Complex 16-bit vector API#

group vect_complex_s16_api

Functions

headroom_t vect_complex_s16_add(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real[], const int16_t c_imag[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#

Add one complex 16-bit vector to another.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

c_real[] and c_imag[] together represent the complex 16-bit input mantissa vector \(\bar c\) . Each \(Re\{c_k\}\) is c_real[k], and each \(Im\{c_k\}\) is c_imag[k].

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[], b_imag[], c_real[] and c_imag[].

length is the number of elements in each of the vectors.

b_shr and c_shr are the signed arithmetic right-shifts applied to each element of \(\bar b\) and \(\bar c\) respectively.

Operation Performed

\[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{16}(\lfloor b_k \cdot 2^{-b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{16}(\lfloor c_k \cdot 2^{-c\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow Re\{b_k'\} + Re\{c_k'\} \\ & Im\{a_k\} \leftarrow Im\{b_k'\} + Im\{c_k'\} \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If \(\bar b\) and \(\bar c\) are the complex 16-bit 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 16-bit 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_s16_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

vect_complex_s16_add_prepare

Parameters:

a_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input vector \(\bar c\)
c_imag – [in] Imaginary part of complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\) , \(\bar b\) and \(\bar c\)
b_shr – [in] Right-shift applied to \(\bar b\)
c_shr – [in] Right-shift applied to \(\bar c\)

Throws ET_LOAD_STORE:

Raised if `a_real`, `a_imag`, `b_real`, `b_imag`, `c_real` or `c_imag` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of output vector \(\bar a\) .

headroom_t vect_complex_s16_add_scalar(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const complex_s16_t c, const unsigned length, const right_shift_t b_shr)#

Add a scalar to a complex 16-bit vector.

a[] and b[]represent the complex 16-bit mantissa vectors \(\bar a\) and \(\bar b\) respectively. Each must begin at a word-aligned address. This operation can be performed safely in-place on b[].

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 right-shift applied to each element of \(\bar b\) .

Operation Performed

\[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{16}(\lfloor b_k \cdot 2^{-b\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow Re\{b_k'\} + Re\{c\} \\ & Im\{a_k\} \leftarrow Im\{b_k'\} + Im\{c\} \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If elements of \(\bar b\) are the complex mantissas of BFP vector \( \bar{b} \cdot 2^{b\_exp}\) , and \(c\) is the mantissa of floating-point value \(c \cdot 2^{c\_exp}\) , then the resulting vector \(\bar a\) are the mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\) .

The function vect_complex_s16_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_s16_add_scalar_prepare(), but is not a parameter to this function. The \(c\_shr\) produced by vect_complex_s16_add_scalar_prepare() is to be applied by the user, and the result passed as input c.

See also

vect_complex_s16_add_scalar_prepare

Parameters:

a_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of 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] Right-shift applied to \(\bar b\)

Throws ET_LOAD_STORE:

Raised if `a` or `b` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of output vector \(\bar a\) .

headroom_t vect_complex_s16_conj_mul(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real[], const int16_t c_imag[], const unsigned length, const right_shift_t a_shr)#

Multiply one complex 16-bit vector element-wise by the complex conjugate of another.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

c_real[] and c_imag[] together represent the complex 16-bit input mantissa vector \(\bar c\) . Each \(Re\{c_k\}\) is c_real[k], and each \(Im\{c_k\}\) is c_imag[k].

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[], b_imag[], c_real[] and c_imag[].

length is the number of elements in each of the vectors.

a_shr is the unsigned arithmetic right-shift applied to the 32-bit accumulators holding the penultimate results.

Operation Performed

\[\begin{split}\begin{aligned} & v_k = \leftarrow Re\{b_k\} \cdot Re\{c_k\} + Im\{b_k\} \cdot Im\{c_k\} \\ & s_k = \leftarrow Im\{b_k\} \cdot Re\{c_k\} - Re\{b_k\} \cdot Im\{c_k\} \\ & Re\{a_k\} \leftarrow round( sat_{16}( v_k \cdot 2^{-a\_shr} ) ) \\ & Im\{a_k\} \leftarrow round( sat_{16}( s_k \cdot 2^{-a\_shr} ) ) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If \(\bar b\) are the complex 16-bit mantissas of a BFP vector \(\bar{b} \cdot 2^{b\_exp}\) and \(c\) is the complex 16-bit mantissa of floating-point 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_s16_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

vect_complex_s16_mul_prepare

Parameters:

a_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input vector \(\bar c\)
c_imag – [in] Imaginary part of complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\) , \(\bar b\) and \(\bar c\)
a_shr – [in] Right-shift applied to 32-bit intermediate results.

