Vol. 1 4-21

DATA TYPES

When a numeric-overflow exception occurs and the exception is masked, the processor sets the OE flag and 
returns one of the values shown in Table 4-10, according to the current rounding mode. See Section 4.8.4, 
“Rounding.”
When numeric overflow occurs and the numeric-overflow exception is not masked, the OE flag is set, a software 
exception handler is invoked, and the source and destination operands either remain unchanged or a biased result 
is stored in the destination operand (depending whether the overflow exception was generated during an 
SSE/SSE2/SSE3 floating-point operation or an x87 FPU operation).

See the following sections for information regarding the numeric overflow exception when detected while executing 
x87 FPU instructions or while executing SSE/SSE2/SSE3 instructions:

•

x87 FPU; Section 8.5.4, “Numeric Overflow Exception (#O)”

•

SIMD floating-point exceptions; Section 11.5.2.4, “Numeric Overflow Exception (#O)”

4.9.1.5  

Numeric Underflow Exception (#U)

The processor detects a potential floating-point numeric underflow condition whenever the result of rounding with 
unbounded exponent (taking into account precision control for x87) is non-zero and tiny; that is, non-zero and less 
than the smallest possible normalized, finite value that will fit into the destination operand. Table 4-11 shows the 
threshold range for numeric underflow for each of the floating-point formats (assuming normalized results); 
underflow occurs when a rounded result falls strictly within the threshold range. The ability to detect and handle 
underflow is provided to prevent a very small result from propagating through a computation and causing another 
exception (such as overflow during division) to be generated at a later time. Results which trigger underflow are 
also potentially less accurate.

Table 4-9.  Numeric Overflow Thresholds

Floating-Point Format

Overflow Thresholds

Single Precision

| x | ≥ 1.0 ∗ 2

128

Double Precision

| x | ≥ 1.0 ∗ 2

1024

Double Extended Precision

| x | ≥ 1.0 ∗ 2

16384

Table 4-10.  Masked Responses to Numeric Overflow

Rounding Mode

Sign of True Result

Result

To nearest

+

+∞

–

–∞

Toward –∞

+

Largest finite positive number

–

–∞

Toward +∞

+

+∞

–

Largest finite negative number

Toward zero

+

Largest finite positive number

–

Largest finite negative number

Table 4-11.  Numeric Underflow (Normalized) Thresholds

Floating-Point Format

Underflow Thresholds*

Single Precision

| x | < 1.0 ∗ 2

−126

Double Precision

| x | < 1.0 ∗ 2

−1022

Double Extended Precision

| x | < 1.0 ∗ 2

−16382

* Where ‘x’ is the result rounded to destination precision with an unbounded exponent range.