Complex 32Bit Vector API#
 group vect_complex_s32_api
Functions

headroom_t vect_complex_s32_add(complex_s32_t a[], const complex_s32_t b[], const complex_s32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Add one complex 32bit vector to another.
a[]
,b[]
andc[]
represent the complex 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
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow Re\{b_k'\} + Re\{c_k'\} \\ & Im\{a_k\} \leftarrow Im\{b_k'\} + Im\{c_k'\} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) and \(\bar c\) are the complex 32bit 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 complex 32bit 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_complex_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] Complex output vector \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
b_shr – [in] Rightshift applied to \(\bar b\)
c_shr – [in] Rightshift applied to \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
a
,b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\).

headroom_t vect_complex_s32_add_scalar(complex_s32_t a[], const complex_s32_t b[], const complex_s32_t c, const unsigned length, const right_shift_t b_shr)#
Add a scalar to a complex 32bit vector.
a[]
andb[]
represent the complex 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 complex 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
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow Re\{b_k'\} + Re\{c\} \\ & Im\{a_k\} \leftarrow Im\{b_k'\} + Im\{c\} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If elements of \(\bar b\) are the complex 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_complex_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_complex_s32_add_scalar_prepare()
, but is not a parameter to this function. The \(c\_shr\) produced byvect_complex_s32_add_scalar_prepare()
is to be applied by the user, and the result passed as inputc
.
See also
 Parameters:
a – [out] Complex output vector \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex input scalar \(c\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shr – [in] Rightshift applied to \(\bar b\)
 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_complex_s32_conj_mul(complex_s32_t a[], const complex_s32_t b[], const complex_s32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Multiply one complex 32bit vector elementwise by the complex conjugate of 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
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow \left( Re\{b_k'\} \cdot Re\{c_k'\} + Im\{b_k'\} \cdot Im\{c_k'\} \right) \cdot 2^{30} \\ & Im\{a_k\} \leftarrow \left( Im\{b_k'\} \cdot Re\{c_k'\}  Re\{b_k'\} \cdot Im\{c_k'\} \right) \cdot 2^{30} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 32bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) and \(c\) is the complex 32bit 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 \(a\_exp = b\_exp + c\_exp + a\_shr\).
The function vect_complex_s32_conj_mul_prepare() can be used to obtain values for \(a\_exp\) and \(a\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
See also
 Parameters:
a – [out] Complex output vector \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
b_shr – [in] Rightshift applied to elements of \(\bar b\).
c_shr – [in] Rightshift applied to elements of \(\bar c\).
 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_complex_s32_headroom(const complex_s32_t x[], const unsigned length)#
Calculate the headroom of a complex 32bit array.
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 a
complex_s32_t
struct is the minimum of the headroom of each of its 32bit fields,re
andim
.The headroom of a
complex_s32_t
array is the minimum of the headroom of each of itscomplex_s32_t
elements.This function efficiently traverses the elements of \(\bar x\) to determine its headroom.
x[]
represents the complex 32bit vector \(\bar x\).x[]
must begin at a wordaligned address.length
is the number of elements inx[]
. Operation Performed
 \[\begin{aligned} min\!\{ HR_{32}\left(x_0\right), HR_{32}\left(x_1\right), ..., HR_{32}\left(x_{length1}\right) \} \end{aligned}\]
 Parameters:
x – [in] Complex input vector \(\bar x\)
length – [in] Number of elements in \(\bar x\)
 Throws ET_LOAD_STORE:
Raised if
x
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of vector \(\bar x\)

