# Image Operations

## Image Operations Overview

Vulkan Image Operations are operations performed by those SPIR-V Image
Instructions which take an `OpTypeImage`

(representing a
`VkImageView`

) or `OpTypeSampledImage`

(representing a
(`VkImageView`

, `VkSampler`

) pair).
Read, write, and atomic operations also take texel coordinates as operands,
and return a value based on a neighborhood of texture elements (*texels*)
within the image.
Query operations return properties of the bound image or of the lookup
itself.
The `Depth`

operand of `OpTypeImage`

is ignored.

Texel is a term which is a combination of the words texture and element. Early interactive computer graphics supported texture operations on textures, a small subset of the image operations on images described here. The discrete samples remain essentially equivalent, however, so we retain the historical term texel to refer to them.

Image Operations include the functionality of the following SPIR-V Image Instructions:

`OpImageSample*`

and`OpImageSparseSample*`

read one or more neighboring texels of the image, and filter the texel values based on the state of the sampler.- Instructions with
`ImplicitLod`

in the name determine the LOD used in the sampling operation based on the coordinates used in neighboring fragments. - Instructions with
`ExplicitLod`

in the name determine the LOD used in the sampling operation based on additional coordinates. - Instructions with
`Proj`

in the name apply homogeneous projection to the coordinates.

- Instructions with
`OpImageFetch`

and`OpImageSparseFetch`

return a single texel of the image. No sampler is used.`OpImage*Gather`

and`OpImageSparse*Gather`

read neighboring texels and return a single component of each.`OpImageRead`

(and`OpImageSparseRead`

) and`OpImageWrite`

read and write, respectively, a texel in the image. No sampler is used.`OpImageSampleFootprintNV`

identifies and returns information about the set of texels in the image that would be accessed by an equivalent`OpImageSample*`

instruction.`OpImage*Dref*`

instructions apply depth comparison on the texel values.`OpImageSparse*`

instructions additionally return a sparse residency code.`OpImageQuerySize`

,`OpImageQuerySizeLod`

,`OpImageQueryLevels`

, and`OpImageQuerySamples`

return properties of the image descriptor that would be accessed. The image itself is not accessed.`OpImageQueryLod`

returns the LOD parameters that would be used in a sample operation. The actual operation is not performed.`OpImageWeightedSampleQCOM`

reads a 2D neighborhood of texels and computes a weighted average using weight values from a separate weight texture.`opImageBlockMatchSADQCOM`

and`opTextureBlockMatchSSD`

compare 2D neighborhoods of texels from two textures.`OpImageBoxFilterQCOM`

reads a 2D neighborhood of texels and computes a weighted average of the texels.`opImageBlockMatchWindowSADQCOM`

and`opImageBlockMatchWindowSSDQCOM`

compare 2D neighborhoods of texels from two textures with the comparison repeated across a window region in the target texture.`opImageBlockMatchGatherSADQCOM`

and`opImageBlockMatchWindowSSDQCOM`

compares four 2D neighborhoods of texels from a target texture with a single 2D neighborhood in the reference texture. The R component of each comparison is gathered and returned in the output.

### Texel Coordinate Systems

Images are addressed by *texel coordinates*.
There are three *texel coordinate systems*:

- normalized texel coordinates [0.0, 1.0]
- unnormalized texel coordinates [0.0, width / height / depth)
- integer texel coordinates [0, width / height / depth)

SPIR-V `OpImageFetch`

, `OpImageSparseFetch`

, `OpImageRead`

,
`OpImageSparseRead`

,
`opImageBlockMatchSADQCOM`

, `opImageBlockMatchSSDQCOM`

,
`opImageBlockMatchWindowSADQCOM`

, `opImageBlockMatchWindowSSDQCOM`

,
and `OpImageWrite`

instructions use integer texel coordinates.

Other image instructions can use either normalized or unnormalized texel
coordinates (selected by the `unnormalizedCoordinates`

state of the
sampler used in the instruction), but there are
limitations on what operations, image
state, and sampler state is supported.
Normalized coordinates are logically
converted to unnormalized as part of
image operations, and certain steps are
only performed on normalized coordinates.
The array layer coordinate is always treated as unnormalized even when other
coordinates are normalized.

Normalized texel coordinates are referred to as (s,t,r,q,a), with the coordinates having the following meanings:

- s: Coordinate in the first dimension of an image.
- t: Coordinate in the second dimension of an image.
- r: Coordinate in the third dimension of an image.
- (s,t,r) are interpreted as a direction vector for Cube images.

- q: Fourth coordinate, for homogeneous (projective) coordinates.
- a: Coordinate for array layer.

The coordinates are extracted from the SPIR-V operand based on the
dimensionality of the image variable and type of instruction.
For `Proj`

instructions, the components are in order (s, [t,] [r,]
q), with t and r being conditionally present based on the
`Dim`

of the image.
For non-`Proj`

instructions, the coordinates are (s [,t] [,r]
[,a]), with t and r being conditionally present based on the
`Dim`

of the image and a being conditionally present based on the
`Arrayed`

property of the image.
Projective image instructions are not supported on `Arrayed`

images.

Unnormalized texel coordinates are referred to as (u,v,w,a), with the coordinates having the following meanings:

- u: Coordinate in the first dimension of an image.
- v: Coordinate in the second dimension of an image.
- w: Coordinate in the third dimension of an image.
- a: Coordinate for array layer.

Only the u and v coordinates are directly extracted from the
SPIR-V operand, because only 1D and 2D (non-`Arrayed`

) dimensionalities
support unnormalized coordinates.
The components are in order (u [,v]), with v being conditionally
present when the dimensionality is 2D.
When normalized coordinates are converted to unnormalized coordinates, all
four coordinates are used.

Integer texel coordinates are referred to as (i,j,k,l,n), with the coordinates having the following meanings:

- i: Coordinate in the first dimension of an image.
- j: Coordinate in the second dimension of an image.
- k: Coordinate in the third dimension of an image.
- l: Coordinate for array layer.
- n: Index of the sample within the texel.

They are extracted from the SPIR-V operand in order (i [,j] [,k] [,l]
[,n]), with j and k conditionally present based on the `Dim`

of the image, and l conditionally present based on the `Arrayed`

property of the image.
n is conditionally present and is taken from the `Sample`

image
operand.

If an accessed image was created from a view using
VkImageViewSlicedCreateInfoEXT and accessed through a
`VK_DESCRIPTOR_TYPE_STORAGE_IMAGE`

descriptor, then the value of k
is incremented by VkImageViewSlicedCreateInfoEXT::`sliceOffset`

,
giving k ← sliceOffset + k.
The image’s accessible range in the third dimension is k < sliceOffset
+ sliceCount.
If VkImageViewSlicedCreateInfoEXT::`sliceCount`

is
`VK_REMAINING_3D_SLICES_EXT`

, the range is inherited from the image’s
depth extent as specified by Image Mip
Level Sizing.

For all coordinate types, unused coordinates are assigned a value of zero.

The Texel Coordinate Systems - For the example shown of an 8×4 texel two dimensional image.

- Normalized texel coordinates:
- The s coordinate goes from 0.0 to 1.0.
- The t coordinate goes from 0.0 to 1.0.

