Expr
====

.. function:: Expr(vnode[] clips, string[] expr[, int format])
   :module: std

   Expr evaluates an expression per pixel for up to 26 input *clips*.
   The expression, *expr*, is written using reverse polish notation and can be
   specified for each plane individually.
   The expression given for the previous plane is used if the *expr* array
   contains fewer expressions than the input clip has planes.
   In practice this means that a single expression will be applied to all planes
   by default.

   Specifying an empty string as the expression enables a fast plane copy from
   the first specified clip, when possible. If it is not possible due to the
   output *format* being incompatible, the plane contents will be undefined.

   Since the expression is evaluated at runtime, there are a few pitfalls. In
   order to keep speed up, the input ranges are not normalized to the usual
   floating point ranges. Instead they are left as is, meaning that an 8 bit
   clip will have values in the 0-255 range and a 10 bit clip will have values
   in the 0-1023 range.
   Note that floating point clips are even more difficult, as most channels are
   stored in the 0-1 range with the exception of U, V, Co and Cg planes, which
   are in the -0.5-0.5 range.
   If you mix clips with different input formats this must be taken into
   consideration.

   When the output format uses integer samples, the result of the expression is
   clamped to the [0, 2**bits_per_sample-1] range.
   When the output format uses float samples, the result of the expression is
   stored without any clamping.

   By default the output *format* is the same as the first input clip's format.
   You can override it by setting *format*. The only restriction is that the
   output *format* must have the same subsampling as the input *clips* and be
   8..16 bit integer or 32 bit float. 16 bit float is also supported on cpus
   with the f16c instructions.

   Logical operators are also a bit special, since everything is done in
   floating point arithmetic.
   All values greater than 0 are considered true for the purpose of comparisons.
   Logical operators return 0.0 for false and 1.0 for true in their operations.

   Since the expression is being evaluated at runtime, there are also the stack
   manipulation operators, *swap* and *dup*. The former swaps the topmost and
   second topmost values, and the latter duplicates the topmost stack value.
   
   These operators also have *swapN* and *dupN* forms that allow a value N
   steps up in the stack to be swapped or duplicated. The top value of the stack
   has index zero meaning that *dup* is equivalent to *dup0* and *swap* is
   equivalent to *swap1*. This is because *swapN* always swaps with the topmost
   value at index 0.
   
   Expressions are converted to byte-code or machine-code by an optimizing
   compiler and are not guaranteed to evaluate in the order originally written.
   The compiler assumes that all input values are finite (i.e neither NaN nor
   INF) and that no operator will produce a non-finite value. Such expressions
   are invalid. This is especially important for the transcendental operators:
   
   * exp - expression must not overflow (i.e. x <= 88)
   * log - input must be finite and non-negative (i.e. x >= 0 && x <= 3e+38)
   * pow - base must be finite and non-negative. Result must not overflow (i.e. x >= 0 && x <= 3e+38; 1e-38 <= result <= 3e+38)

   Clip load operators::

      x-z, a-w

   The operators taking one argument are::

      exp log sqrt sin cos abs not dup dupN

   The operators taking two arguments are::

      + - * / max min pow > < = >= <= and or xor swap swapN

   The operators taking three arguments are::

      ?
      
   For example these operations::
   
      a b c ?
      
      d e <
      
      f abs
      
   Are equivalent to these operations in C::
   
      a ? b : c
      
      d < e
      
      abs(f)

   The sin/cos operators are approximated to within 2e-6 absolute error for
   inputs with magnitude up to 1e5, and there is no accuracy guarantees for
   inputs whose magnitude is larger than 2e5.

   How to average the Y planes of 3 YUV clips and pass through the UV planes
   unchanged (assuming same format)::

      std.Expr(clips=[clipa, clipb, clipc], expr=["x y + z + 3 /", "", ""])

   How to average the Y planes of 3 YUV clips and pass through the UV planes
   unchanged (different formats)::

      std.Expr(clips=[clipa16bit, clipb10bit, clipa8bit],
         expr=["x y 64 * + z 256 * + 3 /", ""])

   Setting the output format because the resulting values are illegal in a 10
   bit clip (note that the U and V planes will contain junk since direct copy
   isn't possible)::

      std.Expr(clips=[clipa10bit, clipb16bit, clipa8bit],
         expr=["x 64 * y + z 256 * + 3 /", ""], format=vs.YUV420P16)