Throws ET_LOAD_STORE:

Raised if `a_real`, `a_imag`, `b_real`, `b_imag`, `c_real` or `c_imag` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s16_headroom(const int16_t b_real[], const int16_t b_imag[], const unsigned length)#

Calculate the headroom of a complex 16-bit array.

The headroom of an N-bit integer is the number of bits that the integer’s value may be left-shifted without any information being lost. Equivalently, it is one less than the number of leading sign bits.

The headroom of a complex_s16_t struct is the minimum of the headroom of each of its 16-bit fields, re and im.

The headroom of a complex_s16_t array is the minimum of the headroom of each of its complex_s16_t elements.

This function efficiently traverses the elements of \(\bar x\) to determine its headroom.

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) .

length is the number of elements in b_real[] and b_imag[].

Operation Performed

\[\begin{aligned} min\!\{ HR_{16}\left(x_0\right), HR_{16}\left(x_1\right), ..., HR_{16}\left(x_{length-1}\right) \} \end{aligned}\]

Parameters:

b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
length – [in] Number of elements in \(\bar x\)

Returns:

Headroom of vector \(\bar x\)

headroom_t vect_complex_s16_mag(int16_t a[], const int16_t b_real[], const int16_t b_imag[], const unsigned length, const right_shift_t b_shr, const int16_t *rot_table, const unsigned table_rows)#

Compute the magnitude of each element of a complex 16-bit vector.

a[] represents the real 16-bit output mantissa vector \(\bar a\) .

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[] or b_imag[].

length is the number of elements in each of the vectors.

b_shr is the signed arithmetic right-shift applied to elements of \(\bar b\) .

rot_table must point to a pre-computed 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_table16_rows;
const extern complex_s16_t rot_table16[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.

Operation Performed

\[\begin{split}\begin{aligned} & v_k \leftarrow b_k \cdot 2^{-b\_shr} \\ & a_k \leftarrow \sqrt { {\left( Re\{v_k\} \right)}^2 + {\left( Im\{v_k\} \right)}^2 } \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If \(\bar b\) are the complex 16-bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) , then the resulting vector \(\bar a\) are the real 16-bit mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\) , where \(a\_exp = b\_exp + b\_shr\) .

The function vect_complex_s16_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

vect_complex_s16_mag_prepare

Parameters:

a – [out] Real output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imag part of complex input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shr – [in] Right-shift appled to \(\bar b\)
rot_table – [in] Pre-computed rotation table required for calculating magnitudes
table_rows – [in] Number of rows in rot_table

Throws ET_LOAD_STORE:

Raised if `a`, `b_real` or `b_imag` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\) .

headroom_t vect_complex_s16_macc(int16_t acc_real[], int16_t acc_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real[], const int16_t c_imag[], const unsigned length, const right_shift_t acc_shr, const right_shift_t bc_sat)#

Multiply one complex 16-bit vector element-wise by another, and add the result to an accumulator.

acc_real[] and acc_imag[] together represent the complex 16-bit accumulator mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is acc_real[k], and each \(Im\{a_k\}\) is acc_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

c_real[] and c_imag[] together represent the complex 16-bit input mantissa vector \(\bar c\) . Each \(Re\{c_k\}\) is c_real[k], and each \(Im\{c_k\}\) is c_imag[k].

Each of the input vectors must begin at a word-aligned address.

length is the number of elements in each of the vectors.

acc_shr is the signed arithmetic right-shift applied to the accumulators \(a_k\) .

bc_sat is the unsigned arithmetic right-shift applied to the product of \(b_k\) and \(c_k\) before being added to the accumulator.

Operation Performed

\[\begin{split}\begin{aligned} & v_k \leftarrow Re\{b_k\} \cdot Re\{c_k\} - Im\{b_k\} \cdot Im\{c_k\} \\ & s_k \leftarrow Im\{b_k\} \cdot Re\{c_k\} + Re\{b_k\} \cdot Im\{c_k\} \\ & \hat{a}_k \leftarrow sat_{16}( a_k \cdot 2^{-acc\_shr} ) \\ & Re\{a_k\} \leftarrow sat_{16}( Re\{\hat{a}_k\} + round( sat_{16}( v_k \cdot 2^{-bc\_sat} ) ) ) \\ & Im\{a_k\} \leftarrow sat_{16}( Im\{\hat{a}_k\} + round( sat_{16}( s_k \cdot 2^{-bc\_sat} ) ) ) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