- Unnormalized texel coordinates:
- The u coordinate within the range 0.0 to 8.0 is within the image, otherwise it is outside the image.
- The v coordinate within the range 0.0 to 4.0 is within the image, otherwise it is outside the image.

- Integer texel coordinates:
- The i coordinate within the range 0 to 7 addresses texels within the image, otherwise it is outside the image.
- The j coordinate within the range 0 to 3 addresses texels within the image, otherwise it is outside the image.

- Also shown for linear filtering:
- Given the unnormalized coordinates (u,v), the four texels
selected are i
_{0}j_{0}, i_{1}j_{0}, i_{0}j_{1}, and i_{1}j_{1}. - The fractions α and β.
- Given the offset Δ
_{i}and Δ_{j}, the four texels selected by the offset are i_{0}j'_{0}, i_{1}j'_{0}, i_{0}j'_{1}, and i_{1}j'_{1}.

- Given the unnormalized coordinates (u,v), the four texels
selected are i

For formats with reduced-resolution components, Δ_{i} and
Δ_{j} are relative to the resolution of the
highest-resolution component, and therefore may be divided by two relative
to the unnormalized coordinate space of the lower-resolution components.

The Texel Coordinate Systems - For the example shown of an 8×4 texel two dimensional image.

- Texel coordinates as above.
Also shown for nearest filtering:
- Given the unnormalized coordinates (u,v), the texel selected is ij.
- Given the offset Δ
_{i}and Δ_{j}, the texel selected by the offset is ij'.

For corner-sampled images, the texel samples are located at the grid intersections instead of the texel centers.

## Conversion Formulas

### RGB to Shared Exponent Conversion

An RGB color (red, green, blue) is transformed to a shared exponent
color (red_{shared}, green_{shared}, blue_{shared}, exp_{shared}) as
follows:

First, the components (red, green, blue) are clamped to
(red_{clamped}, green_{clamped}, blue_{clamped}) as:

- red
_{clamped}= max(0, min(sharedexp_{max}, red)) - green
_{clamped}= max(0, min(sharedexp_{max}, green)) - blue
_{clamped}= max(0, min(sharedexp_{max}, blue))

where:

$\begin{aligned} N & = 9 & \text{number of mantissa bits per component} \\\ B & = 15 & \text{exponent bias} \\\ E\_{max} & = 31 & \text{maximum possible biased exponent value} \\\ sharedexp\_{max} & = \frac{(2^N-1)}{2^N} \times 2^{(E\_{max}-B)} \end{aligned}$NaN, if supported, is handled as in\

IEEE 754-2008 `minNum()`

and `maxNum()`

.
This results in any NaN being mapped to zero.

The largest clamped component, max_{clamped} is determined:

- max
_{clamped}= max(red_{clamped}, green_{clamped}, blue_{clamped})

A preliminary shared exponent exp' is computed:

$\begin{aligned} exp' = \begin{cases} \left \lfloor \log\_2(max\_{clamped}) \right \rfloor + (B+1) & \text{for}\ max\_{clamped} > 2^{-(B+1)} \\\ 0 & \text{for}\ max\_{clamped} \leq 2^{-(B+1)} \end{cases} \end{aligned}$The shared exponent exp_{shared} is computed:

Finally, three integer values in the range 0 to 2^{N} are
computed:

### Shared Exponent to RGB

A shared exponent color (red_{shared}, green_{shared}, blue_{shared},
exp_{shared}) is transformed to an RGB color (red, green, blue) as
follows:

- $red = red\_{shared} \times {2^{(exp\_{shared}-B-N)}}$
- $green = green\_{shared} \times {2^{(exp\_{shared}-B-N)}}$
- $blue = blue\_{shared} \times {2^{(exp\_{shared}-B-N)}}$

where:

- N = 9 (number of mantissa bits per component)
- B = 15 (exponent bias)

## Texel Input Operations

*Texel input instructions* are SPIR-V image instructions that read from an
image.
*Texel input operations* are a set of steps that are performed on state,
coordinates, and texel values while processing a texel input instruction,
and which are common to some or all texel input instructions.
They include the following steps, which are performed in the listed order:

- Validation operations
- Format conversion
- Texel replacement
- Depth comparison
- Conversion to RGBA
- Component swizzle
- Chroma reconstruction
- Y′C
_{B}C_{R}conversion

For texel input instructions involving multiple texels (for sampling or gathering), these steps are applied for each texel that is used in the instruction. Depending on the type of image instruction, other steps are conditionally performed between these steps or involving multiple coordinate or texel values.

If Chroma Reconstruction is implicit,
Texel Filtering instead takes place during
chroma reconstruction, before sampler
Y′C_{B}C_{R} conversion occurs.

The operations described in block matching and weight image sampling are performed before Conversion to RGBA and Component swizzle.

### Texel Input Validation Operations

*Texel input validation operations* inspect instruction/image/sampler state
or coordinates, and in certain circumstances cause the texel value to be
replaced or become undefined:.
There are a series of validations that the texel undergoes.

#### Instruction/Sampler/Image View Validation

There are a number of cases where a SPIR-V instruction can mismatch with the sampler, the image view, or both, and a number of further cases where the sampler can mismatch with the image view. In such cases the value of the texel returned is undefined:.

These cases include:

- The sampler
`borderColor`

is an integer type and the image view`format`

is not one of the VkFormat integer types or a stencil component of a depth/stencil format. - The sampler
`borderColor`

is a float type and the image view`format`

is not one of the VkFormat float types or a depth component of a depth/stencil format. - The sampler
`borderColor`

is one of the opaque black colors (`VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK`

or`VK_BORDER_COLOR_INT_OPAQUE_BLACK`

) and the image view VkComponentSwizzle for any of the VkComponentMapping components is not the identity swizzle, and VkPhysicalDeviceBorderColorSwizzleFeaturesEXT::`borderColorSwizzleFromImage`

feature is not enabled, and VkSamplerBorderColorComponentMappingCreateInfoEXT is not specified. - VkSamplerBorderColorComponentMappingCreateInfoEXT::
`components`

, if specified, has a component swizzle that does not match the component swizzle of the image view, and either component swizzle is not a form of identity swizzle. - VkSamplerBorderColorComponentMappingCreateInfoEXT::
`srgb`

, if specified, does not match the sRGB encoding of the image view. - The sampler
`borderColor`

is a custom color (`VK_BORDER_COLOR_FLOAT_CUSTOM_EXT`

or`VK_BORDER_COLOR_INT_CUSTOM_EXT`

) and the supplied VkSamplerCustomBorderColorCreateInfoEXT::`customBorderColor`

is outside the bounds of the values representable in the image view’s`format`

. - The sampler
`borderColor`

is a custom color (`VK_BORDER_COLOR_FLOAT_CUSTOM_EXT`

or`VK_BORDER_COLOR_INT_CUSTOM_EXT`

) and the image view VkComponentSwizzle for any of the VkComponentMapping components is not the identity swizzle, and VkPhysicalDeviceBorderColorSwizzleFeaturesEXT::`borderColorSwizzleFromImage`

feature is not enabled, and VkSamplerBorderColorComponentMappingCreateInfoEXT is not specified. - The VkImageLayout of any subresource in the image view does not
match the VkDescriptorImageInfo::
`imageLayout`

used to write the image descriptor. - The SPIR-V Image Format is not compatible
with the image view’s
`format`

