Erfc

Applicability

Function Usage

Returns the complementary error function computing result of input x. The integral ranges from x to infinity. The original formula is as follows:

Because the Erfc function does not have an elementary function expression, it is generally calculated by function approximation. An approximate calculation formula is as follows:

where:

R(z) = (((((((z x R0 + R1) x z + R2) x z + R3) x z + R4) x z + R5) x z + R6) x z + R7) x z + R8 is an 8th degree polynomial about z;

S(z) = ((((z + S1) x z + S2) x z + S3) x z + S4) x z + S5 is a 4th degree polynomial about z.

Prototype

• Pass the temporary space through the sharedTmpBuffer input parameter.
  • All or part of the source operand tensors are involved in computation.

    1 2	template <typename T, bool isReuseSource = false> __aicore__ inline void Erfc(const LocalTensor<T>& dstTensor, const LocalTensor<T>& srcTensor, const LocalTensor<uint8_t>& sharedTmpBuffer, const uint32_t calCount)

  • All source operand tensors are involved in computation.

    1 2	template <typename T, bool isReuseSource = false> __aicore__ inline void Erfc(const LocalTensor<T>& dstTensor, const LocalTensor<T>& srcTensor, const LocalTensor<uint8_t>& sharedTmpBuffer)

• Allocate the temporary space through the API framework.
  • All or part of the source operand tensors are involved in computation.

    1 2	template <typename T, bool isReuseSource = false> __aicore__ inline void Erfc(const LocalTensor<T>& dstTensor, const LocalTensor<T>& srcTensor, const uint32_t calCount)

  • All source operand tensors are involved in computation.

    1 2	template <typename T, bool isReuseSource = false> __aicore__ inline void Erfc(const LocalTensor<T>& dstTensor, const LocalTensor<T>& srcTensor)

Due to the complex mathematical computation involved in the internal implementation of this API, additional temporary space is required to store intermediate variables generated during computation. The temporary space can be passed by developers through the sharedTmpBuffer input parameter or allocated through the API framework.

• When the sharedTmpBuffer input parameter is used for passing the temporary space, the tensor serves as the temporary space. In this case, the API framework is not required for temporary space allocation. This enables developers to manage the sharedTmpBuffer space and reuse the buffer after calling the API, so that the buffer is not repeatedly allocated and deallocated, improving the flexibility and buffer utilization.
• When the API framework is used for temporary space allocation, developers do not need to allocate the space, but must reserve the required size for the space.

If sharedTmpBuffer is used, developers must allocate space for the tensor. If the API framework is used, developers must reserve the temporary space. To obtain the size of the temporary space (BufferSize) to be reserved, use the API provided in GetErfcMaxMinTmpSize.

Parameters

Returns

None

Restrictions

• The value range of the input source data must be [-inf, inf]. If the input is not within the range, the output is invalid.
• The source operand address must not overlap the destination operand address.
• The address of sharedTmpBuffer must not overlap the addresses of the source operand and destination operand.
• For details about the operand address alignment requirements, see General Address Alignment Restrictions.

Example

For a complete example, see Erfc operator sample.

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// dstLocal: tensor for storing the computation result
// srcLocal: input tensor involved in computation
// sharedTmpBuffer: temporary buffer for storing intermediate variables during complex internal computation
// The input tensor length is 1,024, the input data type of the operator is half, and the number of actually computed data elements is 512.
AscendC::Erfc(dstLocal, srcLocal, sharedTmpBuffer, 512);

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Input (srcLocal): [0.0           1.0           2.0            3.0           ...]
Output (dstLocal): [1.0000000e+00 1.5729921e-01 4.6777348e-03 2.2090497e-05 ...]