ISO/IEC 23002-7:2021

INTERNATIONAL ISO/IEC
STANDARD 23002-7
First edition
2021-01
Information technology — MPEG video
technologies —
Part 7:
Versatile supplemental enhancement
information messages for coded video
bitstreams
Technologies de l'information — Technologies vidéo MPEG —
Partie 7: Messages d'améliorations complémentaires polyvalents pour
les flux binaires vidéo codés
Reference number
©
ISO/IEC 2021
© ISO/IEC 2021
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ii © ISO/IEC 2021 – All rights reserved

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Abbreviated terms . 8
5 Conventions . 9
5.1 General . 9
5.2 Arithmetic operators . 9
5.3 Logical operators .10
5.4 Relational operators .10
5.5 Bit-wise operators.10
5.6 Assignment operators .11
5.7 Range notation .11
5.8 Mathematical functions .11
5.9 Order of operation precedence .12
5.10 Variables, syntax elements and tables .13
5.11 Text description of logical operations .14
5.12 Processes .15
6 Syntax and semantics .16
6.1 General .16
6.2 Method of specifying syntax in tabular form .17
6.3 Specification of syntax functions and descriptors .18
7 Video usability information parameters .18
7.1 General .18
7.2 VUI parameters syntax .19
7.3 VUI parameters semantics .19
8 SEI messages .27
8.1 General .27
8.2 Filler payload SEI message .28
8.2.1 Filler payload SEI message syntax .28
8.2.2 Filler payload SEI message semantics .28
8.3 User data registered by Recommendation ITU-T T.35 SEI message .28
8.3.1 User data registered by Recommendation ITU-T T.35 SEI message syntax .28
8.3.2 User data registered by Recommendation ITU-T T.35 SEI message semantics .28
8.4 User data unregistered SEI message .29
8.4.1 User data unregistered SEI message syntax .29
8.4.2 User data unregistered SEI message semantics .29
8.5 Film grain characteristics SEI message .29
8.5.1 Film grain characteristics SEI message syntax .29
8.5.2 Film grain characteristics SEI message semantics .30
8.6 Frame packing arrangement SEI message .38
8.6.1 Frame packing arrangement SEI message syntax .38
8.6.2 Frame packing arrangement SEI message semantics .38
8.7 Parameter sets inclusion indication SEI message .47
8.7.1 Parameter sets inclusion indication SEI message syntax .47
8.7.2 Parameter sets inclusion indication SEI message semantics .47
8.8 Decoded picture hash SEI message .48
8.8.1 Decoded picture hash SEI message syntax.48
8.8.2 Decoded picture hash SEI message semantics .48
8.9 Mastering display colour volume SEI message .50
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8.9.1 Mastering display colour volume SEI message syntax .50
8.9.2 Mastering display colour volume SEI message semantics .50
8.10 Content light level information SEI message .52
8.10.1 Content light level information SEI message syntax .52
8.10.2 Content light level information SEI message semantics .52
8.11 Dependent random access point indication SEI message .53
8.11.1 Dependent random access point indication SEI message syntax .53
8.11.2 Dependent random access point indication SEI message semantics .53
8.12 Alternative transfer characteristics information SEI message .54
8.12.1 Alternative transfer characteristics information SEI message syntax.54
8.12.2 Alternative transfer characteristics SEI message semantics .54
8.13 Ambient viewing environment SEI message .54
8.13.1 Ambient viewing environment SEI message syntax .54
8.13.2 Ambient viewing environment SEI message semantics .54
8.14 Content colour volume SEI message .55
8.14.1 Content colour volume SEI message syntax .55
8.14.2 Content colour volume SEI message semantics .55
8.15 Omnidirectional video specific SEI messages .58
8.15.1 Sample location remapping process .58
8.15.2 Equirectangular projection SEI message .68
8.15.3 Generalized cubemap projection SEI message .70
8.15.4 Sphere rotation SEI message .76
8.15.5 Region-wise packing SEI message .78
8.15.6 Omnidirectional viewport SEI message .85
8.16 Frame-field information SEI message .87
8.16.1 Frame-field information SEI message syntax .87
8.16.2 Frame-field information SEI message semantics .87
8.17 Sample aspect ratio information SEI message .90
8.17.1 Sample aspect ratio information SEI message syntax .90
8.17.2 Sample aspect ratio information SEI message semantics .90
8.18 Reserved SEI message .91
8.18.1 Reserved SEI message syntax .91
8.18.2 Reserved SEI message semantics .91
9 Parsing process for k-th order Exp-Golomb codes .91
9.1 General .91
9.2 Mapping process for signed Exp-Golomb codes .92
Bibliography .94
iv © ISO/IEC 2021 – All rights reserved

