Complex 32Bit Block FloatingPoint API#
 group bfp_complex_s32_api
Functions

void bfp_complex_s32_init(bfp_complex_s32_t *a, complex_s32_t *data, const exponent_t exp, const unsigned length, const unsigned calc_hr)#
Initialize a 32bit complex BFP vector.
This function initializes each of the fields of
a
.Unlike
bfp_complex_s16_t
, complex 32bit BFP vectors use a single buffer to store the real and imaginary parts of each mantissa, such that the imaginary part of elementk
follows the real part of elementk
in memory.data
points to the memory buffer used to store elements of the vector, and must be at leastlength * 8
bytes long.exp
is the exponent assigned to the BFP vector. The logical value associated with thek
th complex element of the vector after initialization will be \( \left(data_{2k} + i\cdot data_{2k+1} \right)\cdot2^{exp} \).If
calc_hr
is false,a>hr
is initialized to 0. Otherwise, the headroom of the the BFP vector is calculated and used to initializea>hr
. Parameters:
a – [out] BFP vector struct to initialize
data – [in]
complex_s32_t
buffer used to backa
exp – [in] Exponent of BFP vector
length – [in] Number of elements in BFP vector
calc_hr – [in] Boolean indicating whether the HR of the BFP vector should be calculated

bfp_complex_s32_t bfp_complex_s32_alloc(const unsigned length)#
Dynamically allocate a complex 32bit BFP vector from the heap.
If allocation was unsuccessful, the
data
field of the returned vector will be NULL, and thelength
field will be zero. Otherwise,data
will point to the allocated memory and thelength
field will be the userspecified length. Thelength
argument must not be zero.Neither the BFP exponent, headroom, nor the elements of the allocated mantissa vector are set by this function. To set the BFP vector elements to a known value, use bfp_complex_s32_set() on the retuned BFP vector.
BFP vectors allocated using this function must be deallocated using bfp_complex_s32_dealloc() to avoid a memory leak.
To initialize a BFP vector using static memory allocation, use bfp_complex_s32_init() instead.
See also
Note
Dynamic allocation of BFP vectors relies on allocation from the heap, and offers no guarantees about the execution time. Use of this function in any timecritical section of code is highly discouraged.
 Parameters:
length – [in] The length of the BFP vector to be allocated (in elements)
 Returns:
Complex 32bit BFP vector

void bfp_complex_s32_dealloc(bfp_complex_s32_t *vector)#
Deallocate a complex 32bit BFP vector allocated by bfp_complex_s32_alloc().
Use this function to free the heap memory allocated by bfp_complex_s32_alloc().
BFP vectors whose mantissa buffer was (successfully) dynamically allocated have a flag set which indicates as much. This function can safely be called on any bfp_complex_s32_t which has not had its
flags
ordata
manually manipulated, including:bfp_complex_s32_t resulting from a successful call to bfp_complex_s32_alloc()
bfp_complex_s32_t resulting from an unsuccessful call to bfp_complex_s32_alloc()
bfp_complex_s32_t initialized with a call to bfp_complex_s32_init()
In the latter two cases, this function does nothing. In the former, the
data
,length
andflags
fields ofvector
are cleared to zero.See also
 Parameters:
vector – [in] BFP vector to be deallocated.

void bfp_complex_s32_set(bfp_complex_s32_t *a, const complex_s32_t b, const exponent_t exp)#
Set all elements of a complex 32bit BFP vector to a specified value.
The exponent of
a
is set toexp
, and each element’s mantissa is set tob
.After performing this operation, all elements will represent the same value \(b \cdot 2^{exp}\).
a
must have been initialized (see bfp_complex_s32_init()). Parameters:
a – [out] BFP vector to update
b – [in] New value each complex mantissa is set to
exp – [in] New exponent for the BFP vector