headroom_t vect_complex_s32_macc(complex_s32_t acc[], const complex_s32_t b[], const complex_s32_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 complex 32bit vector elementwise by another, and add the result to an accumulator.
acc[]
represents the complex 32bit accumulator mantissa vector \(\bar a\). Each \(a_k\) isacc[k]
.b[]
andc[]
represent the complex 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
 \[\begin{split}\begin{aligned} & \tilde{b}_k \leftarrow sat_{32}( b_k \cdot 2^{b\_shr} ) \\ & \tilde{c}_k \leftarrow sat_{32}( c_k \cdot 2^{c\_shr} ) \\ & \tilde{a}_k \leftarrow sat_{32}( a_k \cdot 2^{acc\_shr} ) \\ & v_k \leftarrow round( sat_{32}( ( Re\{\tilde{b}_k\} \cdot Re\{\tilde{c}_k\}  Im\{\tilde{b}_k\} \cdot Im\{\tilde{c}_k\} ) \cdot 2^{30}) ) \\ & s_k \leftarrow round( sat_{32}( ( Im\{\tilde{b}_k\} \cdot Re\{\tilde{c}_k\} + Re\{\tilde{b}_k\} \cdot Im\{\tilde{c}_k\} ) \cdot 2^{30}) ) \\ & Re\{a_k\} \leftarrow sat_{32}( Re\{\tilde{a}_k\} + v_k ) \\ & Im\{a_k\} \leftarrow sat_{32}( Im\{\tilde{a}_k\} + s_k ) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 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 \( a\_exp + acc\_shr = b\_exp + c\_exp + b\_shr + c\_shr \).
The function vect_complex_s32_macc_prepare() can be used to obtain values for \(a\_exp\), \(acc\_shr\), \(b\_shr\) and \(c\_shr\) 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] Complex accumulator \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex 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_complex_s32_nmacc(complex_s32_t acc[], const complex_s32_t b[], const complex_s32_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 complex 32bit vector elementwise by another, and subtract the result from an accumulator.
acc[]
represents the complex 32bit accumulator mantissa vector \(\bar a\). Each \(a_k\) isacc[k]
.b[]
andc[]
represent the complex 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
 \[\begin{split}\begin{aligned} & \tilde{b}_k \leftarrow sat_{32}( b_k \cdot 2^{b\_shr} ) \\ & \tilde{c}_k \leftarrow sat_{32}( c_k \cdot 2^{c\_shr} ) \\ & \tilde{a}_k \leftarrow sat_{32}( a_k \cdot 2^{acc\_shr} ) \\ & v_k \leftarrow round( sat_{32}( ( Re\{\tilde{b}_k\} \cdot Re\{\tilde{c}_k\}  Im\{\tilde{b}_k\} \cdot Im\{\tilde{c}_k\} ) \cdot 2^{30}) ) \\ & s_k \leftarrow round( sat_{32}( ( Im\{\tilde{b}_k\} \cdot Re\{\tilde{c}_k\} + Re\{\tilde{b}_k\} \cdot Im\{\tilde{c}_k\} ) \cdot 2^{30}) ) \\ & Re\{a_k\} \leftarrow sat_{32}( Re\{\tilde{a}_k\}  v_k ) \\ & Im\{a_k\} \leftarrow sat_{32}( Im\{\tilde{a}_k\}  s_k ) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 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 \( a\_exp + acc\_shr = b\_exp + c\_exp + b\_shr + c\_shr \).
The function vect_complex_s32_macc_prepare() can be used to obtain values for \(a\_exp\), \(acc\_shr\), \(b\_shr\) and \(c\_shr\) 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] Complex accumulator \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex 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_complex_s32_conj_macc(complex_s32_t acc[], const complex_s32_t b[], const complex_s32_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 complex 32bit vector elementwise by the complex conjugate of another, and add the result to an accumulator.
acc[]
represents the complex 32bit accumulator mantissa vector \(\bar a\). Each \(a_k\) isacc[k]
.b[]
andc[]
represent the complex 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
