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## 1. Introduction

OpenCL (Open Computing Language) is an open royalty-free standard for general purpose parallel programming across CPUs, GPUs, and other processors, giving software developers portable and efficient access to the power of these heterogeneous processing platforms.

Parallel programs in OpenCL may be written in the OpenCL C source language, or may compiled from OpenCL C, OpenCL C++, or other source languages into SPIR-V modules.

All SPIR-V intermediate binary modules are consumed by environments, such as an API, a specific version of an API, or an implementation of an API. The environment describes required support for some SPIR-V capabilities, additional semantics for some SPIR-V instructions, and additional validation rules a module must adhere to in order to be considered valid.

This document describes the environment for implementations of the OpenCL API. It is written for compiler developers who are generating SPIR-V modules to be consumed by the OpenCL API, for implementors of the OpenCL API who are consuming SPIR-V modules, and by software developers who are using SPIR-V modules with the OpenCL API.

## 2. SPIR-V Consumption

This section describes common properties of all OpenCL environments. Subsequent sections describe environments for specific versions of OpenCL, and how an environment may additionally be modified via OpenCL or SPIR-V extensions.

A SPIR-V module passed to an OpenCL environment is interpreted as a series of 32-bit words in host endianness, with literal strings packed as described in the SPIR-V specification. The first few words of the SPIR-V module must be a magic number and a SPIR-V version number, as described in the SPIR-V specification.

### 2.1. Validation Rules

The following are a list of validation rules that apply to SPIR-V modules executing in all OpenCL environments:

• The Execution Model declared in OpEntryPoint must be Kernel.

• The Addressing Model declared in OpMemoryModel must be either Physical32 or Physical64:

• Modules indicating a Physical32 Addressing Model are valid for OpenCL devices reporting 32 for CL_DEVICE_ADDRESS_BITS.

• Modules indicating a Physical64 Addressing Model are valid for OpenCL devices reporting 64 for CL_DEVICE_ADDRESS_BITS.

• The Memory Model declared in OpMemoryModel must be OpenCL.

• For all OpTypeInt integer type-declaration instructions:

• Signedness must be 0, indicating no signedness semantics.

• For all OpTypeImage type-declaration instructions:

• Sampled Type must be OpTypeVoid.

• Sampled must be 0, indicating that the image usage will be known at run time, not at compile time.

• MS must be 0, indicating single-sampled content.

• Arrayed may only be set to 1, indicating arrayed content, when Dim is set to 1D or 2D.

• Image Format must be Unknown, indicating that the image does not have a specified format.

• The optional image Access Qualifier must be present.

• The image write instruction OpImageWrite must not include any optional Image Operands.

• The image read instructions OpImageRead and OpImageSampleExplicitLod must not include the optional Image Operand ConstOffset.

• For all Atomic Instructions:

• Only 32-bit integer types are supported for the Result Type and/or type of Value.

• The Pointer operand must be a pointer to the Function, Workgroup, or CrossWorkGroup Storage Classes. Note that an Atomic Instruction on a pointer to the Function Storage Class is valid, but does not have defined behavior.

• Recursion is not supported. The static function call graph for an entry point must not contain cycles.

• Whether irreducible control flow is legal is implementation defined.

### 2.2. Source Language Encoding

If a SPIR-V module represents a program written in OpenCL C, then the Source Language operand for the OpSource instruction should be OpenCL_C, and the 32-bit literal language Version should describe the version of OpenCL C, encoded MSB to LSB as:

0 | Major Number | Minor Number | Revision Number (optional)

Hence, OpenCL C 1.2 would be encoded as 0x00010200, and OpenCL C 2.0 as 0x00020000.

If a SPIR-V module represents a program written in OpenCL C++, then the Source Language operand for the OpSource instruction should be OpenCL_CPP, and the 32-bit literal language Version should describe the version of OpenCL C++, encoded similarly. Hence, OpenCL C++ 2.2 would be encoded as 0x00020200.

The source language version is purely informational and has no semantic meaning.

### 2.3. Numerical Type Formats

For all OpenCL environments, floating-point types are represented and stored using IEEE-754 semantics. All integer formats are represented and stored using 2’s-complement format.

### 2.4. Supported Types

The following types are supported by OpenCL environments. Note that some types may require additional capabilities, and may not be supported by all OpenCL environments.

OpenCL environments support arrays declared using OpTypeArray, structs declared using OpTypeStruct, functions declared using OpTypeFunction, and pointers declared using OpTypePointer.

#### 2.4.1. Basic Scalar and Vector Types

OpTypeVoid is supported.

The following scalar types are supported by OpenCL environments:

• OpTypeBool

• OpTypeInt, with Width equal to 8, 16, 32, or 64, and with Signedness equal to zero, indicating no signedness semantics.

• OpTypeFloat, with Width equal to 16, 32, or 64.

OpenCL environments support vector types declared using OpTypeVector. The vector Component Type may be any of the scalar types described above. Supported vector Component Counts are 2, 3, 4, 8, or 16.

The following table describes the OpTypeImage image types supported by OpenCL environments:

 Dim Depth Arrayed Description 1D 0 0 A 1D image. 1D 0 1 A 1D image array. 2D 0 0 A 2D image. 2D 1 0 A 2D depth image. 2D 0 1 A 2D image array. 2D 1 1 A 2D depth image array. 3D 0 0 A 3D image. Buffer 0 0 A 1D buffer image.

OpTypeSampler may be used to declare sampler types in OpenCL environments.

#### 2.4.3. Other Data Types

The following table describes other data types that may be used in an OpenCL environment:

 Type Description OpTypeEvent OpenCL event type. OpTypeDeviceEvent OpenCL device-side event type. OpTypePipe OpenCL pipe type OpTypeReserveId OpenCL pipe reservation identifier. OpTypeQueue OpenCL device-side command queue.

### 2.5. Image Channel Order Mapping

The following table describes how the results of the SPIR-V OpImageQueryOrder instruction correspond to the OpenCL host API image channel orders.

Table 3. Image Channel Order mapping
SPIR-V Image Channel Order OpenCL Image Channel Order

R

CL_R

A

CL_A

RG

CL_RG

RA

CL_RA

RGB

CL_RGB

RGBA

CL_RGBA

BGRA

CL_BGRA

ARGB

CL_ARGB

Intensity

CL_INTENSITY

Luminance

CL_LUMINANCE

Rx

CL_Rx

RGx

CL_RGx

RGBx

CL_RGBx

Depth

CL_DEPTH

DepthStencil

CL_DEPTH_STENCIL

sRGB

CL_sRGB

sRGBA

CL_sRGBA

sBGRA

CL_sBGRA

sRGBx

CL_sRGBx

### 2.6. Image Channel Data Type Mapping

The following table describes how the results of the SPIR-V OpImageQueryFormat instruction correspond to the OpenCL host API image channel data types.

Table 4. Image Channel Data Type mapping
SPIR-V Image Channel Data Type OpenCL Image Channel Data Type

SnormInt8

CL_SNORM_INT8

SnormInt16

CL_SNORM_INT16

UnormInt8

CL_UNORM_INT8

UnormInt16

CL_UNORM_INT16

UnormInt24

CL_UNORM_INT24

UnormShort565

CL_UNORM_SHORT_565

UnormShort555

CL_UNORM_SHORT_555

UnormInt101010

CL_UNORM_INT_101010

SignedInt8

CL_SIGNED_INT8

SignedInt16

CL_SIGNED_INT16

SignedInt32

CL_SIGNED_INT32

UnsignedInt8

CL_UNSIGNED_INT8

UnsignedInt16

CL_UNSIGNED_INT16

UnsignedInt32

CL_UNSIGNED_INT32

HalfFloat

CL_HALF_FLOAT

Float

CL_FLOAT

### 2.7. Kernels

An OpFunction in a SPIR-V module that is identified with OpEntryPoint defines an OpenCL kernel that may be invoked using the OpenCL host API enqueue kernel interfaces.

### 2.8. Kernel Return Types

The Result Type for an OpFunction identified with OpEntryPoint must be OpTypeVoid.

### 2.9. Kernel Arguments

An OpFunctionParameter for an OpFunction that is identified with OpEntryPoint defines an OpenCL kernel argument. Allowed types for OpenCL kernel arguments are:

• OpTypeInt

• OpTypeFloat

• OpTypeStruct

• OpTypeVector

• OpTypePointer

• OpTypeSampler

• OpTypeImage

• OpTypePipe

• OpTypeQueue

For OpTypeInt parameters, supported Widths are 8, 16, 32, and 64, and must have no signedness semantics.

For OpTypeFloat parameters, Width must be 32.

For OpTypeStruct parameters, supported structure Member Types are:

• OpTypeInt

• OpTypeFloat

• OpTypeStruct

• OpTypeVector

• OpTypePointer

For OpTypePointer parameters, supported Storage Classes are:

• CrossWorkgroup

• Workgroup

• UniformConstant

OpenCL kernel argument types must have a representation in the OpenCL host API.

Environments that support extensions or optional features may allow additional types in an entry point’s parameter list.

## 3. OpenCL 2.2

An OpenCL 2.2 environment must accept SPIR-V 1.0, 1.1, and 1.2 modules.

### 3.1. Full Profile

An OpenCL 2.2 Full Profile environment is guaranteed to support the following SPIR-V capabilities:

• DeviceEnqueue

• Float16Buffer

• GenericPointer

• Groups

• Int64

• Int16

• Int8

• Kernel

• Pipes

• Vector16

• SubgroupDispatch

• PipeStorage

The following capabilities may be optionally supported:

• ImageBasic, if CL_DEVICE_IMAGE_SUPPORT is CL_TRUE

• Float64, if the device supports double precision floating-point

If ImageBasic is supported then the following capabilities must also be supported:

• LiteralSampler

• Sampled1D

• Image1D

• SampledBuffer

• ImageBuffer

### 3.2. Embedded Profile

An OpenCL 2.2 Embedded Profile environment is guaranteed to support the following SPIR-V capabilities:

• DeviceEnqueue

• Float16Buffer

• GenericPointer

• Groups

• Int16

• Int8

• Kernel

• Pipes

• Vector16

• SubgroupDispatch

• PipeStorage

Furthermore, the following capabilities may optionally be supported:

• ImageBasic, if CL_DEVICE_IMAGE_SUPPORT is CL_TRUE

• Float64, if the device supports double precision floating-point

If ImageBasic is supported then the following capabilities must also be supported:

• LiteralSampler

• Sampled1D

• Image1D

• SampledBuffer

• ImageBuffer

### 3.3. Validation Rules

The following are a list of validation rules for SPIR-V modules executing in an OpenCL 2.2 environment:

Scope for Execution is generally limited to:

• Workgroup

• Subgroup

Scope for Memory is generally limited to:

• CrossDevice

• Device

• Workgroup

• Invocation

Scope for Execution for the OpGroupAsyncCopy and OpGroupWaitEvents instructions is specifically limited to:

• Workgroup

The Pointer operand to all Atomic Instructions may additionally be a pointer to the Generic Storage Class, however behavior is still undefined if the Generic pointer represents a pointer to the Function Storage Class.

## 4. OpenCL 2.1

An OpenCL 2.1 environment must accept SPIR-V 1.0 modules.