Foreword
ISO (the International Organization for Standardization) and IEC (the International Electrotechnical
Commission) form the specialized system for worldwide standardization. National bodies that
are members of ISO or IEC participate in the development of International Standards through
technical committees established by the respective organization to deal with particular fields of
technical activity. ISO and IEC technical committees collaborate in fields of mutual interest. Other
international organizations, governmental and non-governmental, in liaison with ISO and IEC, also
take part in the work.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for
the different types of document should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject
of patent rights. ISO and IEC shall not be held responsible for identifying any or all such patent
rights. Details of any patent rights identified during the development of the document will be in the
Introduction and/or on the ISO list of patent declarations received (see www .iso .org/ patents) or the IEC
list of patent declarations received (see patents.iec.ch).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/
iso/ foreword .html.
This document was prepared by Joint Technical Committee ISO/IEC JTC 1, Information technology,
Subcommittee SC 29, Coding of audio, picture, multimedia and hypermedia information information, in
collaboration with ITU-T. The technically identical text is published as Recommendation ITU-T H.274
(08/2020).
A list of all parts in the ISO/IEC 23002 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
© ISO/IEC 2021 – All rights reserved v

Introduction
The International Organization for Standardization (ISO) and International Electrotechnical
Commission (IEC) draw attention to the fact that it is claimed that compliance with this document may
involve the use of patents.
ISO and IEC take no position concerning the evidence, validity and scope of these patent rights.
The holders of these patent rights have assured ISO and IEC that they are willing to negotiate licences
under reasonable and non-discriminatory terms and conditions with applicants throughout the world.
In this respect, the statements of the holders of these patent rights are registered with ISO and IEC.
Information may be obtained from the patent database available at www .iso .org/ patents.
Attention is drawn to the possibility that some of the elements of this document may be the subject
of patent rights other than those in the patent database. ISO and IEC shall not be held responsible for
identifying any or all such patent rights.
vi © ISO/IEC 2021 – All rights reserved

INTERNATIONAL STANDARD ISO/IEC 23002-7:2021(E)
Information technology — MPEG video technologies —
Part 7:
Versatile supplemental enhancement information
messages for coded video bitstreams
1 Scope
This document specifies the syntax and semantics of video usability information (VUI) parameters and
supplemental enhancement information (SEI) messages. The VUI parameters and SEI messages defined
in this document are designed to be conveyed within coded video bitstreams in a manner specified
in a video coding specification or to be conveyed by other means determined by the specifications for
systems that make use of such coded video bitstreams. This document is particularly intended for use
with coded video bitstreams as specified by Rec. ITU-T H.266 | ISO/IEC 23090-3, although it can also be
used with other types of coded video bitstreams.
VUI parameters and SEI messages can assist in processes related to decoding, display or other purposes.
However, unless otherwise specified in a referencing specification, the interpretation and use of the
VUI parameters and SEI messages specified in this document is not a required functionality of a video
decoder or receiving video system. Although semantics are specified for the VUI parameters and SEI
messages, decoders and receiving video systems can simply ignore the content of the VUI parameters
and SEI messages or can use them in a manner that somewhat differs from what is specified in this
document.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
Recommendation ITU-T H.273 | ISO/IEC 23091-2,Coding-independent code points for video signal
type identification
ISO/CIE 11664-1, Colorimetry — Part 1: CIE standard colorimetric observers
ISO/IEC 11578:1996, Information technology — Open Systems Interconnection — Remote Procedure
Call (RPC)
Recommendation ITU-T T.35:2000, Procedure for the allocation of ITU-T defined codes for non standard
facilities
IETF RFC 1321, The MD5 Message-Digest Algorithm
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
© ISO/IEC 2021 – All rights reserved 1