void bfp_complex_s32_use_exponent(bfp_complex_s32_t *a, const exponent_t exp)#
Modify a complex 32bit BFP vector to use a specified exponent.
This function forces complex BFP vector \(\bar A\) to use a specified exponent. The mantissa vector \(\bar a\) will be bitshifted left or right to compensate for the changed exponent.
This function can be used, for example, before calling a fixedpoint arithmetic function to ensure the underlying mantissa vector has the needed Qformat. As another example, this may be useful when communicating with peripheral devices (e.g. via I2S) that require sample data to be in a specified format.
Note that this sets the current encoding, and does not fix the exponent permanently (i.e. subsequent operations may change the exponent as usual).
If the required fixedpoint Qformat is
QX.Y
, whereY
is the number of fractional bits in the resulting mantissas, then the associated exponent (and value for parameterexp
) isY
.a
points to input BFP vector \(\bar A\), with complex mantissa vector \(\bar a\) and exponent \(a\_exp\).a
is updated in place to produce resulting BFP vector \( \tilde{A} \) with complex mantissa vector \( \tilde{a} \) and exponent \(\tilde{a}\_exp\).exp
is \(\tilde{a}\_exp\), the required exponent. \(\Delta{}p = \tilde{a}\_exp  a\_exp\) is the required change in exponent.If \(\Delta{}p = 0\), the BFP vector is left unmodified.
If \(\Delta{}p > 0\), the required exponent is larger than the current exponent and an arithmetic rightshift of \(\Delta{}p\) bits is applied to the mantissas \(\bar a\). When applying a rightshift, precision may be lost by discarding the \(\Delta{}p\) least significant bits.
If \(\Delta{}p < 0\), the required exponent is smaller than the current exponent and a leftshift of \(\Delta{}p\) bits is applied to the mantissas \(\bar a\). When leftshifting, saturation logic will be applied such that any element that can’t be represented exactly with the new exponent will saturate to the 32bit saturation bounds.
The exponent and headroom of
a
are updated by this function. Operation Performed:
 \[\begin{split}\begin{flalign*} & \Delta{}p = \tilde{a}\_exp  a\_exp \\ & \tilde{a_k} \leftarrow sat_{32}( a_k \cdot 2^{\Delta{}p} ) \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{A} \text{ (in elements) } && \end{flalign*}\end{split}\]
 Parameters:
a – [inout] Input BFP vector \(\bar A\) / Output BFP vector \(\tilde{A}\)
exp – [in] The required exponent, \(\tilde{a}\_exp\)

headroom_t bfp_complex_s32_headroom(bfp_complex_s32_t *b)#
Get the headroom of a complex 32bit BFP vector.
The headroom of a complex vector is the number of bits that the real and imaginary parts of each of its elements can be leftshifted without losing any information. It conveys information about the range of values that vector may contain, which is useful for determining how best to preserve precision in potentially lossy block floatingpoint operations.
In a BFP context, headroom applies to mantissas only, not exponents.
In particular, if the complex 32bit mantissa vector \(\bar x\) has \(N\) bits of headroom, then for any element \(x_k\) of \(\bar x\)
\(2^{31N} \le Re\{x_k\} < 2^{31N}\)
and
\(2^{31N} \le Im\{x_k\} < 2^{31N}\)
And for any element \(X_k = x_k \cdot 2^{x\_exp}\) of a complex BFP vector \(\bar X\)
\(2^{31 + x\_exp  N} \le Re\{X_k\} < 2^{31 + x\_exp  N} \)
and
\(2^{31 + x\_exp  N} \le Im\{X_k\} < 2^{31 + x\_exp  N} \)
This function determines the headroom of
b
, updatesb>hr
with that value, and then returnsb>hr
. Parameters:
b – complex BFP vector to get the headroom of
 Returns:
Headroom of complex BFP vector
b

