Expr

Applies a mathematical function, defined by an expression string, on the pixels of the source clip(s). A different expression may be set for each color channel. Users of MaskTools may be familiar with this concept.

Expr( [clip clip[, ...], string exp[, ...], string format,
      bool optAvx2, bool optSingleMode, bool optSSE2, string scale_inputs, bool clamp_float, bool clamp_float_UV, int lut] )

clip  clip =

One or more source clips. Up to 26 input clips can be specified.

• The first three clips are referenced by lowercase letter x, y and z; use 'a', 'b' ... 'w' for the rest.
• Clips may be YUV(A), RGB(A), or greyscale; 8-16 bit integer or 32 bit float.
• Width, height and color subsampling should be the same; bit depths can be different.

string  exp =

One or more RPN expressions

• A different expression may be set for each color channel (or plane). Plane order is Y-U-V-A or R-G-B-A.

(note: due to a bug, versions prior to r2724 used GBRA ordering)

• When an expression string is not given, the previous one is used.
• The empty string ("") is a valid expression; it causes the plane to be copied (see Expressions below).
• Keyword delimiters are space, but TAB, CR and LF characters are allowed as whitespace as well since 3.7.1

string  format = ""

Set color format of the returned clip.

• Use pixel format strings like "YV12", "YUV420P8", "YUV444P16", "RGBP10".
• By default, the output format is the same as the first clip.

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 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)

string  scale_inputs = "none"

Autoscale any input bit depths to 8-16 bit integer or 32 bit float for internal expression use, the conversion method is either full range (stretch) or limited YUV range (like bit shift). Feature is similar to the one in masktools2 v2.2.15

The primary reason of this feature is the "easy" usage of formerly written expressions optimized for 8 bits.

• "int" : scales limited range videos, only integer formats (8-16bits) to 8 (or bit depth specified by 'i8'..'i16' and 'f32')
• "intf": scales full range videos, only integer formats (8-16bits) to 8 (or bit depth specified by 'i8'..'i16' and 'f32')
• "float" or "floatf" : only scales 32 bit float format to 8 bit range (or bit depth specified by 'i8'..'i16' and 'f32')
• "floatUV": (since v3.5) chroma pre and post shift by 0.5 for 32 bit float pixels, thus having them in the range of 0..1 instead of -0.5..+0.5 during Expr evaluation
• "all": scales videos to 8 (or bit depth specified by 'i8'..'i16' and 'f32') - conversion uses limited_range logic (mul/div by two's power)
• "allf": scales videos to 8 (or bit depth specified by 'i8'..'i16' and 'f32') - conversion uses full scale logic (stretch)
• "none": no magic

E.g. scale_inputs="float" will automatically convert 32 bit float input to 8 bit range (but keeps the floating point precision)

The default 8 bit target range can be overridden by the i10 .. i16 or f32 specifiers at the beginning of the expression string.

The script inside will treat the clip as a 8 bit one. This only affects the internal calculations, the output is properly scaled back.

Note: ymin, ymax, cmin, cmax, range_min, range_max, range_half and range_size internal variables are changed accordingly (this behaviour was fixed in Avs+ > r2900)

bool  clamp_float = false

if true: clamps 32 bit float to valid ranges, which is 0..1 for luma or for RGB color space and -0.5..0.5 for YUV chroma UV channels

Default false: as usual, 32 bit float pixels are not clamped

Until 3.4: Ignored when scale_inputs scales 32bit-float type pixels

From 3.5: not ignored, even when parameter "scale_inputs" auto-scales 32 bit float type pixels to integer

bool  clamp_float_UV = false

Since v3.5

this parameter affects clamping of chroma planes: chroma is clamped between 0..1.0 instead of -0.5..0.5.

Default false: as usual, 32 bit float pixels are not clamped

int  lut = 0

Since v3.7.1

LUT (Look-up Table) mode. LUT is precalculated table. Expression values are calculated for all pixel value combinations in advance.

Then in each frame the resulting pixel value is 'looked up' from the ready-made table, which is indexed by the actual (x) or (x,y) pixel value.

• Default is 0, which means the usual realtime calculation. lut=1: 1D LUT (lutx) lut=2: 2D lut (lutxy)
• 1D luts are available for 8-16 bit inputs. A 8 bit 1D lut need 256 byte memory. A 16 bit 1D lut needs 65536 2-byte-words (131072 bytes)
• 2D luts are available for 8-14 bit inputs. Note: a 14 bit 2D lut needs (2^14)*(2^14)*2 bytes buffer in memory per plane (~1GByte)
• When lut is not available for a given bit depth then Expr will silently fallback to realtime (lut=0) mode.
• In 1D or 2D lut mode some keywords and features are forbidden in the expression: sx, sy, sxr, syr, frameno, time, relative pixel addressing.
• Frame property access works, but is limited to frame #0 which is read before LUT evaluation.
• In lut mode the input clip's bit depths must be the same.