. - The sampler
`unnormalizedCoordinates`

is`VK_TRUE`

and any of the limitations of unnormalized coordinates are violated. - The sampler was created with
`flags`

containing`VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT`

and the image was not created with`flags`

containing`VK_IMAGE_CREATE_SUBSAMPLED_BIT_EXT`

. - The sampler was not created with
`flags`

containing`VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT`

and the image was created with`flags`

containing`VK_IMAGE_CREATE_SUBSAMPLED_BIT_EXT`

. - The sampler was created with
`flags`

containing`VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT`

and is used with a function that is not`OpImageSampleImplicitLod`

or`OpImageSampleExplicitLod`

, or is used with operands`Offset`

or`ConstOffsets`

. - The SPIR-V instruction is one of the
`OpImage*Dref*`

instructions and the sampler`compareEnable`

is`VK_FALSE`

- The SPIR-V instruction is not one of the
`OpImage*Dref*`

instructions and the sampler`compareEnable`

is`VK_TRUE`

- The SPIR-V instruction is one of the
`OpImage*Dref*`

instructions, the image view`format`

is one of the depth/stencil formats, and the image view aspect is not`VK_IMAGE_ASPECT_DEPTH_BIT`

. - The SPIR-V instruction’s image variable’s properties are not compatible
with the image view:
- If the image view’s
`viewType`

is one of`VK_IMAGE_VIEW_TYPE_1D_ARRAY`

,`VK_IMAGE_VIEW_TYPE_2D_ARRAY`

, or`VK_IMAGE_VIEW_TYPE_CUBE_ARRAY`

then the instruction must have`Arrayed`

= 1. Otherwise the instruction must have`Arrayed`

= 0. - If the image was created with VkImageCreateInfo::
`samples`

equal to`VK_SAMPLE_COUNT_1_BIT`

, the instruction must have`MS`

= 0. - If the image was created with VkImageCreateInfo::
`samples`

not equal to`VK_SAMPLE_COUNT_1_BIT`

, the instruction must have`MS`

= 1. - If the
`Sampled`

`Type`

of the`OpTypeImage`

does not match the SPIR-V Type. - If the signedness of any read or sample operation does not match the signedness of the image’s format.

- If the image view’s
- If the image was created with VkImageCreateInfo::
`flags`

containing`VK_IMAGE_CREATE_CORNER_SAMPLED_BIT_NV`

, the sampler addressing modes must only use a VkSamplerAddressMode of`VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE`

. - The SPIR-V instruction is
`OpImageSampleFootprintNV`

with`Dim`

= 2D and`addressModeU`

or`addressModeV`

in the sampler is not`VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE`

. - The SPIR-V instruction is
`OpImageSampleFootprintNV`

with`Dim`

= 3D and`addressModeU`

,`addressModeV`

, or`addressModeW`

in the sampler is not`VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE`

. - The sampler was created with a specified
VkSamplerCustomBorderColorCreateInfoEXT::
`format`

which does not match the VkFormat of the image view(s) it is sampling. - The sampler is sampling an image view of
`VK_FORMAT_B4G4R4A4_UNORM_PACK16`

,`VK_FORMAT_B5G6R5_UNORM_PACK16`

, or`VK_FORMAT_B5G5R5A1_UNORM_PACK16`

format without a specified VkSamplerCustomBorderColorCreateInfoEXT::`format`

.

Only `OpImageSample*`

and `OpImageSparseSample*`

can be used with a
sampler or image view that enables sampler
Y′C_{B}C_{R} conversion.

`OpImageFetch`

, `OpImageSparseFetch`

, `OpImage*Gather`

, and
`OpImageSparse*Gather`

must not be used with a sampler or image view
that enables sampler Y′C_{B}C_{R} conversion.

The `ConstOffset`

and `Offset`

operands must not be used with a
sampler or image view that enables sampler
Y′C_{B}C_{R} conversion.

If the underlying `VkImage`

format has an X component in its format
description, undefined: values are read from those bits.

If the `VkImage`

format and `VkImageView`

format are the same, these
bits will be unused by format conversion and this will have no effect.
However, if the `VkImageView`

format is different, then some bits of the
result may be undefined:.
For example, when a `VK_FORMAT_R10X6_UNORM_PACK16`

`VkImage`

is
sampled via a `VK_FORMAT_R16_UNORM`

`VkImageView`

, the low 6 bits of
the value before format conversion are undefined: and format conversion may
return a range of different values.

Some implementations will return undefined: values in the case where a
sampler uses a VkSamplerAddressMode of
`VK_SAMPLER_ADDRESS_MODE_MIRRORED_REPEAT`

, the sampler is used with
operands `Offset`

, `ConstOffset`

, or `ConstOffsets`

, and the value
of the offset is larger than or equal to the corresponding width, height, or
depth of any accessed image level.

This behavior was not tested prior to Vulkan conformance test suite version 1.3.8.0. Affected implementations will have a conformance test waiver for this issue.

#### Integer Texel Coordinate Validation

Integer texel coordinates are validated against the size of the image level, and the number of layers and number of samples in the image. For SPIR-V instructions that use integer texel coordinates, this is performed directly on the integer coordinates. For instructions that use normalized or unnormalized texel coordinates, this is performed on the coordinates that result after conversion to integer texel coordinates.

If the integer texel coordinates do not satisfy all of the conditions

- 0 ≤ i < w
_{s} - 0 ≤ j < h
_{s} - 0 ≤ k < d
_{s} - 0 ≤ l < layers
- 0 ≤ n < samples

where:

- w
_{s}= width of the image level - h
_{s}= height of the image level - d
_{s}= depth of the image level - layers = number of layers in the image
- samples = number of samples per texel in the image

then the texel fails integer texel coordinate validation.

There are four cases to consider:

- Valid Texel Coordinates
- If the texel coordinates pass validation (that is, the coordinates lie within the image),

then the texel value comes from the value in image memory. - Border Texel
- If the texel coordinates fail validation, and
- If the read is the result of an image sample instruction or image gather instruction, and
- If the image is not a cube image,
or if a sampler created with
`VK_SAMPLER_CREATE_NON_SEAMLESS_CUBE_MAP_BIT_EXT`

is used,

then the texel is a border texel and texel replacement is performed. - Invalid Texel
- If the texel coordinates fail validation, and
- If the read is the result of an image fetch instruction, image read instruction, or atomic instruction,

then the texel is an invalid texel and texel replacement is performed. - Cube Map Edge or Corner

Otherwise the texel coordinates lie beyond the edges or corners of the selected cube map face, and Cube map edge handling is performed.

#### Cube Map Edge Handling

If the texel coordinates lie beyond the edges or corners of the selected
cube map face (as described in the prior section), the following steps are
performed.
Note that this does not occur when using `VK_FILTER_NEAREST`

filtering
within a mip level, since `VK_FILTER_NEAREST`

is treated as using
`VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE`

.

- Cube Map Edge Texel
- If the texel lies beyond the selected cube map face in either only i or only j, then the coordinates (i,j) and the array layer l are transformed to select the adjacent texel from the appropriate neighboring face.

