Slang Standard Library Reference
- Interfaces
  - IArithmetic
    - add
    - div
    - init
    - mod
    - mul
    - neg
    - sub
  - IArithmeticAtomicable
  - IArray
    - getCount
    - subscript
  - IAtomicable
  - IBitAtomicable
  - IBufferDataLayout
  - IComparable
    - equals
    - lessThan
    - lessThanOrEquals
  - IDefaultInitializable
    - init
  - IDiffTensorWrapper
    - loadOnce_backward
    - loadOnce_forward
    - load_backward
    - load_forward
    - storeOnce_backward
    - storeOnce_forward
    - store_backward
    - store_forward
  - IDifferentiable
    - dadd
    - dmul
    - dzero
  - IDifferentiableFunc
    - operator()
  - IDifferentiableMutatingFunc
    - operator()
  - IDifferentiablePtrType
  - IFloat
    - add
    - div
    - init
    - mod
    - mul
    - neg
    - scale
    - sub
    - toFloat
  - IFunc
    - operator()
  - IInteger
    - init
    - toInt
    - toInt64
    - toUInt
    - toUInt64
  - ILogical
    - and
    - bitAnd
    - bitNot
    - bitOr
    - bitXor
    - init
    - not
    - or
    - shl
    - shr
  - IMutatingFunc
    - operator()
  - IRWArray
    - subscript
  - IRangedValue
    - maxValue
    - minValue
  - __BuiltinArithmeticType
  - __BuiltinFloatingPointType
    - getPi
  - __BuiltinIntegerType
  - __BuiltinLogicalType
  - __ITextureShape
    - dimensions
    - flavor
    - planeDimensions
  - __ITextureShape1D2D3D
- Types
  - Buffer types
    - AppendStructuredBuffer
      - Append
      - GetDimensions
    - ByteAddressBuffer
      - GetDimensions
      - Load
      - Load2
      - Load2Aligned
      - Load3
      - Load3Aligned
      - Load4
      - Load4Aligned
      - LoadAligned
    - ConsumeStructuredBuffer
      - Consume
      - GetDimensions
    - RWByteAddressBuffer
      - GetDimensions
      - InterlockedAdd
      - InterlockedAdd64
      - InterlockedAddF16
      - InterlockedAddF16Emulated
      - InterlockedAddF32
      - InterlockedAddF64
      - InterlockedAddI64
      - InterlockedAddU64
      - InterlockedAnd
      - InterlockedAnd64
      - InterlockedAndU64
      - InterlockedCompareExchange
      - InterlockedCompareExchange64
      - InterlockedCompareExchangeFloatBitwise
      - InterlockedCompareExchangeU64
      - InterlockedCompareStore
      - InterlockedCompareStore64
      - InterlockedCompareStoreFloatBitwise
      - InterlockedExchange
      - InterlockedExchange64
      - InterlockedExchangeFloat
      - InterlockedExchangeU64
      - InterlockedMax
      - InterlockedMax64
      - InterlockedMaxU64
      - InterlockedMin
      - InterlockedMin64
      - InterlockedMinU64
      - InterlockedOr
      - InterlockedOr64
      - InterlockedOrU64
      - InterlockedXor
      - InterlockedXor64
      - InterlockedXorU64
      - Load
      - Load2
      - Load2Aligned
      - Load3
      - Load3Aligned
      - Load4
      - Load4Aligned
      - LoadAligned
      - Store
      - Store2
      - Store2Aligned
      - Store3
      - Store3Aligned
      - Store4
      - Store4Aligned
      - StoreAligned
      - _NvInterlockedAddFp16x2
    - RWStructuredBuffer
      - DecrementCounter
      - GetDimensions
      - IncrementCounter
      - Load
      - subscript
    - RasterizerOrderedByteAddressBuffer
      - GetDimensions
      - InterlockedAdd
      - InterlockedAnd
      - InterlockedCompareExchange
      - InterlockedCompareStore
      - InterlockedExchange
      - InterlockedMax
      - InterlockedMin
      - InterlockedOr
      - InterlockedXor
      - Load
      - Load2