Expressions

Expr accepts 1 to 26 source clips, up to four expression strings (one per color plane), an optional output format string, and some debug options. Output video format is inherited from the first clip, when there is no format override. All clips have to match in their width, height and chroma subsampling.

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.
• Example: 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 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. Example: result = x - trunc(x/d)*d. Note: the internal 32-bit float can hold only a 24 bit integer number (approximately)
• Math constant: pi
• Functions: min, max, sqrt, abs, exp, log, pow ^ (synonyms: pow and )
• Function: neg simple negates stack top
• Function: sgn simple signum function -1 if x<0; 0 when x==0; 1 if x>0
• Function: clip three operand function for clipping. Example: x 16 240 clip means min((max(x,16),240)
• Functions: sin cos atan2 tan asin acos atan

  On Intel x86/x64 the functions sin, cos and atan2 have SSE2/AVX2 optimization, the others have not (they make the whole expression to evaluate without SIMD optimization)

• Functions: round, floor, ceil, trunc operators (nearest integer - banker's rounding, round down, round up, round to zero)

  On Intel builds acceleration requires at least SSE4.1 capable processor or else the whole expression is running in C mode.

• Logical: > < = >= <= and or xor not == & | != (synonyms: == and =, & and and, | and or)
• Ternary operator: ? Example: x 128 < x y ?
• Duplicate stack elements: 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_size_a .. range_size_z , etc..) 256, 1024, 4096, 16384, 65536 for integer formats, 1.0 for 32 bit float formats
• range_min, range_max (range_min_a .. range_min_z) chroma/luma plane aware constants for the actual min-max limits
• yrange_min, yrange_half, yrange_max Unlike the luma/chroma plane adaptive "range_min", "range_half", "range_max" these constants always report the luma (Y) values. Since v3.5

When the constant name is ended with _x, _y, _z, _a, etc.. the constant is brought from the specified clip (input clips can be of different formats) When by using parameter "scale_inputs" the input is converted to e.g. 8 bits, these constants are calculated for this internally used bit depth.

Keywords for modifying base bit depth

• i8, i10, i12, i14, i16, f32 (used with scaleb and scalef)

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)

Frame property input

Frame properties (Integer or 32 bit float type) can be accessed within the expressions.

clipletter.frameProperty syntax injects actual frame property values into expression

Example:

x._ColorRange will push the value of _ColorRange frame property on stack (of clip x)

Internal variables

User variables

Variables can freely be used during evaluation for storing and loading intermediate results within the expression.

Variable names must begin with an English letter (a to z, A to Z) or with _ (underscore), followed by one or more underscore, letters or digits.

For example A, X2, _myvar, aa etc..

(until 3.7.1 only uppercase A to Z names were allowed)

Variables names are case sensitive and cannot be already reserved words.

Actions with variables

• Store: varname@

  Actual stack top is assigned to a variable.

• Store and pop from stack: varname^

  Actual stack top is assigned to a variable, then is immediately removed from stack top. Use case: when the value assigned to the variable won't be used immediately.

• Variables can be used by simply giving their names: varname

  The actual content of the variable is pushed onto the stack top.

Example: "x y - A^ x y 0.5 + + B^ A B / C@ x +"

Special predefined variables

• frameno : use current frame number in expression. 0 <= frameno < clip_frame_count.

  A 32 bit integer converted to float, so it is precise only at approximately 24 bits.

• 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

Pixel addressing

Indexed, addressable 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 an pixel would come from off-screen, the 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

Auto-scale inputs with "scale_inputs"

Autoscale works by converting any input bit depths to a common 8-16 integer or 32 bit float bit format for internal expression use, the conversion method is either full range or limited YUV range. Feature is similar to the one in masktools2 v2.2.15

The primary reason of this feature is the "easy" usage of formerly written expressions optimized for 8 bits.

Possible values for scale_inputs

• "int" : scales limited range videos, only integer formats (8-16bits) to 8 (or bit depth specified by 'i8'..'i16','f32')
• "intf": scales full range videos, only integer formats (8-16bits) to 8 (or bit depth specified by 'i8'..'i16','f32')
• "float" or "floatf" : only scales 32 bit float format to 8 bit range (or bit depth specified by 'i8'..'i16','f32')
• "floatUV": (since v3.5) chroma pre and post shift by 0.5 for 32 bit float pixels, thus having them in the range of 0..1 instead of -0.5..+0.5 during Expr evaluation
• "all": scales videos to 8 (or bit depth specified by 'i8'..'i16','f32') - conversion uses limited_range logic (mul/div by two's power)
• "allf": scales videos to 8 (or bit depth specified by 'i8'..'i16','f32') - conversion uses full scale logic (stretch)
• "none": no magic

Usually limited range is for normal YUV videos, full scale is for RGB or known-to-be-fullscale YUV

By default the internal conversion target is 8 bits, so old expressions written for 8 bit videos will probably work.