3.1
AU
access unit
set of PUs that belong to different layers and contain coded pictures associated with the same output time
3.2
APS
adaptation parameter set
syntax structure containing syntax elements that apply to zero or more slices as determined by zero or
more syntax elements found in slice headers
3.3
associated IRAP picture
previous IRAP picture (when present) in decoding order, for a particular picture, in the same layer as the
particular picture
3.4
azimuth circle
circle on a sphere connecting all points with the same azimuth value
Note 1 to entry: An azimuth circle is always a great circle like a longitude line on the earth.
3.5
byte
sequence of 8 bits, within which, when written or read as a sequence of bit values, the left-most and
right-most bits represent the most and least significant bits, respectively, and the bits are written or
read from left to right
3.6
chroma
sample array or single sample representing one of the two colour difference signals related to the
primary colours, represented by the symbols Cb and Cr
Note 1 to entry: The term chroma is used rather than the term chrominance in order to avoid implying the use of
linear light transfer characteristics that is often associated with the term chrominance.
3.7
CLVS
coded layer video sequence
sequence of PUs of the same layer that consists, in decoding order, of a CLVSS PU, followed by zero or
more PUs that are not CLVSS PUs, including all subsequent PUs up to but not including any subsequent PU
that is a CLVSS PU
3.8
CLVSS PU
PU in which the coded picture is a CLVSS picture
3.9
CLVSS
coded layer video sequence start
coded picture that starts a new CLVS as specified in a video coding specification
Note 1 to entry: In Rec. ITU-T H.266 | ISO/IEC 23090-3, a CLVSS picture is an IRAP picture with
NoIncorrectPicOutputFlag equal to 1 or a gradual decoding refresh picture with NoIncorrectPicOutputFlag equal
to 1. In Rec. ITU-T H.265 | ISO/IEC 23008-2, a CLVSS picture is an IRAP picture with NoRaslOutputFlag equal to 1.
3.10
coded picture
coded representation of a picture containing all CTUs of the picture
2 © ISO/IEC 2021 – All rights reserved

