instruction is not the remainder operation specified in IEEE Std 754. It differs from FPREM in the way it rounds the quotient of ST and ST(1 ), when the exponent difference of exp(ST) -exp(ST)1 is less than 64.

FPREM1 works by iterative subtraction, can reduce the exponent of ST by no more than 63 in one execution. If FPREM1 succeeds in producing a remainder that is less than one half the modulus, the function is complete and the C2 flag is cleared. Otherwise, C2 is set, and the result in ST is called the partial remainder. The exponent of the partial remainder is less than the exponent of the original dividend by at least 32. Software can run the instruction again (using the partial remainder in ST as the dividend) until C2 is cleared. A higher-priority interrupting routine that needs the FPU can force a context switch between the instructions in the remainder loop.

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