1 @chapter Expression Evaluation
2 @c man begin EXPRESSION EVALUATION
4 When evaluating an arithmetic expression, FFmpeg uses an internal
5 formula evaluator, implemented through the @file{libavutil/eval.h}
8 An expression may contain unary, binary operators, constants, and
11 Two expressions @var{expr1} and @var{expr2} can be combined to form
12 another expression "@var{expr1};@var{expr2}".
13 @var{expr1} and @var{expr2} are evaluated in turn, and the new
14 expression evaluates to the value of @var{expr2}.
16 The following binary operators are available: @code{+}, @code{-},
17 @code{*}, @code{/}, @code{^}.
19 The following unary operators are available: @code{+}, @code{-}.
21 The following functions are available:
24 Compute hyperbolic sine of @var{x}.
27 Compute hyperbolic cosine of @var{x}.
30 Compute hyperbolic tangent of @var{x}.
33 Compute sine of @var{x}.
36 Compute cosine of @var{x}.
39 Compute tangent of @var{x}.
42 Compute arctangent of @var{x}.
45 Compute arcsine of @var{x}.
48 Compute arccosine of @var{x}.
51 Compute exponential of @var{x} (with base @code{e}, the Euler's number).
54 Compute natural logarithm of @var{x}.
57 Compute absolute value of @var{x}.
60 Compute expression @code{1/(1 + exp(4*x))}.
63 Compute Gauss function of @var{x}, corresponding to
64 @code{exp(-x*x/2) / sqrt(2*PI)}.
67 Return 1.0 if @var{x} is +/-INFINITY, 0.0 otherwise.
70 Return 1.0 if @var{x} is NAN, 0.0 otherwise.
73 Compute the remainder of division of @var{x} by @var{y}.
76 Return the maximum between @var{x} and @var{y}.
79 Return the maximum between @var{x} and @var{y}.
82 Return 1 if @var{x} and @var{y} are equivalent, 0 otherwise.
85 Return 1 if @var{x} is greater than or equal to @var{y}, 0 otherwise.
88 Return 1 if @var{x} is greater than @var{y}, 0 otherwise.
91 Return 1 if @var{x} is lesser than or equal to @var{y}, 0 otherwise.
94 Return 1 if @var{x} is lesser than @var{y}, 0 otherwise.
97 Allow to store the value of the expression @var{expr} in an internal
98 variable. @var{var} specifies the number of the variable where to
99 store the value, and it is a value ranging from 0 to 9. The function
100 returns the value stored in the internal variable.
101 Note, Variables are currently not shared between expressions.
104 Allow to load the value of the internal variable with number
105 @var{var}, which was previously stored with st(@var{var}, @var{expr}).
106 The function returns the loaded value.
108 @item while(cond, expr)
109 Evaluate expression @var{expr} while the expression @var{cond} is
110 non-zero, and returns the value of the last @var{expr} evaluation, or
111 NAN if @var{cond} was always false.
114 Round the value of expression @var{expr} upwards to the nearest
115 integer. For example, "ceil(1.5)" is "2.0".
118 Round the value of expression @var{expr} downwards to the nearest
119 integer. For example, "floor(-1.5)" is "-2.0".
122 Round the value of expression @var{expr} towards zero to the nearest
123 integer. For example, "trunc(-1.5)" is "-1.0".
126 Compute the square root of @var{expr}. This is equivalent to
130 Return 1.0 if @var{expr} is zero, 0.0 otherwise.
133 Compute the power of @var{x} elevated @var{y}, it is equivalent to
134 "(@var{x})^(@var{y})".
137 Return a pseudo random value between 0.0 and 1.0. @var{x} is the index of the
138 internal variable which will be used to save the seed/state.
141 This function is similar to the C function with the same name; it returns
142 "sqrt(@var{x}*@var{x} + @var{y}*@var{y})", the length of the hypotenuse of a
143 right triangle with sides of length @var{x} and @var{y}, or the distance of the
144 point (@var{x}, @var{y}) from the origin.
147 Return the greatest common divisor of @var{x} and @var{y}. If both @var{x} and
148 @var{y} are 0 or either or both are less than zero then behavior is undefined.
151 Evaluate @var{x}, and if the result is non-zero return the result of
152 the evaluation of @var{y}, return 0 otherwise.
155 Evaluate @var{x}, and if the result is zero return the result of the
156 evaluation of @var{y}, return 0 otherwise.
158 @item taylor(expr, x) taylor(expr, x, id)
159 Evaluate a taylor series at x.
160 expr represents the LD(id)-th derivates of f(x) at 0. If id is not specified
162 note, when you have the derivatives at y instead of 0
163 taylor(expr, x-y) can be used
164 When the series does not converge the results are undefined.
166 @item root(expr, max)
167 Finds x where f(x)=0 in the interval 0..max.
168 f() must be continuous or the result is undefined.
171 The following constants are available:
174 area of the unit disc, approximately 3.14
176 exp(1) (Euler's number), approximately 2.718
178 golden ratio (1+sqrt(5))/2, approximately 1.618
181 Assuming that an expression is considered "true" if it has a non-zero
184 @code{*} works like AND
186 @code{+} works like OR
197 In your C code, you can extend the list of unary and binary functions,
198 and define recognized constants, so that they are available for your
201 The evaluator also recognizes the International System number
202 postfixes. If 'i' is appended after the postfix, powers of 2 are used
203 instead of powers of 10. The 'B' postfix multiplies the value for 8,
204 and can be appended after another postfix or used alone. This allows
205 using for example 'KB', 'MiB', 'G' and 'B' as postfix.
207 Follows the list of available International System postfixes, with
208 indication of the corresponding powers of 10 and of 2.