Intel 80286, 80287 manual Output Format, Trigonometric Calculation Examples

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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 104900 by 1.00000000000000010 X 10-4883would 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 - 262 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.

FPTAN 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 1018 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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