3.11
coded slice NAL unit
NAL unit that contains a coded slice
3.12
coded video bitstream
sequence of bits that forms the representation of a sequence of AUs forming one or more CVSs
3.13
CVS
coded video sequence
sequence of AUs that consists, in decoding order, of a CVSS AU, followed by zero or more AUs that are not
CVSS AUs, including all subsequent AUs up to but not including any subsequent AU that is a CVSS AU
3.14
CVSS AU
AU that has a PU for each layer present in the CVS and the coded picture in each PU is a CLVSS picture
3.15
component
array or single sample from one of the three arrays (luma and two chroma) that compose a picture in
4:2:0, 4:2:2, or 4:4:4 colour format or the array or a single sample of the array that compose a picture in
monochrome format
3.16
constituent picture
part of a spatially frame-packed stereoscopic picture that corresponds to one view, or a picture itself
when frame packing is not in use or the temporal interleaving frame packing arrangement is in use
3.17
cropped decoded picture
result of cropping a decoded picture based on the conformance cropping window for the corresponding
coded picture
3.18
decoded picture
decoded picture is derived by decoding a coded picture
3.19
decoder
embodiment of a decoding process
3.20
decoding order
order in which syntax elements are conveyed in the coded video bitstream and are processed by a
decoding process
3.21
decoding process
process that reads a coded video bitstream and derives decoded pictures from it
3.22
elevation circle
circle on a sphere connecting all points with the same elevation value
Note 1 to entry: An elevation circle is similar to a lattitude line on the earth. Except when the elevation value is
zero, an elevation circle is not a great circle like a longitude circle on the earth.
3.23
encoder
embodiment of an encoding process
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3.24
encoding process
process that produces a coded video bitstream
3.25
field
assembly of alternative rows of samples of a frame
3.26
flag
variable or single-bit syntax element that can take one of the two possible values: 0 and 1
3.27
frame
composition of a top field and a bottom field, where sample rows 0, 2, 4, . originate from the top field
and sample rows 1, 3, 5, . originate from the bottom field
3.28
global coordinate axes
coordinate axes associated with omnidirectional video that are associated with an externally
referenceable position and orientation
Note 1 to entry: The global coordinate axes could correspond to the position and orientation of a device or rig
used for omnidirectional audio/video acquisition as well as the position of an observer's head in the three-
dimensional space of the omnidirectional video rendering environment.
3.29
great circle
intersection of a sphere and a plane that passes through the centre point of the sphere
Note 1 to entry: A great circle is also known as an orthodrome or Riemannian circle.
3.30
inter prediction
aspect of the decoding process for a coded picture that makes use of data derived from the decoding
process of one or more previously decoded reference pictures
3.31
IRAP picture
coded picture starting from which all pictures in the same layer in both decoding order and output order
can be decoded without first decoding any picture in the same layer earlier in decoding order in the
coded video bitstream
3.32
layer
set of VCL NAL units that all have a particular value of layer identifier and the associated non-VCL
NAL units, wherein the layer identifier is a variable for which the value is specified by a video coding
specification
Note 1 to entry: In the contexts of Rec. ITU-T H.266 | ISO/IEC 23090-3 and Rec. ITU-T H.265 | ISO/IEC 23008-2,
the layer identifier is the value of the nuh_layer_id syntax element in the NAL unit header.
3.33
leading picture
picture that is in the same layer as the associated IRAP picture and precedes the associated IRAP picture
in output order
3.34
local coordinate axes
coordinate axes having a specified rotation relationship relative to the global coordinate axes
4 © ISO/IEC 2021 – All rights reserved

