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  • @chapter Syntax
    @c man begin SYNTAX
    
    This section documents the syntax and formats employed by the FFmpeg
    libraries and tools.
    
    @anchor{quoting_and_escaping}
    @section Quoting and escaping
    
    FFmpeg adopts the following quoting and escaping mechanism, unless
    explicitly specified. The following rules are applied:
    
    @itemize
    @item
    
    @samp{'} and @samp{\} are special characters (respectively used for
    
    quoting and escaping). In addition to them, there might be other
    special characters depending on the specific syntax where the escaping
    and quoting are employed.
    
    @item
    
    A special character is escaped by prefixing it with a @samp{\}.
    
    All characters enclosed between @samp{''} are included literally in the
    parsed string. The quote character @samp{'} itself cannot be quoted,
    
    so you may need to close the quote and escape it.
    
    @item
    Leading and trailing whitespaces, unless escaped or quoted, are
    removed from the parsed string.
    @end itemize
    
    Note that you may need to add a second level of escaping when using
    the command line or a script, which depends on the syntax of the
    adopted shell language.
    
    The function @code{av_get_token} defined in
    @file{libavutil/avstring.h} can be used to parse a token quoted or
    escaped according to the rules defined above.
    
    The tool @file{tools/ffescape} in the FFmpeg source tree can be used
    to automatically quote or escape a string in a script.
    
    @subsection Examples
    
    @itemize
    @item
    Escape the string @code{Crime d'Amour} containing the @code{'} special
    character:
    @example
    Crime d\'Amour
    @end example
    
    @item
    The string above contains a quote, so the @code{'} needs to be escaped
    when quoting it:
    @example
    'Crime d'\''Amour'
    @end example
    
    @item
    Include leading or trailing whitespaces using quoting:
    @example
    '  this string starts and ends with whitespaces  '
    @end example
    
    @item
    Escaping and quoting can be mixed together:
    @example
    ' The string '\'string\'' is a string '
    @end example
    
    @item
    
    To include a literal @samp{\} you can use either escaping or quoting:
    
    @example
    'c:\foo' can be written as c:\\foo
    @end example
    @end itemize
    
    @anchor{date syntax}
    @section Date
    
    The accepted syntax is:
    @example
    [(YYYY-MM-DD|YYYYMMDD)[T|t| ]]((HH:MM:SS[.m...]]])|(HHMMSS[.m...]]]))[Z]
    now
    @end example
    
    If the value is "now" it takes the current time.
    
    Time is local time unless Z is appended, in which case it is
    interpreted as UTC.
    If the year-month-day part is not specified it takes the current
    year-month-day.
    
    @anchor{time duration syntax}
    @section Time duration
    
    
    There are two accepted syntaxes for expressing time duration.
    
    @example
    [-][@var{HH}:]@var{MM}:@var{SS}[.@var{m}...]
    @end example
    
    @var{HH} expresses the number of hours, @var{MM} the number of minutes
    for a maximum of 2 digits, and @var{SS} the number of seconds for a
    maximum of 2 digits. The @var{m} at the end expresses decimal value for
    @var{SS}.
    
    @emph{or}
    
    
    [-]@var{S}+[.@var{m}...]
    
    @var{S} expresses the number of seconds, with the optional decimal part
    @var{m}.
    
    In both expressions, the optional @samp{-} indicates negative duration.
    
    @subsection Examples
    
    The following examples are all valid time duration:
    
    @table @samp
    @item 55
    55 seconds
    
    @item 12:03:45
    12 hours, 03 minutes and 45 seconds
    
    @item 23.189
    23.189 seconds
    @end table
    
    
    @anchor{video size syntax}
    @section Video size
    Specify the size of the sourced video, it may be a string of the form
    @var{width}x@var{height}, or the name of a size abbreviation.
    