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

vect_complex_s16_macc_prepare

Parameters:

acc_real – [inout] Real part of complex accumulator \(\bar a\)
acc_imag – [inout] Imaginary aprt of complex accumulator \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input vector \(\bar c\)
c_imag – [in] Imaginary part of complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\) , \(\bar b\) and \(\bar c\)
acc_shr – [in] Signed arithmetic right-shift applied to accumulator elements.
bc_sat – [in] Unsigned arithmetic right-shift applied to the products of elements \(b_k\) and \(c_k\)

Throws ET_LOAD_STORE:

Raised if `acc_real`, `acc_imag`, `b_real`, `b_imag`, `c_real` or c_imag is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s16_nmacc(int16_t acc_real[], int16_t acc_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real[], const int16_t c_imag[], const unsigned length, const right_shift_t acc_shr, const right_shift_t bc_sat)#

Multiply one complex 16-bit vector element-wise by another, and subtract the result from an accumulator.

acc_real[] and acc_imag[] together represent the complex 16-bit accumulator mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is acc_real[k], and each \(Im\{a_k\}\) is acc_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

c_real[] and c_imag[] together represent the complex 16-bit input mantissa vector \(\bar c\) . Each \(Re\{c_k\}\) is c_real[k], and each \(Im\{c_k\}\) is c_imag[k].

Each of the input vectors must begin at a word-aligned address.

length is the number of elements in each of the vectors.

acc_shr is the signed arithmetic right-shift applied to the accumulators \(a_k\) .

bc_sat is the unsigned arithmetic right-shift applied to the product of \(b_k\) and \(c_k\) before being subtracted from the accumulator.

Operation Performed

\[\begin{split}\begin{aligned} & v_k \leftarrow Re\{b_k\} \cdot Re\{c_k\} - Im\{b_k\} \cdot Im\{c_k\} \\ & s_k \leftarrow Im\{b_k\} \cdot Re\{c_k\} + Re\{b_k\} \cdot Im\{c_k\} \\ & \hat{a}_k \leftarrow sat_{16}( a_k \cdot 2^{-acc\_shr} ) \\ & Re\{a_k\} \leftarrow sat_{16}( Re\{\hat{a}_k\} - round( sat_{16}( v_k \cdot 2^{-bc\_sat} ) ) ) \\ & Im\{a_k\} \leftarrow sat_{16}( Im\{\hat{a}_k\} - round( sat_{16}( s_k \cdot 2^{-bc\_sat} ) ) ) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

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_nmacc_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

vect_complex_s16_nmacc_prepare

Parameters:

acc_real – [inout] Real part of complex accumulator \(\bar a\)
acc_imag – [inout] Imaginary aprt of complex accumulator \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input vector \(\bar c\)
c_imag – [in] Imaginary part of complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\) , \(\bar b\) and \(\bar c\)
acc_shr – [in] Signed arithmetic right-shift applied to accumulator elements.
bc_sat – [in] Unsigned arithmetic right-shift applied to the products of elements \(b_k\) and \(c_k\)

Throws ET_LOAD_STORE:

Raised if `acc_real`, `acc_imag`, `b_real`, `b_imag`, `c_real` or c_imag is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s16_conj_macc(int16_t acc_real[], int16_t acc_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real[], const int16_t c_imag[], const unsigned length, const right_shift_t acc_shr, const right_shift_t bc_sat)#

Multiply one complex 16-bit vector element-wise by the complex conjugate of another, and add the result to an accumulator.

acc_real[] and acc_imag[] together represent the complex 16-bit accumulator mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is acc_real[k], and each \(Im\{a_k\}\) is acc_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

c_real[] and c_imag[] together represent the complex 16-bit input mantissa vector \(\bar c\) . Each \(Re\{c_k\}\) is c_real[k], and each \(Im\{c_k\}\) is c_imag[k].

Each of the input vectors must begin at a word-aligned address.

length is the number of elements in each of the vectors.

acc_shr is the signed arithmetic right-shift applied to the accumulators \(a_k\) .

bc_sat is the unsigned arithmetic right-shift applied to the product of \(b_k\) and \(c_k^*\) before being added to the accumulator.

Operation Performed

\[\begin{split}\begin{aligned} & v_k \leftarrow Re\{b_k\} \cdot Re\{c_k\} + Im\{b_k\} \cdot Im\{c_k\} \\ & s_k \leftarrow Im\{b_k\} \cdot Re\{c_k\} - Re\{b_k\} \cdot Im\{c_k\} \\ & \hat{a}_k \leftarrow sat_{16}( a_k \cdot 2^{-acc\_shr} ) \\ & Re\{a_k\} \leftarrow sat_{16}( Re\{\hat{a}_k\} + round( sat_{16}( v_k \cdot 2^{-bc\_sat} ) ) ) \\ & Im\{a_k\} \leftarrow sat_{16}( Im\{\hat{a}_k\} + round( sat_{16}( s_k \cdot 2^{-bc\_sat} ) ) ) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

For accumulation to make sense mathematically, \(bc\_sat\) must be chosen such that \( a\_exp + acc\_shr = b\_exp + c\_exp + bc\_sat \) .