void bfp_complex_s32_shl(bfp_complex_s32_t *a, const bfp_complex_s32_t *b, const left_shift_t b_shl)#
Apply a leftshift to the mantissas of a complex 32bit BFP vector.
Each complex mantissa of input BFP vector \(\bar B\) is leftshifted
b_shl
bits and stored in the corresponding element of output BFP vector \(\bar A\).This operation can be used to add or remove headroom from a BFP vector.
b_shl
is the number of bits that the real and imaginary parts of each mantissa will be leftshifted. This shift is signed and arithmetic, so negative values forb_shl
will rightshift the mantissas.a
andb
must have been initialized (see bfp_complex_s32_init()), and must be the same length.This operation can be performed safely inplace on
b
.Note that this operation bypasses the logic protecting the caller from saturation or underflows. Output values saturate to the symmetric 32bit range (the open interval \((2^{31}, 2^{31})\)). To avoid saturation,
b_shl
should be no greater than the headroom ofb
(b>hr
). Operation Performed:
 \[\begin{split}\begin{flalign*} & Re\{a_k\} \leftarrow sat_{32}( \lfloor Re\{b_k\} \cdot 2^{b\_shl} \rfloor ) \\ & Im\{a_k\} \leftarrow sat_{32}( \lfloor Im\{b_k\} \cdot 2^{b\_shl} \rfloor ) \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B} \\ & \qquad\text{ and } b_k \text{ and } a_k \text{ are the } k\text{th mantissas from } \bar{B}\text{ and } \bar{A}\text{ respectively} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Complex output BFP vector \(\bar A\)
b – [in] Complex input BFP vector \(\bar B\)
b_shl – [in] Signed arithmetic leftshift to be applied to mantissas of \(\bar B\).

void bfp_complex_s32_real_mul(bfp_complex_s32_t *a, const bfp_complex_s32_t *b, const bfp_s32_t *c)#
Multiply a complex 32bit BFP vector elementwise by a real 32bit BFP vector.
Each complex output element \(A_k\) of complex output BFP vector \(\bar A\) is set to the complex product of \(B_k\) and \(C_k\), the corresponding elements of complex input BFP vector \(\bar B\) and real input BFP vector \(\bar C\) respectively.
a
,b
andc
must have been initialized (see bfp_complex_s32_init() and bfp_s32_init()), and must be the same length.This operation can be performed safely inplace on
b
. Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow B_k \cdot C_k \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B}\text{ and }\bar{C} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input real BFP vector \(\bar C\)

void bfp_complex_s32_mul(bfp_complex_s32_t *a, const bfp_complex_s32_t *b, const bfp_complex_s32_t *c)#
Multiply one complex 32bit BFP vector elementwise by another.
Each complex output element \(A_k\) of complex output BFP vector \(\bar A\) is set to the complex product of \(B_k\) and \(C_k\), the corresponding elements of complex input BFP vectors \(\bar B\) and \(\bar C\) respectively.
a
,b
andc
must have been initialized (see bfp_complex_s32_init()), and must be the same length.This operation can be performed safely inplace on
b
orc
. Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow B_k \cdot C_k \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B}\text{ and }\bar{C} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input complex BFP vector \(\bar C\)

void bfp_complex_s32_conj_mul(bfp_complex_s32_t *a, const bfp_complex_s32_t *b, const bfp_complex_s32_t *c)#
Multiply one complex 32bit BFP vector elementwise by the complex conjugate of another.
Each complex output element \(A_k\) of complex output BFP vector \(\bar A\) is set to the complex product of \(B_k\), the corresponding element of complex input BFP vectors \(\bar B\), and \((C_k)^*\), the complex conjugate of the corresponding element of complex input BFP vector \(\bar C\).
a
,b
andc
must have been initialized (see bfp_complex_s32_init()), and must be the same length.This operation can be performed safely inplace on
b
orc
. Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow B_k \cdot (C_k)^* \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B}\text{ and }\bar{C} \\ & \qquad\text{and } (C_k)^* \text{ is the complex conjugate of } C_k && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input complex BFP vector \(\bar C\)

void bfp_complex_s32_macc(bfp_complex_s32_t *acc, const bfp_complex_s32_t *b, const bfp_complex_s32_t *c)#
Multiply one complex 32bit BFP vector by another elementwise and add the result to a third vector.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow A_k + (B_k \cdot C_k) \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B}\text{ and }\bar{C} && \end{flalign*}\end{split}\]
 Parameters:
acc – [inout] Input/Output accumulator complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input complex BFP vector \(\bar C\)

