32Bit Vector API#
 group vect_s32_api
Defines

VECT_SQRT_S32_MAX_DEPTH#
Maximum bitdepth that can be calculated by vect_s32_sqrt().
See also
Enums

enum pad_mode_e#
Supported padding modes for convolutions in “same” mode.
Values:

enumerator PAD_MODE_REFLECT#
Vector is reflected at its boundaries, such that
\( \tilde{x}_i \begin{cases} x_{i} & i < 0 \\ x_{2N  2  i} & i \ge N \\ x_i & otherwise \end{cases} \)
For example, if the length \(N\) of input vector \(\bar x\) is \(7\) and the order \(K\) of the filter is \(5\), then
\( \bar{x} = [x_0, x_1, x_2, x_3, x_4, x_5, x_6] \)
\( \tilde{x} = [x_2, x_1, x_0, x_1, x_2, x_3, x_4, x_5, x_6, x_5, x_4] \)
Note that by convention the first element of \(\tilde{x}\) is considered to be at index \(P\), where \(P = \lfloor K/2 \rfloor\).

enumerator PAD_MODE_EXTEND#
Vector is padded using the value of the bounding elements.
\( \tilde{x}_i \begin{cases} x_{0} & i < 0 \\ x_{N1} & i \ge N \\ x_i & otherwise \end{cases} \)
For example, if the length \(N\) of input vector \(\bar x\) is \(7\) and the order \(K\) of the filter is \(5\), then
\( \bar{x} = [x_0, x_1, x_2, x_3, x_4, x_5, x_6] \)
\( \tilde{x} = [x_0, x_0, x_0, x_1, x_2, x_3, x_4, x_5, x_6, x_6, x_6] \)
Note that by convention the first element of \(\tilde{x}\) is considered to be at index \(P\), where \(P = \lfloor K/2 \rfloor\).

enumerator PAD_MODE_ZERO#
Vector is padded with zeroes.
\( \tilde{x}_i \begin{cases} 0 & i < 0 \\ 0 & i \ge N \\ x_i & otherwise \end{cases} \)
For example, if the length \(N\) of input vector \(\bar x\) is \(7\) and the order \(K\) of the filter is \(5\), then
\( \bar{x} = [x_0, x_1, x_2, x_3, x_4, x_5, x_6] \)
\( \tilde{x} = [0, 0, x_0, x_1, x_2, x_3, x_4, x_5, x_6, 0, 0] \)
Note that by convention the first element of \(\tilde{x}\) is considered to be at index \(P\), where \(P = \lfloor K/2 \rfloor\).

enumerator PAD_MODE_REFLECT#
Functions

headroom_t vect_s32_copy(int32_t a[], const int32_t b[], const unsigned length)#
Copy one 32bit vector to another.
This function is effectively a constrained version of
memcpy
.With the constraints below met, this function should be modestly faster than
memcpy
.a[]
is the output vector to which elements are copied.b[]
is the input vector from which elements are copied.a
andb
each must begin at a wordaligned address.length
is the number of elements to be copied.length
must be a multiple of 8. Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow b_k \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\)

headroom_t vect_s32_abs(int32_t a[], const int32_t b[], const unsigned length)#
Compute the elementwise absolute value of a 32bit vector.
a[]
andb[]
represent the 32bit vectors \(\bar a\) and \(\bar b\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
.length
is the number of elements in each of the vectors. Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow sat_{32}(\left b_k \right) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the output vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp\).
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of the output vector \(\bar a\).

int64_t vect_s32_abs_sum(const int32_t b[], const unsigned length)#
Compute the sum of the absolute values of elements of a 32bit vector.
b[]
represents the 32bit mantissa vector \(\bar b\).b[]
must begin at a wordaligned address.length
is the number of elements in \(\bar b\). Operation Performed:
 \[\begin{flalign*} \sum_{k=0}^{length1} sat_{32}(\left b_k \right) && \end{flalign*}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the returned value \(a\) is the 64bit mantissa of floatingpoint value \(a \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp\).
 Additional Details

Internally the sum accumulates into 8 separate 40bit accumulators. These accumulators apply symmetric 40bit saturation logic (with bounds \(\pm (2^{39}1)\)) with each added element. At the end, the 8 accumulators are summed together into the 64bit value \(a\) which is returned by this function. No saturation logic is applied at this final step.
Because symmetric 32bit saturation logic is applied when computing the absolute value, in the corner case where each element is
INT32_MIN
, each of the 8 accumulators can accumulate \(256\) elements before saturation is possible. Therefore, with \(b\_hr\) bits of headroom, no saturation of intermediate results is possible with fewer than \(2^{11 + b\_hr}\) elements in \(\bar b\).If the length of \(\bar b\) is greater than \(2^{11 + b\_hr}\), the sum can be computed piecewise in several calls to this function, with the partial results summed in user code.
 Parameters:
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
is not wordaligned (See Note: Vector Alignment) Returns:
The 64bit sum \(a\)

headroom_t vect_s32_add(int32_t a[], const int32_t b[], const int32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Add together two 32bit vectors.
a[]
,b[]
andc[]
represent the 32bit mantissa vectors \(\bar a\), \(\bar b\) and \(\bar c\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
orc[]
.length
is the number of elements in each of the vectors.b_shr
andc_shr
are the signed arithmetic rightshifts applied to each element of \(\bar b\) and \(\bar c\) respectively. Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' = sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' = sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & a_k \leftarrow sat_{32}\!\left( b_k' + c_k' \right) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) and \(\bar c\) are the mantissas of BFP vectors \( \bar{b} \cdot 2^{b\_exp} \) and \(\bar{c} \cdot 2^{c\_exp}\), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\).
In this case, \(b\_shr\) and \(c\_shr\) must be chosen so that \(a\_exp = b\_exp + b\_shr = c\_exp + c\_shr\). Adding or subtracting mantissas only makes sense if they are associated with the same exponent.
The function vect_s32_add_prepare() can be used to obtain values for \(a\_exp\), \(b\_shr\) and \(c\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
See also
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
b_shr – [in] Rightshift appled to \(\bar b\)
c_shr – [in] Rightshift appled to \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
a
,b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of the output vector \(\bar a\).

headroom_t vect_s32_add_scalar(int32_t a[], const int32_t b[], const int32_t c, const unsigned length, const right_shift_t b_shr)#
Add a scalar to a 32bit vector.
a[]
,b[]
represent the 32bit mantissa vectors \(\bar a\) and \(\bar b\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
.c
is the scalar \(c\) to be added to each element of \(\bar b\).length
is the number of elements in each of the vectors.b_shr
is the signed arithmetic rightshift applied to each element of \(\bar b\). Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' = sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & a_k \leftarrow sat_{32}\!\left( b_k' + c \right) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If elements of \(\bar b\) are the mantissas of BFP vector \( \bar{b} \cdot 2^{b\_exp} \), and \(c\) is the mantissa of floatingpoint value \(c \cdot 2^{c\_exp}\), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\).
In this case, \(b\_shr\) and \(c\_shr\) must be chosen so that \(a\_exp = b\_exp + b\_shr = c\_exp + c\_shr\). Adding or subtracting mantissas only makes sense if they are associated with the same exponent.
The function vect_s32_add_scalar_prepare() can be used to obtain values for \(a\_exp\), \(b\_shr\) and \(c\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
Note that \(c\_shr\) is an output of
vect_s32_add_scalar_prepare()
, but is not a parameter to this function. The \(c\_shr\) produced byvect_s32_add_scalar_prepare()
is to be applied by the user, and the result passed as inputc
.
See also
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Input scalar \(c\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shr – [in] Rightshift appled to \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of the output vector \(\bar a\).