3.35
luma
sample array or single sample representing the monochrome signal related to the primary colours,
represented by the symbol or subscript Y or L
Note 1 to entry: The term luma is used rather than the term luminance in order to avoid implying the use of
linear light transfer characteristics that is often associated with the term luminance. The symbol L is sometimes
used instead of the symbol Y to avoid confusion with the symbol y as used for vertical location.
3.36
NAL unit
syntax structure containing an indication of the type of data that follows and bytes containing that data
in a manner that enables the extraction of a string of data bits from the syntax structure
3.37
non-VCL NAL unit
NAL unit that is not a VCL NAL unit
3.38
omnidirectional video
video content in a format that enables rendering according to the user's viewing orientation, e.g., if
viewed using a head-mounted device, or according to a user's desired viewport, reflecting a potentially
rotated viewing position
3.39
output order
order in which the decoded pictures are output from the decoder (for the decoded pictures that are to be
output from the decoder)
3.40
output time
time when a decoded picture is to be output from the decoder (for the decoded pictures that are to be
output from the decoder)
3.41
packed region
region in a region-wise packed picture that is mapped to a projected region according to a region-
wise packing
3.42
picture
array of luma samples in monochrome format or an array of luma samples and two corresponding
arrays of chroma samples in 4:2:0, 4:2:2, and 4:4:4 colour format
Note 1 to entry: A picture could be either a frame or a field. However, in one CLVS, either all pictures are frames
or all pictures are fields.
3.43
PPS
picture parameter set
A syntax structure containing syntax elements that apply to zero or more entire coded pictures as
determined by a syntax element that is the same for all slices of a picture and found in the picture header
or slice headers of each picture
3.44
PU
picture unit
set of NAL units that contain all VCL NAL units of a coded picture and their associated non-VCL NAL units
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3.45
projected picture
picture that uses a projection format for omnidirectional video
3.46
projected region
region in a projected picture that is mapped to a packed region according to a region-wise packing
3.47
projection
specified correspondence between the colour samples of a projected picture and azimuth and elevation
positions on a sphere
3.48
random access
act of starting the decoding process for a coded video bitstream at a point other than the beginning of
the bitstream
3.49
RASL picture
leading picture that cannot be correctly decoded when the decoding process starts from the associated
IRAP picture
3.50
reference picture
picture that contains samples that could be used for inter prediction in the decoding process of
subsequent pictures in decoding order
3.51
reference picture list
list of reference pictures that is used for inter prediction of a slice
3.52
region-wise packed picture
decoded picture that contains one or more packed regions
Note 1 to entry: A region-wise packed picture could contain a region-wise packing of a projected picture.
3.53
region-wise packing
transformation, resizing, and relocation of packed regions of a region-wise packed picture to remap the
packed regions to projected regions of a projected picture
3.54
sample aspect ratio
indicated width-to-height aspect ratio of the luma samples of the associated decoded pictures
3.55
slice
region of a picture that can be decoded separately from other regions of the same coded picture (although
in some cases the decoding process for the picture might use inter prediction that makes reference to
other previously decoded reference pictures)
3.56
source
term used to describe the video material or some of its attributes before encoding
3.57
sphere coordinates
azimuth and elevation angles identifying a location of a point on a sphere
6 © ISO/IEC 2021 – All rights reserved

3.58
sphere region
region on a sphere, specified either by four great circles or by two azimuth circles and two elevation
circles, or such a region on a rotated sphere after applying yaw, pitch, and roll rotations
3.59
STSA picture
coded picture that enables up-switching, at the coded picture, to the temporal sublayer containing the
coded picture, from the immediately lower temporal sublayer of the same layer when the coded picture
does not belong to the lowest temporal sublayer
Note 1 to entry: An STSA picture does not use pictures in the same layer and with the same temporal sublayer
identifier as the STSA picture for inter prediction reference. Pictures following an STSA picture in decoding order
in the same layer and with the same temporal sublayer identifier as the STSA picture do not use pictures prior to
the STSA picture in decoding order in the same layer and with the same temporal sublayer identifier as the STSA
picture for inter prediction reference. STSA pictures in an independent layer (i.e., a layer that does not depend on
other layers in its decoding) always have a temporal sublayer identifier greater than 0.
3.60
syntax element
element of data represented in a syntax structure
3.61
syntax structure
zero or more syntax elements that are present together in a specified order in a string of data bits,
where the left-most bit is considered to be the first and most significant bit, and the right-most bit is
considered to be the last and least significant bit
3.62
SEI message
syntax structure that provides a particular type of information that assists in processes related to
decoding, display or other purposes but is not needed by the decoding process in order to determine the
values of the samples in decoded pictures
3.63
temporal sublayer
subset of a temporal scalable bitstream, consisting of VCL NAL units with a particular value of temporal
sublayer identifier and the associated non-VCL NAL units
3.64
temporal sublayer identifier
number greater than or equal to 0 defined by a variable for which the value is specified by a video
coding specification such that pictures of all temporal sublayers have a specified temporal output order
relative to each other and pictures with a lower temporal sublayer identifier can be decoded without
reference to pictures with a higher temporal sublayer identifier
3.65
tilt angle
angle indicating the amount of tilt of a sphere region, measured as the amount of rotation of a sphere
region along the axis originating from the sphere origin passing through the centre point of the sphere
region, where the angle value increases clockwise when looking from the origin towards the positive
end of the axis
3.66
trailing picture
coded picture that is associated with an IRAP picture and follows the IRAP picture in both decoding
order and output order
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3.67
VCL NAL unit
collective term for coded slice NAL units and the subset of other NAL units that have reserved values of
NAL unit type identifiers that are classified as VCL NAL units in a referencing specification
3.68
VUI parameters
syntax structure that identifies properties of interpretation of decoded pictures for display purposes,
particularly including colour representation information
3.69
viewport
region of omnidirectional video content suitable for display and viewing by the user
4 Abbreviated terms
AU access unit
APS adaptation parameter set
CRC cyclic redundancy check
CLVS coded layer video sequence
CLVSS coded layer video sequence start
CVS coded video sequence
DRAP dependent random access point
FIR finite impulse response
IRAP intra random access point
NAL network abstraction layer
PPS picture parameter set
PU picture unit
RASL random access skipped leading
RWP region-wise packing
SAR sample aspect ratio
SARI sample aspect ratio information
SEI supplemental enhancement information
STSA step-wise temporal sublayer access
VCL video coding layer
VUI video usability information
8 © ISO/IEC 2021 – All rights reserved