### 4.1. Full Profile

An OpenCL 2.1 Full Profile environment is guaranteed to support the following SPIR-V capabilities:

• DeviceEnqueue

• Float16Buffer

• GenericPointer

• Groups

• Int64

• Int16

• Int8

• Kernel

• Pipes

• Vector16

The following capabilities may be optionally supported:

• ImageBasic, if CL_DEVICE_IMAGE_SUPPORT is CL_TRUE

• Float64, if the device supports double precision floating-point

If ImageBasic is supported then the following capabilities must also be supported:

• LiteralSampler

• Sampled1D

• Image1D

• SampledBuffer

• ImageBuffer

### 4.2. Embedded Profile

An OpenCL 2.1 Embedded Profile environment is guaranteed to support the following SPIR-V capabilities:

• DeviceEnqueue

• Float16Buffer

• GenericPointer

• Groups

• Int16

• Int8

• Kernel

• Pipes

• Vector16

Furthermore, the following capabilities may optionally be supported:

• ImageBasic, if CL_DEVICE_IMAGE_SUPPORT is CL_TRUE

• Float64, if the device supports double precision floating-point

If ImageBasic is supported then the following capabilities must also be supported:

• LiteralSampler

• Sampled1D

• Image1D

• SampledBuffer

• ImageBuffer

### 4.3. Validation Rules

The following are a list of validation rules for SPIR-V modules executing in an OpenCL 2.1 environment:

Scope for Execution is generally limited to:

• Workgroup

• Subgroup

Scope for Memory is generally limited to:

• CrossDevice

• Device

• Workgroup

• Invocation

Scope for Execution for the OpGroupAsyncCopy and OpGroupWaitEvents instructions is specifically limited to:

• Workgroup

The Pointer operand to all Atomic Instructions may additionally be a pointer to the Generic Storage Class, however behavior is still undefined if the Generic pointer represents a pointer to the Function Storage Class.

## 5. OpenCL 2.0

An OpenCL 2.0 environment must accept SPIR-V 1.0 modules if it includes the optional extension cl_khr_il_program in the host API CL_PLATFORM_EXTENSIONS or CL_DEVICE_EXTENSIONS string.

### 5.1. Full Profile

An OpenCL 2.0 Full Profile environment is guaranteed to support the following SPIR-V capabilities:

• DeviceEnqueue

• Float16Buffer

• GenericPointer

• Groups

• Int64

• Int16

• Int8

• Kernel

• Pipes

• Vector16

The following capabilities may be optionally supported:

• ImageBasic, if CL_DEVICE_IMAGE_SUPPORT is CL_TRUE

• Float64, if the device supports double precision floating-point

If ImageBasic is supported then the following capabilities must also be supported:

• LiteralSampler

• Sampled1D

• Image1D

• SampledBuffer

• ImageBuffer

### 5.2. Embedded Profile

An OpenCL 2.0 Embedded Profile environment is guaranteed to support the following SPIR-V capabilities:

• DeviceEnqueue

• Float16Buffer

• GenericPointer

• Groups

• Int16

• Int8

• Kernel

• Pipes

• Vector16

Furthermore, the following capabilities may optionally be supported:

• ImageBasic, if CL_DEVICE_IMAGE_SUPPORT is CL_TRUE

• Float64, if the device supports double precision floating-point

If ImageBasic is supported then the following capabilities must also be supported:

• LiteralSampler

• Sampled1D

• Image1D

• SampledBuffer

• ImageBuffer

### 5.3. Validation Rules

The following are a list of validation rules for SPIR-V modules executing in an OpenCL 2.0 environment:

Scope for Execution is generally limited to:

• Workgroup

Scope for Memory is generally limited to:

• CrossDevice

• Device

• Workgroup

• Invocation

The Pointer operand to all Atomic Instructions may additionally be a pointer to the Generic Storage Class, however behavior is still undefined if the Generic pointer represents a pointer to the Function Storage Class.

## 6. OpenCL 1.2

An OpenCL 1.2 environment must accept SPIR-V 1.0 modules if it includes the optional extension cl_khr_il_program in the host API CL_PLATFORM_EXTENSIONS or CL_DEVICE_EXTENSIONS string.

### 6.1. Full Profile

An OpenCL 1.2 Full Profile environment is guaranteed to support the following SPIR-V capabilities:

• Float16Buffer

• Groups

• Int64

• Int16

• Int8

• Kernel

• Vector16

The following capabilities may be optionally supported:

• ImageBasic, if CL_DEVICE_IMAGE_SUPPORT is CL_TRUE

• Float64, if the device supports double precision floating-point

If ImageBasic is supported then the following capabilities must also be supported:

• LiteralSampler

• Sampled1D

• Image1D

• SampledBuffer

• ImageBuffer

### 6.2. Embedded Profile

An OpenCL 1.2 Embedded Profile environment is guaranteed to support the following SPIR-V capabilities:

• Float16Buffer

• Groups

• Int16

• Int8

• Kernel

• Pipes

• Vector16

The following capabilities may be optionally supported:

• ImageBasic, if CL_DEVICE_IMAGE_SUPPORT is CL_TRUE

• Float64, if the device supports double precision floating-point

If ImageBasic is supported then the following capabilities must also be supported:

• LiteralSampler

• Sampled1D

• Image1D

• SampledBuffer

• ImageBuffer

### 6.3. Validation Rules

The following are a list of validation rules for SPIR-V modules executing in an OpenCL 1.2 environment:

Scope for Execution is generally limited to:

• Workgroup

Scope for Memory is generally limited to:

• CrossDevice

• Device

• Workgroup

• Invocation

The following Group Instructions are not supported:

• OpGroupAll

• OpGroupAny

• OpGroupFMin

• OpGroupUMin

• OpGroupSMin

• OpGroupFMax

• OpGroupUMax

• OpGroupSMax

For the Barrier Instructions OpControlBarrier and OpMemoryBarrier, the Scope for execution must be Workgroup, the Scope for memory must be Workgroup, and the Memory Semantics must be SequentiallyConsistent.

For the Atomic Instructions, the Scope must be Device, and the Memory Semantics must be Relaxed.

## 7. OpenCL Extensions

An OpenCL environment may be modified by OpenCL extensions. For example, some OpenCL extensions may require support for support for additional SPIR-V capabilities or instructions, or by relaxing SPIR-V restrictions. Some OpenCL extensions may modify the OpenCL environment by requiring consumption of a SPIR-V module that uses a SPIR-V extension. In this case, the implementation will include the OpenCL extension in the host API CL_PLATFORM_EXTENSIONS or CL_DEVICE_EXTENSIONS string, but not the corresponding SPIR-V extension.

This section describes how the OpenCL environment is modified by Khronos (khr) OpenCL extensions. Other OpenCL extensions, such as multi-vendor (ext) extensions or vendor-specific extensions, describe how they modify the OpenCL environment in their individual extension specifications. The Khronos OpenCL extensions require no corresponding SPIR-V extensions.

### 7.1. Declaring SPIR-V Extensions

A SPIR-V module declares use of a SPIR-V extension using OpExtension and the name of the SPIR-V extension. For example:

OpExtension "SPV_KHR_extension_name"

Only use of SPIR-V extensions may be declared in a SPIR-V module using OpExtension; there is never a need to declare use of an OpenCL extension in a SPIR-V module using OpExtension.

### 7.2. Full and Embedded Profile Extensions

#### 7.2.1. cl_khr_3d_image_writes

If the OpenCL environment supports the extension cl_khr_3d_image_writes, then the environment must accept Image operands to OpImageWrite that are declared with with dimensionality Dim equal to 3D.

#### 7.2.2. cl_khr_depth_images

If the OpenCL environment supports the extension cl_khr_depth_images, then the environment must accept modules that declare 2D depth image types using OpTypeImage with dimensionality Dim equal to 2D and Depth equal to 1, indicating a depth image. 2D depth images may optionally be Arrayed, if supported.

Additionally, the following Image Channel Orders may be returned by OpImageQueryOrder:

• Depth

#### 7.2.3. cl_khr_device_enqueue_local_arg_types

If the OpenCL environment supports the extension cl_khr_device_enqueue_local_arg_types, then then environment will allow Invoke functions to be passed to OpEnqueueKernel with Workgroup memory pointer parameters of any type.

#### 7.2.4. cl_khr_fp16

If the OpenCL environment supports the extension cl_khr_fp16, then the environment must accept modules that declare the following SPIR-V capabilities:

• Float16

#### 7.2.5. cl_khr_fp64

If the OpenCL environment supports the extension cl_khr_fp64, then the environment must accept modules that declare the following SPIR-V capabilities:

• Float64

#### 7.2.6. cl_khr_gl_depth_images

If the OpenCL environment supports the extension cl_khr_gl_depth_images, then the following Image Channel Orders may additionally be returned by OpImageQueryOrder:

• DepthStencil

Also, the following Image Channel Data Types may additionally be returned by OpImageQueryFormat:

• UnormInt24

#### 7.2.7. cl_khr_gl_msaa_sharing

If the OpenCL environment supports the extension cl_khr_gl_msaa_sharing, then the environment must accept modules that declare 2D multi-sampled image types using OpTypeImage with dimensionality Dim equal to 2D and MS equal to 1, indicating multi-sampled content. 2D multi-sampled images may optionally be Arrayed or Depth images, if supported.

The 2D multi-sampled images may be used with the following instructions:

• OpImageQuerySizeLod

• OpImageQueryFormat

• OpImageQueryOrder

• OpImageQuerySamples

#### 7.2.8. cl_khr_int64_base_atomics and cl_khr_int64_extended_atomics

If the OpenCL environment supports the extension cl_khr_int64_base_atomics or cl_khr_int64_extended_atomics, then the environment must support 64-bit integer operands for all of the SPIR-V Atomic Instructions.

When the WorkgroupMemory Memory Semantic is used the Scope must be Workgroup.

Note: OpenCL environments that consume SPIR-V must support both cl_khr_int64_base_atomics and cl_khr_int64_extended_atomics or neither of these extensions.

#### 7.2.9. cl_khr_mipmap_image

If the OpenCL environment supports the extension cl_khr_mipmap_image, then the environment must accept non-zero optional Lod Image Operands for the following instructions:

• OpImageSampleExplicitLod

• OpImageQuerySizeLod

Note: Implementations that support cl_khr_mipmap_image are not guaranteed to support the ImageMipmap capability, since this extension does not require non-zero optional Lod Image Operands for OpImageWrite.

#### 7.2.10. cl_khr_mipmap_image_writes

If the OpenCL environment supports the extension cl_khr_mipmap_image_writes, then the environment must accept non-zero optional Lod Image Operands for the following instructions:

• OpImageWrite

Note: An implementation that supports cl_khr_mipmap_image_writes must also support cl_khr_mipmap_image, and support for both extensions does guarantee support for the ImageMipmap capability.

#### 7.2.11. cl_khr_subgroups

If the OpenCL environment supports the extension cl_khr_subgroups, then the environment will generally allows the scope for Execution to include:

• Subgroup

However, the Scope for Execution for the OpGroupAsyncCopy and OpGroupWaitEvents instructions still is limited to:

• Workgroup

#### 7.2.12. cl_khr_subgroup_named_barrier

If the OpenCL environment supports the extension cl_khr_subgroup_named_barrier, then the environment must accept modules that declare the following SPIR-V capabilities:

• NamedBarrier

### 7.3. Embedded Profile Extensions

#### 7.3.1. cles_khr_int64

If the OpenCL environment supports the extension cles_khr_int64, then the environment must accept modules that declare the following SPIR-V capabilities:

• Int64

## 8. OpenCL Numerical Compliance

This section describes features of the C++14 and IEEE-754 standards that must be supported by all OpenCL compliant devices.