unsigned vect_s32_argmax(const int32_t b[], const unsigned length)#
Obtain the array index of the maximum element of a 32bit vector.
b[]
represents the 32bit input vector \(\bar b\). It must begin at a wordaligned address.length
is the number of elements in \(\bar b\). Operation Performed:
 \[\begin{split}\begin{flalign*} & a \leftarrow argmax_k\{ b_k \} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Parameters:
b – [in] Input vector \(\bar b\)
length – [in] Number of elemetns in \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
is not wordaligned (See Note: Vector Alignment) Returns:
\(a\), the index of the maximum element of vector \(\bar b\). If there is a tie for the maximum value, the lowest tying index is returned.

unsigned vect_s32_argmin(const int32_t b[], const unsigned length)#
Obtain the array index of the minimum element of a 32bit vector.
b[]
represents the 32bit input vector \(\bar b\). It must begin at a wordaligned address.length
is the number of elements in \(\bar b\). Operation Performed:
 \[\begin{split}\begin{flalign*} & a \leftarrow argmin_k\{ b_k \} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Parameters:
b – [in] Input vector \(\bar b\)
length – [in] Number of elemetns in \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
is not wordaligned (See Note: Vector Alignment) Returns:
\(a\), the index of the minimum element of vector \(\bar b\). If there is a tie for the minimum value, the lowest tying index is returned.

headroom_t vect_s32_clip(int32_t a[], const int32_t b[], const unsigned length, const int32_t lower_bound, const int32_t upper_bound, const right_shift_t b_shr)#
Clamp the elements of a 32bit vector to a specified range.
a[]
andb[]
represent the 32bit vectors \(\bar a\) and \(\bar b\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
.length
is the number of elements in each of the vectors.lower_bound
andupper_bound
are the lower and upper bounds of the clipping range respectively. These bounds are checked for each element of \(\bar b\) only afterb_shr
is applied.b_shr
is the signed arithmetic rightshift applied to elements of \(\bar b\) before being compared to the upper and lower bounds.If \(\bar b\) are the mantissas for a BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the exponent \(a\_exp\) of the output BFP vector \(\bar{a} \cdot 2^{a\_exp}\) is given by \(a\_exp = b\_exp + b\_shr\).
 Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & a_k \leftarrow \begin{cases} lower\_bound & b_k' \le lower\_bound \\ & upper\_bound & b_k' \ge upper\_bound \\ & b_k' & otherwise \end{cases} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the output vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + b\_shr\).
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
lower_bound – [in] Lower bound of clipping range
upper_bound – [in] Upper bound of clipping range
b_shr – [in] Arithmetic rightshift applied to elements of \(\bar b\) prior to clipping
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\)

int64_t vect_s32_dot(const int32_t b[], const int32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Compute the inner product between two 32bit vectors.
b[]
andc[]
represent the 32bit mantissa vectors \(\bar b\) and \(\bar c\) respectively. Each must begin at a wordaligned address.length
is the number of elements in each of the vectors.b_shr
andc_shr
are the signed arithmetic rightshifts applied to each element of \(\bar b\) and \(\bar c\) respectively. Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & a \leftarrow \sum_{k=0}^{length1}\left(round( b_k' \cdot c_k' \cdot 2^{30} ) \right) \\ & \qquad\text{where } a \text{ is returned} && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) and \(\bar c\) are the mantissas of the BFP vectors \( \bar{b} \cdot 2^{b\_exp} \) and \(\bar{c}\cdot 2^{c\_exp}\), then result \(a\) is the 64bit mantissa of the result \(a \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + c\_exp + b\_shr + c\_shr + 30\).
If needed, the bitdepth of \(a\) can then be reduced to 32 bits to get a new result \(a' \cdot 2^{a\_exp'}\) where \(a' = a \cdot 2^{a\_shr}\) and \(a\_exp' = a\_exp + a\_shr\).
The function vect_s32_dot_prepare() can be used to obtain values for \(a\_exp\), \(b\_shr\) and \(c\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
 Additional Details

The 30bit rounding rightshift applied to each of the 64bit products \(b_k \cdot c_k\) is a feature of the hardware and cannot be avoided. As such, if the input vectors \(\bar b\) and \(\bar c\) together have too much headroom (i.e. \(b\_hr + c\_hr\)), the sum may effectively vanish. To avoid this situation, negative values of
b_shr
andc_shr
may be used (with the stipulation that \(b\_shr \ge b\_hr\) and \(c\_shr \ge c\_hr\) if saturation of \(b_k'\) and \(c_k'\) is to be avoided). The less headroom \(b_k'\) and \(c_k'\) have, the greater the precision of the final result.Internally, each product \((b_k' \cdot c_k' \cdot 2^{30})\) accumulates into one of eight 40bit accumulators (which are all used simultaneously) which apply symmetric 40bit saturation logic (with bounds \(\approx 2^{39}\)) with each value added. The saturating arithmetic employed is not associative and no indication is given if saturation occurs at an intermediate step. To avoid satuation errors,
length
should be no greater than \(2^{10+b\_hr+c\_hr}\), where \(b\_hr\) and \(c\_hr\) are the headroom of \(\bar b\) and \(\bar c\) respectively.If the caller’s mantissa vectors are longer than that, the full inner product can be found by calling this function multiple times for partial inner products on subsequences of the input vectors, and adding the results in user code.
In many situations the caller may have a priori knowledge that saturation is impossible (or very nearly so), in which case this guideline may be disregarded. However, such situations are applicationspecific and are well beyond the scope of this documentation, and as such are left to the user’s discretion.
 Parameters:
b – [in] Input vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar b\) and \(\bar c\)
b_shr – [in] Rightshift appled to \(\bar b\)
c_shr – [in] Rightshift appled to \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
The inner product of vectors \(\bar b\) and \(\bar c\), scaled as indicated above.

int64_t vect_s32_energy(const int32_t b[], const unsigned length, const right_shift_t b_shr)#
Calculate the energy (sum of squares of elements) of a 32bit vector.
b[]
represents the 32bit mantissa vector \(\bar b\).b[]
must begin at a wordaligned address.length
is the number of elements in \(\bar b\).b_shr
is the signed arithmetic rightshift applied to elements of \(\bar b\). Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & a \leftarrow \sum_{k=0}^{length1} round((b_k')^2 \cdot 2^{30}) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of the BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then floatingpoint result is \(a \cdot 2^{a\_exp}\), where the 64bit mantissa \(a\) is returned by this function, and \(a\_exp = 30 + 2 \cdot (b\_exp + b\_shr) \).
The function vect_s32_energy_prepare() can be used to obtain values for \(a\_exp\), \(b\_shr\) and \(c\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
 Additional Details