    The following abbreviations are recognized:
    @table @samp
    @item ntsc
    720x480
    @item pal
    720x576
    @item qntsc
    352x240
    @item qpal
    352x288
    @item sntsc
    640x480
    @item spal
    768x576
    @item film
    352x240
    @item ntsc-film
    352x240
    @item sqcif
    128x96
    @item qcif
    176x144
    @item cif
    352x288
    @item 4cif
    704x576
    @item 16cif
    1408x1152
    @item qqvga
    160x120
    @item qvga
    320x240
    @item vga
    640x480
    @item svga
    800x600
    @item xga
    1024x768
    @item uxga
    1600x1200
    @item qxga
    2048x1536
    @item sxga
    1280x1024
    @item qsxga
    2560x2048
    @item hsxga
    5120x4096
    @item wvga
    852x480
    @item wxga
    1366x768
    @item wsxga
    1600x1024
    @item wuxga
    1920x1200
    @item woxga
    2560x1600
    @item wqsxga
    3200x2048
    @item wquxga
    3840x2400
    @item whsxga
    6400x4096
    @item whuxga
    7680x4800
    @item cga
    320x200
    @item ega
    640x350
    @item hd480
    852x480
    @item hd720
    1280x720
    @item hd1080
    1920x1080
    @item 2k
    2048x1080
    @item 2kflat
    1998x1080
    @item 2kscope
    2048x858
    @item 4k
    4096x2160
    @item 4kflat
    3996x2160
    @item 4kscope
    4096x1716
    
    @item nhd
    640x360
    @item hqvga
    240x160
    @item wqvga
    400x240
    @item fwqvga
    432x240
    @item hvga
    480x320
    @item qhd
    960x540
    
    @item 2kdci
    2048x1080
    @item 4kdci
    4096x2160
    
    @end table
    
    @anchor{video rate syntax}
    @section Video rate
    
    Specify the frame rate of a video, expressed as the number of frames
    generated per second. It has to be a string in the format
    @var{frame_rate_num}/@var{frame_rate_den}, an integer number, a float
    number or a valid video frame rate abbreviation.
    
    The following abbreviations are recognized:
    @table @samp
    @item ntsc
    30000/1001
    @item pal
    25/1
    @item qntsc
    30000/1001
    @item qpal
    25/1
    @item sntsc
    30000/1001
    @item spal
    25/1
    @item film
    24/1
    @item ntsc-film
    24000/1001
    @end table
    
    @anchor{ratio syntax}
    @section Ratio
    
    A ratio can be expressed as an expression, or in the form
    @var{numerator}:@var{denominator}.
    
    Note that a ratio with infinite (1/0) or negative value is
    considered valid, so you should check on the returned value if you
    want to exclude those values.
    
    The undefined value can be expressed using the "0:0" string.
    
    @anchor{color syntax}
    @section Color
    
    
    It can be the name of a color as defined below (case insensitive match) or a
    
    @code{[0x|#]RRGGBB[AA]} sequence, possibly followed by @@ and a string
    
    representing the alpha component.
    
    The alpha component may be a string composed by "0x" followed by an
    hexadecimal number or a decimal number between 0.0 and 1.0, which
    
    represents the opacity value (@samp{0x00} or @samp{0.0} means completely
    transparent, @samp{0xff} or @samp{1.0} completely opaque). If the alpha
    component is not specified then @samp{0xff} is assumed.
    
    The string @samp{random} will result in a random color.
    
