Altera Floating-Point - Manual (Page 21)

Meaning Sign Field Exponent Field Mantissa Field
Negative Denormalized 1 All 0’s Non-zero
Positive Infinity 0 All 1’s All 0’s
Negative Infinity 1 All 1’s All 0’s
Not-a-Number (NaN) Don’t care All 1’s Non-zero
Rounding
The IEEE-754 standard defines four types of rounding modes, which are:
• round-to-nearest-even
• round-toward-zero
• round-toward-positive-infinity
• round-toward-negative-infinity
Altera floating-point IP cores support only the most commonly used rounding mode, which is the round-
to-nearest-even mode (
TO_NEAREST
). With round-to-nearest-even, the IP core rounds the result to the
nearest floating-point number. If the result is exactly halfway between two floating-point numbers, the IP
core rounds the result so that the LSB becomes a zero, which is even.
Non-IEEE-754 Standard Format
Only the ALTFP_CONVERT and ALTERA_FP_FUNCTIONS (when the convert function is selected)
support the fixed point format.
The fixed-point data type is similar to the conventional integer data type, except that the fixed-point data
carries a predetermined number of fractional bits. If the width of the fraction is 0, the data becomes a
normal signed integer.
The notation for fixed-point format numbers in this user guide is Qm.f, where Q designates that the
number is in Q format notation, m is the number of bits used to indicate the integer portion of the
number, and f is the number of bits used to indicate the fractional portion of the number.
For example, Q4.12 describes a number with 4 integer bits and 12 fractional bits in a 16-bit word.
The following figures show the difference between the signed-integer format and the fixed-point format
for a 32-bit number.
Figure 1-11: Signed-Integer Format
Sign
bit
Integer bits
31 0
UG-01058
2014.12.19
Rounding 1-15
About Floating-Point IP Cores Altera Corporation
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