This section describes the functionality that must be supported by all OpenCL devices for single precision floating-point numbers. Currently, only single precision floating-point is a requirement. Half precision floating-point is an optional feature indicated by the Float16 capability. Double precision floating-point is also an optional feature indicated by the Float64 capability.

### 8.1. Rounding Modes

Floating-point calculations may be carried out internally with extra precision and then rounded to fit into the destination type. IEEE 754 defines four possible rounding modes:

• Round to nearest even

• Round toward +infinity

• Round toward -infinity

• Round toward zero

The complete set of rounding modes supported by the device are described by the CL_DEVICE_SINGLE_FP_CONFIG, CL_DEVICE_HALF_FP_CONFIG, and CL_DEVICE_DOUBLE_FP_CONFIG device queries.

For double precision operations, Round to nearest even is a required rounding mode, and is therefore the default rounding mode for double precision operations.

For single precision operations, devices supporting the full profile must support Round to nearest even, therefore for full profile devices this is the default rounding mode for single precision operations. Devices supporting the embedded profile may support either Round to nearest even or Round toward zero as the default rounding mode for single precision operations.

For half precision operations, devices may support either Round to nearest even or Round toward zero as the default rounding mode for half precision operations.

Only static selection of rounding mode is supported. Dynamically reconfiguring the rounding mode as specified by the IEEE 754 spec is not supported.

### 8.2. Rounding Modes for Conversions

Results of the following conversion instructions may include an optional FPRoundingMode decoration:

• OpConvertFToU

• OpConvertFToS

• OpConvertSToF

• OpConvertUToF

• OpFConvert

The FPRoundingMode decoration may not be added to results of any other instruction.

If no rounding mode is specified explicitly via an FPRoundingMode decoration, then the default rounding mode for conversion operations is:

• Round to nearest even, for conversions to floating-point types.

• Round toward zero, for conversions from floating-point to integer types.

### 8.3. Out-of-Range Conversions

When a conversion operand is either greater than the greatest representable destination value or less than the least representable destination value, it is said to be out-of-range.

Converting an out-of-range integer to an integer type without a SaturatedConversion decoration follows C99/C++14 conversion rules.

Converting an out-of-range floating point number to an integer type without a SaturatedConversion decoration is implementation-defined.

### 8.4. INF, NaN, and Denormalized Numbers

INFs and NaNs must be supported. Support for signaling NaNs is not required.

Support for denormalized numbers with single precision and half precision floating-point is optional. Denormalized single precision or half precision floating-point numbers passed as the input or produced as the output of single precision or half precision floating-point operations may be flushed to zero. Support for denormalized numbers is required for double precision floating-point.

Support for INFs, NaNs, and denormalized numbers is described by the CL_FP_DENORM and CL_FP_INF_NAN bits in the CL_DEVICE_SINGLE_FP_CONFIG, CL_DEVICE_HALF_FP_CONFIG, and CL_DEVICE_DOUBLE_FP_CONFIG device queries.

### 8.5. Floating-Point Exceptions

Floating-point exceptions are disabled in OpenCL. The result of a floating-point exception must match the IEEE 754 spec for the exceptions-not-enabled case. Whether and when the implementation sets floating-point flags or raises floating-point exceptions is implementation-defined.

This standard provides no method for querying, clearing or setting floating-point flags or trapping raised exceptions. Due to non-performance, non-portability of trap mechanisms, and the impracticality of servicing precise exceptions in a vector context (especially on heterogeneous hardware), such features are discouraged.

Implementations that nevertheless support such operations through an extension to the standard shall initialize with all exception flags cleared and the exception masks set so that exceptions raised by arithmetic operations do not trigger a trap to be taken. If the underlying work is reused by the implementation, the implementation is however not responsible for re-clearing the flags or resetting exception masks to default values before entering the kernel. That is to say that kernels that do not inspect flags or enable traps are licensed to expect that their arithmetic will not trigger a trap. Those kernels that do examine flags or enable traps are responsible for clearing flag state and disabling all traps before returning control to the implementation. Whether or when the underlying work-item (and accompanying global floating-point state if any) is reused is implementation-defined.

### 8.6. Relative Error as ULPs

In this section we discuss the maximum relative error defined as ulp (units in the last place). Addition, subtraction, multiplication, fused multiply-add, and conversion between integer and a single precision floating-point format are IEEE 754 compliant and are therefore correctly rounded. Conversion between floating-point formats and explicit conversions must be correctly rounded.

The ULP is defined as follows:

If x is a real number that lies between two finite consecutive floating-point numbers a and b, without being equal to one of them, then ulp(x) = |b - a|, otherwise ulp(x) is the distance between the two non-equal finite floating-point numbers nearest x. Moreover, ulp(NaN) is NaN.

Attribution: This definition was taken with consent from Jean-Michel Muller with slight clarification for behavior at zero. Refer to: On the definition of ulp(x).

0 ULP is used for math functions that do not require rounding. The reference value used to compute the ULP value is the infinitely precise result.

#### 8.6.1. ULP Values for Math Instructions - Full Profile

The ULP Values for Math Instructions table below describes the minimum accuracy of floating-point math arithmetic instructions for full profile devices given as ULP values.

Table 5. ULP Values for Math Instructions - Full Profile
SPIR-V Instruction Minimum Accuracy - Float64 Minimum Accuracy - Float32 Minimum Accuracy - Float16

Correctly rounded

Correctly rounded

Correctly rounded

OpFSub

Correctly rounded

Correctly rounded

Correctly rounded

OpFMul

Correctly rounded

Correctly rounded

Correctly rounded

OpFDiv

Correctly rounded

<= 2.5 ulp

Correctly rounded

OpExtInst acos

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst acosh

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst acospi

<= 5 ulp

<= 5 ulp

<= 2 ulp

OpExtInst asin

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst asinh

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst asinpi

<= 5 ulp

<= 5 ulp

<= 2 ulp

OpExtInst atan

<= 5 ulp

<= 5 ulp

<= 2 ulp

OpExtInst atanh

<= 5 ulp

<= 5 ulp

<= 2 ulp

OpExtInst atanpi

<= 5 ulp

<= 5 ulp

<= 2 ulp

OpExtInst atan2

<= 6 ulp

<= 6 ulp

<= 2 ulp

OpExtInst atan2pi

<= 6 ulp

<= 6 ulp

<= 2 ulp

OpExtInst cbrt

<= 2 ulp

<= 2 ulp

<= 2 ulp

OpExtInst ceil

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst copysign

0 ulp

0 ulp

0 ulp

OpExtInst cos

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst cosh

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst cospi

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst erfc

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst erf

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst exp

<= 3 ulp

<= 3 ulp

<= 2 ulp

OpExtInst exp2

<= 3 ulp

<= 3 ulp

<= 2 ulp

OpExtInst exp10

<= 3 ulp

<= 3 ulp

<= 2 ulp

OpExtInst expm1

<= 3 ulp

<= 3 ulp

<= 2 ulp

OpExtInst fabs

0 ulp

0 ulp

0 ulp

OpExtInst fdim

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst floor

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst fma

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst fmax

0 ulp

0 ulp

0 ulp

OpExtInst fmin

0 ulp

0 ulp

0 ulp

OpExtInst fmod

0 ulp

0 ulp

0 ulp

OpExtInst fract

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst frexp

0 ulp

0 ulp

0 ulp

OpExtInst hypot

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst ilogb

0 ulp

0 ulp

0 ulp

OpExtInst ldexp

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst lgamma

Implementation-defined

Implementation-defined

Implementation-defined

OpExtInst lgamma_r

Implementation-defined

Implementation-defined

Implementation-defined

OpExtInst log

<= 3 ulp

<= 3 ulp

<= 2 ulp

OpExtInst log2

<= 3 ulp

<= 3 ulp

<= 2 ulp

OpExtInst log10

<= 3 ulp

<= 3 ulp

<= 2 ulp

OpExtInst log1p

<= 2 ulp

<= 2 ulp

<= 2 ulp

OpExtInst logb

0 ulp

0 ulp

0 ulp

Implemented either as a correctly rounded fma, or as a multiply followed by an add, both of which are correctly rounded

Implemented either as a correctly rounded fma, or as a multiply followed by an add, both of which are correctly rounded

Implemented either as a correctly rounded fma, or as a multiply followed by an add, both of which are correctly rounded

OpExtInst maxmag

0 ulp

0 ulp

0 ulp

OpExtInst minmag

0 ulp

0 ulp

0 ulp

OpExtInst modf

0 ulp

0 ulp

0 ulp

OpExtInst nan

0 ulp

0 ulp

0 ulp

OpExtInst nextafter

0 ulp

0 ulp

0 ulp

OpExtInst pow

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst pown

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst powr

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst remainder

0 ulp

0 ulp

0 ulp

OpExtInst remquo

0 ulp for the remainder, at least the lower 7 bits of the integral quotient

0 ulp for the remainder, at least the lower 7 bits of the integral quotient

0 ulp for the remainder, at least the lower 7 bits of the integral quotient

OpExtInst rint

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst rootn

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst round

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst rsqrt

<= 2 ulp

<= 2 ulp

<= 1 ulp

OpExtInst sin

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst sincos

<= 4 ulp for sine and cosine values

<= 4 ulp for sine and cosine values

<= 2 ulp for sine and cosine values

OpExtInst sinh

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst sinpi

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst sqrt

Correctly rounded

<= 3 ulp

Correctly rounded

OpExtInst tan

<= 5 ulp

<= 5 ulp

<= 2 ulp

OpExtInst tanh

<= 5 ulp

<= 5 ulp

<= 2 ulp

OpExtInst tanpi

<= 6 ulp

<= 6 ulp

<= 2 ulp

OpExtInst tgamma

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst trunc

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst half_cos

<= 8192 ulp

OpExtInst half_divide

<= 8192 ulp

OpExtInst half_exp

<= 8192 ulp

OpExtInst half_exp2

<= 8192 ulp

OpExtInst half_exp10

<= 8192 ulp

OpExtInst half_log

<= 8192 ulp

OpExtInst half_log2

<= 8192 ulp

OpExtInst half_log10

<= 8192 ulp

OpExtInst half_powr

<= 8192 ulp

OpExtInst half_recip

<= 8192 ulp

OpExtInst half_rsqrt

<= 8192 ulp

OpExtInst half_sin

<= 8192 ulp

OpExtInst half_sqrt

<= 8192 ulp

OpExtInst half_tan

<= 8192 ulp

OpExtInst native_cos

Implementation-defined

OpExtInst native_divide

Implementation-defined

OpExtInst native_exp

Implementation-defined

OpExtInst native_exp2

Implementation-defined

OpExtInst native_exp10

Implementation-defined

OpExtInst native_log

Implementation-defined

OpExtInst native_log2

Implementation-defined

OpExtInst native_log10

Implementation-defined

OpExtInst native_powr

Implementation-defined

OpExtInst native_recip

Implementation-defined

OpExtInst native_rsqrt

Implementation-defined

OpExtInst native_sin

Implementation-defined

OpExtInst native_sqrt

Implementation-defined

OpExtInst native_tan

Implementation-defined

#### 8.6.2. ULP Values for Math Instructions - Embedded Profile

The ULP Values for Math instructions for Embedded Profile table below describes the minimum accuracy of floating-point math arithmetic operations given as ULP values for the embedded profile.

