Expr

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AVS+
This feature is specific to AviSynthPlus.

It is not supported in other AviSynth versions.

/// TODO DESCRIPTION

Syntax and Parameters

Expr( [clip clip[, ...], string exp[, ...], string format,
      bool optAvx2, bool optSingleMode, bool optSSE2] )

clip   =
One or more source clips. Up to 26 input clips can be specified. First three clips are referenced by lowercase letter x, y and z. Use letters 'a', 'b' ... 'w' for the rest.
Clips has to be of YUV(A), RGB(A), or greyscale 8-16 integer or 32 bit float. Width, height and color subsamping should be the same. Bit depths can be different.
string   =
One or more RPN expressions
up to "number of planes" strings which hold the expression strings. When an expression string is not given, previous one is used. Empty string means the plane is copied.
string  format = ?
Optional named format argument
This parameter overrides the output format defined by the first clip. Use pixel format strings like "YV12", "YUV420P8", "YUV444P16", "RGBP10".
bool   optAvx2 = (auto)
If false, disable AVX2.
Enables/Disables AVX2 code generation if available. Do nothing if AVX2 is not supported in Avisynth.
bool   optSingleMode = false
If true, generate assembly code using only one XMM/YMM register set instead of two; default false.
Expr generates assembly code that normally uses two 128 (SSE2) or 256 bit (AVX2) registers ("lanes"), thus processing 8 (SSE2)/16 (AVX2) pixels per internal cycle.
Experimental parameter, optSingleMode=true makes the internal compiler to generate instructions for only one register (4/8 pixels - SSE2/AVX2). The parameter was introduced to test the speed of x86 code using one working register. Very-very complex expressions would use too many XMM/YMM registers which are then "swapped" to memory slots, that could be slow. Using optSingleMode = true may result in using less registers with no need for swapping them to memory slots.
bool   optSSE2 = (auto)
If false, disable SSE2.
Enables/Disables SSE2 code generation when in non-AVX2 mode. Setting optSSE2=false and optAVX2=false forces expression processing in a slow interpreted way (C language)

/// TODO: formatting, sections and titles

Expr accepts 1 to 26 clips as inputs and up to four expression strings, an optional video format overrider, and some debug parameters. Output video format is inherited from the first clip, when there is no format override. All clips have to match their dimensions and plane subsamplings.

Expressions are evaluated on each plane, Y, U, V (and A) or R, G, B (,A). When an expression string is not specified, the previous expression is used for that plane. Except for plane A (alpha) which is copied by default. When an expression is an empty string ("") then the relevant plane will be copied (if the output clip bit depth is similar). When an expression is a single clip reference letter ("x") and the source/target bit depth is similar, then the relevant plane will be copied. When an expression is constant (after constant folding), then the relevant plane will be filled with an optimized memory fill method.

 Example: Expr(clip,"255","128,"128") fills all three planes.
 Example2: Expr(clip,"x","range_half,"range_half") copies luma, fills U and V with 128/512/... (bit depth dependent)

Other optimizations: do not call GetFrame for input clips that are not referenced or plane-copied

Expressions are written in Reverse Polish Notation (RPN).

Expressions use 32 bit float precision internally.

For 8..16 bit formats output is rounded and clamped from the internal 32 bit float representation to valid 8, 10, ... 16 bits range. 32 bit float output is not clamped at all.