- Cube Map Corner Texel
- If the texel lies beyond the selected cube map face in both i and j, then there is no unique neighboring face from which to read that texel. The texel should be replaced by the average of the three values of the adjacent texels in each incident face. However, implementations may replace the cube map corner texel by other methods. The methods are subject to the constraint that for linear filtering if the three available texels have the same value, the resulting filtered texel must have that value, and for cubic filtering if the twelve available samples have the same value, the resulting filtered texel must have that value.

#### Sparse Validation

If the texel reads from an unbound region of a sparse image, the texel is a
*sparse unbound texel*, and processing continues with
texel replacement.

#### Layout Validation

If all planes of a *disjoint* *multi-planar* image are not in the same
image layout, the image must not be sampled
with sampler Y′C_{B}C_{R} conversion enabled.

### Format Conversion

Texels undergo a format conversion from the VkFormat of the image view to a vector of either floating-point or signed or unsigned integer components, with the number of components based on the number of components present in the format.

- Color formats have one, two, three, or four components, according to the format.
- Depth/stencil formats are one component.
The depth or stencil component is selected by the
`aspectMask`

of the image view.

Each component is converted based on its type and size (as defined in the Format Definition section for each VkFormat), using the appropriate equations in 16-Bit Floating-Point Numbers, Unsigned 11-Bit Floating-Point Numbers, Unsigned 10-Bit Floating-Point Numbers, Fixed-Point Data Conversion, and Shared Exponent to RGB. Signed integer components smaller than 32 bits are sign-extended.

If the image view format is sRGB, the color components are first converted
as if they are UNORM, and then sRGB to linear conversion is applied to the
R, G, and B components as described in the `sRGB EOTF`

section of the
Khronos Data Format Specification.
The A component, if present, is unchanged.

If
VkSamplerYcbcrConversionYcbcrDegammaCreateInfoQCOM::`enableYDegamma`

is equal to `VK_TRUE`

, then sRGB to linear conversion is applied to the
G component as described in the `sRGB EOTF`

section of the
Khronos Data Format Specification.
If
VkSamplerYcbcrConversionYcbcrDegammaCreateInfoQCOM::`enableCbCrDegamma`

is equal to `VK_TRUE`

, then sRGB to linear conversion is applied to the
R and B components as described in the `sRGB EOTF`

section of the
Khronos Data Format Specification.
The A component, if present, is unchanged.

If the image view format is block-compressed, then the texel value is first decoded, then converted based on the type and number of components defined by the compressed format.

### Texel Replacement

A texel is replaced if it is one (and only one) of:

- a border texel,
- an invalid texel, or
- a sparse unbound texel.

Border texels are replaced with a value based on the image format and the
`borderColor`

of the sampler.
The border color is:

Sampler | Corresponding Border Color |
---|---|

The custom border color (U) may be rounded by implementations prior
to texel replacement, but the error introduced by such a rounding must not
exceed one ULP of the image’s `format`

.

The names `VK_BORDER_COLOR_*_TRANSPARENT_BLACK`

,
`VK_BORDER_COLOR_*_OPAQUE_BLACK`

, and
`VK_BORDER_COLOR_*_OPAQUE_WHITE`

are meant to describe which components
are zeros and ones in the vocabulary of compositing, and are not meant to
imply that the numerical value of `VK_BORDER_COLOR_INT_OPAQUE_WHITE`

is
a saturating value for integers.

This is substituted for the texel value by replacing the number of components in the image format

Texel Aspect or Format | Component Assignment |
---|---|

Depth aspect | |

Stencil aspect | |

One component color format | |

Two component color format | |

Three component color format | |

Four component color format | |

Single component alpha format |

† S = B_{g} may be substituted as the replacement method by the
implementation when VkSamplerCreateInfo::`borderColor`

is
`VK_BORDER_COLOR_INT_CUSTOM_EXT`

and
VkSamplerCustomBorderColorCreateInfoEXT::`format`

is
`VK_FORMAT_UNDEFINED`

.
Implementations should use S = B_{r} as the replacement method.

The value returned by a read of an invalid texel is undefined:, unless that
read operation is from a buffer resource and the `robustBufferAccess`

feature is enabled.
In that case, an invalid texel is replaced as described by the
`robustBufferAccess`

feature.
If the access is to an image resource and the x, y, z, or layer coordinate
validation fails and
the `robustImageAccess`

feature is
enabled, then zero must be returned for the R, G, and B components, if
present.
Either zero or one must be returned for the A component, if present.
If
If the `robustImageAccess2`

feature is
enabled, zero values must be returned.
If only the sample index was invalid, the values returned are undefined:.

Additionally, if the `robustImageAccess`

feature is enabled,
but the `robustImageAccess2`

feature is
not,
any invalid texels may be expanded to four components prior to texel
replacement.
This means that components not present in the image format may be replaced
with 0 or may undergo conversion to RGBA as
normal.

Loads from a null descriptor return a four component color value of all zeros. However, for storage images and storage texel buffers using an explicit SPIR-V Image Format, loads from a null descriptor may return an alpha value of 1 (float or integer, depending on format) if the format does not include alpha.

If the
VkPhysicalDeviceSparseProperties::`residencyNonResidentStrict`

property is `VK_TRUE`

, a sparse unbound texel is replaced with 0 or 0.0
values for integer and floating-point components of the image format,
respectively.

If `residencyNonResidentStrict`

is `VK_FALSE`

, the value of the
sparse unbound texel is undefined:.

### Depth Compare Operation

If the image view has a depth/stencil format, the depth component is
selected by the `aspectMask`

, and the operation is an `OpImage*Dref*`

instruction, a depth comparison is performed.
The result is 1.0 if the comparison evaluates to true, and
0.0 otherwise.
This value replaces the depth component D.

The compare operation is selected by the VkCompareOp value set by
VkSamplerCreateInfo::`compareOp`

.
The reference value from the SPIR-V operand D_{ref} and the texel depth
value D_{tex} are used as the *reference* and *test* values,
respectively, in that operation.

If the image being sampled has an unsigned normalized fixed-point format,
then D_{ref} is clamped to [0,1] before the compare operation.

### Conversion to RGBA

The texel is expanded from one, two, or three components to four components based on the image base color:

Texel Aspect or Format | RGBA Color |
---|---|

Depth aspect | |

Stencil aspect | |

One component color format | |

Two component color format | |

Three component color format | |

Four component color format | |

One alpha component color format |

where one = 1.0f for floating-point formats and depth aspects, and one = 1 for integer formats and stencil aspects.

### Component Swizzle

All texel input instructions apply a *swizzle* based on:

- the VkComponentSwizzle enums in the
`components`

member of the VkImageViewCreateInfo structure for the image being read if sampler Y′C_{B}C_{R}conversion is not enabled, and - the VkComponentSwizzle enums in the
`components`

member of the VkSamplerYcbcrConversionCreateInfo structure for the sampler Y′C_{B}C_{R}conversion if sampler Y′C_{B}C_{R}conversion is enabled.