Table 6. ULP Values for Math Instructions - Embedded Profile
SPIR-V Instruction Minimum Accuracy - Float64 Minimum Accuracy - Float32 Minimum Accuracy - Float16

Correctly rounded

Correctly rounded

Correctly rounded

OpFSub

Correctly rounded

Correctly rounded

Correctly rounded

OpFMul

Correctly rounded

Correctly rounded

Correctly rounded

OpFDiv

<= 3 ulp

<= 3 ulp

<= 1 ulp

OpExtInst acos

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst acosh

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst acospi

<= 5 ulp

<= 5 ulp

<= 3 ulp

OpExtInst asin

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst asinh

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst asinpi

<= 5 ulp

<= 5 ulp

<= 3 ulp

OpExtInst atan

<= 5 ulp

<= 5 ulp

<= 3 ulp

OpExtInst atanh

<= 5 ulp

<= 5 ulp

<= 3 ulp

OpExtInst atanpi

<= 5 ulp

<= 5 ulp

<= 3 ulp

OpExtInst atan2

<= 6 ulp

<= 6 ulp

<= 3 ulp

OpExtInst atan2pi

<= 6 ulp

<= 6 ulp

<= 3 ulp

OpExtInst cbrt

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst ceil

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst copysign

0 ulp

0 ulp

0 ulp

OpExtInst cos

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst cosh

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst cospi

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst erfc

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst erf

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst exp

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst exp2

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst exp10

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst expm1

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst fabs

0 ulp

0 ulp

0 ulp

OpExtInst fdim

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst floor

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst fma

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst fmax

0 ulp

0 ulp

0 ulp

OpExtInst fmin

0 ulp

0 ulp

0 ulp

OpExtInst fmod

0 ulp

0 ulp

0 ulp

OpExtInst fract

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst frexp

0 ulp

0 ulp

0 ulp

OpExtInst hypot

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst ilogb

0 ulp

0 ulp

0 ulp

OpExtInst ldexp

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst lgamma

Implementation-defined

Implementation-defined

Implementation-defined

OpExtInst lgamma_r

Implementation-defined

Implementation-defined

Implementation-defined

OpExtInst log

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst log2

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst log10

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst log1p

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst logb

0 ulp

0 ulp

0 ulp

Implemention-defined

Implemention-defined

Implemention-defined

OpExtInst maxmag

0 ulp

0 ulp

0 ulp

OpExtInst minmag

0 ulp

0 ulp

0 ulp

OpExtInst modf

0 ulp

0 ulp

0 ulp

OpExtInst nan

0 ulp

0 ulp

0 ulp

OpExtInst nextafter

0 ulp

0 ulp

0 ulp

OpExtInst pow

<= 16 ulp

<= 16 ulp

<= 5 ulp

OpExtInst pown

<= 16 ulp

<= 16 ulp

<= 5 ulp

OpExtInst powr

<= 16 ulp

<= 16 ulp

<= 5 ulp

OpExtInst remainder

0 ulp

0 ulp

0 ulp

OpExtInst remquo

0 ulp for the remainder, at least the lower 7 bits of the integral quotient

0 ulp for the remainder, at least the lower 7 bits of the integral quotient

0 ulp for the remainder, at least the lower 7 bits of the integral quotient

OpExtInst rint

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst rootn

<= 16 ulp

<= 16 ulp

<= 5 ulp

OpExtInst round

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst rsqrt

<= 4 ulp

<= 4 ulp

<= 1 ulp

OpExtInst sin

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst sincos

<= 4 ulp for sine and cosine values

<= 4 ulp for sine and cosine values

<= 2 ulp for sine and cosine values

OpExtInst sinh

<= 4 ulp

<= 4 ulp

<= 3 ulp

OpExtInst sinpi

<= 4 ulp

<= 4 ulp

<= 2 ulp

OpExtInst sqrt

<= 4 ulp

<= 4 ulp

<= 1 ulp

OpExtInst tan

<= 5 ulp

<= 5 ulp

<= 3 ulp

OpExtInst tanh

<= 5 ulp

<= 5 ulp

<= 3 ulp

OpExtInst tanpi

<= 6 ulp

<= 6 ulp

<= 3 ulp

OpExtInst tgamma

<= 16 ulp

<= 16 ulp

<= 4 ulp

OpExtInst trunc

Correctly rounded

Correctly rounded

Correctly rounded

OpExtInst half_cos

<= 8192 ulp

OpExtInst half_divide

<= 8192 ulp

OpExtInst half_exp

<= 8192 ulp

OpExtInst half_exp2

<= 8192 ulp

OpExtInst half_exp10

<= 8192 ulp

OpExtInst half_log

<= 8192 ulp

OpExtInst half_log2

<= 8192 ulp

OpExtInst half_log10

<= 8192 ulp

OpExtInst half_powr

<= 8192 ulp

OpExtInst half_recip

<= 8192 ulp

OpExtInst half_rsqrt

<= 8192 ulp

OpExtInst half_sin

<= 8192 ulp

OpExtInst half_sqrt

<= 8192 ulp

OpExtInst half_tan

<= 8192 ulp

OpExtInst native_cos

Implementation-defined

OpExtInst native_divide

Implementation-defined

OpExtInst native_exp

Implementation-defined

OpExtInst native_exp2

Implementation-defined

OpExtInst native_exp10

Implementation-defined

OpExtInst native_log

Implementation-defined

OpExtInst native_log2

Implementation-defined

OpExtInst native_log10

Implementation-defined

OpExtInst native_powr

Implementation-defined

OpExtInst native_recip

Implementation-defined

OpExtInst native_rsqrt

Implementation-defined

OpExtInst native_sin

Implementation-defined

OpExtInst native_sqrt

Implementation-defined

OpExtInst native_tan

Implementation-defined

#### 8.6.3. ULP Values for Math Instructions - Unsafe Math Optimizations Enabled

The ULP Values for Math Instructions with Unsafe Math Optimizations table below describes the minimum accuracy of commonly used single precision floating-point math arithmetic instructions given as ULP values if the -cl-unsafe-math-optimizations compiler option is specified when compiling or building the OpenCL program.

For derived implementations, the operations used in the derivation may themselves be relaxed according to the ULP Values for Math Instructions with Unsafe Math Optimizations table.

The minimum accuracy of math functions not defined in the ULP Values for Math Instructions with Unsafe Math Optimizations table when the -cl-unsafe-math-optimizations compiler option is specified is as defined in the ULP Values for Math Instructions for Full Profile table when operating in the full profile, and as defined in the ULP Values for Math instructions for Embedded Profile table when operating in the embedded profile.

Table 7. ULP Values for Single Precision Math Instructions with -cl-unsafe-math-optimizations
SPIR-V Instruction Minimum Accuracy

OpFDiv for 1.0 / x

<= 2.5 ulp for x in the domain of 2-126 to 2126 for the full profile, and <= 3 ulp for the embedded profile.

OpFDiv for x / y

<= 2.5 ulp for x in the domain of 2-62 to 262 and y in the domain of 2-62 to 262 for the full profile, and <= 3 ulp for the embedded profile.

OpExtInst acos

<= 4096 ulp

OpExtInst acosh

Implemented as log( x + sqrt(x*x - 1) ).

OpExtInst acospi

Implemented as acos(x) * M_PI_F. For non-derived implementations, the error is <= 8192 ulp.

OpExtInst asin

<= 4096 ulp

OpExtInst asinh

Implemented as log( x + sqrt(x*x + 1) ).

OpExtInst asinpi

Implemented as asin(x) * M_PI_F. For non-derived implementations, the error is <= 8192 ulp.

OpExtInst atan

<= 4096 ulp

OpExtInst atanh

Defined for x in the domain (-1, 1). For x in [-2-10, 2-10], implemented as x. For x outside of [-2-10, 2-10], implemented as 0.5f * log( (1.0f + x) / (1.0f - x) ). For non-derived implementations, the error is <= 8192 ulp.

OpExtInst atanpi

Implemented as atan(x) * M_1_PI_F. For non-derived implementations, the error is <= 8192 ulp.

OpExtInst atan2

Implemented as atan(y/x) for x > 0, atan(y/x) + M_PI_F for x < 0 and y > 0, and atan(y/x) - M_PI_F for x < 0 and y < 0.

OpExtInst atan2pi

Implemented as atan2(y, x) * M_1_PI_F. For non-derived implementations, the error is <= 8192 ulp.

OpExtInst cbrt

Implemented as rootn(x, 3). For non-derived implementations, the error is <= 8192 ulp.

OpExtInst cos

For x in the domain [-π, π], the maximum absolute error is <= 2-11 and larger otherwise.

OpExtInst cosh

Defined for x in the domain [-∞, ∞] and implemented as 0.5f * ( exp(x) + exp(-x) ). For non-derived implementations, the error is <= 8192 ULP.

OpExtInst cospi

For x in the domain [-1, 1], the maximum absolute error is <= 2-11 and larger otherwise.

OpExtInst exp

<= 3 + floor( fabs(2 * x) ) ulp for the full profile, and <= 4 ulp for the embedded profile.

OpExtInst exp2

<= 3 + floor( fabs(2 * x) ) ulp for the full profile, and <= 4 ulp for the embedded profile.

OpExtInst exp10

Derived implementations implement this as exp2( x * log2(10) ). For non-derived implementations, the error is <= 8192 ulp.

OpExtInst expm1

Derived implementations implement this as exp(x) - 1. For non-derived implementations, the error is <= 8192 ulp.

OpExtInst log

For x in the domain [0.5, 2] the maximum absolute error is <= 2-21; otherwise the maximum error is <=3 ulp for the full profile and <= 4 ulp for the embedded profile

OpExtInst log2

For x in the domain [0.5, 2] the maximum absolute error is <= 2-21; otherwise the maximum error is <=3 ulp for the full profile and <= 4 ulp for the embedded profile

OpExtInst log10

For x in the domain [0.5, 2] the maximum absolute error is <= 2-21; otherwise the maximum error is <=3 ulp for the full profile and <= 4 ulp for the embedded profile

OpExtInst log1p

Derived implementations implement this as log(x + 1). For non-derived implementations, the error is <= 8192 ulp.

OpExtInst pow

Undefined for x = 0 and y = 0. Undefined for x < 0 and non-integer y. Undefined for x < 0 and y outside the domain [-224, 224]. For x > 0 or x < 0 and even y, derived implementations implement this as exp2( y * log2(x) ). For x < 0 and odd y, derived implementations implement this as -exp2( y * log2(fabs(x) ). For x == 0 and nonzero y, derived implementations return zero. For non-derived implementations, the error is <= 8192 ULP.

On some implementations, powr() or pown() may perform faster than pow(). If x is known to be >= 0, consider using powr() in place of pow(), or if y is known to be an integer, consider using pown() in place of pow().

OpExtInst pown

Defined only for integer values of y. Undefined for x = 0 and y = 0. For x >= 0 or x < 0 and even y, derived implementations implement this as exp2( y * log2(x) ). For x < 0 and odd y, derived implementations implement this as -exp2( y * log2( fabs(x) ) ). For non-derived implementations, the error is <= 8192 ulp.

OpExtInst powr

Defined only for x >= 0. Undefined for x = 0 and y = 0. Derived implementations implement this as exp2( y * log2(x) ). For non-derived implementations, the error is <= 8192 ulp.

