Intel 80286, 80287 manual Exception Considerations, Special Instructions, Description of Operation

NUMERIC PROGRAMMING EXAMPLES

Exception Considerations

Care is taken inside the function to avoid generating exceptions. Any possible numeric value will be accepted. The only exceptions possible would occur if insufficient space exists on the numeric register stack.

The value passed in the numeric stack is checked for existence, type (NaN or infinity), and status (unnormal, denormal, zero, sign). The string size is tested for a minimum and maximum value. If the top of the register stack is empty, or the string size is too small, the function will return with an error code.

Overflow and underflow is avoided inside the function for very large or very small numbers.

Special Instructions

The functions demonstrate the operation of several numeric instructions, different data types, and precision control. Shown are instructions for automatic conversion to BCD, calculating the value of 10 raised to an integer value, establishing and maintaining concurrency, data synchronization, and use of directed rounding on the NPX.

Without the extended precision data type and built-in exponential function, the double precision accuracy of this function could not be attained with the size and speed of the shown example.

The function relies on the numeric BCD data type for conversion from binary floating-point to decimal. It is not difficult to unpack the BCD digits into separate ASCII decimal digits. The major work involves scaling the floating-point value to the comparatively limited range of BCD values. To print a 9-digit result requires accurately scaling the given value to an integer between 108 and 109 • For example, the number +0.123456789 requires a scaling factor of 109 to produce the value + 123456789.0, which can be stored in 9 BCD digits. The scale factor must be an exact power of 10 to avoid to changing any of the printed digit values.

These routines should exactly convert all values exactly representable in decimal in the field size given. Integer values that fit in the given string size will not be scaled, but directly stored into the BCD form. Noninteger values exactly representable in decimal within the string size limits will also be exactly converted. For example, 0.125 is exactly representable in binary or decimal. To convert this floating- point value to decimal, the scaling factor will be 1000, resulting in 125. When scaling a value, the function must keep track of where the decimal point lies in the final decimal value.

Description of Operation

Converting a floating-point number to decimal ASCII takes three major steps: identifying the magni- tude of the number, scaling it for the BCD data type, and converting the BCD data type to a decimal ASCII string.

Identifying the magnitude of the result requires finding the value X such that the number is repre- sented by 1* lOX, where 1.0 < = I < 10.0. Scaling the number requires multiplying it by a scaling factor lOS, so that the result is an integer requiring no more decimal digits than provided for in the ASCII string.

Once scaled, the numeric rounding modes and BCD conversion put the number in a form easy to convert to decimal ASCII by host software.

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