void bfp_complex_s32_nmacc(bfp_complex_s32_t *acc, const bfp_complex_s32_t *b, const bfp_complex_s32_t *c)#
Multiply one complex 32bit BFP vector by another elementwise and subtract the result from a third vector.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow A_k  (B_k \cdot C_k) \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B}\text{ and }\bar{C} && \end{flalign*}\end{split}\]
 Parameters:
acc – [inout] Input/Output accumulator complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input complex BFP vector \(\bar C\)

void bfp_complex_s32_conj_macc(bfp_complex_s32_t *acc, const bfp_complex_s32_t *b, const bfp_complex_s32_t *c)#
Multiply one complex 32bit BFP vector by the complex conjugate of another elementwise and add the result to a third vector.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow A_k + (B_k \cdot C_k^*) \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B}\text{ and }\bar{C} \\ & \qquad\text{and } (C_k)^* \text{ is the complex conjugate of } C_k && \end{flalign*}\end{split}\]
 Parameters:
acc – [inout] Input/Output accumulator complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input complex BFP vector \(\bar C\)

void bfp_complex_s32_conj_nmacc(bfp_complex_s32_t *acc, const bfp_complex_s32_t *b, const bfp_complex_s32_t *c)#
Multiply one complex 32bit BFP vector by the complex conjugate of another elementwise and subtract the result from a third vector.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow A_k  (B_k \cdot C_k^*) \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B}\text{ and }\bar{C} \\ & \qquad\text{and } (C_k)^* \text{ is the complex conjugate of } C_k && \end{flalign*}\end{split}\]
 Parameters:
acc – [inout] Input/Output accumulator complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input complex BFP vector \(\bar C\)

void bfp_complex_s32_real_scale(bfp_complex_s32_t *a, const bfp_complex_s32_t *b, const float_s32_t alpha)#
Multiply a complex 32bit BFP vector by a real scalar.
Each complex output element \(A_k\) of complex output BFP vector \(\bar A\) is set to the complex product of \(B_k\), the corresponding element of complex input BFP vector \(\bar B\), and real scalar \(\alpha\cdot 2^{\alpha\_exp}\), where \(\alpha\) and \(\alpha\_exp\) are the mantissa and exponent respectively of parameter
alpha
.a
andb
must have been initialized (see bfp_complex_s32_init()), and must be the same length.This operation can be performed safely inplace on
b
. Operation Performed:
 \[\begin{flalign*} \bar{A} \leftarrow \bar{B} \cdot \left( \alpha \cdot 2^{\alpha\_exp} \right) && \end{flalign*}\]
 Parameters:
a – [out] Output complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
alpha – [in] Real scalar by which \(\bar B\) is multiplied

void bfp_complex_s32_scale(bfp_complex_s32_t *a, const bfp_complex_s32_t *b, const float_complex_s32_t alpha)#
Multiply a complex 32bit BFP vector by a complex scalar.
Each complex output element \(A_k\) of complex output BFP vector \(\bar A\) is set to the complex product of \(B_k\), the corresponding element of complex input BFP vector \(\bar B\), and complex scalar \(\alpha\cdot 2^{\alpha\_exp}\), where \(\alpha\) and \(\alpha\_exp\) are the complex mantissa and exponent respectively of parameter
alpha
.a
andb
must have been initialized (see bfp_complex_s32_init()), and must be the same length.This operation can be performed safely inplace on
b
. Operation Performed:
 \[\begin{flalign*} \bar{A} \leftarrow \bar{B} \cdot \left( \alpha \cdot 2^{\alpha\_exp} \right) && \end{flalign*}\]
 Parameters:
a – [out] Output complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
alpha – [in] Complex scalar by which \(\bar B\) is multiplied

void bfp_complex_s32_add(bfp_complex_s32_t *a, const bfp_complex_s32_t *b, const bfp_complex_s32_t *c)#
Add one complex 32bit BFP vector to another.
Each complex output element \(A_k\) of complex output BFP vector \(\bar A\) is set to the sum of \(B_k\) and \(C_k\), the corresponding elements of complex input BFP vectors \(\bar B\) and \(\bar C\) respectively.
a
,b
andc
must have been initialized (see bfp_complex_s32_init()), and must be the same length.This operation can be performed safely inplace on
b
orc
. Operation Performed:
 \[\begin{flalign*} \bar{A} \leftarrow \bar{B} + \bar{C} && \end{flalign*}\]
 Parameters:
a – [out] Output complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input complex BFP vector \(\bar C\)