OpExtInst rootn

Defined for x > 0 when y is non-zero, derived implementations implement this case as exp2( log2(x) / y ). Defined for x < 0 when y is odd, derived implementations implement this case as -exp2( log2(-x) / y ). Defined for x = +/-0 when y > 0, derived implementations will return +0 in this case. For non-derived implementations, the error is <= 8192 ULP.

OpExtInst sin

For x in the domain [-π, π], the maximum absolute error is <= 2-11 and larger otherwise.

OpExtInst sincos

ulp values as defined for sin(x) and cos(x).

OpExtInst sinh

Defined for x in the domain [-∞, ∞]. For x in [-2-10, 2-10], derived implementations implement as x. For x outside of [-2-10, 2-10], derived implement as 0.5f * ( exp(x) - exp(-x) ). For non-derived implementations, the error is <= 8192 ULP.

OpExtInst sinpi

For x in the domain [-1, 1], the maximum absolute error is <= 2-11 and larger otherwise.

OpExtInst tan

Derived implementations implement this as sin(x) * ( 1.0f / cos(x) ). For non-derived implementations, the error is <= 8192 ulp.

OpExtInst tanh

Defined for x in the domain [-∞, ∞]. For x in [-2-10, 2-10], derived implementations implement as x. For x outside of [-2-10, 2-10], derived implementations implement as (exp(x) - exp(-x)) / (exp(x) + exp(-x)). For non-derived implementations, the error is <= 8192 ULP.

OpExtInst tanpi

Derived implementations implement this as tan(x * M_PI_F). For non-derived implementations, the error is <= 8192 ulp for x in the domain [-1, 1].

for x * y + z

Implemented either as a correctly rounded fma or as a multiply and an add both of which are correctly rounded.

### 8.7. Edge Case Behavior

The edge case behavior of the math functions shall conform to sections F.9 and G.6 of ISO/IEC 9899:TC 2, except where noted below in the Additional Requirements Beyond ISO/IEC 9899:TC2 section.

#### 8.7.1. Additional Requirements Beyond ISO/IEC 9899:TC2

Functions that return a NaN with more than one NaN operand shall return one of the NaN operands. Functions that return a NaN operand may silence the NaN if it is a signaling NaN. A non-signaling NaN shall be converted to a non-signaling NaN. A signaling NaN shall be converted to a NaN, and should be converted to a non-signaling NaN. How the rest of the NaN payload bits or the sign of NaN is converted is undefined.

The usual allowances for rounding error (Relative Error as ULPs section) or flushing behavior (Edge Case Behavior in Flush To Zero Mode section) shall not apply for those values for which section F.9 of ISO/IEC 9899:,TC2, or Additional Requirements Beyond ISO/IEC 9899:TC2 and Edge Case Behavior in Flush To Zero Mode sections below (and similar sections for other floating-point precisions) prescribe a result (e.g. ceil( -1 < x < 0 ) returns -0). Those values shall produce exactly the prescribed answers, and no other. Where the ± symbol is used, the sign shall be preserved. For example, sin(±0) = ±0 shall be interpreted to mean sin(+0) is +0 and sin(-0) is -0.

• OpExtInst acospi:

• acospi( 1 ) = +0.

• acospi( x ) returns a NaN for | x | > 1.

• OpExtInst asinpi:

• asinpi( ±0 ) = ±0.

• asinpi( x ) returns a NaN for | x | > 1.

• OpExtInst atanpi:

• atanpi( ±0 ) = ±0.

• atanpi ( ±∞ ) = ±0.5.

• OpExtInst atan2pi:

• atan2pi ( ±0, -0 ) = ±1.

• atan2pi ( ±0, +0 ) = ± 0.

• atan2pi ( ±0, x ) returns ± 1 for x < 0.

• atan2pi ( ±0, x) returns ± 0 for x > 0.

• atan2pi ( y, ±0 ) returns -0.5 for y < 0.

• atan2pi ( y, ±0 ) returns 0.5 for y > 0.

• atan2pi ( ±y, -∞ ) returns ± 1 for finite y > 0.

• atan2pi ( ±y, +∞ ) returns ± 0 for finite y > 0.

• atan2pi ( ±∞, x ) returns ± 0.5 for finite x.

• atan2pi (±∞, -∞ ) returns ±0.75.

• atan2pi (±∞, +∞ ) returns ±0.25.

• OpExtInst ceil:

• ceil( -1 < x < 0 ) returns -0.

• OpExtInst cospi:

• cospi( ±0 ) returns 1

• cospi( n + 0.5 ) is +0 for any integer n where n + 0.5 is representable.

• cospi( ±∞ ) returns a NaN.

• OpExtInst exp10:

• exp10( ±0 ) returns 1.

• exp10( -∞ ) returns +0.

• exp10( +∞ ) returns +∞.

• OpExtInst distance:

• distance(x, y) calculates the distance from x to y without overflow or extraordinary precision loss due to underflow.

• OpExtInst fdim:

• fdim( any, NaN ) returns NaN.

• fdim( NaN, any ) returns NaN.

• OpExtInst fmod:

• fmod( ±0, NaN ) returns NaN.

• OpExtInst fract:

• fract( x, iptr) shall not return a value greater than or equal to 1.0, and shall not return a value less than 0.

• fract( +0, iptr ) returns +0 and +0 in iptr.

• fract( -0, iptr ) returns -0 and -0 in iptr.

• fract( +inf, iptr ) returns +0 and +inf in iptr.

• fract( -inf, iptr ) returns -0 and -inf in iptr.

• fract( NaN, iptr ) returns the NaN and NaN in iptr.

• OpExtInst frexp:

• frexp( ±∞, exp ) returns ±∞ and stores 0 in exp.

• frexp( NaN, exp ) returns the NaN and stores 0 in exp.

• OpExtInst length:

• length calculates the length of a vector without overflow or extraordinary precision loss due to underflow.

• OpExtInst lgamma_r:

• lgamma_r( x, signp ) returns 0 in signp if x is zero or a negative integer.

• OpExtInst nextafter:

• nextafter( -0, y > 0 ) returns smallest positive denormal value.

• nextafter( +0, y < 0 ) returns smallest negative denormal value.

• OpExtInst normalize:

• normalize shall reduce the vector to unit length, pointing in the same direction without overflow or extraordinary precision loss due to underflow.

• normalize( v ) returns v if all elements of v are zero.

• normalize( v ) returns a vector full of NaNs if any element is a NaN.

• normalize( v ) for which any element in v is infinite shall proceed as if the elements in v were replaced as follows:

for( i = 0; i < sizeof(v) / sizeof(v[0] ); i++ )
v[i] = isinf(v[i] )  ?  copysign(1.0, v[i]) : 0.0 * v [i];
• OpExtInst pow:

• pow( ±0, -∞ ) returns +∞

• OpExtInst pown:

• pown( x, 0 ) is 1 for any x, even zero, NaN or infinity.

• pown( ±0, n ) is ±∞ for odd n < 0.

• pown( ±0, n ) is +∞ for even n < 0.

• pown( ±0, n ) is +0 for even n > 0.

• pown( ±0, n ) is ±0 for odd n > 0.

• OpExtInst powr:

• powr( x, ±0 ) is 1 for finite x > 0.

• powr( ±0, y ) is +∞ for finite y < 0.

• powr( ±0, -∞) is +∞.

• powr( ±0, y ) is +0 for y > 0.

• powr( +1, y ) is 1 for finite y.

• powr( x, y ) returns NaN for x < 0.

• powr( ±0, ±0 ) returns NaN.

• powr( +∞, ±0 ) returns NaN.

• powr( +1, ±∞ ) returns NaN.

• powr( x, NaN ) returns the NaN for x >= 0.

• powr( NaN, y ) returns the NaN.

• OpExtInst rint:

• rint( -0.5 <= x < 0 ) returns -0.

• OpExtInst remquo:

• remquo(x, y, &quo) returns a NaN and 0 in quo if x is ±∞, or if y is 0 and the other argument is non-NaN or if either argument is a NaN.

• OpExtInst rootn:

• rootn( ±0, n ) is ±∞ for odd n < 0.

• rootn( ±0, n ) is +∞ for even n < 0.

• rootn( ±0, n ) is +0 for even n > 0.

• rootn( ±0, n ) is ±0 for odd n > 0.

• rootn( x, n ) returns a NaN for x < 0 and n is even.

• rootn( x, 0 ) returns a NaN.

• OpExtInst round:

• round( -0.5 < x < 0 ) returns -0.

• OpExtInst sinpi:

• sinpi( ±0 ) returns ±0.

• sinpi( +n) returns +0 for positive integers n.

• sinpi( -n ) returns -0 for negative integers n.

• sinpi( ±∞ ) returns a NaN.

• OpExtInst tanpi:

• tanpi( ±0 ) returns ±0.

• tanpi( ±∞ ) returns a NaN.

• tanpi( n ) is copysign( 0.0, n ) for even integers n.

• tanpi( n ) is copysign( 0.0, - n) for odd integers n.

• tanpi( n + 0.5 ) for even integer n is +∞ where n + 0.5 is representable.

• tanpi( n + 0.5 ) for odd integer n is -∞ where n + 0.5 is representable.

• OpExtInst trunc:

• trunc( -1 < x < 0 ) returns -0.

#### 8.7.2. Changes to ISO/IEC 9899: TC2 Behavior

OpExtInst modf behaves as though implemented by:

gentype modf( gentype value, gentype *iptr )
{
*iptr = trunc( value );
return copysign( isinf( value ) ? 0.0 : value - *iptr, value );
}

OpExtInst rint always rounds according to round to nearest even rounding mode even if the caller is in some other rounding mode.

#### 8.7.3. Edge Case Behavior in Flush To Zero Mode

If denormals are flushed to zero, then a function may return one of four results:

1. Any conforming result for non-flush-to-zero mode.

2. If the result given by 1 is a sub-normal before rounding, it may be flushed to zero.

3. Any non-flushed conforming result for the function if one or more of its sub-normal operands are flushed to zero.

4. If the result of 3 is a sub-normal before rounding, the result may be flushed to zero.

In each of the above cases, if an operand or result is flushed to zero, the sign of the zero is undefined.

If subnormals are flushed to zero, a device may choose to conform to the following edge cases for OpExtInst nextafter instead of those listed in Additional Requirements Beyond ISO/IEC 9899:TC2 section:

• nextafter ( +smallest normal, y < +smallest normal ) = +0.

• nextafter ( -smallest normal, y > -smallest normal ) = -0.

• nextafter ( -0, y > 0 ) returns smallest positive normal value.

• nextafter ( +0, y < 0 ) returns smallest negative normal value.

For clarity, subnormals or denormals are defined to be the set of representable numbers in the range 0 < x < TYPE_MIN and -TYPE_MIN < x < -0. They do not include ±0. A non-zero number is said to be sub-normal before rounding if, after normalization, its radix-2 exponent is less than (TYPE_MIN_EXP - 1). [1]

## 9. Image Addressing and Filtering

This section describes how image operations behave in an OpenCL environment.

### 9.1. Image Coordinates

Let wt, ht and dt be the width, height (or image array size for a 1D image array) and depth (or image array size for a 2D image array) of the image in pixels. Let coord.xy (also referred to as (s,t)) or coord.xyz (also referred to as (s,t,r)) be the coordinates specified to an image read instruction (such as OpImageRead) or an image write instruction (such as OpImageWrite).

If image coordinates specified to an image read instruction are normalized (as specified in the sampler), the s, t, and r coordinate values are multiplied by wt, ht and dt respectively to generate the unnormalized coordinate values. For image arrays, the image array coordinate (i.e. t if it is a 1D image array or r if it is a 2D image array) specified to the image read instruction must always be the unnormalized image coordinate value.

