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Warning

SpinalHDL floating-point support is under development and only partially used/tested, if you have any bugs with it, or you think that some functionality is missing, please create a Github issue. Also, please do not use undocumented features in your code.

Floating

Description

The Floating type corresponds to IEEE-754 encoded numbers. A second type called RecFloating helps in simplifying your design by recoding the floating-point value simplify some edge cases in IEEE-754 floating-point.

It’s composed of a sign bit, an exponent field and a mantissa field. The widths of the different fields are defined in the IEEE-754 or de-facto standards.

This type can be used with the following import:

import spinal.lib.experimental.math._

IEEE-754 floating format

The numbers are encoded into IEEE-754 floating-point format.

Recoded floating format

Since IEEE-754 has some quirks about denormalized numbers and special values, Berkeley proposed another way of recoding floating-point values.

The mantissa is modified so that denormalized values can be treated the same as the normalized ones.

The exponent field is one bit larger that one of the IEEE-754 number.

The sign bit is kept unchanged between the two encodings.

Examples can be found here

Zero

The zero is encoded with the three leading zeros of the exponent field being set to zero.

Denormalized values

Denormalized values are encoded in the same way as a normal floating-point number. The mantissa is shifted so that the first one becomes implicit. The exponent is encoded as 107 (decimal) plus the index of the highest bit set to 1.

Normalized values

The recoded mantissa for normalized values is exactly the same as the original IEEE-754 mantissa. The recoded exponent is encoded as 130 (decimal) plus the original exponent value.

Infinity

The recoded mantissa value is treated as don’t care. The recoded exponent three highest bits is 6 (decimal), the rest of the exponent can be treated as don’t care.

NaN

The recoded mantissa for normalized values is exactly the same as the original IEEE-754 mantissa. The recoded exponent three highest bits is 7 (decimal), the rest of the exponent can be treated as don’t care.

Declaration

The syntax to declare a floating-point number is as follows:

IEEE-754 Number

Syntax	Description
Floating(exponentSize: Int, mantissaSize: Int)	IEEE-754 Floating-point value with a custom exponent and mantissa size
Floating16()	IEEE-754 Half precision floating-point number
Floating32()	IEEE-754 Single precision floating-point number
Floating64()	IEEE-754 Double precision floating-point number
Floating128()	IEEE-754 Quad precision floating-point number

Recoded floating-point number

Syntax	Description
RecFloating(exponentSize: Int, mantissaSize: Int)	Recoded Floating-point value with a custom exponent and mantissa size
RecFloating16()	Recoded Half precision floating-point number
RecFloating32()	Recoded Single precision floating-point number
RecFloating64()	Recoded Double precision floating-point number
RecFloating128()	Recoded Quad precision floating-point number

Operators

The following operators are available for the Floating and RecFloating types:

Type cast

Operator	Description	Return
x.asBits	Binary cast to Bits	Bits(w(x) bits)
x.asBools	Cast into a array of Bool	Vec(Bool(),width(x))
x.toUInt(size: Int)	Return the corresponding UInt (with truncation)	UInt
x.toSInt(size: Int)	Return the corresponding SInt (with truncation)	SInt
x.fromUInt	Return the corresponding Floating (with truncation)	UInt
x.fromSInt	Return the corresponding Floating (with truncation)	SInt