void bfp_complex_s32_add_scalar(bfp_complex_s32_t *a, const bfp_complex_s32_t *b, const float_complex_s32_t c)#
Add a complex scalar to a complex 32bit BFP vector.
Add a real scalar \(c\) to input BFP vector \(\bar B\) and store the result in BFP vector \(\bar A\).
a
, andb
must have been initialized (see bfp_complex_s32_init()), and must be the same length.This operation can be performed safely inplace on
b
. Operation Performed:
 \[\begin{flalign*} \bar{A} \leftarrow \bar{B} + c && \end{flalign*}\]
 Parameters:
a – [out] Output complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input complex scalar \(c\)

void bfp_complex_s32_sub(bfp_complex_s32_t *a, const bfp_complex_s32_t *b, const bfp_complex_s32_t *c)#
Subtract one complex 32bit BFP vector from another.
Each complex output element \(A_k\) of complex output BFP vector \(\bar A\) is set to the difference between \(B_k\) and \(C_k\), the corresponding elements of complex input BFP vectors \(\bar B\) and \(\bar C\) respectively.
a
,b
andc
must have been initialized (see bfp_complex_s32_init()), and must be the same length.This operation can be performed safely inplace on
b
orc
. Operation Performed:
 \[\begin{flalign*} \bar{A} \leftarrow \bar{B}  \bar{C} && \end{flalign*}\]
 Parameters:
a – [out] Output complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)
c – [in] Input complex BFP vector \(\bar C\)

void bfp_complex_s32_to_bfp_complex_s16(bfp_complex_s16_t *a, const bfp_complex_s32_t *b)#
Convert a complex 32bit BFP vector to a complex 16bit BFP vector.
Each complex 16bit output element \(A_k\) of complex output BFP vector \(\bar A\) is set to the value of \(B_k\), the corresponding element of complex 32bit input BFP vector \(\bar B\), with its bitdepth reduced to 16 bits.
a
andb
must have been initialized (see bfp_complex_s16_init() and bfp_complex_s32_init()), and must be the same length.This function preserves as much precision as possible.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \overset{16bit}{\longleftarrow} B_k \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output complex 16bit BFP vector \(\bar A\)
b – [in] Input complex 32bit BFP vector \(\bar B\)

void bfp_complex_s32_squared_mag(bfp_s32_t *a, const bfp_complex_s32_t *b)#
Get the squared magnitude of each element of a complex 32bit BFP vector.
Each element \(A_k\) of real output BFP vector \(\bar A\) is set to the squared magnitude of \(B_k\), the corresponding element of complex input BFP vector \(\bar B\).
a
andb
must have been initialized (see bfp_s32_init() bfp_complex_s32_init()), and must be the same length. Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow B_k \cdot (B_k)^* \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B} \\ & \qquad\text{ and } (B_k)^* \text{ is the complex conjugate of } B_k && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output real BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)

void bfp_complex_s32_mag(bfp_s32_t *a, const bfp_complex_s32_t *b)#
Get the magnitude of each element of a complex 32bit BFP vector.
Each element \(A_k\) of real output BFP vector \(\bar A\) is set to the magnitude of \(B_k\), the corresponding element of complex input BFP vector \(\bar B\).
a
andb
must have been initialized (see bfp_s32_init() bfp_complex_s32_init()), and must be the same length. Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow \left B_k \right \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B} && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output real BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)

float_complex_s64_t bfp_complex_s32_sum(const bfp_complex_s32_t *b)#
Get the sum of elements of a complex 32bit BFP vector.
The elements of complex input BFP vector \(\bar B\) are summed together. The result is a complex 64bit floatingpoint scalar \(a\), which is returned.
b
must have been initialized (see bfp_complex_s32_init()). Operation Performed:
 \[\begin{split}\begin{flalign*} & a \leftarrow \sum_{k=0}^{N1} \left( b_k \cdot 2^{B\_exp} \right) \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B} && \end{flalign*}\end{split}\]
 Parameters:
b – [in] Input complex BFP vector \(\bar B\)
 Returns:
\(a\), the sum of vector \(\bar B\)’s elements

