LogSumExp

Functions
float16_t	arm_logsumexp_dot_prod_f16 (const float16_t *pSrcA, const float16_t *pSrcB, uint32_t blockSize, float16_t *pTmpBuffer)
	Dot product with log arithmetic.
float32_t	arm_logsumexp_dot_prod_f32 (const float32_t *pSrcA, const float32_t *pSrcB, uint32_t blockSize, float32_t *pTmpBuffer)
	Dot product with log arithmetic.
float16_t	arm_logsumexp_f16 (const float16_t *in, uint32_t blockSize)
	Computation of the LogSumExp.
float32_t	arm_logsumexp_f32 (const float32_t *in, uint32_t blockSize)
	Computation of the LogSumExp.

Description

LogSumExp optimizations to compute sum of probabilities with Gaussian distributions

Function Documentation

arm_logsumexp_dot_prod_f16()

float16_t arm_logsumexp_dot_prod_f16	(	const float16_t *	pSrcA,
		const float16_t *	pSrcB,
		uint32_t	blockSize,
		float16_t *	pTmpBuffer
	)

Dot product with log arithmetic.

Vectors are containing the log of the samples

Parameters

[in]	*pSrcA	points to the first input vector
[in]	*pSrcB	points to the second input vector
[in]	blockSize	number of samples in each vector
[in]	*pTmpBuffer	temporary buffer of length blockSize

Returns

The log of the dot product.

arm_logsumexp_dot_prod_f32()

float32_t arm_logsumexp_dot_prod_f32	(	const float32_t *	pSrcA,
		const float32_t *	pSrcB,
		uint32_t	blockSize,
		float32_t *	pTmpBuffer
	)

Dot product with log arithmetic.

Vectors are containing the log of the samples

Parameters

[in]	*pSrcA	points to the first input vector
[in]	*pSrcB	points to the second input vector
[in]	blockSize	number of samples in each vector
[in]	*pTmpBuffer	temporary buffer of length blockSize

Returns

The log of the dot product.

arm_logsumexp_f16()

float16_t arm_logsumexp_f16	(	const float16_t *	in,
		uint32_t	blockSize
	)

Computation of the LogSumExp.

In probabilistic computations, the dynamic of the probability values can be very wide because they come from gaussian functions. To avoid underflow and overflow issues, the values are represented by their log. In this representation, multiplying the original exp values is easy : their logs are added. But adding the original exp values is requiring some special handling and it is the goal of the LogSumExp function.

If the values are x1...xn, the function is computing:

ln(exp(x1) + ... + exp(xn)) and the computation is done in such a way that rounding issues are minimised.

The max xm of the values is extracted and the function is computing: xm + ln(exp(x1 - xm) + ... + exp(xn - xm))

Parameters

[in]	*in	Pointer to an array of input values.
[in]	blockSize	Number of samples in the input array.

Returns

LogSumExp

arm_logsumexp_f32()

float32_t arm_logsumexp_f32	(	const float32_t *	in,
		uint32_t	blockSize
	)

Computation of the LogSumExp.

In probabilistic computations, the dynamic of the probability values can be very wide because they come from gaussian functions. To avoid underflow and overflow issues, the values are represented by their log. In this representation, multiplying the original exp values is easy : their logs are added. But adding the original exp values is requiring some special handling and it is the goal of the LogSumExp function.

If the values are x1...xn, the function is computing:

ln(exp(x1) + ... + exp(xn)) and the computation is done in such a way that rounding issues are minimised.

The max xm of the values is extracted and the function is computing: xm + ln(exp(x1 - xm) + ... + exp(xn - xm))

Parameters

[in]	*in	Pointer to an array of input values.
[in]	blockSize	Number of samples in the input array.

Returns

LogSumExp