    The following names of colors are recognized:
    @table @samp
    @item AliceBlue
    0xF0F8FF
    @item AntiqueWhite
    0xFAEBD7
    @item Aqua
    0x00FFFF
    @item Aquamarine
    0x7FFFD4
    @item Azure
    0xF0FFFF
    @item Beige
    0xF5F5DC
    @item Bisque
    0xFFE4C4
    @item Black
    0x000000
    @item BlanchedAlmond
    0xFFEBCD
    @item Blue
    0x0000FF
    @item BlueViolet
    0x8A2BE2
    @item Brown
    0xA52A2A
    @item BurlyWood
    0xDEB887
    @item CadetBlue
    0x5F9EA0
    @item Chartreuse
    0x7FFF00
    @item Chocolate
    0xD2691E
    @item Coral
    0xFF7F50
    @item CornflowerBlue
    0x6495ED
    @item Cornsilk
    0xFFF8DC
    @item Crimson
    0xDC143C
    @item Cyan
    0x00FFFF
    @item DarkBlue
    0x00008B
    @item DarkCyan
    0x008B8B
    @item DarkGoldenRod
    0xB8860B
    @item DarkGray
    0xA9A9A9
    @item DarkGreen
    0x006400
    @item DarkKhaki
    0xBDB76B
    @item DarkMagenta
    0x8B008B
    @item DarkOliveGreen
    0x556B2F
    @item Darkorange
    0xFF8C00
    @item DarkOrchid
    0x9932CC
    @item DarkRed
    0x8B0000
    @item DarkSalmon
    0xE9967A
    @item DarkSeaGreen
    0x8FBC8F
    @item DarkSlateBlue
    0x483D8B
    @item DarkSlateGray
    0x2F4F4F
    @item DarkTurquoise
    0x00CED1
    @item DarkViolet
    0x9400D3
    @item DeepPink
    0xFF1493
    @item DeepSkyBlue
    0x00BFFF
    @item DimGray
    0x696969
    @item DodgerBlue
    0x1E90FF
    @item FireBrick
    0xB22222
    @item FloralWhite
    0xFFFAF0
    @item ForestGreen
    0x228B22
    @item Fuchsia
    0xFF00FF
    @item Gainsboro
    0xDCDCDC
    @item GhostWhite
    0xF8F8FF
    @item Gold
    0xFFD700
    @item GoldenRod
    0xDAA520
    @item Gray
    0x808080
    @item Green
    0x008000
    @item GreenYellow
    0xADFF2F
    @item HoneyDew
    0xF0FFF0
    @item HotPink
    0xFF69B4
    @item IndianRed
    0xCD5C5C
    @item Indigo
    0x4B0082
    @item Ivory
    0xFFFFF0
    @item Khaki
    0xF0E68C
    @item Lavender
    0xE6E6FA
    @item LavenderBlush
    0xFFF0F5
    @item LawnGreen
    0x7CFC00
    @item LemonChiffon
    0xFFFACD
    @item LightBlue
    0xADD8E6
    @item LightCoral
    0xF08080
    @item LightCyan
    0xE0FFFF
    @item LightGoldenRodYellow
    0xFAFAD2
    @item LightGreen
    0x90EE90
    @item LightGrey
    0xD3D3D3
    @item LightPink
    0xFFB6C1
    @item LightSalmon
    0xFFA07A
    @item LightSeaGreen
    0x20B2AA
    @item LightSkyBlue
    0x87CEFA
    @item LightSlateGray
    0x778899
    @item LightSteelBlue
    0xB0C4DE
    @item LightYellow
    0xFFFFE0
    @item Lime
    0x00FF00
    @item LimeGreen
    0x32CD32
    @item Linen
    0xFAF0E6
    @item Magenta
    0xFF00FF
    @item Maroon
    0x800000
    @item MediumAquaMarine
    0x66CDAA
    @item MediumBlue
    0x0000CD
    @item MediumOrchid
    0xBA55D3
    @item MediumPurple
    0x9370D8
    @item MediumSeaGreen
    0x3CB371
    @item MediumSlateBlue
    0x7B68EE
    @item MediumSpringGreen
    0x00FA9A
    @item MediumTurquoise
    0x48D1CC
    @item MediumVioletRed
    0xC71585
    @item MidnightBlue
    0x191970
    @item MintCream
    0xF5FFFA
    @item MistyRose
    0xFFE4E1
    @item Moccasin
    0xFFE4B5
    @item NavajoWhite
    0xFFDEAD
    @item Navy
    0x000080
    @item OldLace
    0xFDF5E6
    @item Olive
    0x808000
    @item OliveDrab
    0x6B8E23
    @item Orange
    0xFFA500
    @item OrangeRed
    0xFF4500
    @item Orchid
    0xDA70D6
    @item PaleGoldenRod
    0xEEE8AA
    @item PaleGreen
    0x98FB98
    @item PaleTurquoise
    0xAFEEEE
    @item PaleVioletRed
    0xD87093
    @item PapayaWhip
    0xFFEFD5
    @item PeachPuff
    0xFFDAB9
    @item Peru
    0xCD853F
    @item Pink
    0xFFC0CB
    @item Plum
    0xDDA0DD
    @item PowderBlue
    0xB0E0E6
    @item Purple
    0x800080
    @item Red
    0xFF0000
    @item RosyBrown
    0xBC8F8F
    @item RoyalBlue
    0x4169E1
    @item SaddleBrown
    0x8B4513
    @item Salmon
    0xFA8072
    @item SandyBrown
    0xF4A460
    @item SeaGreen
    0x2E8B57
    @item SeaShell
    0xFFF5EE
    @item Sienna
    0xA0522D
    @item Silver
    0xC0C0C0
    @item SkyBlue
    0x87CEEB
    @item SlateBlue
    0x6A5ACD
    @item SlateGray
    0x708090
    @item Snow
    0xFFFAFA
    @item SpringGreen
    0x00FF7F
    @item SteelBlue
    0x4682B4
    @item Tan
    0xD2B48C
    @item Teal
    0x008080
    @item Thistle
    0xD8BFD8
    @item Tomato
    0xFF6347
    @item Turquoise
    0x40E0D0
    @item Violet
    0xEE82EE
    @item Wheat
    0xF5DEB3
    @item White
    0xFFFFFF
    @item WhiteSmoke
    0xF5F5F5
    @item Yellow
    0xFFFF00
    @item YellowGreen
    0x9ACD32
    @end table
    
    @anchor{channel layout syntax}
    @section Channel Layout
    
    A channel layout specifies the spatial disposition of the channels in
    a multi-channel audio stream. To specify a channel layout, FFmpeg
    makes use of a special syntax.
    