void bfp_complex_s32_conjugate(bfp_complex_s32_t *a, const bfp_complex_s32_t *b)#
Get the complex conjugate of each element of a complex 32bit BFP vector.
Each element \(A_k\) of complex output BFP vector \(\bar A\) is set to the complex conjugate of \(B_k\), the corresponding element of complex input BFP vector \(\bar B\).
 Operation Performed:
 \[\begin{split}\begin{flalign*} & A_k \leftarrow B_k^* \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B}\text{ and }\bar{C} \\ & \qquad\text{and } B_k^* \text{ is the complex conjugate of } B_k && \end{flalign*}\end{split}\]
 Parameters:
a – [out] Output complex BFP vector \(\bar A\)
b – [in] Input complex BFP vector \(\bar B\)

float_s64_t bfp_complex_s32_energy(const bfp_complex_s32_t *b)#
Get the energy of a complex 32bit BFP vector.
The energy of a complex 32bit BFP vector here is the sum of the squared magnitudes of each of the vector’s elements.
 Operation Performed:
 \[\begin{split}\begin{flalign*} & a \leftarrow \sum_{k=0}^{N1} \left( \leftb_k \cdot 2^{B\_exp}\right^2 \right) \\ & \qquad\text{for } k \in 0\ ...\ (N1) \\ & \qquad\text{where } N \text{ is the length of } \bar{B} && \end{flalign*}\end{split}\]
 Parameters:
b – [in] Input complex BFP vector \(\bar B\)
 Returns:
\(a\), the energy of vector \(\bar B\)

void bfp_complex_s32_make(bfp_complex_s32_t *a, const bfp_s32_t *b, const bfp_s32_t *c)#
Create complex 32bit BFP vector from real and imaginary parts.
Create a complex 32bit BFP vector as the sum of a real vector \(\bar B\) and imaginary vector \(\bar{C} i\).
a
,b
andc
must have been initialized (see bfp_complex_s32_init() and bfp_s32_init()), must be the same length.&a>data[0]
must be a doublewordaligned address. Operation Performed:
 \[\begin{flalign*} & \bar{A} \leftarrow \bar{B} + \bar{C} i && \end{flalign*}\]
 Parameters:
a – [out] Complex BFP output vector \(\bar A\)
b – [in] Real BFP input vector \(\bar B\)
c – [in] Real BFP input vector \(\bar C\)

void bfp_complex_s32_real_part(bfp_s32_t *a, const bfp_complex_s32_t *b)#
Extract the real part of a complex 32bit BFP vector.
This function populates the real 32bit BFP vector \(\bar A\) with the real part of complex 32bit BFP vector \(\bar B\).
&b>data[0]
must be a doublewordaligned address. Operation Performed:
 \[\begin{flalign*} & \bar{A} \leftarrow {Real}\{\bar{B}\} && \end{flalign*}\]
 Parameters:
a – [out] Real BFP output vector \(\bar A\)
b – [in] Complex BFP input vector \(\bar B\)

void bfp_complex_s32_imag_part(bfp_s32_t *a, const bfp_complex_s32_t *b)#
Extract the imaginary part of a complex 32bit BFP vector.
This function populates the real 32bit BFP vector \(\bar A\) with the imaginary part of complex 32bit BFP vector \(\bar B\).
&b>data[0]
must be a doublewordaligned address. Operation Performed:
 \[\begin{flalign*} & \bar{A} \leftarrow {Imag}\{\bar{B}\} && \end{flalign*}\]
 Parameters:
a – [out] Real BFP output vector \(\bar A\)
b – [in] Complex BFP input vector \(\bar B\)

void bfp_complex_s32_init(bfp_complex_s32_t *a, complex_s32_t *data, const exponent_t exp, const unsigned length, const unsigned calc_hr)#