5 Conventions
5.1 General
The term "this document" is used to refer to this Recommendation | International Standard.
In this document, the following verbal forms are used:
— “shall” indicates a requirement. When used to express a mandatory constraint on the values of syntax
elements or the values of variables derived from these syntax elements, it is the responsibility of the
encoder to ensure that the constraint is fulfilled.
— “should” indicates a recommendation. It is used to refer to behaviour of an implementation that is
encouraged to be followed under anticipated ordinary circumstances, but is not a requirement for
conformance to this document.
— “may” indicates a permission.
— “can” indicates a possibility or a capability.
Information marked as “NOTE” is intended to assist the understanding or use of the document. “Notes
to entry” used in Clause 3 provide additional information that supplements the terminological data and
can contain provisions relating to the use of a term.
The word "reserved" is used to specify that some values of a particular syntax element are for future
use by ITU-T | ISO/IEC and shall not be used in syntax structures conforming to this document, but
could potentially be used in syntax structures conforming to future editions of this document by
ITU-T | ISO/IEC.
The word "unspecified" is used to describe some values of a particular syntax element to indicate
that the values have no specified meaning in this document and are not expected to have a specified
meaning in future editions of this document by ITU-T | ISO/IEC.
The mathematical operators used in this document are similar to those used in the C programming
language. However, the results of integer division and arithmetic shift operations are defined more
precisely, and additional operations are defined, such as exponentiation and real-valued division.
Numbering and counting conventions generally begin from 0, e.g., "the first" is equivalent to the 0-th,
"the second" is equivalent to the 1-th, etc.
5.2 Arithmetic operators
+ addition
− subtraction (as a two-argument operator) or negation (as a unary prefix operator)
* multiplication, including matrix multiplication
y
x exponentiation
Specifies x to the power of y. In other contexts, such notation is used for superscripting not
intended for interpretation as exponentiation.
/ integer division with truncation of the result toward zero
For example, 7 / 4 and −7 / −4 are truncated to 1 and −7 / 4 and 7 / −4 are truncated to −1.
÷ division in mathematical equations where no truncation or rounding is intended
© ISO/IEC 2021 – All rights reserved 9

x
division in mathematical equations where no truncation or rounding is intended
y
y
summation of f( i ) with i taking all integer values from x up to and including y
f( i )
∑
i = x
x % y modulus
Remainder of x divided by y, defined only for integers x and y with x >= 0 and y > 0
5.3 Logical operators
x && y Boolean logical "and" of x and y
x | | y Boolean logical "or" of x and y
! Boolean logical "not"
x ? y : z if x is TRUE or not equal to 0, evaluates to the value of y;
otherwise, evaluates to the value of z
5.4 Relational operators
> greater than
>= greater than or equal to
< less than
<= less than or equal to
= = equal to
!= not equal to
When a relational operator is applied to a syntax element or variable that has been assigned the value
"na" (not applicable), the value "na" is treated as a distinct value for the syntax element or variable. The
value "na" is considered not to be equal to any other value.
5.5 Bit-wise operators
& bit-wise "and"
When operating on integer arguments, operates on a two's complement representation of the
integer value. When operating on a binary argument that contains fewer bits than another ar-
gument, the shorter argument is extended by adding more significant bits equal to 0.
| bit-wise "or"
When operating on integer arguments, operates on a two's complement representation of the
integer value. When operating on a binary argument that contains fewer bits than another ar-
gument, the shorter argument is extended by adding more significant bits equal to 0.
10 © ISO/IEC 2021 – All rights reserved