Image coordinates specified to an image write instruction are always unnormalized image coordinate values.

Let (u,v,w) represent the unnormalized image coordinate values.

If values in (s,t,r) or (u,v,w) are INF or NaN, the behavior of the image read instruction or image write instruction is undefined.

### 9.2. Addressing and Filter Modes

After generating the image coordinate (u,v,w) we apply the appropriate addressing and filter mode to generate the appropriate sample locations to read from the image.

#### 9.2.1. Clamp and None Addressing Modes

We first describe how the addressing and filter modes are applied to generate the appropriate sample locations to read from the image if the addressing mode is CL_ADDRESS_CLAMP, CL_ADDRESS_CLAMP_TO_EDGE, or CL_ADDRESS_NONE.

##### Nearest Filtering

When the filter mode is CL_FILTER_NEAREST, the result of the image read instruction is the image element that is nearest (in Manhattan distance) to the image element location (i,j,k). The image element location (i,j,k) is computed as:

\begin{aligned} i & = address\_mode((int)floor(u))\\ j & = address\_mode((int)floor(v))\\ k & = address\_mode((int)floor(w)) \end{aligned}

For a 3D image, the image element at location (i,j,k) becomes the color value. For a 2D image, the image element at location (i,j) becomes the color value.

The below table describes the address_mode function.

Table 8. Addressing Modes to Generate Texel Location

CL_ADDRESS_CLAMP

clamp (coord, -1, size)

CL_ADDRESS_CLAMP_TO_EDGE

clamp (coord, 0, size - 1)

CL_ADDRESS_NONE

coord

The size term in the table above is wt for u, ht for v and dt for w.

The clamp function used in the table above is defined as:

\begin{aligned} clamp(a, b, c) & = return (a < b) ? b : ((a > c) ? c : a) \end{aligned}

If the addressing mode is CL_ADDRESS_CLAMP or CL_ADDRESS_CLAMP_TO_EDGE, and the selected texel location (i,j,k) refers to a location outside the image, the border color is used as the color value for the texel.

Otherwise, if the addressing mode is CL_ADDRESS_NONE and the selected texel location (i,j,k) refers to a location outside the image, the color value for the texel is undefined.

##### Linear Filtering

When the filter mode is CL_FILTER_LINEAR, a 2 x 2 square of image elements (for a 2D image) or a 2 x 2 x 2 cube of image elements (for a 3D image is selected). This 2 x 2 square or 2 x 2 x 2 cube is obtained as follows.

Let:

\begin{aligned} i0 & = address\_mode((int)floor(u - 0.5))\\ j0 & = address\_mode((int)floor(v - 0.5))\\ k0 & = address\_mode((int)floor(w - 0.5))\\ i1 & = address\_mode((int)floor(u - 0.5) + 1)\\ j1 & = address\_mode((int)floor(v - 0.5) + 1)\\ k1 & = address\_mode((int)floor(w - 0.5) + 1)\\ a & = frac(u - 0.5)\\ b & = frac(v - 0.5)\\ c & = frac(w - 0.5) \end{aligned}

The frac function determines the fractional part of x and is computed as:

\begin{aligned} frac(x) & = x - floor(x) \end{aligned}

For a 3D image, the color value is computed as:

$\begin{array}{rcl} T &=& (1 - a) \times (1 - b) \times (1 - c) \times T_{i0j0k0}\\ & & {} + a \times (1 - b) \times (1 - c) \times T_{i1j0k0}\\ & & {} + (1 - a) \times b \times (1 - c) \times T_{i0j1k0}\\ & & {} + a \times b \times (1 - c) \times T_{i1j1k0}\\ & & {} + (1 - a) \times (1 - b) \times c \times T_{i0j0k1}\\ & & {} + a \times (1 - b) \times c \times T_{i1j0k1}\\ & & {} + (1 - a) \times b \times c \times T_{i0j1k1}\\ & & {} + a \times b \times c \times T_{i1j1k1} \end{array}$

where Tijk is the image element at location (i,j,k) in the 3D image.

For a 2D image, the color value is computed as:

$\begin{array}{rcl} T &=& (1 - a) \times (1 - b) \times T_{i0j0}\\ & & {} + a \times (1 - b) \times T_{i1j0}\\ & & {} + (1 - a) \times b \times T_{i0j1}\\ & & {} + a \times b \times T_{i1j1} \end{array}$

where Tij is the image element at location (i,j) in the 2D image.

If the addressing mode is CL_ADDRESS_CLAMP or CL_ADDRESS_CLAMP_TO_EDGE, and any of the selected Tijk or Tij refers to a location outside the image, the border color is used as the image element.

Otherwise, if the addressing mode is CL_ADDRESS_NONE, and any of the selected Tijk or Tij refers to a location outside the image, the color value is undefined.

If the image channel type is CL_FLOAT or CL_HALF_FLOAT, and any of the image elements Tijk or Tij is INF or NaN, the color value is undefined.

We now discuss how the addressing and filter modes are applied to generate the appropriate sample locations to read from the image if the addressing mode is CL_ADDRESS_REPEAT.

##### Nearest Filtering

When filter mode is CL_FILTER_NEAREST, the result of the image read instruction is the image element that is nearest (in Manhattan distance) to the image element location (i,j,k). The image element location (i,j,k) is computed as:

$\begin{array}{l} u = (s - floor(s)) \times w_t\\ i = (int)floor(u)\\ if\ (i > w_t - 1)\\ \qquad i = i - w_t\\ v = (t - floor(t)) \times h_t\\ j = (int)floor(v)\\ if\ (j > h_t - 1)\\ \qquad j = j - h_t\\ w = (r - floor(r)) \times d_t\\ k = (int)floor(w)\\ if\ (k > d_t - 1)\\ \qquad k = k - d_t \end{array}$

For a 3D image, the image element at location (i, j, k) becomes the color value. For a 2D image, the image element at location (i, j) becomes the color value.

##### Linear Filtering

When filter mode is CL_FILTER_LINEAR, a 2 x 2 square of image elements for a 2D image or a 2 x 2 x 2 cube of image elements for a 3D image is selected. This 2 x 2 square or 2 x 2 x 2 cube is obtained as follows.

Let

$\begin{array}{l} u = (s - floor(s)) \times w_t\\ i0 = (int)floor(u - 0.5)\\ i1 = i0 + 1\\ if (i0 < 0)\\ i0 = w_t + i0\\ if\ (i1 > w_t - 1)\\ \qquad i1 = i1 - w_t\\ v = (t - floor(t)) \times h_t\\ j0 = (int)floor(v - 0.5)\\ j1 = j0 + 1\\ if (j0 < 0)\\ j0 = h_t + j0\\ if\ (j1 > h_t - 1)\\ \qquad j1 = j1 - h_t\\ w = (r - floor(r)) \times d_t\\ k0 = (int)floor(w - 0.5)\\ k1 = k0 + 1\\ if (k0 < 0)\\ \qquad k0 = d_t + k0\\ if\ (k1 > d_t - 1)\\ \qquad k1 = k1 - d_t\\ a = frac(u - 0.5)\\ b = frac(v - 0.5)\\ c = frac(w - 0.5) \end{array}$

For a 3D image, the color value is computed as:

$\begin{array}{rcl} T &=& (1 - a) \times (1 - b) \times (1 - c) \times T_{i0j0k0}\\ & & {} + a \times (1 - b) \times (1 - c) \times T_{i1j0k0}\\ & & {} + (1 - a) \times b \times (1 - c) \times T_{i0j1k0}\\ & & {} + a \times b \times (1 - c) \times T_{i1j1k0}\\ & & {} + (1 - a) \times (1 - b) \times c \times T_{i0j0k1}\\ & & {} + a \times (1 - b) \times c \times T_{i1j0k1}\\ & & {} + (1 - a) \times b \times c \times T_{i0j1k1}\\ & & {} + a \times b \times c \times T_{i1j1k1} \end{array}$

where Tijk is the image element at location (i,j,k) in the 3D image.

For a 2D image, the color value is computed as:

$\begin{array}{rcl} T &=&(1 - a) \times (1 - b) \times T_{i0j0}\\ & & {} + a \times (1 - b) \times T_{i1j0}\\ & & {} + (1 - a) \times b \times T_{i0j1}\\ & & {} + a \times b \times T_{i1j1} \end{array}$

where Tij is the image element at location (i,j) in the 2D image.

If the image channel type is CL_FLOAT or CL_HALF_FLOAT, and any of the image elements Tijk or Tij is INF or NaN, the color value is undefined.

#### 9.2.3. Mirrored Repeat Addressing Mode

We now discuss how the addressing and filter modes are applied to generate the appropriate sample locations to read from the image if the addressing mode is CL_ADDRESS_MIRRORED_REPEAT. The CL_ADDRESS_MIRRORED_REPEAT addressing mode causes the image to be read as if it is tiled at every integer seam, with the interpretation of the image data flipped at each integer crossing.

##### Nearest Filtering

When filter mode is CL_FILTER_NEAREST, the result of the image read instruction is the image element that is nearest (in Manhattan distance) to the image element location (i,j,k). The image element location (i,j,k) is computed as:

$\begin{array}{rcl} s' &=& 2.0f \times rint(0.5f \times s)\\ s &=& fabs(s - s)\\ u &=& s' \times w_t\\ i &=& (int)floor(u)\\ i &=& min(i, w_t - 1)\\ t' &=& 2.0f \times rint(0.5f \times t)\\ t &=& fabs(t - t)\\ v &=& t' \times h_t\\ j &=& (int)floor(v)\\ j &=& min(j, h_t - 1)\\ r' &=& 2.0f \times rint(0.5f \times r)\\ r &=& fabs(r - r)\\ w &=& r' \times d_t\\ k &=& (int)floor(w)\\ k &=& min(k, d_t - 1) \end{array}$

For a 3D image, the image element at location (i, j, k) becomes the color value. For a 2D image, the image element at location (i, j) becomes the color value.

##### Linear Filtering

When filter mode is CL_FILTER_LINEAR, a 2 x 2 square of image elements for a 2D image or a 2 x 2 x 2 cube of image elements for a 3D image is selected. This 2 x 2 square or 2 x 2 x 2 cube is obtained as follows.

Let

$\begin{array}{rcl} s' &=& 2.0f \times rint(0.5f \times s)\\ s &=& fabs(s - s)\\ u &=& s' \times w_t\\ i0 &=& (int)floor(u - 0.5f)\\ i1 &=& i0 + 1\\ i0 &=& max(i0, 0)\\ i1 &=& min(i1, w_t - 1)\\ t' &=& 2.0f \times rint(0.5f \times t)\\ t &=& fabs(t - t)\\ v &=& t' \times h_t\\ j0 &=& (int)floor(v - 0.5f)\\ j1 &=& j0 + 1\\ j0 &=& max(j0, 0)\\ j1 &=& min(j1, h_t - 1)\\ r' &=& 2.0f \times rint(0.5f \times r)\\ r &=& fabs(r - r)\\ w &=& r' \times d_t\\ k0 &=& (int)floor(w - 0.5f)\\ k1 &=& k0 + 1\\ k0 &=& max(k0, 0)\\ k1 &=& min(k1, d_t - 1)\\ a &=& frac(u - 0.5)\\ b &=& frac(v - 0.5)\\ c &=& frac(w - 0.5) \end{array}$

For a 3D image, the color value is computed as:

$\begin{array}{rcl} T &=& (1 - a) \times (1 - b) \times (1 - c) \times T_{i0j0k0}\\ & & {} + a \times (1 - b) \times (1 - c) \times T_{i1j0k0}\\ & & {} + (1 - a) \times b \times (1 - c) \times T_{i0j1k0}\\ & & {} + a \times b \times (1 - c) \times T_{i1j1k0}\\ & & {} + (1 - a) \times (1 - b) \times c \times T_{i0j0k1}\\ & & {} + a \times (1 - b) \times c \times T_{i1j0k1}\\ & & {} + (1 - a) \times b \times c \times T_{i0j1k1}\\ & & {} + a \times b \times c \times T_{i1j1k1} \end{array}$

where Tijk is the image element at location (i,j,k) in the 3D image.