    Individual channels are identified by an id, as given by the table
    below:
    @table @samp
    @item FL
    front left
    @item FR
    front right
    @item FC
    front center
    @item LFE
    low frequency
    @item BL
    back left
    @item BR
    back right
    @item FLC
    front left-of-center
    @item FRC
    front right-of-center
    @item BC
    back center
    @item SL
    side left
    @item SR
    side right
    @item TC
    top center
    @item TFL
    top front left
    @item TFC
    top front center
    @item TFR
    top front right
    @item TBL
    top back left
    @item TBC
    top back center
    @item TBR
    top back right
    @item DL
    downmix left
    @item DR
    downmix right
    @item WL
    wide left
    @item WR
    wide right
    @item SDL
    surround direct left
    @item SDR
    surround direct right
    @item LFE2
    low frequency 2
    @end table
    
    Standard channel layout compositions can be specified by using the
    following identifiers:
    @table @samp
    @item mono
    FC
    @item stereo
    FL+FR
    @item 2.1
    FL+FR+LFE
    @item 3.0
    FL+FR+FC
    @item 3.0(back)
    FL+FR+BC
    @item 4.0
    FL+FR+FC+BC
    @item quad
    FL+FR+BL+BR
    @item quad(side)
    FL+FR+SL+SR
    @item 3.1
    FL+FR+FC+LFE
    @item 5.0
    FL+FR+FC+BL+BR
    @item 5.0(side)
    FL+FR+FC+SL+SR
    @item 4.1
    FL+FR+FC+LFE+BC
    @item 5.1
    FL+FR+FC+LFE+BL+BR
    @item 5.1(side)
    FL+FR+FC+LFE+SL+SR
    @item 6.0
    FL+FR+FC+BC+SL+SR
    @item 6.0(front)
    FL+FR+FLC+FRC+SL+SR
    @item hexagonal
    FL+FR+FC+BL+BR+BC
    @item 6.1
    FL+FR+FC+LFE+BC+SL+SR
    @item 6.1
    FL+FR+FC+LFE+BL+BR+BC
    @item 6.1(front)
    FL+FR+LFE+FLC+FRC+SL+SR
    @item 7.0
    FL+FR+FC+BL+BR+SL+SR
    @item 7.0(front)
    FL+FR+FC+FLC+FRC+SL+SR
    @item 7.1
    FL+FR+FC+LFE+BL+BR+SL+SR
    @item 7.1(wide)
    FL+FR+FC+LFE+BL+BR+FLC+FRC
    @item 7.1(wide-side)
    FL+FR+FC+LFE+FLC+FRC+SL+SR
    @item octagonal
    FL+FR+FC+BL+BR+BC+SL+SR
    @item downmix
    DL+DR
    @end table
    
    A custom channel layout can be specified as a sequence of terms, separated by
    '+' or '|'. Each term can be:
    @itemize
    @item
    the name of a standard channel layout (e.g. @samp{mono},
    @samp{stereo}, @samp{4.0}, @samp{quad}, @samp{5.0}, etc.)
    
    @item
    the name of a single channel (e.g. @samp{FL}, @samp{FR}, @samp{FC}, @samp{LFE}, etc.)
    
    @item
    a number of channels, in decimal, optionally followed by 'c', yielding
    the default channel layout for that number of channels (see the
    function @code{av_get_default_channel_layout})
    
    @item
    a channel layout mask, in hexadecimal starting with "0x" (see the
    @code{AV_CH_*} macros in @file{libavutil/channel_layout.h}.
    @end itemize
    
    Starting from libavutil version 53 the trailing character "c" to
    specify a number of channels will be required, while a channel layout
    mask could also be specified as a decimal number (if and only if not
    followed by "c").
    
    See also the function @code{av_get_channel_layout} defined in
    @file{libavutil/channel_layout.h}.
    
