Vol. 1 4-19

DATA TYPES

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Divide-by-zero (#Z)

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Denormalized operand (#D)

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Numeric overflow (#O)

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Numeric underflow (#U)

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Inexact result (precision) (#P)

The nomenclature of “#” symbol followed by one or two letters (for example, #P) is used in this manual to indicate 
exception conditions. It is merely a short-hand form and is not related to assembler mnemonics.

NOTE

All of the exceptions listed above except the denormal-operand exception (#D) are defined in IEEE 
Standard 754.

The invalid-operation, divide-by-zero and denormal-operand exceptions are pre-computation exceptions (that is, 
they are detected before any arithmetic operation occurs). The numeric-underflow, numeric-overflow and preci-
sion exceptions are post-computation exceptions.
Each of the six exception classes has a corresponding flag bit (IE, ZE, OE, UE, DE, or PE) and mask bit (IM, ZM, OM, 
UM, DM, or PM). When one or more floating-point exception conditions are detected, the processor sets the appro-
priate flag bits, then takes one of two possible courses of action, depending on the settings of the corresponding 
mask bits:

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Mask bit set. Handles the exception automatically, producing a predefined (and often times usable) result, 
while allowing program execution to continue undisturbed.

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Mask bit clear. Invokes a software exception handler to handle the exception.

The masked (default) responses to exceptions have been chosen to deliver a reasonable result for each exception 
condition and are generally satisfactory for most floating-point applications. By masking or unmasking specific 
floating-point exceptions, programmers can delegate responsibility for most exceptions to the processor and 
reserve the most severe exception conditions for software exception handlers. 
Because the exception flags are “sticky,” they provide a cumulative record of the exceptions that have occurred 
since they were last cleared. A programmer can thus mask all exceptions, run a calculation, and then inspect the 
exception flags to see if any exceptions were detected during the calculation.
In the IA-32 architecture, floating-point exception flag and mask bits are implemented in two different locations: 

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x87 FPU status word and control word. The flag bits are located at bits 0 through 5 of the x87 FPU status word 
and the mask bits are located at bits 0 through 5 of the x87 FPU control word (see Figures 8-4 and 8-6).

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MXCSR register. The flag bits are located at bits 0 through 5 of the MXCSR register and the mask bits are 
located at bits 7 through 12 of the register (see Figure 10-3).

Although these two sets of flag and mask bits perform the same function, they report on and control exceptions for 
different execution environments within the processor. The flag and mask bits in the x87 FPU status and control 
words control exception reporting and masking for computations performed with the x87 FPU instructions; the 
companion bits in the MXCSR register control exception reporting and masking for SIMD floating-point computa-
tions performed with the SSE/SSE2/SSE3 instructions.
Note that when exceptions are masked, the processor may detect multiple exceptions in a single instruction, 
because it continues executing the instruction after performing its masked response. For example, the processor 
can detect a denormalized operand, perform its masked response to this exception, and then detect numeric 
underflow.
See Section 4.9.2, “Floating-Point Exception Priority,” for a description of the rules for exception precedence when 
more than one floating-point exception condition is detected for an instruction.

4.9.1 

Floating-Point Exception Conditions

The following sections describe the various conditions that cause a floating-point exception to be generated and the 
masked response of the processor when these conditions are detected. The Intel® 64 and IA-32 Architectures