The swizzle can rearrange the components of the texel, or substitute zero or one for any components. It is defined as follows for each color component:

$\begin{aligned} Color'\_{component} & = \begin{cases} Color\_r & \text{for RED swizzle} \\\ Color\_g & \text{for GREEN swizzle} \\\ Color\_b & \text{for BLUE swizzle} \\\ Color\_a & \text{for ALPHA swizzle} \\\ 0 & \text{for ZERO swizzle} \\\ one & \text{for ONE swizzle} \\\ identity & \text{for IDENTITY swizzle} \end{cases} \end{aligned}$where:

$\begin{aligned} one & = \begin{cases} & 1.0\text{f} & \text{for floating-point components} \\\ & 1 & \text{for integer components} \\\ \end{cases} \\\ identity & = \begin{cases} & Color\_r & \text{for}\ component = r \\\ & Color\_g & \text{for}\ component = g \\\ & Color\_b & \text{for}\ component = b \\\ & Color\_a & \text{for}\ component = a \\\ \end{cases} \end{aligned}$If the border color is one of the `VK_BORDER_COLOR_*_OPAQUE_BLACK`

enums
and the VkComponentSwizzle is not the
identity swizzle for all
components, the value of the texel after swizzle is undefined:.

If the image view has a depth/stencil format and the
VkComponentSwizzle is `VK_COMPONENT_SWIZZLE_ONE`

, and
`VkPhysicalDeviceMaintenance5PropertiesKHR`

::`depthStencilSwizzleOneSupport`

is not set to `VK_TRUE`

, the value of the texel after swizzle is
undefined:.

### Sparse Residency

`OpImageSparse*`

instructions return a structure which includes a
*residency code* indicating whether any texels accessed by the instruction
are sparse unbound texels.
This code can be interpreted by the `OpImageSparseTexelsResident`

instruction which converts the residency code to a boolean value.

### Chroma Reconstruction

In some color models, the color representation is defined in terms of
monochromatic light intensity (often called `luma`

) and color differences
relative to this intensity, often called `chroma`

.
It is common for color models other than RGB to represent the chroma
components at lower spatial resolution than the luma component.
This approach is used to take advantage of the eye’s lower spatial
sensitivity to color compared with its sensitivity to brightness.
Less commonly, the same approach is used with additive color, since the
green component dominates the eye’s sensitivity to light intensity and the
spatial sensitivity to color introduced by red and blue is lower.

Lower-resolution components are `downsampled`

by resizing them to a lower
spatial resolution than the component representing luminance.
This process is also commonly known as `chroma subsampling`

.
There is one luminance sample in each texture texel, but each chrominance
sample may be shared among several texels in one or both texture dimensions.

`_444`

formats do not spatially downsample chroma values compared with luma: there are unique chroma samples for each texel.`_422`

formats have downsampling in the x dimension (corresponding to*u*or*s*coordinates): they are sampled at half the resolution of luma in that dimension.`_420`

formats have downsampling in the x dimension (corresponding to*u*or*s*coordinates) and the y dimension (corresponding to*v*or*t*coordinates): they are sampled at half the resolution of luma in both dimensions.

The process of reconstructing a full color value for texture access involves
accessing both chroma and luma values at the same location.
To generate the color accurately, the values of the lower-resolution
components at the location of the luma samples are reconstructed from the
lower-resolution sample locations, an operation known here as `chroma reconstruction`

irrespective of the actual color model.

The location of the chroma samples relative to the luma coordinates is
determined by the `xChromaOffset`

and `yChromaOffset`

members of the
VkSamplerYcbcrConversionCreateInfo structure used to create the
sampler Y′C_{B}C_{R} conversion.

The following diagrams show the relationship between unnormalized (*u*,*v*)
coordinates and (*i*,*j*) integer texel positions in the luma component
(shown in black, with circles showing integer sample positions) and the
texel coordinates of reduced-resolution chroma components, shown as crosses
in red.

If the chroma values are reconstructed at the locations of the luma samples
by means of interpolation, chroma samples from outside the image bounds are
needed; these are determined according to Wrapping Operation.
These diagrams represent this by showing the bounds of the `chroma texel`

extending beyond the image bounds, and including additional chroma sample
positions where required for interpolation.
The limits of a sample for `NEAREST`

sampling is shown as a grid.

Reconstruction is implemented in one of two ways:

If the format of the image that is to be sampled sets
`VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT`

,
or the VkSamplerYcbcrConversionCreateInfo’s
`forceExplicitReconstruction`

is set to `VK_TRUE`

, reconstruction is
performed as an explicit step independent of filtering, described in the
Explicit Reconstruction section.

If the format of the image that is to be sampled does not set
`VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT`

and if the VkSamplerYcbcrConversionCreateInfo’s
`forceExplicitReconstruction`

is set to `VK_FALSE`

, reconstruction
is performed as an implicit part of filtering prior to color model
conversion, with no separate post-conversion texel filtering step, as
described in the Implicit Reconstruction
section.

#### Explicit Reconstruction

- If the
`chromaFilter`

member of the VkSamplerYcbcrConversionCreateInfo structure is`VK_FILTER_NEAREST`

:- If the format’s R and B components are reduced in resolution in just
width by a factor of two relative to the G component (i.e. this is a
`_422`

format), the $\tau\_{ijk}\[level]$ values accessed by texel filtering are reconstructed as follows:$\begin{aligned} \tau\_R'(i, j) & = \tau\_R(\left\lfloor{i\times 0.5}\right\rfloor, j)\[level] \\\ \tau\_B'(i, j) & = \tau\_B(\left\lfloor{i\times 0.5}\right\rfloor, j)\[level] \end{aligned}$ - If the format’s R and B components are reduced in resolution in width
and height by a factor of two relative to the G component (i.e. this is
a
`_420`

format), the $\tau\_{ijk}\[level]$ values accessed by texel filtering are reconstructed as follows:$\begin{aligned} \tau\_R'(i, j) & = \tau\_R(\left\lfloor{i\times 0.5}\right\rfloor, \left\lfloor{j\times 0.5}\right\rfloor)\[level] \\\ \tau\_B'(i, j) & = \tau\_B(\left\lfloor{i\times 0.5}\right\rfloor, \left\lfloor{j\times 0.5}\right\rfloor)\[level] \end{aligned}$`xChromaOffset`

and`yChromaOffset`

have no effect if`chromaFilter`

is`VK_FILTER_NEAREST`

for explicit reconstruction.

- If the format’s R and B components are reduced in resolution in just
width by a factor of two relative to the G component (i.e. this is a
- If the
`chromaFilter`

member of the VkSamplerYcbcrConversionCreateInfo structure is`VK_FILTER_LINEAR`

:- If the format’s R and B components are reduced in resolution in just
width by a factor of two relative to the G component (i.e. this is a
`_422`

format):- If
`xChromaOffset`

is`VK_CHROMA_LOCATION_COSITED_EVEN`

:$\tau\_{RB}'(i,j) = \begin{cases} \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)\[level], & 0.5 \times i = \left\lfloor{0.5 \times i}\right\rfloor\\\ 0.5\times\tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)\[level] + \\\ 0.5\times\tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor + 1,j)\[level], & 0.5 \times i \neq \left\lfloor{0.5 \times i}\right\rfloor \end{cases}$ - If
`xChromaOffset`

is`VK_CHROMA_LOCATION_MIDPOINT`

:$\tau\_{RB}'(i,j) = \begin{cases} 0.25 \times \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor - 1,j)\[level] + \\\ 0.75 \times \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)\[level], & 0.5 \times i = \left\lfloor{0.5 \times i}\right\rfloor\\\ 0.75 \times \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)\[level] + \\\ 0.25 \times \tau\_{RB}(\left\lfloor{i\times 0.5}\right\rfloor + 1,j)\[level], & 0.5 \times i \neq \left\lfloor{0.5 \times i}\right\rfloor \end{cases}$