The 30bit rounding rightshift applied to each element of the 64bit products \((b_k')^2\) is a feature of the hardware and cannot be avoided. As such, if the input vector \(\bar b\) has too much headroom (i.e. \(2\cdot b\_hr\)), the sum may effectively vanish. To avoid this situation, negative values of
b_shr
may be used (with the stipulation that \(b\_shr \ge b\_hr\) if satuartion of \(b_k'\) is to be avoided). The less headroom \(b_k'\) has, the greater the precision of the final result.Internally, each product \((b_k')^2 \cdot 2^{30}\) accumulates into one of eight 40bit accumulators (which are all used simultaneously) which apply symmetric 40bit saturation logic (with bounds \(\approx 2^{39}\)) with each value added. The saturating arithmetic employed is not associative and no indication is given if saturation occurs at an intermediate step. To avoid saturation errors,
length
should be no greater than \(2^{10+2\cdot b\_hr}\), where \(b\_hr\) is the headroom of \(\bar b\).If the caller’s mantissa vector is longer than that, the full result can be found by calling this function multiple times for partial results on subsequences of the input, and adding the results in user code.
In many situations the caller may have a priori knowledge that saturation is impossible (or very nearly so), in which case this guideline may be disregarded. However, such situations are applicationspecific and are well beyond the scope of this documentation, and as such are left to the user’s discretion.
 Parameters:
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in \(\bar b\)
b_shr – [in] Rightshift appled to \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
is not wordaligned (See Note: Vector Alignment) Returns:
64bit mantissa of vector \(\bar b\)’s energy

headroom_t vect_s32_headroom(const int32_t x[], const unsigned length)#
Calculate the headroom of a 32bit vector.
The headroom of an Nbit integer is the number of bits that the integer’s value may be leftshifted without any information being lost. Equivalently, it is one less than the number of leading sign bits.
The headroom of an
int32_t
array is the minimum of the headroom of each of itsint32_t
elements.This function efficiently traverses the elements of
a[]
to determine its headroom.x[]
represents the 32bit vector \(\bar x\).x[]
must begin at a wordaligned address.length
is the number of elements inx[]
. Operation Performed:
 \[\begin{flalign*} min\!\{ HR_{32}\left(x_0\right), HR_{32}\left(x_1\right), ..., HR_{32}\left(x_{length1}\right) \} && \end{flalign*}\]
 Parameters:
x – [in] Input vector \(\bar x\)
length – [in] The number of elements in
x[]
 Throws ET_LOAD_STORE:
Raised if
x
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of vector \(\bar x\)

headroom_t vect_s32_inverse(int32_t a[], const int32_t b[], const unsigned length, const unsigned scale)#
Compute the inverse of elements of a 32bit vector.
a[]
andb[]
represent the 32bit mantissa vectors \(\bar a\) and \(\bar b\) respectively. Each vector must begin at a wordaligned address. This operation can be performed safely inplace onb[]
.length
is the number of elements in each of the vectors.scale
is a scaling parameter used to maximize the precision of the result. Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow \lfloor\frac{2^{scale}}{b_k}\rfloor \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = scale  b\_exp\).
The function vect_s32_inverse_prepare() can be used to obtain values for \(a\_exp\) and \(scale\).
See also
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
scale – [in] Scale factor applied to dividend when computing inverse
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\)

int32_t vect_s32_max(const int32_t b[], const unsigned length)#
Find the maximum value in a 32bit vector.
b[]
represents the 32bit vector \(\bar b\). It must begin at a wordaligned address.length
is the number of elements in \(\bar b\). Operation Performed:
 \[\begin{flalign*} max\{ x_0, x_1, ..., x_{length1} \} && \end{flalign*}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the returned value \(a\) is the 32bit mantissa of floatingpoint value \(a \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp\).
 Parameters:
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
is not wordaligned (See Note: Vector Alignment) Returns:
Maximum value from \(\bar b\)

headroom_t vect_s32_max_elementwise(int32_t a[], const int32_t b[], const int32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Get the elementwise maximum of two 32bit vectors.
a[]
,b[]
andc[]
represent the 32bit mantissa vectors \(\bar a\), \(\bar b\) and \(\bar c\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
, but not onc[]
.length
is the number of elements in each of the vectors.b_shr
andc_shr
are the signed arithmetic rightshifts applied to each element of \(\bar b\) and \(\bar c\) respectively. Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & a_k \leftarrow max(b_k', c_k') \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) and \(\bar c\) are the mantissas of BFP vectors \( \bar{b} \cdot 2^{b\_exp} \) and \(\bar{c} \cdot 2^{c\_exp}\), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + b\_shr = c\_exp + c\_shr\).
The function vect_2vec_prepare() can be used to obtain values for \(a\_exp\), \(b\_shr\) and \(c\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
Warning
For correct operation, this function requires at least 1 bit of headroom in each mantissa vector after the shifts have been applied.
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
b_shr – [in] Rightshift appled to \(\bar b\)
c_shr – [in] Rightshift appled to \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
a
,b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of vector \(\bar a\)

int32_t vect_s32_min(const int32_t b[], const unsigned length)#
Find the minimum value in a 32bit vector.
b[]
represents the 32bit vector \(\bar b\). It must begin at a wordaligned address.length
is the number of elements in \(\bar b\). Operation Performed:
 \[\begin{flalign*} max\{ x_0, x_1, ..., x_{length1} \} && \end{flalign*}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the returned value \(a\) is the 32bit mantissa of floatingpoint value \(a \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp\).
 Parameters:
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
is not wordaligned (See Note: Vector Alignment) Returns:
Minimum value from \(\bar b\)

headroom_t vect_s32_min_elementwise(int32_t a[], const int32_t b[], const int32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Get the elementwise minimum of two 32bit vectors.
a[]
,b[]
andc[]
represent the 32bit mantissa vectors \(\bar a\), \(\bar b\) and \(\bar c\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
, but not onc[]
.length
is the number of elements in each of the vectors.b_shr
andc_shr
are the signed arithmetic rightshifts applied to each element of \(\bar b\) and \(\bar c\) respectively. Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & a_k \leftarrow min(b_k', c_k') \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) and \(\bar c\) are the mantissas of BFP vectors \( \bar{b} \cdot 2^{b\_exp} \) and \(\bar{c} \cdot 2^{c\_exp}\), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + b\_shr = c\_exp + c\_shr\).
The function vect_2vec_prepare() can be used to obtain values for \(a\_exp\), \(b\_shr\) and \(c\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
Warning
For correct operation, this function requires at least 1 bit of headroom in each mantissa vector after the shifts have been applied.
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
b_shr – [in] Rightshift appled to \(\bar b\)
c_shr – [in] Rightshift appled to \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
a
,b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of vector \(\bar a\)