For a 2D image, the color value is computed as:

$\begin{array}{rcl} T &=& (1 - a) \times (1 - b) \times T_{i0j0}\\ & & {} + a \times (1 - b) \times T_{i1j0}\\ & & {} + (1 - a) \times b \times T_{i0j1}\\ & & {} + a \times b \times T_{i1j1} \end{array}$

where Tij is the image element at location (i,j) in the 2D image.

For a 1D image, the color value is computed as:

$\begin{array}{rcl} T &=& (1 - a) \times T_i0 + a \times T_i1 \end{array}$

where Ti is the image element at location (i) in the 1D image.

If the image channel type is CL_FLOAT or CL_HALF_FLOAT and any of the image elements Tijk or Tij is INF or NaN, the color value is undefined.

### 9.3. Precision of Addressing and Filter Modes

If the sampler is specified as using unnormalized coordinates (floating-point or integer coordinates), filter mode set to CL_FILTER_NEAREST and addressing mode set to one of the following modes - CL_ADDRESS_CLAMP, CL_ADDRESS_CLAMP_TO_EDGE or CL_ADDRESS_NONE - the location of the image element in the image given by (i,j,k) will be computed without any loss of precision.

For all other sampler combinations of normalized or unnormalized coordinates, filter modes, and addressing modes, the relative error or precision of the addressing mode calculations and the image filter operation are not defined. To ensure precision of image addressing and filter calculations across any OpenCL device for these sampler combinations, developers may unnormalize the image coordinate in the kernel, and then implement the linear filter in the kernel with appropriate read image instructions with a sampler that uses unnormalized coordinates, filter mode set to CL_FILTER_NEAREST, addressing mode set to CL_ADDRESS_CLAMP, CL_ADDRESS_CLAMP_TO_EDGE or CL_ADDRESS_NONE, and finally performing the interpolation of color values read from the image to generate the filtered color value.

### 9.4. Conversion Rules

In this section we discuss conversion rules that are applied when reading and writing images in a kernel.

#### 9.4.1. Conversion Rules for Normalized Integer Channel Data Types

In this section we discuss converting normalized integer channel data types to half-precision and single-precision floating-point values and vice-versa.

##### Converting Normalized Integer Channel Data Types to Half Precision Floating-point Values

For images created with image channel data type of CL_UNORM_INT8 and CL_UNORM_INT16, image read instructions will convert the channel values from an 8-bit or 16-bit unsigned integer to normalized half precision floating-point values in the range [0.0h …​ 1.0h].

For images created with image channel data type of CL_SNORM_INT8 and CL_SNORM_INT16, image read instructions will convert the channel values from an 8-bit or 16-bit signed integer to normalized half precision floating-point values in the range [-1.0h …​ 1.0h].

These conversions are performed as follows:

• CL_UNORM_INT8 (8-bit unsigned integer) → half

$normalized\_half\_value(x)=round\_to\_half(\frac{x}{255})$
• CL_UNORM_INT_101010 (10-bit unsigned integer) → half

$normalized\_half\_value(x)=round\_to\_half(\frac{x}{1023})$
• CL_UNORM_INT16 (16-bit unsigned integer) → half

$normalized\_half\_value(x)=round\_to\_half(\frac{x}{65535})$
• CL_SNORM_INT8 (8-bit signed integer) → half

$normalized\_half\_value(x)=max(-1.0h, round\_to\_half(\frac{x}{127}))$
• CL_SNORM_INT16 (16-bit signed integer) → half

$normalized\_half\_value(x)=max(-1.0h, round\_to\_half(\frac{x}{32767}))$

The precision of the above conversions is <= 1.5 ulp except for the following cases:

For CL_UNORM_INT8:

• 0 must convert to 0.0h, and

• 255 must convert to 1.0h

For CL_UNORM_INT_101010:

• 0 must convert to 0.0h, and

• 1023 must convert to 1.0h

For CL_UNORM_INT16:

• 0 must convert to 0.0h, and

• 65535 must convert to 1.0h

For CL_SNORM_INT8:

• -128 and -127 must convert to -1.0h,

• 0 must convert to 0.0h, and

• 127 must convert to 1.0h

For CL_SNORM_INT16:

• -32768 and -32767 must convert to -1.0h,

• 0 must convert to 0.0h, and

• 32767 must convert to 1.0h

##### Converting Half Precision Floating-point Values to Normalized Integer Channel Data Types

For images created with image channel data type of CL_UNORM_INT8 and CL_UNORM_INT16, image write instructions will convert the half precision floating-point color value to an 8-bit or 16-bit unsigned integer.

For images created with image channel data type of CL_SNORM_INT8 and CL_SNORM_INT16, image write instructions will convert the half precision floating-point color value to an 8-bit or 16-bit signed integer.

OpenCL implementations may choose to approximate the rounding mode used in the conversions described below. When approximate rounding is used instead of the preferred rounding, the result of the conversion must satisfy the bound given below.

The conversions from half precision floating-point values to normalized integer values are performed is as follows:

• halfCL_UNORM_INT8 (8-bit unsigned integer)

\begin{aligned} & f(x)=max(0,min(255,255 \times x))\\ \\ & f_{preferred}(x) = \begin{cases} round\_to\_nearest\_even\_uint8(f(x)) & x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & x = \infty \text{ or } x = NaN \end{cases}\\ & f_{approx}(x) = \begin{cases} round\_to\_impl\_uint8(f(x)) & x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & x = \infty \text{ or } x = NaN \end{cases}\\ \\ & |f(x) - f_{approx}(x)|\leq 0.6, x \neq \infty \text{ and } x \neq NaN \end{aligned}
• halfCL_UNORM_INT16 (16-bit unsigned integer)

\begin{aligned} & f(x)=max(0,min(65535,65535 \times x))\\ \\ & f_{preferred}(x) = \begin{cases} round\_to\_nearest\_even\_uint16(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ & f_{approx}(x) = \begin{cases} round\_to\_impl\_uint16(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ \\ & |f(x) - f_{approx}(x)|\leq 0.6, x \neq \infty \text{ and } x \neq NaN \end{aligned}
• halfCL_SNORM_INT8 (8-bit signed integer)

\begin{aligned} & f(x)=max(-128,min(127,127 \times x))\\ \\ & f_{preferred}(x) = \begin{cases} round\_to\_nearest\_even\_int8(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ & f_{approx}(x) = \begin{cases} round\_to\_impl\_int8(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ \\ & |f(x) - f_{approx}(x)|\leq 0.6, x \neq \infty \text{ and } x \neq NaN \end{aligned}
• halfCL_SNORM_INT16 (16-bit signed integer)

\begin{aligned} & f(x)=max(-32768,min(32767,32767 \times x))\\ \\ & f_{preferred}(x) = \begin{cases} round\_to\_nearest\_even\_int16(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ & f_{approx}(x) = \begin{cases} round\_to\_impl\_int16(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ \\ & |f(x) - f_{approx}(x)|\leq 0.6, x \neq \infty \text{ and } x \neq NaN \end{aligned}
##### Converting Normalized Integer Channel Data Types to Floating-point Values

For images created with image channel data type of CL_UNORM_INT8 and CL_UNORM_INT16, image read instructions will convert the channel values from an 8-bit or 16-bit unsigned integer to normalized floating-point values in the range [0.0f …​ 1.0f].

For images created with image channel data type of CL_SNORM_INT8 and CL_SNORM_INT16, image read instructions will convert the channel values from an 8-bit or 16-bit signed integer to normalized floating-point values in the range [-1.0f …​ 1.0f].

These conversions are performed as follows:

• CL_UNORM_INT8 (8-bit unsigned integer) → float

$normalized\_float\_value(x)=round\_to\_float(\frac{x}{255})$
• CL_UNORM_INT_101010 (10-bit unsigned integer) → float

$normalized\_float\_value(x)=round\_to\_float(\frac{x}{1023})$
• CL_UNORM_INT16 (16-bit unsigned integer) → float

$normalized\_float\_value(x)=round\_to\_float(\frac{x}{65535})$
• CL_SNORM_INT8 (8-bit signed integer) → float

$normalized\_float\_value(x)=max(-1.0f, round\_to\_float(\frac{x}{127}))$
• CL_SNORM_INT16 (16-bit signed integer) → float

$normalized\_float\_value(x)=max(-1.0f, round\_to\_float(\frac{x}{32767}))$

The precision of the above conversions is <= 1.5 ulp except for the following cases.

For CL_UNORM_INT8:

• 0 must convert to 0.0f, and

• 255 must convert to 1.0f

For CL_UNORM_INT_101010:

• 0 must convert to 0.0f, and

• 1023 must convert to 1.0f

For CL_UNORM_INT16:

• 0 must convert to 0.0f, and

• 65535 must convert to 1.0f

For CL_SNORM_INT8:

• -128 and -127 must convert to -1.0f,

• 0 must convert to 0.0f, and

• 127 must convert to 1.0f

For CL_SNORM_INT16:

• -32768 and -32767 must convert to -1.0f,

• 0 must convert to 0.0f, and

• 32767 must convert to 1.0f

##### Converting Floating-point Values to Normalized Integer Channel Data Types

For images created with image channel data type of CL_UNORM_INT8 and CL_UNORM_INT16, image write instructions will convert the floating-point color value to an 8-bit or 16-bit unsigned integer.

For images created with image channel data type of CL_SNORM_INT8 and CL_SNORM_INT16, image write instructions will convert the floating-point color value to an 8-bit or 16-bit signed integer.

OpenCL implementations may choose to approximate the rounding mode used in the conversions described below. When approximate rounding is used instead of the preferred rounding, the result of the conversion must satisfy the bound given below.