This internal working bit-depth can be overwritten by the i8, i10, i12, i14, i16 and f32 specifiers.

When using autoscale mode, scaleb and scalef keywords are meaningless for 8-16 bits, because there is nothing to scale. 32 bit (float) values will be scaled however when "float", "floatUV", "all", "allf" is specified.

Different conversion methods cannot be set for converting before and after the expression. Neither can you specify different methods for distinct input clips (e.g. x is full, y is limited is not supported).

How it works:

• 8-32 bit inputs ar all scaled to a common bit depth value, which bit depth is 8 by default and can be set to 10, 12, 14, 16 or 32 bits by the 'i10'..'i16','f32' keywords.
  

For example: scale_inputs="all" converts any inputs to 8 bit range. No truncation occurs however (no precision loss), because even a 16 bit data is converted to 8 bit in floating point precision, using division by 256.0 (2^16/2^8).

So the conversion is _not_ a simple shift-right-8 in the integer domain, which would lose precision.

• Calculates expression
• Scales the internal result back to the original video bit depth.
  Clamping (clipping to valid range) and converting to an integer output (if applicable) occurs here.

The predefined constants such as 'range_max', etc. will behave according to the internal working bit depth

Important note!

This feature was created for easy porting earlier 8-bit-video-only lut expressions. You have to understand how it works internally.

Let's see a 16bit input in "all" and "allf" mode (target is the default 8 bits)

Limited range 16->8 bits conversion has a factor of 1/256.0 (Instead of shift right 8 in integer domain, float-division is used or else it would lose presision)

Full range 16->8 bits conversion has a factor of 255.0/65535 (chroma is a bit different, since it is converted by moving into signed domain and back such as in (x-32768)*(127/32767)+128)

Using bit shifts (really it's division and multiplication by 2^8=256.0):

result = calculate_value(input / 256.0) * 256.0

Full scale 16-8-16 bit mode ('intf', 'allf'):

result = calculate_value(input / 65535.0 * 255.0 ) / 255.0 * 65535.0

chroma: result = (calculate_value((input-32768) / 32767.0 * 127.0 + 128 ) - 128) / 127.0 * 32767.0 + 32768

Use scale_inputs = "all" ("int", "float") for YUV videos with 'limited' range e.g. in 8 bits: Y=16..235, UV=16..240).

Use scale_inputs = "allf" (intf, floatf) for RGB or YUV videos with 'full' range e.g. in 8 bits: channels 0..255.

When input is 32bit float, the 0..1.0 (luma) and -0.5..0.5 (chroma) channel is scaled to 0..255 (8 bits), 0..1023 (i10 mode), 0..4095 (i12 mode), 0..16383(i14 mode), 0..65535(i16 mode) then back.

Compared to MaskTools

Compared to MaskTools2 version 2.2.15, Expr has functionality similar to mt_lut, mt_lutxy, mt_lutxyz, mt_lutxyza and mt_lutspa.

MaskTools2 is very slow for 10+ bit clips, when a LUT (lookup table) cannot be used for memory size reasons, thus the expression is evaluated/interpreted at runtime for each pixel. MaskTools2 (from v2.2.15) however is able to pass the expressions to this Avisynth+ 'Expr' filter with its 'use_expr' parameter, by passing the expression strings, and clamp_float and scale_inputs parameter.

The JIT compiler in Expr (adapted from VapourSynth) turns the expression calculation into realtime assembly code which is much faster and basically bit depth independent.

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, mt_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)
• 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

Examples

Average three clips:

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

When input clips to have more planes than an implicitely specified output format:

 Expr(aYV12Clip, "x 255.0 /", format="Y32") # target is Y only which needs only Y plane from YV12

Y-plane-only clip(s) can be used as source planes when a non-subsampled (rgb or 444) output format is specified:

 Expr(Y, "x", "x 2.0 /", "x 3.0 /", format="RGBPS") # r, g and b expression uses Y plane
 Expr(Grey_r, Grey_g, Grey_b, "x", "y 2.0 /", "z 3.0 /", format="RGBPS") # r, g and b expression uses Y plane

Using spatial feature:

 c = Expr(clip_for_format, "sxr syr 1 sxr - 1 syr - * * * 4096 scaleb *", "", "")

Mandelbrot zoomer (original code and idea from here: https://forum.doom9.org/showthread.php?p=1738391#post1738391 )

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")

For other ideas of spatial variables, see MaskTools2:mt_lutspa