headroom_t vect_s32_mul(int32_t a[], const int32_t b[], const int32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Multiply one 32bit vector elementwise by another.
a[]
,b[]
andc[]
represent the 32bit mantissa vectors \(\bar a\), \(\bar b\) and \(\bar c\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
orc[]
.length
is the number of elements in each of the vectors.b_shr
andc_shr
are the signed arithmetic rightshifts applied to each element of \(\bar b\) and \(\bar c\) respectively. Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & a_k \leftarrow sat_{32}(round(b_k' \cdot c_k' \cdot 2^{30})) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) and \(\bar c\) are the mantissas of BFP vectors \( \bar{b} \cdot 2^{b\_exp} \) and \(\bar{c} \cdot 2^{c\_exp}\), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + c\_exp + b\_shr + c\_shr + 30\).
The function vect_s32_mul_prepare() can be used to obtain values for \(a\_exp\), \(b\_shr\) and \(c\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
b_shr – [in] Rightshift appled to \(\bar b\)
c_shr – [in] Rightshift appled to \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
a
,b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of vector \(\bar a\)

headroom_t vect_s32_macc(int32_t acc[], const int32_t b[], const int32_t c[], const unsigned length, const right_shift_t acc_shr, const right_shift_t b_shr, const right_shift_t c_shr)#
Multiply one 32bit vector elementwise by another, and add the result to an accumulator.
acc[]
represents the 32bit accumulator mantissa vector \(\bar a\). Each \(a_k\) isacc[k]
.b[]
andc[]
represent the 32bit input mantissa vectors \(\bar b\) and \(\bar c\), where each \(b_k\) isb[k]
and each \(c_k\) isc[k]
.Each of the input vectors must begin at a wordaligned address.
length
is the number of elements in each of the vectors.acc_shr
,b_shr
andc_shr
are the signed arithmetic rightshifts applied to input elements \(a_k\), \(b_k\) and \(c_k\). Operation Performed:
 \[\begin{split}\begin{flalign*} & \tilde{b}_k \leftarrow sat_{32}( b_k \cdot 2^{b\_shr} ) \\ & \tilde{c}_k \leftarrow sat_{32}( c_k \cdot 2^{c\_shr} ) \\ & \tilde{a}_k \leftarrow sat_{32}( a_k \cdot 2^{acc\_shr} ) \\ & v_k \leftarrow round( sat_{32}( \tilde{b}_k \cdot \tilde{c}_k \cdot 2^{30} ) ) \\ & a_k \leftarrow sat_{32}( \tilde{a}_k + v_k ) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If inputs \(\bar b\) and \(\bar c\) are the mantissas of BFP vectors \( \bar{b} \cdot 2^{b\_exp} \) and \(\bar{c} \cdot 2^{c\_exp}\), and input \(\bar a\) is the accumulator BFP vector \(\bar{a} \cdot 2^{a\_exp}\), then the output values of \(\bar a\) have the exponent \(2^{a\_exp + acc\_shr}\).
For accumulation to make sense mathematically, \(bc\_sat\) must be chosen such that \( a\_exp + acc\_shr = b\_exp + c\_exp + bc\_sat \).
The function vect_complex_s16_macc_prepare() can be used to obtain values for \(a\_exp\), \(acc\_shr\) and \(bc\_sat\) based on the input exponents \(a\_exp\), \(b\_exp\) and \(c\_exp\) and the input headrooms \(a\_hr\), \(b\_hr\) and \(c\_hr\).
See also
 Parameters:
acc – [inout] Accumulator \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
acc_shr – [in] Signed arithmetic rightshift applied to accumulator elements.
b_shr – [in] Signed arithmetic rightshift applied to elements of \(\bar b\)
c_shr – [in] Signed arithmetic rightshift applied to elements of \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
acc
,b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of the output vector \(\bar a\)

headroom_t vect_s32_nmacc(int32_t acc[], const int32_t b[], const int32_t c[], const unsigned length, const right_shift_t acc_shr, const right_shift_t b_shr, const right_shift_t c_shr)#
Multiply one 32bit vector elementwise by another, and subtract the result from an accumulator.
acc[]
represents the 32bit accumulator mantissa vector \(\bar a\). Each \(a_k\) isacc[k]
.b[]
andc[]
represent the 32bit input mantissa vectors \(\bar b\) and \(\bar c\), where each \(b_k\) isb[k]
and each \(c_k\) isc[k]
.Each of the input vectors must begin at a wordaligned address.
length
is the number of elements in each of the vectors.acc_shr
,b_shr
andc_shr
are the signed arithmetic rightshifts applied to input elements \(a_k\), \(b_k\) and \(c_k\). Operation Performed:
 \[\begin{split}\begin{flalign*} & \tilde{b}_k \leftarrow sat_{32}( b_k \cdot 2^{b\_shr} ) \\ & \tilde{c}_k \leftarrow sat_{32}( c_k \cdot 2^{c\_shr} ) \\ & \tilde{a}_k \leftarrow sat_{32}( a_k \cdot 2^{acc\_shr} ) \\ & v_k \leftarrow round( sat_{32}( \tilde{b}_k \cdot \tilde{c}_k \cdot 2^{30} ) ) \\ & a_k \leftarrow sat_{32}( \tilde{a}_k  v_k ) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If inputs \(\bar b\) and \(\bar c\) are the mantissas of BFP vectors \( \bar{b} \cdot 2^{b\_exp} \) and \(\bar{c} \cdot 2^{c\_exp}\), and input \(\bar a\) is the accumulator BFP vector \(\bar{a} \cdot 2^{a\_exp}\), then the output values of \(\bar a\) have the exponent \(2^{a\_exp + acc\_shr}\).
For accumulation to make sense mathematically, \(bc\_sat\) must be chosen such that \( a\_exp + acc\_shr = b\_exp + c\_exp + bc\_sat \).
The function vect_complex_s16_macc_prepare() can be used to obtain values for \(a\_exp\), \(acc\_shr\) and \(bc\_sat\) based on the input exponents \(a\_exp\), \(b\_exp\) and \(c\_exp\) and the input headrooms \(a\_hr\), \(b\_hr\) and \(c\_hr\).
See also
 Parameters:
acc – [inout] Accumulator \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
acc_shr – [in] Signed arithmetic rightshift applied to accumulator elements.
b_shr – [in] Signed arithmetic rightshift applied to elements of \(\bar b\)
c_shr – [in] Signed arithmetic rightshift applied to elements of \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
acc
,b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of the output vector \(\bar a\)

headroom_t vect_s32_rect(int32_t a[], const int32_t b[], const unsigned length)#
Rectify the elements of a 32bit vector.
a[]
andb[]
represent the 32bit mantissa vectors \(\bar a\) and \(\bar b\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
.length
is the number of elements in each of the vectors. Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow \begin{cases} b_k & b_k > 0 \\ & 0 & b_k \leq 0 \end{cases} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the output vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp\).
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of the output vector \(\bar a\)