 \[\begin{split}\begin{aligned} & \tilde{b}_k \leftarrow sat_{32}( b_k \cdot 2^{b\_shr} ) \\ & \tilde{c}_k \leftarrow sat_{32}( c_k \cdot 2^{c\_shr} ) \\ & \tilde{a}_k \leftarrow sat_{32}( a_k \cdot 2^{acc\_shr} ) \\ & v_k \leftarrow round( sat_{32}( ( Re\{\tilde{b}_k\} \cdot Re\{\tilde{c}_k\} + Im\{\tilde{b}_k\} \cdot Im\{\tilde{c}_k\} ) \cdot 2^{30}) ) \\ & s_k \leftarrow round( sat_{32}( ( Im\{\tilde{b}_k\} \cdot Re\{\tilde{c}_k\}  Re\{\tilde{b}_k\} \cdot Im\{\tilde{c}_k\} ) \cdot 2^{30}) ) \\ & Re\{a_k\} \leftarrow sat_{32}( Re\{\tilde{a}_k\} + v_k ) \\ & Im\{a_k\} \leftarrow sat_{32}( Im\{\tilde{a}_k\} + s_k ) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 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 \( a\_exp + acc\_shr = b\_exp + c\_exp + b\_shr + c\_shr \).
The function vect_complex_s32_conj_macc_prepare() can be used to obtain values for \(a\_exp\), \(acc\_shr\), \(b\_shr\) and \(c\_shr\) 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] Complex accumulator \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex 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_complex_s32_conj_nmacc(complex_s32_t acc[], const complex_s32_t b[], const complex_s32_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 complex 32bit vector elementwise by the complex conjugate of another, and subtract the result from an accumulator.
acc[]
represents the complex 32bit accumulator mantissa vector \(\bar a\). Each \(a_k\) isacc[k]
.b[]
andc[]
represent the complex 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
 \[\begin{split}\begin{aligned} & \tilde{b}_k \leftarrow sat_{32}( b_k \cdot 2^{b\_shr} ) \\ & \tilde{c}_k \leftarrow sat_{32}( c_k \cdot 2^{c\_shr} ) \\ & \tilde{a}_k \leftarrow sat_{32}( a_k \cdot 2^{acc\_shr} ) \\ & v_k \leftarrow round( sat_{32}( ( Re\{\tilde{b}_k\} \cdot Re\{\tilde{c}_k\} + Im\{\tilde{b}_k\} \cdot Im\{\tilde{c}_k\} ) \cdot 2^{30}) ) \\ & s_k \leftarrow round( sat_{32}( ( Im\{\tilde{b}_k\} \cdot Re\{\tilde{c}_k\}  Re\{\tilde{b}_k\} \cdot Im\{\tilde{c}_k\} ) \cdot 2^{30}) ) \\ & Re\{a_k\} \leftarrow sat_{32}( Re\{\tilde{a}_k\}  v_k ) \\ & Im\{a_k\} \leftarrow sat_{32}( Im\{\tilde{a}_k\}  s_k ) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 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 \( a\_exp + acc\_shr = b\_exp + c\_exp + b\_shr + c\_shr \).
The function vect_complex_s32_conj_nmacc_prepare() can be used to obtain values for \(a\_exp\), \(acc\_shr\), \(b\_shr\) and \(c\_shr\) 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] Complex accumulator \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex 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_complex_s32_mag(int32_t a[], const complex_s32_t b[], const unsigned length, const right_shift_t b_shr, const complex_s32_t *rot_table, const unsigned table_rows)#
Compute the magnitude of each element of a complex 32bit vector.
a[]
represents the real 32bit output mantissa vector \(\bar a\).b[]
represents the complex 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 \(\bar b\).rot_table
must point to a precomputed table of complex vectors used in calculating the magnitudes.table_rows
is the number of rows in the table. This library is distributed with a default version of the required rotation table. The following symbols can be used to refer to it in user code:const extern unsigned rot_table32_rows; const extern complex_s32_t rot_table32[30][4];
Faster computation (with reduced precision) can be achieved by generating a smaller version of the table. A python script is provided to generate this table.
 Todo:
Point to documentation page on generating this table.
 Operation Performed
 \[\begin{split}\begin{aligned} & v_k \leftarrow b_k \cdot 2^{b\_shr} \\ & a_k \leftarrow \sqrt { {\left( Re\{v_k\} \right)}^2 + {\left( Im\{v_k\} \right)}^2 } \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 32bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \), then the resulting vector \(\bar a\) are the real 32bit mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + b\_shr\).
The function vect_complex_s32_mag_prepare() can be used to obtain values for \(a\_exp\) and \(b\_shr\) based on the input exponent \(b\_exp\) and headroom \(b\_hr\).