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    @chapter Expression Evaluation
    @c man begin EXPRESSION EVALUATION
    
    
    When evaluating an arithmetic expression, FFmpeg uses an internal
    
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    formula evaluator, implemented through the @file{libavutil/eval.h}
    interface.
    
    An expression may contain unary, binary operators, constants, and
    functions.
    
    Two expressions @var{expr1} and @var{expr2} can be combined to form
    another expression "@var{expr1};@var{expr2}".
    @var{expr1} and @var{expr2} are evaluated in turn, and the new
    expression evaluates to the value of @var{expr2}.
    
    The following binary operators are available: @code{+}, @code{-},
    @code{*}, @code{/}, @code{^}.
    
    The following unary operators are available: @code{+}, @code{-}.
    
    The following functions are available:
    @table @option
    
    @item abs(x)
    Compute absolute value of @var{x}.
    
    @item acos(x)
    Compute arccosine of @var{x}.
    
    @item asin(x)
    Compute arcsine of @var{x}.
    
    @item atan(x)
    Compute arctangent of @var{x}.
    
    
    @item between(x, min, max)
    Return 1 if @var{x} is greater than or equal to @var{min} and lesser than or
    equal to @var{max}, 0 otherwise.
    
    
    @item bitand(x, y)
    @item bitor(x, y)
    Compute bitwise and/or operation on @var{x} and @var{y}.
    
    The results of the evaluation of @var{x} and @var{y} are converted to
    integers before executing the bitwise operation.
    
    Note that both the conversion to integer and the conversion back to
    floating point can lose precision. Beware of unexpected results for
    large numbers (usually 2^53 and larger).
    
    
    @item ceil(expr)
    Round the value of expression @var{expr} upwards to the nearest
    integer. For example, "ceil(1.5)" is "2.0".
    
    @item clip(x, min, max)
    Return the value of @var{x} clipped between @var{min} and @var{max}.
    
    
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    @item cos(x)
    
    Compute cosine of @var{x}.
    
    
    @item cosh(x)
    Compute hyperbolic cosine of @var{x}.
    
    @item eq(x, y)
    Return 1 if @var{x} and @var{y} are equivalent, 0 otherwise.
    
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    @item exp(x)
    
    Compute exponential of @var{x} (with base @code{e}, the Euler's number).
    
    
    @item floor(expr)
    Round the value of expression @var{expr} downwards to the nearest
    integer. For example, "floor(-1.5)" is "-2.0".
    
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    @item gauss(x)
    
    Compute Gauss function of @var{x}, corresponding to
    @code{exp(-x*x/2) / sqrt(2*PI)}.
    
    
    @item gcd(x, y)
    Return the greatest common divisor of @var{x} and @var{y}. If both @var{x} and
    @var{y} are 0 or either or both are less than zero then behavior is undefined.
    
    @item gt(x, y)
    Return 1 if @var{x} is greater than @var{y}, 0 otherwise.
    
    @item gte(x, y)
    Return 1 if @var{x} is greater than or equal to @var{y}, 0 otherwise.
    
    @item hypot(x, y)
    This function is similar to the C function with the same name; it returns
    "sqrt(@var{x}*@var{x} + @var{y}*@var{y})", the length of the hypotenuse of a
    right triangle with sides of length @var{x} and @var{y}, or the distance of the
    point (@var{x}, @var{y}) from the origin.
    
    @item if(x, y)
    Evaluate @var{x}, and if the result is non-zero return the result of
    the evaluation of @var{y}, return 0 otherwise.
    
    @item if(x, y, z)
    Evaluate @var{x}, and if the result is non-zero return the evaluation
    result of @var{y}, otherwise the evaluation result of @var{z}.
    
    @item ifnot(x, y)
    Evaluate @var{x}, and if the result is zero return the result of the
    evaluation of @var{y}, return 0 otherwise.
    
    @item ifnot(x, y, z)
    Evaluate @var{x}, and if the result is zero return the evaluation
    result of @var{y}, otherwise the evaluation result of @var{z}.
    
    @item isinf(x)
    Return 1.0 if @var{x} is +/-INFINITY, 0.0 otherwise.
    
    @item isnan(x)
    Return 1.0 if @var{x} is NAN, 0.0 otherwise.
    
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    @item ld(var)
    
    Load the value of the internal variable with number
    
    @var{var}, which was previously stored with st(@var{var}, @var{expr}).
    
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    The function returns the loaded value.
    
    
    @item log(x)
    Compute natural logarithm of @var{x}.
    