      - Load2Aligned
      - Load3
      - Load3Aligned
      - Load4
      - Load4Aligned
      - LoadAligned
      - Store
      - Store2
      - Store2Aligned
      - Store3
      - Store3Aligned
      - Store4
      - Store4Aligned
      - StoreAligned
    - RasterizerOrderedStructuredBuffer
      - DecrementCounter
      - GetDimensions
      - IncrementCounter
      - Load
      - subscript
    - StructuredBuffer
      - GetDimensions
      - Load
      - subscript
  - Math types
    - matrix
      - Differential
      - T
      - add
      - dadd
      - div
      - dmul
      - dzero
      - equals
      - getCount
      - init
      - lessThan
      - lessThanOrEquals
      - mod
      - mul
      - neg
      - scale
      - sub
      - toFloat
    - vector
      - Differential
      - Element
      - add
      - and
      - bitAnd
      - bitNot
      - bitOr
      - bitXor
      - dadd
      - div
      - dmul
      - dzero
      - equals
      - getCount
      - init
      - lessThan
      - lessThanOrEquals
      - mod
      - mul
      - neg
      - not
      - or
      - scale
      - shl
      - shr
      - sub
      - toFloat
      - toInt
      - toInt64
      - toUInt
      - toUInt64
  - Miscelaneous types
    - DefaultDataLayout
    - MemoryOrder
    - NativeString
      - getBuffer
      - getLength
      - init
      - length
    - ScalarDataLayout
    - SideEffectBehavior
    - Std140DataLayout
    - Std430DataLayout
    - __Shape1D
      - dimensions
      - flavor
      - planeDimensions
    - __Shape2D
      - dimensions
      - flavor
      - planeDimensions
    - __Shape3D
      - dimensions
      - flavor
      - planeDimensions
    - __ShapeBuffer
      - dimensions
      - flavor
      - planeDimensions
    - __ShapeCube
      - dimensions
      - flavor
      - planeDimensions
    - string
  - Ray-tracing
    - BuiltInTriangleIntersectionAttributes
      - barycentrics
    - CANDIDATE_TYPE
    - COMMITTED_STATUS
    - HitObject
      - GetAttributes
      - GetCurrentTime
      - GetGeometryIndex
      - GetHitKind
      - GetInstanceID
      - GetInstanceIndex
      - GetObjectRayDirection
      - GetObjectRayOrigin
      - GetObjectToWorld
      - GetPrimitiveIndex
      - GetRayDesc
      - GetShaderRecordBufferHandle
      - GetShaderTableIndex
      - GetWorldToObject
      - Invoke
      - IsHit
      - IsMiss
      - IsNop
      - LoadLocalRootTableConstant
      - MakeHit
      - MakeMiss
      - MakeMotionHit
      - MakeMotionMiss
      - MakeNop
      - TraceMotionRay
      - TraceRay
      - init
    - RAY_FLAG
    - RayDesc
      - Direction
      - Origin
      - TMax
      - TMin
    - RayQuery
      - Abort
      - CandidateGeometryIndex
      - CandidateGetIntersectionTriangleVertexPositions
      - CandidateInstanceContributionToHitGroupIndex
      - CandidateInstanceID
      - CandidateInstanceIndex
      - CandidateObjectRayDirection
      - CandidateObjectRayOrigin
      - CandidateObjectToWorld3x4
      - CandidateObjectToWorld4x3
      - CandidatePrimitiveIndex
      - CandidateProceduralPrimitiveNonOpaque
      - CandidateRayBarycentrics
      - CandidateRayFrontFace
      - CandidateRayGeometryIndex
      - CandidateRayInstanceCustomIndex
      - CandidateRayInstanceId
      - CandidateRayInstanceShaderBindingTableRecordOffset
      - CandidateRayObjectRayDirection
      - CandidateRayObjectRayOrigin
      - CandidateRayObjectToWorld
      - CandidateRayPrimitiveIndex
      - CandidateRayWorldToObject
