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-@chapter Expression Evaluation
-@c man begin EXPRESSION EVALUATION
-
-When evaluating an arithmetic expression, FFmpeg uses an internal
-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 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 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.
-
-@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".
-
-@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.
-
-@item ld(var)
-Allow to load the value of the internal variable with number
-@var{var}, which was previously stored with st(@var{var}, @var{expr}).
-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)
-Allow to 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.
-
-@item time(0)
-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.
-@end table
-
-The following constants are available:
-@table @option
-@item PI
-area of the unit disc, approximately 3.14
-@item E
-exp(1) (Euler's number), approximately 2.718
-@item PHI
-golden ratio (1+sqrt(5))/2, approximately 1.618
-@end table
-
-Assuming that an expression is considered "true" if it has a non-zero
-value, note that:
-
-@code{*} works like AND
-
-@code{+} works like OR
-
-For example the construct:
-@example
-if (A AND B) then C
-@end example
-is equivalent to:
-@example
-if(A*B, C)
-@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
-indication of the corresponding powers of 10 and of 2.
-@table @option
-@item y
-10^-24 / 2^-80
-@item z
-10^-21 / 2^-70
-@item a
-10^-18 / 2^-60
-@item f
-10^-15 / 2^-50
-@item p
-10^-12 / 2^-40
-@item n
-10^-9 / 2^-30
-@item u
-10^-6 / 2^-20
-@item m
-10^-3 / 2^-10
-@item c
-10^-2
-@item d
-10^-1
-@item h
-10^2
-@item k
-10^3 / 2^10
-@item K
-10^3 / 2^10
-@item M
-10^6 / 2^20
-@item G
-10^9 / 2^30
-@item T
-10^12 / 2^40
-@item P
-10^15 / 2^40
-@item E
-10^18 / 2^50
-@item Z
-10^21 / 2^60
-@item Y
-10^24 / 2^70
-@end table
-
-@c man end