See also
 Parameters:
a – [out] Real output vector \(\bar a\)
b – [in] Complex input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shr – [in] Rightshift appled to \(\bar b\)
rot_table – [in] Precomputed rotation table required for calculating magnitudes
table_rows – [in] Number of rows in
rot_table
 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_complex_s32_mul(complex_s32_t a[], const complex_s32_t b[], const complex_s32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Multiply one complex 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
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow \left( Re\{b_k'\} \cdot Re\{c_k'\}  Im\{b_k'\} \cdot Im\{c_k'\} \right) \cdot 2^{30} \\ & Im\{a_k\} \leftarrow \left( Im\{b_k'\} \cdot Re\{c_k'\} + Re\{b_k'\} \cdot Im\{c_k'\} \right) \cdot 2^{30} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 32bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) and \(c\) is the complex 32bit 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 \(a\_exp = b\_exp + c\_exp + b\_shr + c\_shr\).
The function vect_complex_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 \(c\_hr\).
See also
 Parameters:
a – [out] Complex output vector \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex 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_complex_s32_real_mul(complex_s32_t a[], const complex_s32_t b[], const int32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Multiply a complex 32bit vector elementwise by a real 32bit vector.
a[]
andb[]
represent the complex 32bit mantissa vectors \(\bar a\) and \(\bar b\) respectively.c[]
represents the real 32bit mantissa vector \(\bar c\).a[]
,b[]
, andc[]
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.b_shr
andc_shr
are the signed arithmetic rightshifts applied to each element of \(\bar b\) and \(\bar c\) respectively. Operation Performed
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow \left( Re\{b_k'\} \cdot c_k' \right) \cdot 2^{30} \\ & Im\{a_k\} \leftarrow \left( Im\{b_k'\} \cdot c_k' \right) \cdot 2^{30} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 32bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) and \(c\) is the complex 32bit 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 \(a\_exp = b\_exp + c\_exp + b\_shr + c\_shr\).
The function vect_complex_s32_real_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 \(c\_hr\).
See also
 Parameters:
a – [out] Complex output vector \(\bar a\).
b – [in] Complex input vector \(\bar b\).
c – [in] Real 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_complex_s32_real_scale(complex_s32_t a[], const complex_s32_t b[], const int32_t c, const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Multiply a complex 32bit vector by a real scalar.
a[]
andb[]
represent the complex 32bit mantissa vectors \(\bar a\) and \(\bar b\) respectively.c
represents the real 32bit scale factor \(c\).a[]
andb[]
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.b_shr
andc_shr
are the signed arithmetic rightshift applied to each element of \(\bar b\) and to \(c\). Operation Performed
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow Re\{b_k'\} \cdot c \\ & Im\{a_k\} \leftarrow Im\{b_k'\} \cdot c \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 16bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) and \(c\) is the complex 16bit 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 \(a\_exp = b\_exp + c\_exp + b\_shr + c\_shr\).
The function vect_complex_s32_real_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 \(c\_hr\).
 Parameters:
a – [out] Complex output vector \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\), and \(\bar c\)
b_shr – [in] Rightshift applied 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 the output vector \(\bar a\).