Expr language/RPN elements

Clips: letters x, y, z, a, ... w. x is the first clip parameter, y is the second one, etc.
Math: * / + -
 % (modulo), like fmod. result = x - trunc(x/d)*d. Note: float can hold only a 24 bit integer number (approximately)
Math constant: pi
Functions: min, max, sqrt, abs, neg, exp, log, pow ^ (synonyms: "pow" and "^")
Functions: sin cos tan asin acos atan (no SSE2/AVX2 optimization when they appear in Expr)
Logical: > < = >= <= and or xor not == & | != (synonyms: "==" and "=", "&" and "and", "|" and "or")
Ternary operator: ? TODO: example
Duplicate stack: dup, dupN (dup1, dup2, ...)
Swap stack elements: swap, swapN (swap1, swap2, ...)
Scale by bit shift: scaleb (operand is treated as being a number in 8 bit range unless i8..i16 or f32 is specified)
Scale by full scale stretch: scalef (operand is treated as being a number in 8 bit range unless i8..i16 or f32 is specified)
Bit-depth aware constants
ymin, ymax (ymin_a .. ymin_z for individual clips) - the usual luma limits (16..235 or scaled equivalents)
cmin, cmax (cmin_a .. cmin_z) - chroma limits (16..240 or scaled equivalents)
range_half (range_half_a .. range_half_z) - half of the range, (128 or scaled equivalents)
range_size, range_half, range_max (range_size_a .. range_size_z , etc..)
Keywords for modifying base bit depth for scaleb and scalef: i8, i10, i12, i14, i16, f32
Spatial input variables in expr syntax:
sx, sy (absolute x and y coordinates, 0 to width-1 and 0 to height-1)
sxr, syr (relative x and y coordinates, from 0 to 1.0)
internal variables uppercase A to Z for storing and loading intermediate results within the expression
Store: A@ .. Z@
Store and pop from stack: A^ .. Z^
Use: A..Z
 Example: "x y - A^ x y 0.5 + + B^ A B / C@ x +"
'frameno' : use current frame number in expression. 0 <= frameno < clip_frame_count
'time' : calculation: time = frameno/clip_frame_count. Use relative time position in expression. 0 <= time < frameno/clip_frame_count
'width', 'height': clip width and clip height
Indexable source clip pixels by relative x,y positions.
Syntax: x[a,b] where
'x': source clip letter a..z
'a': horizontal shift. -width < a < width
'b': vertical shift. -height < b < height
'a' and 'b' should be constant. e.g.: "x[-1,-1] x[-1,0] x[-1,1] y[0,-10] + + + 4 /"

When a resulting pixels would come from off-screen the off-screen pixels are cloned from the edge. Optimized version of indexed pixels require SSSE3, and no AVX2 version is available. Non-SSSE3 falls back to C for the whole expression

Example (original code and idea from here: https://forum.doom9.org/showthread.php?p=1738391#post1738391 )
Mandelbrot zoomer
 a="X dup * Y dup * - A + T^ X Y 2 * * B + 2 min Y^ T 2 min X^ "
 b=a+a
 c=b+b
 blankclip(width=960,height=640,length=1600,pixel_type="YUV420P8")
 Expr("sxr 3 * 2 - -1.2947627 - 1.01 frameno ^ / -1.2947627 + A@ X^ syr 2 * 1 - 0.4399695 "+\
 "- 1.01 frameno ^ / 0.4399695  + B@ Y^ "+c+c+c+c+c+b+a+"X dup * Y dup * + 4 < 0 255 ?","128","128")
Comparing Expr to current masktools2 (2.2.12) version

Expr has similar functionality as mt_lut, mt_lutxy, mt_lutxyz, mt_lutxyza and mt_lutspa in masktools2.

Masktools2 however is very slow when no lut (lookup table) can be used for 10+ bit clips. The expression is evaluated in an interpreted way for each pixel.

The JIT compiler in Expr turnes the expression calculation into realtime assembly code which is much faster and basically bit depth indepentent.

In Expr:
Up to 26 clips are allowed (x,y,z,a,b,...w). Masktools handles only up to 4 clips with its mt_lut, my_lutxy, mt_lutxyz, mt_lutxyza
Clips with different bit depths are allowed
Works with 32 bit floats instead of 64 bit double internally
Less functions (e.g. no bit shifts)
No float clamping and float-to-8bit-and-back load/store option
Logical 'false' is 0 instead of -1
The ymin, ymax, etc built-in constants can have a _X suffix, where X is the corresponding clip designator letter. E.g. cmax_z, range_half_x
mt_lutspa-like functionality is available through "sx", "sy", "sxr", "syr" internal predefined variables
No y= u= v= parameters with negative values for filling plane with constant value, constant expressions are changed into optimized "fill" mode
Example:

Average three clips:

 c = Expr(clip1, clip2, clip3, "x y + z + 3 /") 

Using spatial feature:

 c = Expr(clip1, clip2, clip3, "sxr syr 1 sxr - 1 syr - * * * 4096 scaleb *", "", "")

For other ideas of spatial variables, look at the ideas at http://avisynth.nl/index.php/MaskTools2/mt_lutspa

Changes

r2574 (20171219) new: Indexable source clip pixels by relative x,y positions like x[-1,1]

new functions: sin cos tan asin acos atan
new operator: % (modulo)
new: Variables: uppercase letters A..Z for storing and reuse temporary results, frequently used computations.
new: predefined expr variables 'frameno', 'time', 'width', 'height'
fix: jitasm code generation at specific circumstances

r2544 (20171115) optimization; fix scalef
r2542 (20171114) first added
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