@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 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