headroom_t vect_s32_scale(int32_t a[], const int32_t b[], const unsigned length, const int32_t c, const right_shift_t b_shr, const right_shift_t c_shr)#
Multiply a 32bit vector by a scalar.
a[]
andb[]
represent the 32bit mantissa vectors \(\bar a\) and \(\bar b\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
.length
is the number of elements in each of the vectors.c
is the 32bit scalar \(c\) by which each element of \(\bar b\) is multiplied.b_shr
andc_shr
are the signed arithmetic rightshifts applied to each element of \(\bar b\) and to \(c\). Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & a_k \leftarrow sat_{32}(round(c \cdot b_k' \cdot 2^{30})) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) and \(c\) is the mantissa of floatingpoint value \(c \cdot 2^{c\_exp}\), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + c\_exp + b\_shr + c\_shr + 30\).
The function vect_s32_scale_prepare() can be used to obtain values for \(a\_exp\), \(b\_shr\) and \(c\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
See also
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
c – [in] Scalar to be multiplied by elements of \(\bar b\)
b_shr – [in] Rightshift appled to \(\bar b\)
c_shr – [in] Rightshift applied to \(c\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\)

void vect_s32_set(int32_t a[], const int32_t b, const unsigned length)#
Set all elements of a 32bit vector to the specified value.
a[]
represents the 32bit output vector \(\bar a\).a[]
must begin at a wordaligned address.b
is the new value to set each element of \(\bar a\) to. Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow b \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(b\) is the mantissa of floatingpoint value \(b \cdot 2^{b\_exp}\), then the output vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp\).
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] New value for the elements of \(\bar a\)
length – [in] Number of elements in \(\bar a\)
 Throws ET_LOAD_STORE:
Raised if
a
is not wordaligned (See Note: Vector Alignment)

headroom_t vect_s32_shl(int32_t a[], const int32_t b[], const unsigned length, const left_shift_t b_shl)#
Leftshift the elements of a 32bit vector by a specified number of bits.
a[]
andb[]
represent the 32bit vectors \(\bar a\) and \(\bar b\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
.length
is the number of elements in vectors \(\bar a\) and \(\bar b\).b_shl
is the signed arithmetic leftshift applied to each element of \(\bar b\). Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shl} \rfloor) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(\bar{a} = \bar{b} \cdot 2^{b\_shl}\) and \(a\_exp = b\_exp\).
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shl – [in] Arithmetic leftshift applied to elements of \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\)

headroom_t vect_s32_shr(int32_t a[], const int32_t b[], const unsigned length, const right_shift_t b_shr)#
Rightshift the elements of a 32bit vector by a specified number of bits.
a[]
andb[]
represent the 32bit vectors \(\bar a\) and \(\bar b\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
.length
is the number of elements in vectors \(\bar a\) and \(\bar b\).b_shr
is the signed arithmetic rightshift applied to each element of \(\bar b\). Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(\bar{a} = \bar{b} \cdot 2^{b\_shr}\) and \(a\_exp = b\_exp\).
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shr – [in] Arithmetic rightshift applied to elements of \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\)

headroom_t vect_s32_sqrt(int32_t a[], const int32_t b[], const unsigned length, const right_shift_t b_shr, const unsigned depth)#
Compute the square root of elements of a 32bit vector.
a[]
andb[]
represent the 32bit mantissa vectors \(\bar a\) and \(\bar b\) respectively. Each vector must begin at a wordaligned address. This operation can be performed safely inplace onb[]
.length
is the number of elements in each of the vectors.b_shr
is the signed arithmetic rightshift applied to elements of \(\bar b\).depth
is the number of most significant bits to calculate of each \(a_k\). For example, adepth
value of 8 will only compute the 8 most significant byte of the result, with the remaining 3 bytes as 0. The maximum value for this parameter isVECT_SQRT_S32_MAX_DEPTH
(31). The time cost of this operation is approximately proportional to the number of bits computed. Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & a_k \leftarrow \sqrt{ b_k' } \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \\ & \qquad\text{ where } sqrt() \text{ computes the first } depth \text{ bits of the square root.} && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = (b\_exp + b\_shr  30)/2\).
Note that because exponents must be integers, that means \(b\_exp + b\_shr\) must be even.
The function vect_s32_sqrt_prepare() can be used to obtain values for \(a\_exp\) and \(b\_shr\) based on the input exponent \(b\_exp\) and headroom \(b\_hr\).
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shr – [in] Rightshift appled to \(\bar b\)
depth – [in] Number of bits of each output value to compute
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\)

headroom_t vect_s32_sub(int32_t a[], const int32_t b[], const int32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Subtract one 32bit vector from another.
a[]
,b[]
andc[]
represent the 32bit mantissa vectors \(\bar a\), \(\bar b\) and \(\bar c\) respectively. Each must begin at a wordaligned address. This operation can be performed safely inplace onb[]
orc[]
.length
is the number of elements in each of the vectors.b_shr
andc_shr
are the signed arithmetic rightshifts applied to each element of \(\bar b\) and \(\bar c\) respectively. Operation Performed:
 \[\begin{split}\begin{flalign*} & b_k' = sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' = sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & a_k \leftarrow sat_{32}\!\left( b_k'  c_k' \right) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) and \(\bar c\) are the mantissas of BFP vectors \( \bar{b} \cdot 2^{b\_exp} \) and \(\bar{c} \cdot 2^{c\_exp}\), then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\).
In this case, \(b\_shr\) and \(c\_shr\) must be chosen so that \(a\_exp = b\_exp + b\_shr = c\_exp + c\_shr\). Adding or subtracting mantissas only makes sense if they are associated with the same exponent.
The function vect_s32_sub_prepare() can be used to obtain values for \(a\_exp\), \(b\_shr\) and * \(c\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
See also
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
b_shr – [in] Rightshift appled to \(\bar b\)
c_shr – [in] Rightshift appled to \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
a
,b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\)

int64_t vect_s32_sum(const int32_t b[], const unsigned length)#
Sum the elements of a 32bit vector.
b[]
represents the 32bit mantissa vector \(\bar b\).b[]
must begin at a wordaligned address.length
is the number of elements in \(\bar b\). Operation Performed:
 \[\begin{flalign*} a \leftarrow \sum_{k=0}^{length1} b_k && \end{flalign*}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the returned value \(a\) is the 64bit mantissa of floatingpoint value \(a \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp\).
 Additional Details

Internally, each element accumulates into one of eight 40bit accumulators (which are all used simultaneously) which apply symmetric 40bit saturation logic (with bounds \(\approx 2^{39}\)) with each value added. The saturating arithmetic employed is not associative and no indication is given if saturation occurs at an intermediate step. To avoid the possibility of saturation errors,
length
should be no greater than \(2^{11+b\_hr}\), where \(b\_hr\) is the headroom of \(\bar b\).If the caller’s mantissa vector is longer than that, the full result can be found by calling this function multiple times for partial results on subsequences of the input, and adding the results in user code.
In many situations the caller may have a priori knowledge that saturation is impossible (or very nearly so), in which case this guideline may be disregarded. However, such situations are applicationspecific and are well beyond the scope of this documentation, and as such are left to the user’s discretion.
 Parameters:
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vector \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
is not wordaligned (See Note: Vector Alignment) Returns:
64bit mantissa of the sum, \(a\).

