Intel 80287, 80286 manual Overview of Numeric Processing Denormalized Operand

OVERVIEW OF NUMERIC PROCESSING

DENORMALIZED OPERAND

If an instruction attempts to operate on a denormal, the NPX reports the denormalized operand excep- tion. This exception allows users to implement in software an option of the proposed IEEE standard specifying that operands must be prenormalized before they are used.

NUMERIC OVERFLOW AND UNDERFLOW

If the exponent of a numeric result is too large for the destination real format, the 80287 signals a numeric overflow. Conversely, if the exponent of a result is too small to be represented in the destina- tion format, a numeric underflow is signaled. If either of these exceptions occur, the result of the operation is outside the range of the destination real format.

Typical algorithms are most likely to produce extremely large and small numbers in the calculation of intermediate, rather than final, results. Because of the great range of the temporary real format (recommended as the destination format for intermediates), overflow and underflow are relatively rare events in most 80287 applications.

INEXACT RESULT

If the result of an operation is not exactly representable in the destination format, the 80287 rounds the number and reports the precision exception. For example, the fraction 113 cannot be precisely repre- sented in binary form. This exception occurs frequently and indicates that some (generally acceptable) accuracy has been lost; it is provided for applications that need to perform exact arithmetic only.

HANDLING NUMERIC ERRORS

When numeric errors occur, the NPX takes one of two possible courses of action:

•The NPX can itself handle the error, producing the most reasonable result and allowing numeric program execution to continue undisturbed.

•A software exception handler can be invoked by the CPU to handle the error.

Each of the six exception conditions described above has a corresponding flag bit in the 80287 status word and a mask bit in the 80287 control word. If an exception is masked (the corresponding mask bit in the control word = 1), the 80287 takes an appropriate default action and continues with the compu- tation. If the exception is unmasked (mask=O), the 80287 asserts the ERROR output to the 80286 to signal the exception and invoke a software exception handler.

The NPX reports ari exception by setting the corresponding flag in the NPX status word to 1. The NPX then checks the corresponding exception mask in the control word to determine if it should

"field" the exception (mask= 1), or if it sho~it.1 :siguill the 6x~eptio" to the CPU to in~7cke 2. soft'.l!f!.!e exception handler (mask=O).

If the mask is set, the exception is said to be masked (from user software), and the NPX executes its on-chip masked response for that exception. If the mask is not set (mask=O), the exception is unmasked, and the NPX performs its unmasked response. The masked response always produces a standard result, then proceeds with the instruction. The unmasked response always traps to a software exception handler, allowing the CPU to recognize and take action on the exception. Table 1-17 gives a complete descrip- tion of all exception conditions and the NPX's masked response.

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