The conversions from half precision floating-point values to normalized integer values are performed is as follows:

• floatCL_UNORM_INT8 (8-bit unsigned integer)

\begin{aligned} & f(x)=max(0,min(255,255 \times x))\\ \\ & f_{preferred}(x) = \begin{cases} round\_to\_nearest\_even\_uint8(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ & f_{approx}(x) = \begin{cases} round\_to\_impl\_uint8(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ \\ & |f(x) - f_{approx}(x)|\leq 0.6, x \neq \infty \text{ and } x \neq NaN \end{aligned}
• floatCL_UNORM_INT_101010 (10-bit unsigned integer)

\begin{aligned} & f(x)=max(0,min(1023,1023 \times x))\\ \\ & f_{preferred}(x) = \begin{cases} round\_to\_nearest\_even\_uint10(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ & f_{approx}(x) = \begin{cases} round\_to\_impl\_uint10(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ \\ & |f(x) - f_{approx}(x)|\leq 0.6, x \neq \infty \text{ and } x \neq NaN \end{aligned}
• floatCL_UNORM_INT16 (16-bit unsigned integer)

\begin{aligned} & f(x)=max(0,min(65535,65535 \times x))\\ \\ & f_{preferred}(x) = \begin{cases} round\_to\_nearest\_even\_uint16(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ & f_{approx}(x) = \begin{cases} round\_to\_impl\_uint16(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ \\ & |f(x) - f_{approx}(x)|\leq 0.6, x \neq \infty \text{ and } x \neq NaN \end{aligned}
• floatCL_SNORM_INT8 (8-bit signed integer)

\begin{aligned} & f(x)=max(-128,min(127,127 \times x))\\ \\ & f_{preferred}(x) = \begin{cases} round\_to\_nearest\_even\_uint8(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ & f_{approx}(x) = \begin{cases} round\_to\_impl\_uint8(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ \\ & |f(x) - f_{approx}(x)|\leq 0.6, x \neq \infty \text{ and } x \neq NaN \end{aligned}
• floatCL_SNORM_INT16 (16-bit signed integer)

\begin{aligned} & f(x)=max(-32768,min(32767,32767 \times x))\\ \\ & f_{preferred}(x) = \begin{cases} round\_to\_nearest\_even\_uint16(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ & f_{approx}(x) = \begin{cases} round\_to\_impl\_uint16(f(x)) & \quad x \neq \infty \text{ and } x \neq NaN\\ \text{implementation-defined} & \quad x = \infty \text{ or } x = NaN \end{cases}\\ \\ & |f(x) - f_{approx}(x)|\leq 0.6, x \neq \infty \text{ and } x \neq NaN \end{aligned}

#### 9.4.2. Conversion Rules for Half Precision Floating-point Channel Data Type

For images created with a channel data type of CL_HALF_FLOAT, the conversions of half to float and half to half are lossless. Conversions from float to half round the mantissa using the round to nearest even or round to zero rounding mode. Denormalized numbers for the half data type which may be generated when converting a float to a half may be flushed to zero. A float NaN must be converted to an appropriate NaN in the half type. A float INF must be converted to an appropriate INF in the half type.

#### 9.4.3. Conversion Rules for Floating-point Channel Data Type

The following rules apply for reading and writing images created with channel data type of CL_FLOAT.

• NaNs may be converted to a NaN value(s) supported by the device.

• Denorms can be flushed to zero.

• All other values must be preserved.

#### 9.4.4. Conversion Rules for Signed and Unsigned 8-bit, 16-bit and 32-bit Integer Channel Data Types

For images created with image channel data type of CL_SIGNED_INT8, CL_SIGNED_INT16 and CL_SIGNED_INT32, image read instructions will return the unmodified integer values stored in the image at specified location.

Likewise, for images created with image channel data type of CL_UNSIGNED_INT8, CL_UNSIGNED_INT16 and CL_UNSIGNED_INT32, image read instructions will return the unmodified unsigned integer values stored in the image at specified location.

Image write instructions will perform one of the following conversions:

• 32 bit signed integer → CL_SIGNED_INT8 (8-bit signed integer):

$int8\_value(x) = clamp(x, -128, 127)$
• 32 bit signed integer → CL_SIGNED_INT16 (16-bit signed integer):

$int16\_value(x) = clamp(x, -32768, 32767)$
• 32 bit signed integer → CL_SIGNED_INT32 (32-bit signed integer):

$int32\_value(x) = x \quad \text{(no conversion)}$
• 32 bit unsigned integer → CL_UNSIGNED_INT8 (8-bit unsigned integer):

$uint8\_value(x) = clamp(x, 0, 255)$
• 32 bit unsigned integer → CL_UNSIGNED_INT16 (16-bit unsigned integer):

$uint16\_value(x) = clamp(x, 0, 65535)$
• 32 bit unsigned integer → CL_UNSIGNED_INT32 (32-bit unsigned integer):

$uint32\_value(x) = x \quad \text{(no conversion)}$

The conversions described in this section must be correctly saturated.

#### 9.4.5. Conversion Rules for sRGBA and sBGRA Images

Standard RGB data, which roughly displays colors in a linear ramp of luminosity levels such that an average observer, under average viewing conditions, can view them as perceptually equal steps on an average display. All 0s maps to 0.0f, and all 1s maps to 1.0f. The sequence of unsigned integer encodings between all 0s and all 1s represent a nonlinear progression in the floating-point interpretation of the numbers between 0.0f to 1.0f. For more detail, see the SRGB color standard.

Conversion from sRGB space is automatically done the image read instruction if the image channel order is one of the sRGB values described above. When reading from an sRGB image, the conversion from sRGB to linear RGB is performed before filtering is applied. If the format has an alpha channel, the alpha data is stored in linear color space. Conversion to sRGB space is automatically done by the image write instruction if the image channel order is one of the sRGB values described above and the device supports writing to sRGB images.

If the format has an alpha channel, the alpha data is stored in linear color space.

1. The following process is used by image read instructions to convert a normalized 8-bit unsigned integer sRGB color value x to a floating-point linear RGB color value y:

1. Convert a normalized 8-bit unsigned integer sRGB value x to a floating-point sRGB value r as per rules described in Converting Normalized Integer Channel Data Types to Floating-point Values section.

$r=normalized\_float\_value(x)$
2. Convert a floating-point sRGB value r to a floating-point linear RGB color value y:

\begin{aligned} & c_{linear}(x) = \begin{cases} \frac{r}{12.92} & \quad r \geq 0 \text{ and } r \leq 0.04045\\ (\frac{r + 0.055}{1.055})^{2.4} & \quad r > 0.04045 \text{ and } \leq 1 \end{cases}\\ \\ & y = c_{linear}(r) \end{aligned}
2. The following process is used by image write instructions to convert a linear RGB floating-point color value y to a normalized 8-bit unsigned integer sRGB value x:

1. Convert a floating-point linear RGB value y to a normalized floating point sRGB value r:

\begin{aligned} & c_{linear}(x) = \begin{cases} 0 & \quad y \geq NaN \text{ or } y < 0\\ 12.92 \times y & \quad y \geq 0 \text{ and } y < 0.0031308\\ 1.055 \times y^{(\frac{1}{2.4})} & \quad y \geq 0.0031308 \text{ and } y \leq 1\\ 1 & \quad y > 1 \end{cases}\\ \\ & r = c_{sRGB}(y) \end{aligned}
2. Convert a normalized floating-point sRGB value r to a normalized 8-bit unsigned integer sRGB value x as per rules described in Converting Floating-point Values to Normalized Integer Channel Data Types section.

\begin{aligned} & g(r) = \begin{cases} f_{preferred}(r) & \quad \text{if rounding mode is round to even}\\ f_{approx}(r) & \quad \text{if implementation-defined rounding mode} \end{cases}\\ \\ & x = g(r) \end{aligned}

The accuracy required when converting a normalized 8-bit unsigned integer sRGB color value x to a floating-point linear RGB color value y is given by:

$|x-255 \times c_{sRGB}(y)|\leq 0.5$

The accuracy required when converting a linear RGB floating-point color value y to a normalized 8-bit unsigned integer sRGB value x is given by:

$|x-255 \times c_{sRGB}(y)|\leq 0.6$

### 9.5. Selecting an Image from an Image Array

Let (u,v,w) represent the unnormalized image coordinate values for reading from and/or writing to a 2D image in a 2D image array.

When read using a sampler, the 2D image layer selected is computed as:

$layer = clamp(rint(w), 0, d_t - 1)$

otherwise the layer selected is computed as:

$layer = w$

(since w is already an integer) and the result is undefined if w is not one of the integers 0, 1, …​ dt - 1.

Let (u,v) represent the unnormalized image coordinate values for reading from and/or writing to a 1D image in a 1D image array.

When read using a sampler, the 1D image layer selected is computed as:

$layer = clamp(rint(v), 0, h_t - 1)$

otherwise the layer selected is computed as:

$layer = v$

(since v is already an integer) and the result is undefined if v is not one of the integers 0, 1, …​ ht - 1.

### 9.6. Data Format for Reading and Writing Images

This section describes how image element data is returned by an image read instruction or passed as the Texel data that is written by an image write instruction:

For the following image channel orders, the data is a four component vector type:

Table 9. Mapping Image Data to Vector Components
Image Channel Order Components

R, Rx

(R, 0, 0, 1)

A

(0, 0, 0, A)

RG, RGx

(R, G, 0, 1)

RGB, RGBx, sRGB, sRGBx

(R, G, B, 1)

RGBA, BGRA, ARGB, ABGR, sRGBA, sBGRA

(R, G, B, A)

Intensity

(I, I, I, I)

Luminance

(L, L, L, 1)

For the following image channel orders, the data is a scalar type:

Table 10. Scalar Image Data
Image Channel Order Scalar Value

Depth

D

DepthStencil

D

The following table describes the mapping from image channel data type to the data vector component type or scalar type:

Table 11. Image Data Types
Image Channel Order Data Type

SnormInt8, SnormInt16,
UnormInt8, UnormInt16,
UnormShort565, UnormShort555,
UnormInt101010, UnormInt101010_2,
UnormInt24,
HalfFloat,
Float

OpTypeFloat, with Width equal to 16 or 32.

SignedInt8, SignedInt16, SignedInt32,
UnsignedInt8, UnsignedInt16, UnsignedInt32

OpTypeInt, with Width equal to 32.

### 9.7. Sampled and Sampler-less Reads

SPIR-V instructions that read from an image without a sampler (such as OpImageRead) behave exactly the same as the corresponding image read instruction with a sampler that has Sampler Filter Mode set to Nearest, Non-Normalized coordinates, and Sampler Addressing Mode set to None.

There is one exception for cases where the image being read has Image Format equal to a floating-point type (such as R32f). In this exceptional case, when channel data values are denormalized, the non-sampler image read instruction may return the denormalized data, while the sampler image read instruction may flush denormalized channel data values to zero. The coordinates must be between 0 and image size in that dimension, non inclusive.

## 10. Normative References

1. IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2008, http://dx.doi.org/10.1109/IEEESTD.2008.4610935 , August, 2008.

2. “ISO/IEC 9899:1999 - Programming Languages - C”, with technical corrigenda TC1 and TC2, https://www.iso.org/standard/29237.html .

3. “ISO/IEC 14882:2014 - Information technology - Programming languages - C++”, https://www.iso.org/standard/64029.html .

4. “The OpenCL Specification, Version 2.2”, https://www.khronos.org/registry/OpenCL/ .

5. “The OpenCL C Specification, Version 2.0”, https://www.khronos.org/registry/OpenCL/ .

6. “The OpenCL C++ 1.0 Specification”, https://www.khronos.org/registry/OpenCL/ .

7. “The OpenCL Extension Specification, Version 2.2”, https://www.khronos.org/registry/OpenCL/ .

8. “SPIR-V Specification, Version 1.2, Unified”, https://www.khronos.org/registry/spir-v/ .

9. Jean-Michel Muller. On the definition of ulp(x). RR-5504, INRIA. 2005, pp.16. <inria-00070503>

10. “IEC 61966-2-1:1999 Multimedia systems and equipment - Colour measurement and management - Part 2-1: Colour management - Default RGB colour space - sRGB”, https://webstore.iec.ch/publication/6169 .

1. Here TYPE_MIN and TYPE_MIN_EXP should be substituted by constants appropriate to the floating-point type under consideration, such as FLT_MIN and FLT_MIN_EXP for float.