headroom_t vect_complex_s32_scale(complex_s32_t a[], const complex_s32_t b[], const int32_t c_real, const int32_t c_imag, const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Multiply a complex 32bit vector by a complex 32bit scalar.
a[]
andb[]
represent the complex 32bit mantissa vectors \(\bar a\) and \(\bar b\) respectively.c
represents the complex 32bit scale factor \(c\).a[]
andb[]
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.b_shr
andc_shr
are the signed arithmetic rightshifts applied to each element of \(\bar b\) and to \(c\). Operation Performed
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow \left( Re\{v_k\} \cdot Re\{c\}  Im\{v_k\} \cdot Im\{c\} \right) \cdot 2^{30} \\ & Im\{a_k\} \leftarrow \left( Re\{v_k\} \cdot Im\{c\} + Im\{v_k\} \cdot Re\{c\} \right) \cdot 2^{30} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 32bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) and \(c\) is the complex 32bit 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 \(a\_exp = b\_exp + c\_exp + b\_shr + c\_shr\).
The function vect_complex_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] Complex output vector \(\bar a\).
b – [in] Complex input vector \(\bar b\).
c_real – [in] Real part of \(c\)
c_imag – [in] Imaginary part of \(c\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\).
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 the output vector \(\bar a\).

void vect_complex_s32_set(complex_s32_t a[], const int32_t b_real, const int32_t b_imag, const unsigned length)#
Set each element of a complex 32bit vector to a specified value.
a[]
represents a complex 32bit vector \(\bar a\).a[]
must begin at a wordaligned address.b_real
andb_imag
are the real and imaginary parts to which each element will be set.length
is the number of elements ina[]
. Operation Performed
 \[\begin{split}\begin{aligned} & a_k \leftarrow b\_real + j\cdot b\_imag \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \\ & \qquad\text{ where } j^2 = 1 \end{aligned}\end{split}\]
 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] Complex output vector \(\bar a\)
b_real – [in] Value to set real part of elements of \(\bar a\) to
b_imag – [in] Value to set imaginary part of elements of \(\bar a\) to
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_complex_s32_shl(complex_s32_t a[], const complex_s32_t b[], const unsigned length, const left_shift_t b_shl)#
Leftshift each element of a complex 32bit vector by a specified number of bits.
a[]
andb[]
represent the complex 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 \(\bar a\) and \(\bar b\).b_shl
is the signed arithmetic leftshift applied to each element of \(\bar b\). Operation Performed
 \[\begin{split}\begin{aligned} & Re\{a_k\} \leftarrow sat_{32}(\lfloor Re\{b_k\} \cdot 2^{b\_shl} \rfloor) \\ & Im\{a_k\} \leftarrow sat_{32}(\lfloor Im\{b_k\} \cdot 2^{b\_shl} \rfloor) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 32bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \), then the resulting vector \(\bar a\) are the complex 32bit 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] Complex output vector \(\bar a\)
b – [in] Complex input vector \(\bar b\)
length – [in] Number of elements in vector \(\bar b\)
b_shl – [in] Leftshift applied to \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s32_shr(complex_s32_t a[], const complex_s32_t b[], const unsigned length, const right_shift_t b_shr)#
Rightshift each element of a complex 32bit vector by a specified number of bits.
a[]
andb[]
represent the complex 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 \(\bar a\) and \(\bar b\).b_shr
is the signed arithmetic rightshift applied to each element of \(\bar b\). Operation Performed
 \[\begin{split}\begin{aligned} & Re\{a_k\} \leftarrow sat_{32}(\lfloor Re\{b_k\} \cdot 2^{b\_shr} \rfloor) \\ & Im\{a_k\} \leftarrow sat_{32}(\lfloor Im\{b_k\} \cdot 2^{b\_shr} \rfloor) \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 32bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \), then the resulting vector \(\bar a\) are the complex 32bit 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] Complex output vector \(\bar a\)
b – [in] Complex input vector \(\bar b\)
length – [in] Number of elements in vector \(\bar b\)
b_shr – [in] Rightshift applied to \(\bar b\)
 Throws ET_LOAD_STORE:
Raised if
a
orb
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s32_squared_mag(int32_t a[], const complex_s32_t b[], const unsigned length, const right_shift_t b_shr)#
Computes the squared magnitudes of elements of a complex 32bit vector.
a[]
represents the complex 32bit mantissa vector \(\bar a\).b[]
represents the real 32bit mantissa vector \(\bar b\). Each must begin at a wordaligned address.length
is the number of elements in each of the vectors.b_shr
is the signed arithmetic rightshift appled to each element of \(\bar b\). Operation Performed
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & a_k \leftarrow ((Re\{b_k'\})^2 + (Im\{b_k'\})^2)\cdot 2^{30} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 32bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \), then the resulting vector \(\bar a\) are the real 32bit mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = 2 \cdot (b\_exp + b\_shr)\).
The function vect_complex_s32_squared_mag_prepare() can be used to obtain values for \(a\_exp\) and \(b\_shr\) based on the input exponent \(b\_exp\) and headroom \(b\_hr\).
See also
 Parameters:
a – [out] Complex output vector \(\bar a\)
b – [in] Complex 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
is not double wordaligned orb
is not wordaligned (See Note: Vector Alignment)

