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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