void vect_s32_zip(complex_s32_t a[], const int32_t b[], const int32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Interleave the elements of two vectors into a single vector.
Elements of 32bit input vectors \(\bar b\) and \(\bar c\) are interleaved into 32bit output vector \(\bar a\). Each element of \(\bar b\) has a rightshift of \(b\_shr\) applied, and each element of \(\bar c\) has a rightshift of \(c\_shr\) applied.
Alternatively (and equivalently), this function can be conceived of as taking two real vectors \(\bar b\) and \(\bar c\) and forming a new complex vector \(\bar a\) where \(\bar{a} = \bar{b} + i\cdot\bar{c}\).
If vectors \(\bar b\) and \(\bar c\) each have \(N\) elements, then the resulting \(\bar a\) will have either \(2N\)
int32_t
elements or (equivalently) \(N\)complex_s32_t
elements (and must have space for such).Each element \(b_k\) of \(\bar b\) will end up as end up as element \(a_{2k}\) of \(\bar a\) (with the bitshift applied). Each element \(c_k\) will end up as element \(a_{2k+1}\) of \(\bar a\).
a[]
is the output vector \(\bar a\).b[]
andc[]
are the input vectors \(\bar b\) and \(\bar c\) respectively.a
,b
andc
must each begin at a double wordaligned (8 byte) address. (seeDWORD_ALIGNED
).length
is the number \(N\) ofint32_t
elements in \(\bar b\) and \(\bar c\).b_shr
is the signed arithmetic rightshift applied to elements of \(\bar b\).c_shr
is the signed arithmetic rightshift applied to elements of \(\bar c\). Operation Performed:
 \[\begin{split}\begin{flalign*} & Re{a_{k}} \leftarrow sat_{32}( b_k \cdot 2^{b\_shr} \\ & Im{a_{k}} \leftarrow sat_{32}( c_k \cdot 2^{c\_shr} \\ & \qquad\text{ for }k\in 0\ ...\ (N1) && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] Number of elements \(N\) in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
b_shr – [in] Signed arithmetic rightshift applied to elements of \(\bar b\)
c_shr – [in] Signed arithmetic rightshift applied to elements of \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
a
,b
orc
is not double wordaligned (See Note: Vector Alignment)

void vect_s32_unzip(int32_t a[], int32_t b[], const complex_s32_t c[], const unsigned length)#
Deinterleave the real and imaginary parts of a complex 32bit vector into two separate vectors.
Complex 32bit input vector \(\bar c\) has its real and imaginary parts (which correspond to the even and oddindexed elements, if reinterpreted as an
int32_t
array) split apart to create real 32bit output vectors \(\bar a\) and \(\bar b\), such that \(\bar{a} = Re{\bar{c}}\) and \(\bar{b} = Im{\bar{c}}\).a[]
andb[]
are the real output vectors \(\bar a\) and \(\bar b\) which receive the real and imaginary parts respectively of \(\bar c\).a
andb
must each begin at a wordaligned address.c[]
is the complex input vector \(\bar c\).c
must begin at a double wordaligned address.length
is the number \(N\) ofint32_t
elements in \(\bar a\) and \(\bar b\) and the number ofcomplex_s32_t
in \(\bar c\). Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k = Re\{c_k\} \\ & b_k = Im\{c_k\} \\ & \qquad\text{ for }k\in 0\ ...\ (N1) && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output vector \(\bar a\)
b – [out] Output vector \(\bar b\)
c – [in] Input vector \(\bar c\)
length – [in] The number of elements \(N\) in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Throws ET_LOAD_STORE:
Raised if
c
is not double wordaligned (See Note: Vector Alignment)

headroom_t vect_s32_convolve_valid(int32_t y[], const int32_t x[], const int32_t b_q30[], const unsigned x_length, const unsigned b_length)#
Convolve a 32bit vector with a short kernel.
32bit input vector \(\bar x\) is convolved with a short fixedpoint kernel \(\bar b\) to produce 32bit output vector \(\bar y\). In other words, this function applies the \(K\)thorder FIR filter with coefficients given by \(\bar b\) to the input signal \(\bar x\). The convolution is “valid” in the sense that no output elements are emitted where the filter taps extend beyond the bounds of the input vector, resulting in an output vector \(\bar y\) with fewer elements.
The maximum filter order \(K\) supported by this function is \(7\).
y[]
is the output vector \(\bar y\). If input \(\bar x\) has \(N\) elements, and the filter has \(K\) elements, then \(\bar y\) has \(N2P\) elements, where \(P = \lfloor K / 2 \rfloor\).x[]
is the input vector \(\bar x\) with length \(N\).b_q30[]
is the vector \(\bar b\) of filter coefficients. The coefficients of \(\bar b\) are encoded in a Q2.30 fixedpoint format. The effective value of the \(i\)th coefficient is then \(b_i \cdot 2^{30}\).x_length
is the length \(N\) of \(\bar x\) in elements.b_length
is the length \(K\) of \(\bar b\) in elements (i.e. the number of filter taps).b_length
must be one of \( \{ 1, 3, 5, 7 \} \). Operation Performed:
 \[\begin{split}\begin{flalign*} & y_k \leftarrow \sum_{l=0}^{K1} (x_{(k+l)} \cdot b_l \cdot 2^{30} ) \\ & \qquad\text{ for }k\in 0\ ...\ (N2P) \\ & \qquad\text{ where }P = \lfloor K/2 \rfloor && \end{flalign*}\end{split}\]
 Additional Details

To avoid the possibility of saturating any output elements, \(\bar b\) may be constrained such that \( \sum_{i=0}^{K1} \leftb_i\right \leq 2^{30} \).
This operation can be applied safely inplace on
x[]
.
 Parameters:
y – [out] Output vector \(\bar y\)
x – [in] Input vector \(\bar x\)
b_q30 – [in] Filter coefficient vector \(\bar b\)
x_length – [in] The number of elements \(N\) in vector \(\bar x\)
b_length – [in] The number of elements \(K\) in \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
x
ory
orb_q30
is not wordaligned (See Note: Vector Alignment)

headroom_t vect_s32_convolve_same(int32_t y[], const int32_t x[], const int32_t b_q30[], const unsigned x_length, const unsigned b_length, const pad_mode_e padding_mode)#
Convolve a 32bit vector with a short kernel.
32bit input vector \(\bar x\) is convolved with a short fixedpoint kernel \(\bar b\) to produce 32bit output vector \(\bar y\). In other words, this function applies the \(K\)thorder FIR filter with coefficients given by \(\bar b\) to the input signal \(\bar x\). The convolution mode is “same” in that the input vector is effectively padded such that the input and output vectors are the same length. The padding behavior is one of those given by pad_mode_e.
The maximum filter order \(K\) supported by this function is \(7\).
y[]
andx[]
are the output and input vectors \(\bar y\) and \(\bar x\) respectively.b_q30[]
is the vector \(\bar b\) of filter coefficients. The coefficients of \(\bar b\) are encoded in a Q2.30 fixedpoint format. The effective value of the \(i\)th coefficient is then \(b_i \cdot 2^{30}\).x_length
is the length \(N\) of \(\bar x\) and \(\bar y\) in elements.b_length
is the length \(K\) of \(\bar b\) in elements (i.e. the number of filter taps).b_length
must be one of \( \{ 1, 3, 5, 7 \} \).padding_mode
is one of the values from the pad_mode_e enumeration. The padding mode indicates the filter input values for filter taps that have extended beyond the bounds of the input vector \(\bar x\). See pad_mode_e for a list of supported padding modes and associated behaviors. Operation Performed:
 \[\begin{split}\begin{flalign*} & \tilde{x}_i = \begin{cases} \text{determined by padding mode} & i < 0 \\ \text{determined by padding mode} & i \ge N \\ x_i & otherwise \end{cases} \\ & y_k \leftarrow \sum_{l=0}^{K1} (\tilde{x}_{(k+lP)} \cdot b_l \cdot 2^{30} ) \\ & \qquad\text{ for }k\in 0\ ...\ (N2P) \\ & \qquad\text{ where }P = \lfloor K/2 \rfloor && \end{flalign*}\end{split}\]
 Additional Details