^ bit-wise "exclusive or"
When operating on integer arguments, operates on a two's complement representation of the
integer value. When operating on a binary argument that contains fewer bits than another ar-
gument, the shorter argument is extended by adding more significant bits equal to 0.
x >> y arithmetic right shift of a two's complement integer representation of x by y binary digits
This function is defined only for non-negative integer values of y. Bits shifted into the most
significant bits (MSBs) as a result of the right shift have a value equal to the MSB of x prior to
the shift operation.
x << y arithmetic left shift of a two's complement integer representation of x by y binary digits
This function is defined only for non-negative integer values of y. Bits shifted into the least sig-
nificant bits (LSBs) as a result of the left shift have a value equal to 0.
5.6 Assignment operators
= assignment operator
++ increment, i.e., x++ is equivalent to x = x + 1; when used in an array index, evaluates to the value
of the variable prior to the increment operation
− − decrement, i.e., x− − is equivalent to x = x − 1; when used in an array index, evaluates to the
value of the variable prior to the decrement operation
+= increment by amount specified, i.e., x += 3 is equivalent to x = x + 3, and x += (−3) is equivalent
to x = x + (−3)
−= decrement by amount specified, i.e., x −= 3 is equivalent to x = x − 3, and x −= (−3) is equivalent
to x = x − (−3)
5.7 Range notation
x = y.z x takes on integer values starting from y to z, inclusive, with x, y, and z being integer numbers
and z being greater than y
5.8 Mathematical functions
x; x> =0

Abs( x ) =  (1)

−x; x< 0

Asin( x ) trigonometric inverse sine function, operating on an argument x that is in the range of −1.0
to 1.0, inclusive, with an output value in the range of −π÷2 to π÷2, inclusive, in units of radians (2)
Atan( x ) trigonometric inverse tangent function, operating on an argument x, with an output value
in the range of −π÷2 to π÷2, inclusive, in units of radians (3)
© ISO/IEC 2021 – All rights reserved 11




y
 

Atan ; x > 0
 

x
 

y

 
Atan +π
 

; x < 0 && y >= 0
 x 

Atan2( y, x ) =  (4)

y ; x < 0 && y < 0
 

Atan −π
 

 x 

 π
+

; x = = 0 && y >= 0

 π ; otherwiise
−


Ceil( x ) smallest integer greater than or equal to x (5)
x; z < x


Clip3( x, y, z ) = y; z > y (6)


z; otherwise

Cos( x ) trigonometric cosine function operating on an argument x in units of radians (7)
Floor( x ) largest integer less than or equal to x (8)
Ln( x ) natural logarithm of x (the base-e logarithm, where e is the natural logarithm base constant
2.718 281 828.) (9)
x; x >= y

Max( x, y ) =  (10)

y; x < y

Round( x ) = Sign( x ) * Floor( Abs( x ) + 0.5 ) (11)
1; x > 0


Sign( x ) = 0 ;x = = 0 (12)


−1; x < 0

Sin( x ) trigonometric sine function operating on an argument x in units of radians (13)
Sqrt( x ) square root of x (14)
Tan( x ) trigonometric tangent function operating on an argument x in units of radians (15)
5.9 Order of operation precedence
When order of precedence in an expression is not indicated explicitly by use of parentheses, the
foll
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