- If
- If the format’s R and B components are reduced in resolution in width
and height by a factor of two relative to the G component (i.e. this is
a
`_420`

format), a similar relationship applies. Due to the number of options, these formulae are expressed more concisely as follows:$\begin{aligned} i\_{RB} & = \begin{cases} 0.5 \times (i) & \textrm{xChromaOffset = COSITED}\\*\textrm{EVEN} \\\ 0.5 \times (i - 0.5) & \textrm{xChromaOffset = MIDPOINT} \end{cases}\\\ j*{RB} & = \begin{cases} 0.5 \times (j) & \textrm{yChromaOffset = COSITED}\\*\textrm{EVEN} \\\ 0.5 \times (j - 0.5) & \textrm{yChromaOffset = MIDPOINT} \end{cases}\\\ \\\ i*{floor} & = \left\lfloor i\_{RB} \right\rfloor \\\ j\_{floor} & = \left\lfloor j\_{RB} \right\rfloor \\\ \\\ i\_{frac} & = i\_{RB} - i\_{floor} \\\ j\_{frac} & = j\_{RB} - j\_{floor} \end{aligned}$$\begin{aligned} \tau\_{RB}'(i,j) = & \tau\_{RB}( i\_{floor}, j\_{floor})\[level] & \times & ( 1 - i\_{frac} ) & & \times & ( 1 - j\_{frac} ) & + \\\ & \tau\_{RB}( 1 + i\_{floor}, j\_{floor})\[level] & \times & ( i\_{frac} ) & & \times & ( 1 - j\_{frac} ) & + \\\ & \tau\_{RB}( i\_{floor}, 1 + j\_{floor})\[level] & \times & ( 1 - i\_{frac} ) & & \times & ( j\_{frac} ) & + \\\ & \tau\_{RB}( 1 + i\_{floor}, 1 + j\_{floor})\[level] & \times & ( i\_{frac} ) & & \times & ( j\_{frac} ) & \end{aligned}$

- If the format’s R and B components are reduced in resolution in just
width by a factor of two relative to the G component (i.e. this is a

In the case where the texture itself is bilinearly interpolated as described
in Texel Filtering, thus requiring four
full-color samples for the filtering operation, and where the reconstruction
of these samples uses bilinear interpolation in the chroma components due to
`chromaFilter`

=`VK_FILTER_LINEAR`

, up to nine chroma samples may be
required, depending on the sample location.

#### Implicit Reconstruction

Implicit reconstruction takes place by the samples being interpolated, as
required by the filter settings of the sampler, except that
`chromaFilter`

takes precedence for the chroma samples.

If `chromaFilter`

is `VK_FILTER_NEAREST`

, an implementation may
behave as if `xChromaOffset`

and `yChromaOffset`

were both
`VK_CHROMA_LOCATION_MIDPOINT`

, irrespective of the values set.

This will not have any visible effect if the locations of the luma samples coincide with the location of the samples used for rasterization.

The sample coordinates are adjusted by the downsample factor of the component (such that, for example, the sample coordinates are divided by two if the component has a downsample factor of two relative to the luma component):

$\begin{aligned} u\_{RB}' (422/420) &= \begin{cases} 0.5\times (u + 0.5), & \textrm{xChromaOffset = COSITED}\\*\textrm{EVEN} \\\ 0.5\times u, & \textrm{xChromaOffset = MIDPOINT} \end{cases} \\\ v*{RB}' (420) &= \begin{cases} 0.5\times (v + 0.5), & \textrm{yChromaOffset = COSITED}\\\_\textrm{EVEN} \\\ 0.5\times v, & \textrm{yChromaOffset = MIDPOINT} \end{cases} \end{aligned}$### Sampler Y′C_{B}C_{R} Conversion

Sampler Y′C_{B}C_{R} conversion performs the following operations, which an
implementation may combine into a single mathematical operation:

#### Sampler Y′C_{B}C_{R} Range Expansion

Sampler Y′C_{B}C_{R} range expansion is applied to color component values after
all texel input operations which are not specific to sampler Y′C_{B}C_{R}
conversion.
For example, the input values to this stage have been converted using the
normal format conversion rules.

The input values to this stage may have been converted using sRGB to linear
conversion if `ycbcrDegamma`

is enabled.

Sampler Y′C_{B}C_{R} range expansion is not applied if `ycbcrModel`

is
`VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY`

.
That is, the shader receives the vector C'_{rgba} as output by the Component
Swizzle stage without further modification.

For other values of `ycbcrModel`

, range expansion is applied to the
texel component values output by the Component
Swizzle defined by the `components`

member of
VkSamplerYcbcrConversionCreateInfo.
Range expansion applies independently to each component of the image.
For the purposes of range expansion and Y′C_{B}C_{R} model conversion, the R and
B components contain color difference (chroma) values and the G component
contains luma.
The A component is not modified by sampler Y′C_{B}C_{R} range expansion.

The range expansion to be applied is defined by the `ycbcrRange`

member
of the VkSamplerYcbcrConversionCreateInfo structure:

- If
`ycbcrRange`

is`VK_SAMPLER_YCBCR_RANGE_ITU_FULL`

, the following transformations are applied:$\begin{aligned} Y' &= C'*{rgba}\[G] \\\ C\_B &= C'*{rgba}\[B] - {{2^{(n-1)}}\over{(2^n) - 1}} \\\ C\_R &= C'\_{rgba}\[R] - {{2^{(n-1)}}\over{(2^n) - 1}} \end{aligned}$These formulae correspond to the

`full range`

encoding in the`Quantization schemes`

chapter of the Khronos Data Format Specification.Should any future amendments be made to the ITU specifications from which these equations are derived, the formulae used by Vulkan may also be updated to maintain parity.

- If
`ycbcrRange`

is`VK_SAMPLER_YCBCR_RANGE_ITU_NARROW`

, the following transformations are applied:$\begin{aligned} Y' &= {{C'*{rgba}\[G] \times (2^n-1) - 16\times 2^{n-8}}\over{219\times 2^{n-8}}} \\\ C\_B &= {{C'*{rgba}\[B] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \\\ C\_R &= {{C'\_{rgba}\[R] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \end{aligned}$These formulae correspond to the

`narrow range`

encoding in the`Quantization schemes`

chapter of the Khronos Data Format Specification. *n*is the bit-depth of the components in the format.

The precision of the operations performed during range expansion must be at least that of the source format.

An implementation may clamp the results of these range expansion operations
such that Y′ falls in the range [0,1], and/or such that C_{B} and C_{R}
fall in the range [-0.5,0.5].

#### Sampler Y′C_{B}C_{R} Model Conversion

The range-expanded values are converted between color models, according to
the color model conversion specified in the `ycbcrModel`

member:

`VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY`

The color components are not modified by the color model conversion
since they are assumed already to represent the desired color model in
which the shader is operating; Y′C_{B}C_{R} range expansion is also ignored.

`VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_IDENTITY`

The color components are not modified by the color model conversion and
are assumed to be treated as though in Y′C_{B}C_{R} form both in memory and
in the shader; Y′C_{B}C_{R} range expansion is applied to the components as
for other Y′C_{B}C_{R} models, with the vector (C_{R},Y′,C_{B},A)
provided to the shader.

`VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_709`

The color components are transformed from a Y′C_{B}C_{R} representation to an
R′G′B′ representation as described in the BT.709 Y′C_{B}C_{R}
conversion section of the Khronos Data Format
Specification.

`VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_601`

The color components are transformed from a Y′C_{B}C_{R} representation to an
R′G′B′ representation as described in the BT.601 Y′C_{B}C_{R}
conversion section of the Khronos Data Format
Specification.

`VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_2020`

The color components are transformed from a Y′C_{B}C_{R} representation to an
R′G′B′ representation as described in the BT.2020 Y′C_{B}C_{R}
conversion section of the Khronos Data Format
Specification.

In this operation, each output component is dependent on each input component.

An implementation may clamp the R′G′B′ results of these conversions to the range [0,1].

The precision of the operations performed during model conversion must be at least that of the source format.

The alpha component is not modified by these model conversions.

Sampling operations in a non-linear color space can introduce color and
intensity shifts at sharp transition boundaries.
To avoid this issue, the technically precise color correction sequence
described in the `Introduction to Color Conversions`

chapter of the
Khronos Data Format Specification may be performed as
follows:

- Calculate the unnormalized texel coordinates corresponding to the desired sample position.
- For a
`minFilter`

or`magFilter`

of`VK_FILTER_NEAREST`

:- Calculate (
*i*,*j*) for the sample location as described under the`nearest filtering`

formulae in (u,v,w,a) to (i,j,k,l,n) Transformation and Array Layer Selection - Calculate the normalized texel coordinates corresponding to these integer coordinates.
- Sample using sampler Y′C
_{B}C_{R}conversion at this location.

- Calculate (
- For a
`minFilter`

or`magFilter`

of`VK_FILTER_LINEAR`

:- Calculate (
*i*,_{[0,1]}*j*) for the sample location as described under the_{[0,1]}`linear filtering`

formulae in (u,v,w,a) to (i,j,k,l,n) Transformation and Array Layer Selection - Calculate the normalized texel coordinates corresponding to these integer coordinates.
- Sample using sampler Y′C
_{B}C_{R}conversion at each of these locations. - Convert the non-linear A′R′G′B′ outputs of the Y′C
_{B}C_{R}conversions to linear ARGB values as described in the`Transfer Functions`

chapter of the Khronos Data Format Specification. - Interpolate the linear ARGB values using the α and
β values described in the
`linear filtering`

section of (u,v,w,a) to (i,j,k,l,n) Transformation and Array Layer Selection and the equations in Texel Filtering.

- Calculate (

The additional calculations and, especially, additional number of sampling
operations in the `VK_FILTER_LINEAR`

case can be expected to have a
performance impact compared with using the outputs directly.
Since the variations from `correct`

results are subtle for most content,
the application author should determine whether a more costly implementation
is strictly necessary.

If `chromaFilter`

, and `minFilter`

or `magFilter`

are both
`VK_FILTER_NEAREST`

, these operations are redundant and sampling using
sampler Y′C_{B}C_{R} conversion at the desired
sample coordinates will produce the `correct`

results without further
processing.

## Texel Output Operations

*Texel output instructions* are SPIR-V image instructions that write to an
image.
*Texel output operations* are a set of steps that are performed on state,
coordinates, and texel values while processing a texel output instruction,
and which are common to some or all texel output instructions.
They include the following steps, which are performed in the listed order:

### Texel Output Validation Operations

*Texel output validation operations* inspect instruction/image state or
coordinates, and in certain circumstances cause the write to have no effect.
There are a series of validations that the texel undergoes.

#### Texel Format Validation

If the image format of the `OpTypeImage`

is not
compatible with the `VkImageView`

’s
`format`

, the write causes the contents of the image’s memory to become
undefined:.

#### Texel Type Validation

If the `Sampled`

`Type`

of the `OpTypeImage`

does not match the
SPIR-V Type, the write causes the value of the texel to
become undefined:.
For integer types, if the signedness of the
access does not match the signedness of the accessed resource, the write
causes the value of the texel to become undefined:.

### Integer Texel Coordinate Validation

The integer texel coordinates are validated according to the same rules as for texel input coordinate validation.

If the texel fails integer texel coordinate validation, then the write has no effect.

### Sparse Texel Operation

If the texel attempts to write to an unbound region of a sparse image, the
texel is a sparse unbound texel.
In such a case, if the
VkPhysicalDeviceSparseProperties::`residencyNonResidentStrict`

property is `VK_TRUE`

, the sparse unbound texel write has no effect.
If `residencyNonResidentStrict`

is `VK_FALSE`

, the write may have a
side effect that becomes visible to other accesses to unbound texels in any
resource, but will not be visible to any device memory allocated by the
application.

### Texel Output Format Conversion

If the image format is sRGB, a linear to sRGB conversion is applied to the
R, G, and B components as described in the `sRGB EOTF`

section of the
Khronos Data Format Specification.
The A component, if present, is unchanged.

Texels then undergo a format conversion from the floating-point, signed, or unsigned integer type of the texel data to the VkFormat of the image view. If the number of components in the texel data is larger than the number of components in the format, additional components are discarded.

Each component is converted based on its type and size (as defined in the Format Definition section for each VkFormat). Floating-point outputs are converted as described in Floating-Point Format Conversions and Fixed-Point Data Conversion. Integer outputs are converted such that their value is preserved. The converted value of any integer that cannot be represented in the target format is undefined:.

If the `VkImageView`

format has an X component in its format
description, undefined: values are written to those bits.

If the underlying `VkImage`

format has an X component in its format
description, undefined: values are also written to those bits, even if
result format conversion produces a valid value for those bits because the
`VkImageView`

format is different.

## Normalized Texel Coordinate Operations

If the image sampler instruction provides normalized texel coordinates, some of the following operations are performed.

### Projection Operation

For `Proj`

image operations, the normalized texel coordinates
(s,t,r,q,a) and (if present) the D_{ref} coordinate are
transformed as follows:

### Derivative Image Operations

Derivatives are used for LOD selection.
These derivatives are either implicit (in an `ImplicitLod`

image
instruction in a
mesh, task,
compute, or
fragment shader) or explicit (provided explicitly by shader to the image
instruction in any shader).

For implicit derivatives image instructions, the derivatives of texel coordinates are calculated in the same manner as derivative operations. That is:

$\begin{aligned} \partial{s}/\partial{x} & = dPdx(s), & \partial{s}/\partial{y} & = dPdy(s), & \text{for 1D, 2D, Cube, or 3D image} \\\ \partial{t}/\partial{x} & = dPdx(t), & \partial{t}/\partial{y} & = dPdy(t), & \text{for 2D, Cube, or 3D image} \\\ \partial{r}/\partial{x} & = dPdx(r), & \partial{r}/\partial{y} & = dPdy(r), & \text{for Cube or 3D image} \end{aligned}$Partial derivatives not defined above for certain image dimensionalities are set to zero.