To avoid the possibility of saturating any output elements, \(\bar b\) may be constrained such that \( \sum_{i=0}^{K1} \leftb_i\right \leq 2^{30} \).
Note
Unlike vect_s32_convolve_valid(), this operation cannot be performed safely inplace on
x[]
 Parameters:
y – [out] Output vector \(\bar y\)
x – [in] Input vector \(\bar x\)
b_q30 – [in] Filter coefficient vector \(\bar b\)
x_length – [in] The number of elements \(N\) in vector \(\bar x\)
b_length – [in] The number of elements \(K\) in \(\bar b\)
padding_mode – [in] The padding mode to be applied at signal boundaries
 Throws ET_LOAD_STORE:
Raised if
x
ory
orb_q30
is not wordaligned (See Note: Vector Alignment)

void vect_s32_merge_accs(int32_t a[], const split_acc_s32_t b[], const unsigned length)#
Merge a vector of split 32bit accumulators into a vector of int32_t’s.
Convert a vector of split_acc_s32_t into a vector of
int32_t
. This is useful when a function (e.g.mat_mul_s8_x_s8_yield_s32
) outputs a vector of accumulators in the XS3 VPU’s native split 32bit format, which has the upper half of each accumulator in the first 32 bytes and the lower half in the following 32 bytes.This function is most efficient (in terms of cycles/accumulator) when
length
is a multiple ofIn any case,
length
will be rounded up such that a multiple of 16 accumulators will always be merged.
This function can safely merge accumulators inplace.
 Parameters:
a – [out] Output vector of int32_t
b – [in] Input vector of split_acc_s32_t
length – [in] Number of accumulators to merge
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not wordaligned (See Note: Vector Alignment)

void vect_s32_split_accs(split_acc_s32_t a[], const int32_t b[], const unsigned length)#
Split a vector of
int32_t
’s into a vector ofsplit_acc_s32_t
.Convert a vector of
int32_t
into a vector of split_acc_s32_t, the native format for the XS3 VPU’s 32bit accumulators. This is useful when a function (e.g.mat_mul_s8_x_s8_yield_s32
) takes in a vector of accumulators in that native format.This function is most efficient (in terms of cycles/accumulator) when
length
is a multiple ofIn any case,
length
will be rounded up such that a multiple of 16 accumulators will always be merged.
This function can safely split accumulators inplace.
 Parameters:
a – [out] Output vector of split_acc_s32_t
b – [in] Input vector of int32_t
length – [in] Number of accumulators to merge
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not wordaligned (See Note: Vector Alignment)

void vect_split_acc_s32_shr(split_acc_s32_t a[], const unsigned length, const right_shift_t shr)#
Apply a rightshift to the elements of a 32bit split accumulator vector.
This function may be used in conjunction with chunk_s16_accumulate() or bfp_s16_accumulate() to avoid saturation of accumulators.
This function updates \(\bar a\) inplace.
 Parameters:
a – [inout] Accumulator vector \(\bar a\)
length – [in] Number of elements of \(\bar a\)
shr – [in] Number of bits to rightshift the elements of \(\bar a\)
 Throws ET_LOAD_STORE:
Raised if
a
is not doublewordaligned (See Note: Vector Alignment)

void vect_q30_power_series(int32_t a[], const q2_30 b[], const int32_t c[], const unsigned term_count, const unsigned length)#
Compute a power series sum on a vector of Q2.30 values.
This function is used to compute a power series summation on a vector \(\bar b\). \(\bar b\) contains Q2.30 values. \(\bar c\) is a vector containing coefficients to be multiplied by powers of \(\bar b\), and may have any associated exponent. The output is vector \(\bar a\) and has the same exponent as \(\bar c\).
c[]
is an array with shape(term_count, VPU_INT32_EPV)
, where the second axis contains the same value replicated across allVPU_INT32_EPV
elements. That is,c[k][i] = c[k][j]
fori
andj
in0..(VPU_INT32_EPV1)
. This is for performance reasons. (For the purpose of this explanation, \(\bar c\) is considered to be singledimensional, without redundancy.) Operation Performed:
 \[\begin{split}\begin{flalign*} & b_{k,0} = 2^{30} \\ & b_{k,i} = round\left(\frac{b_{k,i1}\cdot{}b_k}{2^{30}}\right)\qquad\text{for }i \in {1..(N1)} \\ & a_k \leftarrow \sum_{i=0}^{N1} round\left( \frac{b_{k,i}\cdot c_i}{2^{30}} \right) \\ & \qquad\text{for }k \in {0..\mathtt{length}1} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
c – [in] Coefficient vector \(\bar c\)
term_count – [in] Number of power series terms, \(N\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)

void vect_float_s32_log_base(q8_24 a[], const float_s32_t b[], const q2_30 inv_ln_base_q30, const unsigned length)#
Compute the logarithm (in the specified base) of a vector of
float_s32_t
.This function computes the logarithm of a vector \(\bar b\) of
float_s32_t
values. The base of the computed logarithm is given by parameterinv_ln_base_q30
. The result is written to output \(\bar a\), a vector of Q8.24 values.If the desired base is \(D\), then
inv_ln_base_q30
, represented here by \(R\), should be \(\mathtt{Q30}\left(\frac{1}{ln\left(D\right)}\right)\). That is: the inverse of the natural logarithm of the desired base, expressed as a Q2.30 value. Typically the desired base is known at compile time, so this value will usually be a precomputed constant.The resulting \(a_k\) for \(b_k \le 0\) is undefined.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow log_{D}\left(b_k\right) \\ & \qquad\text{for }k \in {0..\mathtt{length}1} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output Q8.24 vector \(\bar a\)
b – [in] Input vector \(\bar b\)
inv_ln_base_q30 – [in] Coefficient \(R\) converting from natural log to desired base \(D\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not double wordaligned (See Note: Vector Alignment)

void vect_float_s32_log(q8_24 a[], const float_s32_t b[], const unsigned length)#
Compute the natural logarithm of a vector of
float_s32_t
.This function computes the natural logarithm of a vector \(\bar b\) of
float_s32_t
values. The result is written to output \(\bar a\), a vector of Q8.24 values.The resulting \(a_k\) for \(b_k \le 0\) is undefined.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow ln\left(b_k\right) \\ & \qquad\text{for }k \in {0..\mathtt{length}1} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output Q8.24 vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not double wordaligned (See Note: Vector Alignment)

