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 non-zero return the evaluation
156 result of @var{y}, otherwise the evaluation result of @var{z}.
159 Evaluate @var{x}, and if the result is zero return the result of the
160 evaluation of @var{y}, return 0 otherwise.
163 Evaluate @var{x}, and if the result is zero return the evaluation
164 result of @var{y}, otherwise the evaluation result of @var{z}.
166 @item taylor(expr, x) taylor(expr, x, id)
167 Evaluate a taylor series at x.
168 expr represents the LD(id)-th derivates of f(x) at 0. If id is not specified
170 note, when you have the derivatives at y instead of 0
171 taylor(expr, x-y) can be used
172 When the series does not converge the results are undefined.
175 Return the current (wallclock) time in seconds.
177 @item root(expr, max)
178 Finds x where f(x)=0 in the interval 0..max.
179 f() must be continuous or the result is undefined.
182 The following constants are available:
185 area of the unit disc, approximately 3.14
187 exp(1) (Euler's number), approximately 2.718
189 golden ratio (1+sqrt(5))/2, approximately 1.618
192 Assuming that an expression is considered "true" if it has a non-zero
195 @code{*} works like AND
197 @code{+} works like OR
199 For example the construct:
208 In your C code, you can extend the list of unary and binary functions,
209 and define recognized constants, so that they are available for your
212 The evaluator also recognizes the International System unit prefixes.
213 If 'i' is appended after the prefix, binary prefixes are used, which
214 are based on powers of 1024 instead of powers of 1000.
215 The 'B' postfix multiplies the value by 8, and can be appended after a
216 unit prefix or used alone. This allows using for example 'KB', 'MiB',
217 'G' and 'B' as number postfix.
219 The list of available International System prefixes follows, with
220 indication of the corresponding powers of 10 and of 2.