      - CandidateTriangleBarycentrics
      - CandidateTriangleFrontFace
      - CandidateTriangleRayT
      - CandidateType
      - CandidateWorldToObject3x4
      - CandidateWorldToObject4x3
      - CommitNonOpaqueTriangleHit
      - CommitProceduralPrimitiveHit
      - CommittedGeometryIndex
      - CommittedGetIntersectionTriangleVertexPositions
      - CommittedInstanceContributionToHitGroupIndex
      - CommittedInstanceID
      - CommittedInstanceIndex
      - CommittedObjectRayDirection
      - CommittedObjectRayOrigin
      - CommittedObjectToWorld3x4
      - CommittedObjectToWorld4x3
      - CommittedPrimitiveIndex
      - CommittedRayBarycentrics
      - CommittedRayFrontFace
      - CommittedRayGeometryIndex
      - CommittedRayInstanceCustomIndex
      - CommittedRayInstanceId
      - CommittedRayInstanceShaderBindingTableRecordOffset
      - CommittedRayObjectRayDirection
      - CommittedRayObjectRayOrigin
      - CommittedRayObjectToWorld
      - CommittedRayPrimitiveIndex
      - CommittedRayT
      - CommittedRayWorldToObject
      - CommittedStatus
      - CommittedTriangleBarycentrics
      - CommittedTriangleFrontFace
      - CommittedWorldToObject3x4
      - CommittedWorldToObject4x3
      - Proceed
      - RayFlags
      - RayTMin
      - TraceRayInline
      - WorldRayDirection
      - WorldRayOrigin
      - init
    - RaytracingAccelerationStructure
  - Sampler types
    - SamplerComparisonState
    - SamplerState
  - Scalar types
    - float16_t
    - float32_t
    - float64_t
    - int32_t
    - size_t
    - ssize_t
    - uint32_t
    - usize_t
  - Stage IO types
    - InputPatch
      - subscript
    - LineStream
      - Append
      - RestartStrip
    - OutputIndices
      - subscript
    - OutputPatch
      - subscript
    - OutputPrimitives
      - subscript
    - OutputVertices
      - _metalSetVertex
      - _setVertex
      - subscript
    - PointStream
      - Append
      - RestartStrip
    - SubpassInput
    - SubpassInputMS
    - TextureFootprint
      - _isSingleLevel
      - isSingleLevel
    - TextureFootprint2D
    - TextureFootprint3D
    - TriangleStream
      - Append
      - RestartStrip
  - Texture types
    - Buffer
    - FeedbackTexture2D
    - FeedbackTexture2DArray
    - RWBuffer
    - RWSampler1D
    - RWSampler1DArray
    - RWSampler2D
    - RWSampler2DArray
    - RWSampler2DMS
    - RWSampler2DMSArray
    - RWSampler3D
    - RWTexture1D
    - RWTexture1DArray
    - RWTexture2D
    - RWTexture2DArray
    - RWTexture2DMS
    - RWTexture2DMSArray
    - RWTexture3D
    - RasterizerOrderedBuffer
    - RasterizerOrderedSampler1D
    - RasterizerOrderedSampler1DArray
    - RasterizerOrderedSampler2D
    - RasterizerOrderedSampler2DArray
    - RasterizerOrderedSampler3D
    - RasterizerOrderedTexture1D
    - RasterizerOrderedTexture1DArray
    - RasterizerOrderedTexture2D
    - RasterizerOrderedTexture2DArray
    - RasterizerOrderedTexture3D
    - SAMPLER_FEEDBACK_MIN_MIP
    - SAMPLER_FEEDBACK_MIP_REGION_USED
    - Sampler1D
    - Sampler1DArray
    - Sampler1DArrayShadow
    - Sampler1DShadow
    - Sampler2D
    - Sampler2DArray
    - Sampler2DArrayShadow
    - Sampler2DMS
    - Sampler2DMSArray
    - Sampler2DShadow
    - Sampler3D
    - Sampler3DArrayShadow
    - Sampler3DShadow
    - SamplerCube
    - SamplerCubeArray
    - SamplerCubeArrayShadow
    - SamplerCubeShadow
    - Texture1D
    - Texture1DArray
    - Texture2D
    - Texture2DArray
    - Texture2DMS
    - Texture2DMSArray
    - Texture3D
