@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 sinh(x)
Compute hyperbolic sine of @var{x}.
@item cosh(x)
Compute hyperbolic cosine of @var{x}.
@item tanh(x)
Compute hyperbolic tangent of @var{x}.
@item sin(x)
Compute sine of @var{x}.
@item cos(x)
Compute cosine of @var{x}.
@item tan(x)
Compute tangent of @var{x}.
@item atan(x)
Compute arctangent of @var{x}.
@item asin(x)
Compute arcsine of @var{x}.
@item acos(x)
Compute arccosine of @var{x}.
@item exp(x)
Compute exponential of @var{x} (with base @code{e}, the Euler's number).
@item log(x)
Compute natural logarithm of @var{x}.
@item abs(x)
Compute absolute value of @var{x}.
@item squish(x)
Compute expression @code{1/(1 + exp(4*x))}.
@item gauss(x)
Compute Gauss function of @var{x}, corresponding to
@code{exp(-x*x/2) / sqrt(2*PI)}.
@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 mod(x, y)
Compute the remainder of division of @var{x} by @var{y}.
@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 eq(x, y)
Return 1 if @var{x} and @var{y} are equivalent, 0 otherwise.
@item gte(x, y)
Return 1 if @var{x} is greater than or equal to @var{y}, 0 otherwise.
@item gt(x, y)
Return 1 if @var{x} is greater 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 lt(x, y)
Return 1 if @var{x} is lesser than @var{y}, 0 otherwise.
@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 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 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.
@item ceil(expr)
Round the value of expression @var{expr} upwards to the nearest
integer. For example, "ceil(1.5)" is "2.0".
@item floor(expr)
Round the value of expression @var{expr} downwards to the nearest
integer. For example, "floor(-1.5)" is "-2.0".
@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 sqrt(expr)
Compute the square root of @var{expr}. This is equivalent to
"(@var{expr})^.5".
@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 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 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 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 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 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 taylor(expr, x) taylor(expr, x, id)
Evaluate a taylor series at x.
expr represents the LD(id)-th derivates of f(x) at 0. If id is not specified
then 0 is assumed.
note, when you have the derivatives at y instead of 0
taylor(expr, x-y) can be used
When the series does not converge the results are undefined.
@item root(expr, max)
Finds x where f(x)=0 in the interval 0..max.
f() must be continuous or the result is undefined.
@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
and the construct:
@example
if A then B else C
@end example
is equivalent to
@example
if(A,B) + ifnot(A,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 number
postfixes. If 'i' is appended after the postfix, powers of 2 are used
instead of powers of 10. The 'B' postfix multiplies the value for 8,
and can be appended after another postfix or used alone. This allows
using for example 'KB', 'MiB', 'G' and 'B' as postfix.
Follows the list of available International System postfixes, with
indication of the corresponding powers of 10 and of 2.
@table @option
@item y
-24 / -80
@item z
-21 / -70
@item a
-18 / -60
@item f
-15 / -50
@item p
-12 / -40
@item n
-9 / -30
@item u
-6 / -20
@item m
-3 / -10
@item c
-2
@item d
-1
@item h
2
@item k
3 / 10
@item K
3 / 10
@item M
6 / 20
@item G
9 / 30
@item T
12 / 40
@item P
15 / 40
@item E
18 / 50
@item Z
21 / 60
@item Y
24 / 70
@end table
@c man end