    @item lt(x, y)
    Return 1 if @var{x} is lesser than @var{y}, 0 otherwise.
    
    @item lte(x, y)
    Return 1 if @var{x} is lesser than or equal to @var{y}, 0 otherwise.
    
    @item max(x, y)
    Return the maximum between @var{x} and @var{y}.
    
    @item min(x, y)
    Return the maximum between @var{x} and @var{y}.
    
    @item mod(x, y)
    Compute the remainder of division of @var{x} by @var{y}.
    
    
    @item not(expr)
    Return 1.0 if @var{expr} is zero, 0.0 otherwise.
    
    
    @item pow(x, y)
    Compute the power of @var{x} elevated @var{y}, it is equivalent to
    "(@var{x})^(@var{y})".
    
    @item print(t)
    @item print(t, l)
    Print the value of expression @var{t} with loglevel @var{l}. If
    @var{l} is not specified then a default log level is used.
    Returns the value of the expression printed.
    
    Prints t with loglevel l
    
    
    @item random(x)
    Return a pseudo random value between 0.0 and 1.0. @var{x} is the index of the
    internal variable which will be used to save the seed/state.
    
    
    @item root(expr, max)
    Find an input value for which the function represented by @var{expr}
    with argument @var{ld(0)} is 0 in the interval 0..@var{max}.
    
    The expression in @var{expr} must denote a continuous function or the
    result is undefined.
    
    @var{ld(0)} is used to represent the function input value, which means
    that the given expression will be evaluated multiple times with
    various input values that the expression can access through
    @code{ld(0)}. When the expression evaluates to 0 then the
    corresponding input value will be returned.
    
    @item sin(x)
    Compute sine of @var{x}.
    
    @item sinh(x)
    Compute hyperbolic sine of @var{x}.
    
    @item sqrt(expr)
    Compute the square root of @var{expr}. This is equivalent to
    "(@var{expr})^.5".
    
    @item squish(x)
    Compute expression @code{1/(1 + exp(4*x))}.
    
    @item st(var, expr)
    
    Store the value of the expression @var{expr} in an internal
    
    variable. @var{var} specifies the number of the variable where to
    store the value, and it is a value ranging from 0 to 9. The function
    returns the value stored in the internal variable.
    Note, Variables are currently not shared between expressions.
    
    @item tan(x)
    Compute tangent of @var{x}.
    
    @item tanh(x)
    Compute hyperbolic tangent of @var{x}.
    
    @item taylor(expr, x)
    @item taylor(expr, x, id)
    Evaluate a Taylor series at @var{x}, given an expression representing
    the @code{ld(id)}-th derivative of a function at 0.
    
    When the series does not converge the result is undefined.
    
    @var{ld(id)} is used to represent the derivative order in @var{expr},
    which means that the given expression will be evaluated multiple times
    with various input values that the expression can access through
    @code{ld(id)}. If @var{id} is not specified then 0 is assumed.
    
    Note, when you have the derivatives at y instead of 0,
    @code{taylor(expr, x-y)} can be used.
    
    Return the current (wallclock) time in seconds.
    
    @item trunc(expr)
    Round the value of expression @var{expr} towards zero to the nearest
    integer. For example, "trunc(-1.5)" is "-1.0".
    
    @item while(cond, expr)
    Evaluate expression @var{expr} while the expression @var{cond} is
    non-zero, and returns the value of the last @var{expr} evaluation, or
    NAN if @var{cond} was always false.
    
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    @end table
    
    
    The following constants are available:
    @table @option
    @item PI
    
    area of the unit disc, approximately 3.14
    
    exp(1) (Euler's number), approximately 2.718
    
    golden ratio (1+sqrt(5))/2, approximately 1.618
    
    Assuming that an expression is considered "true" if it has a non-zero
    value, note that:
    
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    @code{*} works like AND
    
    @code{+} works like OR
    
    
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    @example
    
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    @end example
    
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    @example
    
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    @end example
    
    In your C code, you can extend the list of unary and binary functions,
    and define recognized constants, so that they are available for your
    expressions.
    
    
    The evaluator also recognizes the International System unit prefixes.
    If 'i' is appended after the prefix, binary prefixes are used, which
    are based on powers of 1024 instead of powers of 1000.
    The 'B' postfix multiplies the value by 8, and can be appended after a
    unit prefix or used alone. This allows using for example 'KB', 'MiB',
    'G' and 'B' as number postfix.
    
    The list of available International System prefixes follows, with