    - TextureBuffer
    - TextureCube
    - TextureCubeArray
    - WSampler1D
    - WSampler1DArray
    - WSampler2D
    - WSampler2DArray
    - WSampler3D
    - WTexture1D
    - WTexture1DArray
    - WTexture2D
    - WTexture2DArray
    - WTexture3D
    - _Texture
      - CalculateLevelOfDetail
      - CalculateLevelOfDetailUnclamped
      - Coords
      - Footprint
      - FootprintGranularity
      - Gather
      - GatherAlpha
      - GatherBlue
      - GatherCmp
      - GatherCmpAlpha
      - GatherCmpBlue
      - GatherCmpGreen
      - GatherCmpRed
      - GatherGreen
      - GatherRed
      - GetDimensions
      - GetSamplePosition
      - InterlockedAddF32
      - Load
      - Sample
      - SampleBias
      - SampleCmp
      - SampleCmpLevelZero
      - SampleGrad
      - SampleLevel
      - Store
      - TextureCoord
      - WriteSamplerFeedback
      - WriteSamplerFeedbackBias
      - WriteSamplerFeedbackGrad
      - WriteSamplerFeedbackLevel
      - queryFootprintCoarse
      - queryFootprintCoarseBias
      - queryFootprintCoarseBiasClamp
      - queryFootprintCoarseClamp
      - queryFootprintCoarseGrad
      - queryFootprintCoarseGradClamp
      - queryFootprintCoarseLevel
      - queryFootprintFine
      - queryFootprintFineBias
      - queryFootprintFineBiasClamp
      - queryFootprintFineClamp
      - queryFootprintFineGrad
      - queryFootprintFineGradClamp
      - queryFootprintFineLevel
      - subscript
  - Array
    - Differential
    - dadd
    - dmul
    - dzero
    - getCount
  - Atomic
    - add
    - and
    - compareExchange
    - decrement
    - exchange
    - increment
    - load
    - max
    - min
    - or
    - store
    - sub
    - xor
  - AtomicAdd
    - diff
    - loadOnce_backward
    - loadOnce_forward
    - load_backward
    - load_forward
    - storeOnce_backward
    - storeOnce_forward
    - store_backward
    - store_forward
  - ConstantBuffer
  - DiffTensorView
    - diff
    - dims
    - init
    - load
    - loadOnce
    - primal
    - size
    - store
    - storeOnce
    - stride
    - subscript
  - DifferentialPair
    - Differential
    - DifferentialElementType
    - d
    - dadd
    - dmul
    - dzero
    - getDifferential
    - getPrimal
    - init
    - p
    - v
  - DifferentialPtrPair
    - Differential
    - DifferentialElementType
    - d
    - init
    - p
    - v
  - NullDifferential
    - Differential
    - dadd
    - dmul
    - dummy
    - dzero
  - Optional
    - hasValue
    - init
    - value
  - ParameterBlock
  - Ptr
    - init
    - subscript
  - String
    - getLength
    - init
    - length
  - TensorView
    - InterlockedAdd
    - InterlockedAnd
    - InterlockedCompareExchange
    - InterlockedExchange
    - InterlockedMax
    - InterlockedMin
    - InterlockedOr
    - InterlockedXor
    - data_ptr
    - data_ptr_at
    - dims
    - init
    - load
    - size
    - store
    - stride
    - subscript
  - TorchTensor
    - alloc
    - data_ptr
    - dims
    - emptyLike
    - fillValue
    - fillZero
    - getView
    - size
    - stride
    - zerosLike
  - Tuple
    - Differential
    - dadd
    - dmul
    - dzero
    - equals
    - init
    - lessThan
    - lessThanOrEquals
  - _AttributeTargets
- Attributes
  - AutoPyBindCUDA
  - BackwardDerivative
  - BackwardDerivativeOf
  - BackwardDifferentiable
  - COM
  - CUDADeviceExport
  - CUDAHost
  - CUDAKernel
  - CudaDeviceExport
  - CudaHost
  - CudaKernel
  - DerivativeGroupLinear
  - DerivativeGroupQuad
  - DerivativeMember
  - Differentiable