For explicit LOD image instructions, if the optional SPIR-V operand
`Grad`

is provided, then the operand values are used for the derivatives.
The number of components present in each derivative for a given image
dimensionality matches the number of partial derivatives computed above.

If the optional SPIR-V operand `Lod`

is provided, then derivatives are
set to zero, the cube map derivative transformation is skipped, and the
scale factor operation is skipped.
Instead, the floating-point scalar coordinate is directly assigned to
λ_{base} as described in LOD Operation.

If the image or sampler object used by an implicit derivative image
instruction is not uniform across the quad and
`quadDivergentImplicitLod`

is not
supported, then the derivative and LOD values are undefined:.
Implicit derivatives are well-defined when the image and sampler and control
flow are uniform across the quad, even if they diverge between different
quads.

If `quadDivergentImplicitLod`

is
supported, then derivatives and implicit LOD values are well-defined even if
the image or sampler object are not uniform within a quad.
The derivatives are computed as specified above, and the implicit LOD
calculation proceeds for each shader invocation using its respective image
and sampler object.

### Cube Map Face Selection and Transformations

For cube map image instructions, the (s,t,r) coordinates are treated
as a direction vector (r_{x},r_{y},r_{z}).
The direction vector is used to select a cube map face.
The direction vector is transformed to a per-face texel coordinate system
(s_{face},t_{face}), The direction vector is also used to transform the
derivatives to per-face derivatives.

### Cube Map Face Selection

The direction vector selects one of the cube map’s faces based on the largest magnitude coordinate direction (the major axis direction). Since two or more coordinates can have identical magnitude, the implementation must have rules to disambiguate this situation.

The rules should have as the first rule that r_{z} wins over
r_{y} and r_{x}, and the second rule that r_{y} wins over
r_{x}.
An implementation may choose other rules, but the rules must be
deterministic and depend only on (r_{x},r_{y},r_{z}).

The layer number (corresponding to a cube map face), the coordinate
selections for s_{c}, t_{c}, r_{c}, and the selection of
derivatives, are determined by the major axis direction as specified in the
following two tables.

Major Axis Direction | Layer Number | Cube Map Face | |||
---|---|---|---|---|---|

Positive X | |||||

Negative X | |||||

Positive Y | |||||

Negative Y | |||||

Positive Z | |||||

Negative Z |

Major Axis Direction | ||||||
---|---|---|---|---|---|---|

### Cube Map Coordinate Transformation

$\begin{aligned}
s\_{\textit{face}} & =
\frac{1}{2} \times \frac{s\_c}{|r\_c|} + \frac{1}{2} \\\
t\_{\textit{face}} & =
\frac{1}{2} \times \frac{t\_c}{|r\_c|} + \frac{1}{2} \\\
\end{aligned}$### Cube Map Derivative Transformation

$\begin{aligned}
\frac{\partial{s\_{\textit{face}}}}{\partial{x}} &=
\frac{\partial}{\partial{x}} \left ( \frac{1}{2} \times \frac{s\_{c}}{|r\_{c}|}
\+ \frac{1}{2}\right ) \\\
\frac{\partial{s\_{\textit{face}}}}{\partial{x}} &=
\frac{1}{2} \times \frac{\partial}{\partial{x}}
\left ( \frac{s\_{c}}{|r\_{c}|} \right ) \\\
\frac{\partial{s\_{\textit{face}}}}{\partial{x}} &=
\frac{1}{2} \times
\left (
\frac{
|r\_{c}| \times \partial{s\_c}/\partial{x}
-s\_c \times {\partial{r\_{c}}}/{\partial{x}}}
{\left ( r\_{c} \right )^2}
\right )
\end{aligned}$$\begin{aligned}
\frac{\partial{s\_{\textit{face}}}}{\partial{y}} &=
\frac{1}{2} \times
\left (
\frac{
|r\_{c}| \times \partial{s\_c}/\partial{y}
-s\_c \times {\partial{r\_{c}}}/{\partial{y}}}
{\left ( r\_{c} \right )^2}
\right )\\\
\frac{\partial{t\_{\textit{face}}}}{\partial{x}} &=
\frac{1}{2} \times
\left (
\frac{
|r\_{c}| \times \partial{t\_c}/\partial{x}
-t\_c \times {\partial{r\_{c}}}/{\partial{x}}}
{\left ( r\_{c} \right )^2}
\right ) \\\
\frac{\partial{t\_{\textit{face}}}}{\partial{y}} &=
\frac{1}{2} \times
\left (
\frac{
|r\_{c}| \times \partial{t\_c}/\partial{y}
-t\_c \times {\partial{r\_{c}}}/{\partial{y}}}
{\left ( r\_{c} \right )^2}
\right )
\end{aligned}$### Scale Factor Operation, LOD Operation and Image Level(s) Selection

LOD selection can be either explicit (provided explicitly by the image
instruction) or implicit (determined from a scale factor calculated from the
derivatives).
The LOD must be computed with `mipmapPrecisionBits`

of accuracy.

#### Scale Factor Operation

The magnitude of the derivatives are calculated by:

- m
_{ux}= |∂s/∂x| × w_{base} - m
_{vx}= |∂t/∂x| × h_{base} - m
_{wx}= |∂r/∂x| × d_{base} - m
_{uy}= |∂s/∂y| × w_{base} - m
_{vy}= |∂t/∂y| × h_{base} - m
_{wy}= |∂r/∂y| × d_{base}

where:

- ∂t/∂x = ∂t/∂y = 0 (for 1D images)
- ∂r/∂x = ∂r/∂y = 0 (for 1D, 2D or Cube images)

and:

- w
_{base}= image.w - h
_{base}= image.h - d
_{base}= image.d

(for the `baseMipLevel`

, from the image descriptor).

For corner-sampled images, the w_{base}, h_{base}, and
d_{base} are instead:

- w
_{base}= image.w - 1 - h
_{base}= image.h - 1 - d
_{base}= image.d - 1

A point sampled in screen space has an elliptical footprint in texture
space.
The minimum and maximum scale factors (ρ_{min}, ρ_{max}) should
be the minor and major axes of this ellipse.

The *scale factors* ρ_{x} and ρ_{y}, calculated from the
magnitude of the derivatives in x and y, are used to compute the minimum and
maximum scale factors.

ρ_{x} and ρ_{y} may be approximated with functions
f_{x} and f_{y}, subject to the following constraints:

The minimum and maximum scale factors (ρ_{min},ρ_{max}) are
determined by:

- ρ
_{max}= max(ρ_{x}, ρ_{y}) - ρ
_{min}= min(ρ_{x}, ρ_{y})

The ratio of anisotropy is determined by:

- η = min(ρ
_{max}/ρ_{min}, max_{Aniso})

where:

- sampler.max
_{Aniso}=`maxAnisotropy`

(from sampler descriptor) - limits.max
_{Aniso}=`maxSamplerAnisotropy`

(from physical device limits) - max
_{Aniso}= min(sampler.max_{Aniso}, limits.max_{Aniso})

If ρ_{max} = ρ_{min} = 0, then all the partial derivatives are
zero, the fragment’s footprint in texel space is a point, and η
should be treated as 1.
If ρ_{}