Vol. 1 8-29

PROGRAMMING WITH THE X87 FPU

The flag (DE) for this exception is bit 1 of the x87 FPU status word, and the mask bit (DM) is bit 1 of the x87 FPU 
control word.
When a denormal-operand exception occurs and the exception is masked, the x87 FPU sets the DE flag, then 
proceeds with the instruction. The denormal operand in single- or double-precision floating-point format is auto-
matically normalized when converted to the double extended-precision floating-point format. Subsequent opera-
tions will benefit from the additional precision of the internal double extended-precision floating-point format.
When a denormal-operand exception occurs and the exception is not masked, the DE flag is set and a software 
exception handler is invoked (see Section 8.7, “Handling x87 FPU Exceptions in Software”). The top-of-stack 
pointer (TOP) and source operands remain unchanged.
For additional information about the denormal-operation exception, see Section 4.9.1.2, “Denormal Operand 
Exception (#D).”

8.5.3 

Divide-By-Zero Exception (#Z)

The x87 FPU reports a floating-point divide-by-zero exception whenever an instruction attempts to divide a finite 
non-zero operand by 0. The flag (ZE) for this exception is bit 2 of the x87 FPU status word, and the mask bit (ZM) 
is bit 2 of the x87 FPU control word. The FDIV, FDIVP, FDIVR, FDIVRP, FIDIV, and FIDIVR instructions and the other 
instructions that perform division internally (FYL2X and FXTRACT) can report the divide-by-zero exception. 
When a divide-by-zero exception occurs and the exception is masked, the x87 FPU sets the ZE flag and returns the 
values shown in Table 8-10. If the divide-by-zero exception is not masked, the ZE flag is set, a software exception 
handler is invoked (see Section 8.7, “Handling x87 FPU Exceptions in Software”), and the top-of-stack pointer 
(TOP) and source operands remain unchanged.

8.5.4 

Numeric Overflow Exception (#O)

The x87 FPU reports a floating-point numeric overflow exception (#O) whenever the rounded result of an arith-
metic instruction exceeds the largest allowable finite value that will fit into the floating-point format of the destina-
tion operand. (See Section 4.9.1.4, “Numeric Overflow Exception (#O),” for additional information about the 
numeric overflow exception.)
When using the x87 FPU, numeric overflow can occur on arithmetic operations where the result is stored in an x87 
FPU data register. It can also occur on store floating-point operations (using the FST and FSTP instructions), where 
a within-range value in a data register is stored in memory in a single-precision or double-precision floating-point 
format. The numeric overflow exception cannot occur when storing values in an integer or BCD integer format. 
Instead, the invalid-arithmetic-operand exception is signaled.
The flag (OE) for the numeric-overflow exception is bit 3 of the x87 FPU status word, and the mask bit (OM) is bit 
3 of the x87 FPU control word. 
When a numeric-overflow exception occurs and the exception is masked, the x87 FPU sets the OE flag and returns 
one of the values shown in Table 4-10. The value returned depends on the current rounding mode of the x87 FPU 
(see Section 8.1.5.3, “Rounding Control Field”).
The action that the x87 FPU takes when numeric overflow occurs and the numeric-overflow exception is not 
masked, depends on whether the instruction is supposed to store the result in memory or on the register stack.

•

Destination is a memory location — The OE flag is set and a software exception handler is invoked (see 
Section 8.7, “Handling x87 FPU Exceptions in Software”). The top-of-stack pointer (TOP) and source and 
destination operands remain unchanged. Because the data in the stack is in double extended-precision format, 

Table 8-11.  Divide-By-Zero Conditions and the Masked Responses to Them

Condition

Masked Response

Divide or reverse divide operation with a 

0 divisor.

Returns an ∞ signed with the exclusive OR of the sign of the two operands to the 

destination operand.

FYL2X instruction.

Returns an ∞ signed with the opposite sign of the non-zero operand to the destination 

operand.

FXTRACT instruction.

ST(1) is set to –∞; ST(0) is set to 0 with the same sign as the source operand.