  - DllExport
  - DllImport
  - Flags
  - ForceInline
  - ForceUnroll
  - ForwardDerivative
  - ForwardDerivativeOf
  - ForwardDifferentiable
  - KnownBuiltin
  - MaxIters
  - NoDiffThis
  - NonUniformReturn
  - NumThreads
  - OverloadRank
  - PreferCheckpoint
  - PreferRecompute
  - PrimalSubstitute
  - PrimalSubstituteOf
  - PyExport
  - RequirePrelude
  - Shader
  - SpecializationConstant
  - Specialize
  - TorchEntryPoint
  - TreatAsDifferentiable
  - UnscopedEnum
  - WaveSize
  - allow
  - allow_uav_condition
  - anyValueSize
  - branch
  - builtin
  - call
  - constref
  - deprecated
  - disable_array_flattening
  - domain
  - earlydepthstencil
  - fastopt
  - flatten
  - forcecase
  - format
  - gl_binding
  - instance
  - loop
  - maxtessfactor
  - maxvertexcount
  - mutating
  - noRefInline
  - noinline
  - nonmutating
  - numthreads
  - open
  - outputcontrolpoints
  - outputtopology
  - partitioning
  - patchconstantfunc
  - payload
  - push_constant
  - require
  - sealed
  - shader
  - shader_record
  - spv_target_env_1_3
  - unroll
  - vk_binding
  - vk_constant_id
  - vk_image_format
  - vk_location
  - vk_push_constant
  - vk_shader_record
  - vk_specialization_constant
  - vk_spirv_instruction
- Global Declarations
  - Atomic functions
    - InterlockedAdd
    - InterlockedAnd
    - InterlockedCompareExchange
    - InterlockedCompareExchangeFloatBitwise
    - InterlockedCompareStore
    - InterlockedCompareStoreFloatBitwise
    - InterlockedExchange
    - InterlockedMax
    - InterlockedMin
    - InterlockedOr
    - InterlockedXor
  - Memory and control barriers
    - AllMemoryBarrier
    - AllMemoryBarrierWithGroupSync
    - DeviceMemoryBarrier
    - DeviceMemoryBarrierWithGroupSync
    - GroupMemoryBarrier
    - GroupMemoryBarrierWithGroupSync
  - Bit operation functions
    - countbits
    - firstbithigh
    - firstbitlow
    - reversebits
  - Conversion functions
    - asdouble
    - asfloat
    - asfloat16
    - asint
    - asint16
    - asuint
    - asuint16
    - bit_cast
    - f16tof32
    - f32tof16
    - f32tof16_
    - reinterpret
  - Derivative functions
    - ddx
    - ddx_coarse
    - ddx_fine
    - ddy
    - ddy_coarse
    - ddy_fine
    - fwidth
  - Math functions
    - abs
    - acos
    - acosh
    - asin
    - asinh
    - atan
    - atan2
    - atanh
    - ceil
    - clamp
    - copysign
    - copysign_double
    - copysign_float
    - copysign_half
    - cos
    - cosh
    - cospi
    - cross
    - degrees
    - determinant
    - distance
    - divide
    - dot
    - dot2add
    - dot4add_i8packed
    - dot4add_u8packed
    - dst
    - exp
    - exp10
    - exp2
    - fabs
    - faceforward
    - fdim
    - floor
    - fma
    - fmax
    - fmax3
    - fmedian3
    - fmin
    - fmin3
    - fmod
    - frac
    - fract
    - frexp
    - isfinite
    - isinf
    - isnan
    - ldexp
    - length
    - lerp
    - lit
    - log
    - log10
    - log2
    - mad
    - max
    - max3
    - median3
    - min
    - min3
    - modf
    - msad4
    - mul
    - noise
    - normalize
    - pow
    - powr
    - radians
    - rcp
    - reflect
    - refract
    - rint
    - round
    - rsqrt
    - saturate
    - sign
    - sin
    - sincos
    - sinh
    - sinpi
    - smoothstep
    - sqrt
    - step
    - tan
    - tanh
    - tanpi
    - transpose
    - trunc
  - Mesh shading
    - DispatchMesh
    - SetMeshOutputCounts
  - Ray-tracing
    - AcceptHitAndEndSearch
    - CANDIDATE_NON_OPAQUE_TRIANGLE
    - CANDIDATE_PROCEDURAL_PRIMITIVE