headroom_t vect_complex_s32_sub(complex_s32_t a[], const complex_s32_t b[], const complex_s32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#
Subtract one complex 32bit vector from another.
a[]
,b[]
andc[]
represent the complex 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
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{32}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{32}(\lfloor c_k \cdot 2^{c\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow Re\{b_k'\}  Re\{c_k'\} \\ & Im\{a_k\} \leftarrow Im\{b_k'\}  Im\{c_k'\} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) and \(\bar c\) are the complex 32bit 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 complex 32bit 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_complex_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] Complex output vector \(\bar a\)
b – [in] Complex input vector \(\bar b\)
c – [in] Complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\), \(\bar b\) and \(\bar c\)
b_shr – [in] Rightshift applied to \(\bar b\)
c_shr – [in] Rightshift applied to \(\bar c\)
 Throws ET_LOAD_STORE:
Raised if
a
,b
orc
is not wordaligned (See Note: Vector Alignment) Returns:
Headroom of output vector \(\bar a\).

void vect_complex_s32_sum(complex_s64_t *a, const complex_s32_t b[], const unsigned length, const right_shift_t b_shr)#
Compute the sum of elements of a complex 32bit vector.
a
is the complex 64bit mantissa of the resulting sum.b[]
represents the complex 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 unsigned arithmetic rightshift appled to each element of \(\bar b\).b_shr
cannot be negative. Operation Performed
 \[\begin{split}\begin{aligned} & b_k' \leftarrow b_k \cdot 2^{b\_shr} \\ & Re\{a\} \leftarrow \sum_{k=0}^{length1} \left( Re\{b_k'\} \right) \\ & Im\{a\} \leftarrow \sum_{k=0}^{length1} \left( Im\{b_k'\} \right) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then \(a\) is the complex 64bit mantissa of floatingpoint value \(a \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + b\_shr\).
The function vect_complex_s32_sum_prepare() can be used to obtain values for \(a\_exp\) and \(b\_shr\) based on the input exponents \(b\_exp\) and \(c\_exp\) and the input headrooms \(b\_hr\) and \(c\_hr\).
 Additional Details

Internally the sum accumulates into four separate complex 40bit accumulators. These accumulators apply symmetric 40bit saturation logic (with bounds \(\pm 2^{39}1\)) with each added element. At the end, the 4 accumulators are summed together into the 64bit fields of
a
. No saturation logic is applied at this final step.In the most extreme case, each \(b_k\) may be \(2^{31}\). \(256\) of these added into the same accumulator is \(2^{39}\) which would saturate to \(2^{39}+1\), introducing 1 LSb of error (which may or may not be acceptable given a particular circumstance). The final result for each part then may be as large as \(4\cdot(2^{39}+1) = 2^{41}+4 \), each fitting into a 42bit signed integer.
See also
 Parameters:
a – [out] Complex sum \(a\)
b – [in] Complex input vector \(\bar b\).
length – [in] Number of elements in vector \(\bar b\).
b_shr – [in] Rightshift appled to \(\bar b\).
 Throws ET_LOAD_STORE:
Raised if
b
is not wordaligned (See Note: Vector Alignment)

