Binary16 Internal Representation

Packed FP16 Representation

The standard 16-bit IEEE-754 encoding used to store or communicate a binary16 value.

Internal FP16 Representation

A hardware-friendly form in which the encoded fields are transformed into information such as sign, unbiased exponent, working significand, and classification for arithmetic processing.

FP16 Unpacking

The process of converting a packed 16-bit FP16 encoding into fields and derived information convenient for the arithmetic datapath.

FP16 Packing

The process of constructing the final 16-bit IEEE-754 binary16 encoding from a prepared sign, stored exponent, fraction, and classification.

The arithmetic datapath benefits from an explicit significand and unbiased exponent rather than repeatedly interpreting the packed IEEE fields.

Why is an FP16 value unpacked before ordinary floating-point arithmetic?

Field Extraction

The first unpacking step in which the sign, stored exponent, and fraction are separated from the 16-bit FP16 word.

The hidden leading 1 is restored.

What does the unpacker add to the fraction when constructing the significand of a normal FP16 value?

{1'b1, Fraction}

How is the 11-bit internal significand of a normal FP16 value constructed?

{1'b0, Fraction}

How is the internal significand constructed when the FP16 value is not normal?

StoredExponent - 15

How does the Proteus unpacker calculate the unbiased exponent of a normal FP16 value?

-14

What unbiased exponent does the Proteus unpacker assign to a subnormal value?

-14

What placeholder effective exponent does the Proteus unpacker assign to signed zero?

Because zero has a zero significand, so the assigned exponent does not change its numerical value.

Why is assigning an effective exponent of -14 to signed zero harmless in the Proteus unpacker?

0

What exponent placeholder does the Proteus unpacker provide for Infinity or NaN?

Infinity and NaN must be recognized from their classification rather than interpreted through the ordinary finite-number exponent datapath.

Why must arithmetic hardware not treat the unpacker's exponent placeholder for Infinity or NaN as a numerical exponent?

Classification-Aware Unpacking

Unpacking in which the construction of internal arithmetic information depends on whether the encoded operand is normal, subnormal, zero, infinity, or NaN.

The classification signals tell later hardware whether the unpacked exponent and significand should participate in ordinary finite arithmetic.

Why does classification information accompany the unpacked numerical fields?

NaN Payload Preservation

The practice of retaining the NaN fraction information while converting the encoded NaN into an internal representation.

The lower 10 bits continue to contain the supplied fraction even though the leading internal significand bit is zero.

How does the Proteus unpacker preserve NaN payload information in its significand output?

FP16 Packer

A module that converts prepared floating-point result information back into the standard 16-bit binary16 encoding.

The packer expects earlier stages such as normalization and rounding to prepare the normal result's exponent and fraction.

Why is the FP16 packer not responsible for performing ordinary normalization and rounding?

For a normal result, the packer stores the sign, prepared biased exponent, and 10-bit fraction while omitting the implicit leading 1.

How does the packer encode a prepared normal finite result?

For a zero result, it forces the exponent and fraction to zero while preserving the supplied sign.

How does the packer preserve signed zero?

For an infinity result, it uses exponent 11111, fraction zero, and preserves the supplied sign.

How does the packer construct positive or negative Infinity?

The quiet bit of the NaN fraction is forced to 1.

What does the Proteus packer enforce when packing a quiet NaN?

The quiet bit is cleared, and if that would leave the entire fraction zero, another payload bit is set.

How does the Proteus packer prevent a signaling NaN from accidentally being encoded as Infinity?

Canonical Quiet NaN Fallback

The safe output policy in which the packer produces a canonical quiet NaN if it receives an unsupported or invalid internal classification.

Unpack → Process → Pack

The fundamental FP16 datapath pattern in which an IEEE encoding is translated into arithmetic-friendly information, processed internally, and converted back into an IEEE encoding.