    - COMMITTED_NOTHING
    - COMMITTED_PROCEDURAL_PRIMITIVE_HIT
    - COMMITTED_TRIANGLE_HIT
    - CallShader
    - DispatchRaysDimensions
    - DispatchRaysIndex
    - GeometryIndex
    - HIT_KIND_TRIANGLE_BACK_FACE
    - HIT_KIND_TRIANGLE_FRONT_FACE
    - HitKind
    - HitTriangleVertexPosition
    - IgnoreHit
    - InstanceID
    - InstanceIndex
    - ObjectRayDirection
    - ObjectRayOrigin
    - ObjectToWorld
    - ObjectToWorld3x4
    - ObjectToWorld4x3
    - PrimitiveIndex
    - RAY_FLAG_ACCEPT_FIRST_HIT_AND_END_SEARCH
    - RAY_FLAG_CULL_BACK_FACING_TRIANGLES
    - RAY_FLAG_CULL_FRONT_FACING_TRIANGLES
    - RAY_FLAG_CULL_NON_OPAQUE
    - RAY_FLAG_CULL_OPAQUE
    - RAY_FLAG_FORCE_NON_OPAQUE
    - RAY_FLAG_FORCE_OPAQUE
    - RAY_FLAG_NONE
    - RAY_FLAG_SKIP_CLOSEST_HIT_SHADER
    - RAY_FLAG_SKIP_PROCEDURAL_PRIMITIVES
    - RAY_FLAG_SKIP_TRIANGLES
    - RayCurrentTime
    - RayFlags
    - RayTCurrent
    - RayTMin
    - ReportHit
    - ReportHitOptix
    - TraceMotionRay
    - TraceRay
    - WorldRayDirection
    - WorldRayOrigin
    - WorldToObject
    - WorldToObject3x4
    - WorldToObject4x3
  - Tessellation functions
    - Process2DQuadTessFactorsAvg
    - Process2DQuadTessFactorsMax
    - Process2DQuadTessFactorsMin
    - ProcessIsolineTessFactors
    - ProcessQuadTessFactorsAvg
    - ProcessQuadTessFactorsMax
    - ProcessQuadTessFactorsMin
    - ProcessTriTessFactorsAvg
    - ProcessTriTessFactorsMax
    - ProcessTriTessFactorsMin
  - Wave and quad functions
    - QuadReadAcrossDiagonal
    - QuadReadAcrossX
    - QuadReadAcrossY
    - QuadReadLaneAt
    - WaveActiveAllEqual
    - WaveActiveAllTrue
    - WaveActiveAnyTrue
    - WaveActiveBallot
    - WaveActiveBitAnd
    - WaveActiveBitOr
    - WaveActiveBitXor
    - WaveActiveCountBits
    - WaveActiveMax
    - WaveActiveMin
    - WaveActiveProduct
    - WaveActiveSum
    - WaveBroadcastLaneAt
    - WaveGetActiveMulti
    - WaveGetConvergedMulti
    - WaveGetLaneCount
    - WaveGetLaneIndex
    - WaveIsFirstLane
    - WaveMatch
    - WaveMultiPrefixBitAnd
    - WaveMultiPrefixBitOr
    - WaveMultiPrefixBitXor
    - WaveMultiPrefixCountBits
    - WaveMultiPrefixProduct
    - WaveMultiPrefixSum
    - WavePrefixCountBits
    - WavePrefixProduct
    - WavePrefixSum
    - WaveReadLaneAt
    - WaveReadLaneFirst
    - WaveShuffle
    - _WaveCountBits
  - CheckAccessFullyMapped
  - D3DCOLORtoUBYTE4
  - EvaluateAttributeAtCentroid
  - EvaluateAttributeAtSample
  - EvaluateAttributeSnapped
  - GetAttributeAtVertex
  - GetRenderTargetSampleCount
  - GetRenderTargetSamplePosition
  - IsHelperLane
  - NonUniformResourceIndex
  - ReorderThread
  - WorkgroupSize
  - abort
  - all
  - any
  - bitfieldExtract
  - bitfieldInsert
  - clip
  - concat
  - createDynamicObject
  - cudaBlockDim
  - cudaBlockIdx
  - cudaThreadIdx
  - debugBreak
  - detach
  - diffPair
  - getRealtimeClock
  - getRealtimeClockLow
  - getStringHash
  - isDifferentialNull
  - loadAligned
  - makeArrayFromElement
  - makeTuple
  - nextafter
  - printf
  - select
  - static_assert
  - storeAligned
  - syncTorchCudaStream
  - unmodified
  - unused
  - updateDiff
  - updatePair
  - updatePrimal
  - workgroupUniformLoad

updatePair

Description

Signature

void updatePair<T>(
    inout DifferentialPair<T> p,
    T newPrimal,
    T.Differential newDiff)
    where T : IDifferentiable;

updatePair

Description

Signature

Generic Parameters

T: IDifferentiable

Parameters

p : DifferentialPair<T>

newPrimal : T

newDiff : T.Differential