void vect_complex_s32_tail_reverse(complex_s32_t x[], const unsigned length)#
Reverses the order of the tail of a complex 32bit vector.
Reverses the order of elements in the tail of the complex 32bit vector \(\bar x\). The tail of \(\bar x\), in this context, is all elements of \(\bar x\) except for \(x_0\). In other words, the first element \(x_0\) remains where it is, and the remaining \(length1\) elements are rearranged to have their order reversed.
This function is used when performing a forward or inverse FFT on a single sequence of real values (i.e. the mono FFT), and operates inplace on
x[]
. Parameter Details

x[]
represents the complex 32bit vector \(\bar x\), which is both an input to and an output of this function.x[]
must begin at a wordaligned address.length
is the number of elements in \(\bar x\).
 Operation Performed
 \[\begin{split}\begin{aligned} & x_0 \leftarrow x_0 \\ & x_k \leftarrow x_{length  k} \\ & \qquad\text{ for }k\in 1\ ...\ (length1) \end{aligned}\end{split}\]
See also
 Parameters:
x – [inout] Complex vector to have its tail reversed.
length – [in] Number of elements in \(\bar x\)
 Throws ET_LOAD_STORE:
Raised if
x
is not wordaligned (See Note: Vector Alignment)

headroom_t vect_complex_s32_conjugate(complex_s32_t a[], const complex_s32_t b[], const unsigned length)#
Get the complex conjugate of a complex 32bit vector.
The complex conjugate of a complex scalar \(z = x + yi\) is \(z^* = x  yi\). This function computes the complex conjugate of each element of \(\bar b\) (negates the imaginary part of each element) and places the result in \(\bar a\).
a[]
is the complex 32bit output vector \(\bar a\).b[]
is the complex 32bit input vector \(\bar b\).Both
a
andb
must point to wordaligned addresses.length
is the number of elements in \(\bar a\) and \(\bar b\). Operation Performed
 \[\begin{split}\begin{aligned} & Re\{a_k\} \leftarrow Re\{b_k\} \\ & Im\{a_k\} \leftarrow  Im\{b_k\} \\ & \qquad\text{ for }k\in 1\ ...\ (length1) \end{aligned}\end{split}\]
 Parameters:
a – [out] Complex 32bit output vector \(\bar a\)
b – [in] Complex 32bit 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 \(\bar a\).

void vect_complex_s32_to_vect_complex_s16(int16_t a_real[], int16_t a_imag[], const complex_s32_t b[], const unsigned length, const right_shift_t b_shr)#
Convert a complex 32bit vector into a complex 16bit vector.
This function converts a complex 32bit mantissa vector \(\bar b\) into a complex 16bit mantissa vector \(\bar a\). Conceptually, the output BFP vector \(\bar{a}\cdot 2^{a\_exp}\) represents the same value 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 then be given by
\( a\_exp = b\_exp + b\_shr \)
 Parameter Details

a_real[]
anda_imag[]
together represent the complex 16bit output mantissa vector \(\bar a\), with the real part of each \(a_k\) going ina_real[]
and the imaginary part going ina_imag[]
.b[]
represents the complex 32bit mantissa vector \(\bar b\).a_real[]
,a_imag[]
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
 \[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{16}(\lfloor b_k \cdot 2^{b\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow Re\{b_k'\} \\ & Im\{a_k\} \leftarrow Im\{b_k'\} \\ & \qquad\text{ for }k\in 0\ ...\ (length1) \end{aligned}\end{split}\]
 Block FloatingPoint

If \(\bar b\) are the complex 32bit mantissas of a BFP vector \(\bar{b} \cdot 2^{b\_exp}\), then the resulting vector \(\bar a\) are the complex 16bit mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\), where \(a\_exp = b\_exp + b\_shr\).
 Parameters:
a_real – [out] Real part of complex output vector \(\bar a\).
a_imag – [out] Imaginary part of complex output vector \(\bar a\).
b – [in] Complex 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_real
,a_imag
orb
are not wordaligned (See Note: Vector Alignment)

headroom_t vect_complex_s32_add(complex_s32_t a[], const complex_s32_t b[], const complex_s32_t c[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#