User's Manual

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NUMERIC PROGRAMMING EXAMPLES
FINAL ADJUSTMENTS
It is possible that the power function (GeLPowec10) could produce a scaling value such that it forms
a scaled result larger than the
ASCII field could allow. For example, scaling 9.9999999999999999 X
10
4900
by 1.00000000000000010 X 10-
4883
would produce 1.00000000000000009 X 10". The scale
factor
is within the accuracy of the NPX and the result is within the conversion accuracy, but it cannot
be represented in BCD format. This
is why there is a post-scaling test on the magnitude of the result.
The result can be multiplied or divided by
10, depending on whether the result was too small or too
large, respectively.
Output Format
For maximum flexibility in output formats, the position of the decimal point is indicated by a binary
integer called the power value.
If the power value is zero, then the decimal point is assumed to be at
the right of the rightmost digit. Power values greater than zero indicate
how many trailing zeros are
not shown. For each unit below zero, move the decimal point to the left in the string.
The last step of the conversion
is storing the result in BCD and indicating where the decimal point lies.
The BCD string
is then unpacked into ASCII decimal characters. The ASCII sign is set corresponding
to the sign of the original value.
TRIGONOMETRIC CALCULATION EXAMPLES
The 80287 instruction set does not provide a complete set of trigonometric'functions that can be used
directly
in calculations. Rather, the basic building blocks for implementing trigonometric functions are
provided by the
FPTAN and FPREM instructions. The example in figure 4-7 shows how three trigon-
ometric functions (sine, cosine, and tangent) can
be implementing using the 80287. All three functions
accept a valid angle argument between - 2
62
and + 262. These functions may be called from
PL/M-286, Pascal-286, FORTRAN-286, or ASM286 routines.
These trigonometric functions use the partial tangent instruction together with trigonometric identities
to calculate the result. They are accurate to within
16 units of the low 4 bits of an extended precision
value. The functions are coded for speed and small size, with tradeoffs available for greater accuracy.
FPT AN and FPREM
These trigonometric functions use the FPTAN instruction of the NPX. FPTAN requires that the angle
argument be between
0 and 7r / 4 radians, 0 to 45 degrees. The FPREM instruction is used to reduce
the argument down to this range. The
low three quotient bits set by FPREM identify which octant the
original angle was in.
One FPREM instruction iteration can reduce angles of 10
18
radians or less in magnitude to 7r / 4! Larger
values can
be reduced, but the meaning of the result is questionable, because any errors in the least
significant bits of
that value represent changes of 45 degrees or more in the reduced angle.
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