void vect_float_s32_log2(q8_24 a[], const float_s32_t b[], const unsigned length)#
Compute the base 2 logarithm of a vector of
float_s32_t
.This function computes the base 2 logarithm of a vector \(\bar b\) of
float_s32_t
values. The result is written to output \(\bar a\), a vector of Q8.24 values.The resulting \(a_k\) for \(b_k \le 0\) is undefined.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow log_2\left(b_k\right) \\ & \qquad\text{for }k \in {0..\mathtt{length}1} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output Q8.24 vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not double wordaligned (See Note: Vector Alignment)

void vect_float_s32_log10(q8_24 a[], const float_s32_t b[], const unsigned length)#
Compute the base 10 logarithm of a vector of
float_s32_t
.This function computes the base 10 logarithm of a vector \(\bar b\) of
float_s32_t
values. The result is written to output \(\bar a\), a vector of Q8.24 values.The resulting \(a_k\) for \(b_k \le 0\) is undefined.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow log_{10}\left(b_k\right) \\ & \qquad\text{for }k \in {0..\mathtt{length}1} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output Q8.24 vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not double wordaligned (See Note: Vector Alignment)

void vect_s32_log_base(q8_24 a[], const int32_t b[], const exponent_t b_exp, const q2_30 inv_ln_base_q30, const unsigned length)#
Compute the logarithm (in the specified base) of a block floatingpoint vector.
This function computes the logarithm of the block floatingpoint vector \(\bar{b}\cdot 2^{b\_exp}\). The base of the computed logarithm is given by parameter
inv_ln_base_q30
. The result is written to output \(\bar a\), a vector of Q8.24 values.If the desired base is \(D\), then
inv_ln_base_q30
, represented here by \(R\), should be \(\mathtt{Q30}\left(\frac{1}{ln\left(D\right)}\right)\). That is: the inverse of the natural logarithm of the desired base, expressed as a Q2.30 value. Typically the desired base is known at compile time, so this value will usually be a precomputed constant.The resulting \(a_k\) for \(b_k \le 0\) is undefined.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow log_{D}\left(b_k\cdot 2^{b\_exp}\right) \\ & \qquad\text{for }k \in {0..\mathtt{length}1} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output Q8.24 vector \(\bar a\)
b – [in] Input mantissa vector \(\bar b\)
b_exp – [in] Exponent associated with \(\bar b\)
inv_ln_base_q30 – [in] Coefficient \(R\) converting from natural log to desired base \(D\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not double wordaligned (See Note: Vector Alignment)

void vect_s32_log(q8_24 a[], const int32_t b[], const exponent_t b_exp, const unsigned length)#
Compute the natural logarithm of a block floatingpoint vector.
This function computes the natural logarithm of the block floatingpoint vector \(\bar{b}\cdot 2^{b\_exp}\). The result is written to output \(\bar a\), a vector of Q8.24 values.
The resulting \(a_k\) for \(b_k \le 0\) is undefined.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow ln\left(b_k\cdot 2^{b\_exp}\right) \\ & \qquad\text{for }k \in {0..\mathtt{length}1} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output Q8.24 vector \(\bar a\)
b – [in] Input mantissa vector \(\bar b\)
b_exp – [in] Exponent associated with \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not double wordaligned (See Note: Vector Alignment)

void vect_s32_log2(q8_24 a[], const int32_t b[], const exponent_t b_exp, const unsigned length)#
Compute the base 2 logarithm of a block floatingpoint vector.
This function computes the base 2 logarithm of the block floatingpoint vector \(\bar{b}\cdot 2^{b\_exp}\). The result is written to output \(\bar a\), a vector of Q8.24 values.
The resulting \(a_k\) for \(b_k \le 0\) is undefined.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow log_2\left(b_k\cdot 2^{b\_exp}\right) \\ & \qquad\text{for }k \in {0..\mathtt{length}1} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output Q8.24 vector \(\bar a\)
b – [in] Input mantissa vector \(\bar b\)
b_exp – [in] Exponent associated with \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not double wordaligned (See Note: Vector Alignment)

void vect_s32_log10(q8_24 a[], const int32_t b[], const exponent_t b_exp, const unsigned length)#
Compute the base 10 logarithm of a block floatingpoint vector.
This function computes the base 10 logarithm of the block floatingpoint vector \(\bar{b}\cdot 2^{b\_exp}\). The result is written to output \(\bar a\), a vector of Q8.24 values.
The resulting \(a_k\) for \(b_k \le 0\) is undefined.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow log_{10}\left(b_k\cdot 2^{b\_exp}\right) \\ & \qquad\text{for }k \in {0..\mathtt{length}1} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output Q8.24 vector \(\bar a\)
b – [in] Input mantissa vector \(\bar b\)
b_exp – [in] Exponent associated with \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
b
ora
is not double wordaligned (See Note: Vector Alignment)

void vect_q30_exp_small(q2_30 a[], const q2_30 b[], const unsigned length)#
Compute \(e^x\) for Q2.30 value near \(0\).
This function computes \(e^{b_k \cdot 2^{30}}\) for each \(b_k\) in input vector \(\bar b\). The results are placed in output vector \(\bar a\) as Q2.30 values.
This function is meant to compute \(e^x\) for values of \(x\) in the interval \( \left[0.5, 0.5\right] \). The error grows quickly outside of this range.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow \frac{ e^{b_k \cdot 2^{30}} }{ 2^{30} } \\ & \qquad\text{for }k \in {0..(\mathtt{length}1)} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)

void vect_s32_to_vect_s16(int16_t a[], const int32_t b[], const unsigned length, const right_shift_t b_shr)#
Convert a 32bit vector to a 16bit vector.
This function converts a 32bit mantissa vector \(\bar b\) into a 16bit mantissa vector \(\bar a\). Conceptually, the output BFP vector \(\bar{a}\cdot 2^{a\_exp}\) represents the same values as the input BFP vector \(\bar{b}\cdot 2^{b\_exp}\), only with a reduced bitdepth.
In most cases \(b\_shr\) should be \(16  b\_hr\), where \(b\_hr\) is the headroom of the 32bit input mantissa vector \(\bar b\).
The output exponent \(a\_exp\) will be given by
\( a\_exp = b\_exp + b\_shr \)
 Parameter Details

a[]
represents the 16bit output mantissa vector \(\bar a\).b[]
represents the 32bit input mantissa vector \(\bar b\).a[]
andb[]
must each begin at a wordaligned address.length
is the number of elements in each of the vectors.b_shr
is the signed arithmetic rightshift applied to elements of \(\bar b\).
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a_k \leftarrow sat_{16}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) && \end{flalign*}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the 32bit mantissas of a BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the resulting vector \(\bar a\) are the 16bit mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + b\_shr\).
See also
 Parameters:
a – [out] Output vector \(\bar a\)
b – [in] Input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shr – [in] Rightshift appled to \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment)

VECT_SQRT_S32_MAX_DEPTH#