See also

vect_complex_s16_conj_macc_prepare

Parameters:

acc_real – [inout] Real part of complex accumulator \(\bar a\)
acc_imag – [inout] Imaginary aprt of complex accumulator \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input vector \(\bar c\)
c_imag – [in] Imaginary part of complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\) , \(\bar b\) and \(\bar c\)
acc_shr – [in] Signed arithmetic right-shift applied to accumulator elements.
bc_sat – [in] Unsigned arithmetic right-shift applied to the products of elements \(b_k\) and \(c_k^*\)

Throws ET_LOAD_STORE:

Raised if `acc_real`, `acc_imag`, `b_real`, `b_imag`, `c_real` or c_imag is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s16_conj_nmacc(int16_t acc_real[], int16_t acc_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real[], const int16_t c_imag[], const unsigned length, const right_shift_t acc_shr, const right_shift_t bc_sat)#

Multiply one complex 16-bit vector element-wise by the complex conjugate of another, and subtract the result from an accumulator.

acc_real[] and acc_imag[] together represent the complex 16-bit accumulator mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is acc_real[k], and each \(Im\{a_k\}\) is acc_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

c_real[] and c_imag[] together represent the complex 16-bit input mantissa vector \(\bar c\) . Each \(Re\{c_k\}\) is c_real[k], and each \(Im\{c_k\}\) is c_imag[k].

Each of the input vectors must begin at a word-aligned address.

length is the number of elements in each of the vectors.

acc_shr is the signed arithmetic right-shift applied to the accumulators \(a_k\) .

bc_sat is the unsigned arithmetic right-shift applied to the product of \(b_k\) and \(c_k^*\) before being subtracted from the accumulator.

Operation Performed

\[\begin{split}\begin{aligned} & v_k \leftarrow Re\{b_k\} \cdot Re\{c_k\} + Im\{b_k\} \cdot Im\{c_k\} \\ & s_k \leftarrow Im\{b_k\} \cdot Re\{c_k\} - Re\{b_k\} \cdot Im\{c_k\} \\ & \hat{a}_k \leftarrow sat_{16}( a_k \cdot 2^{-acc\_shr} ) \\ & Re\{a_k\} \leftarrow sat_{16}( Re\{\hat{a}_k\} - round( sat_{16}( v_k \cdot 2^{-bc\_sat} ) ) ) \\ & Im\{a_k\} \leftarrow sat_{16}( Im\{\hat{a}_k\} - round( sat_{16}( s_k \cdot 2^{-bc\_sat} ) ) ) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

For accumulation to make sense mathematically, \(bc\_sat\) must be chosen such that \( a\_exp + acc\_shr = b\_exp + c\_exp + bc\_sat \) .

See also

vect_complex_s16_conj_nmacc_prepare

Parameters:

acc_real – [inout] Real part of complex accumulator \(\bar a\)
acc_imag – [inout] Imaginary aprt of complex accumulator \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input vector \(\bar c\)
c_imag – [in] Imaginary part of complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\) , \(\bar b\) and \(\bar c\)
acc_shr – [in] Signed arithmetic right-shift applied to accumulator elements.
bc_sat – [in] Unsigned arithmetic right-shift applied to the products of elements \(b_k\) and \(c_k^*\)

Throws ET_LOAD_STORE:

Raised if `acc_real`, `acc_imag`, `b_real`, `b_imag`, `c_real` or c_imag is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s16_mul(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real[], const int16_t c_imag[], const unsigned length, const right_shift_t a_shr)#

Multiply one complex 16-bit vector element-wise by another.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

c_real[] and c_imag[] together represent the complex 16-bit input mantissa vector \(\bar c\) . Each \(Re\{c_k\}\) is c_real[k], and each \(Im\{c_k\}\) is c_imag[k].

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[], b_imag[], c_real[] and c_imag[].

length is the number of elements in each of the vectors.

a_shr is the unsigned arithmetic right-shift applied to the 32-bit accumulators holding intermediate results.

Operation Performed

\[\begin{split}\begin{aligned} & v_k = \leftarrow Re\{b_k\} \cdot Re\{c_k\} - Im\{b_k\} \cdot Im\{c_k\} \\ & s_k = \leftarrow Im\{b_k\} \cdot Re\{c_k\} + Re\{b_k\} \cdot Im\{c_k\} \\ & Re\{a_k\} \leftarrow round( sat_{16}( v_k \cdot 2^{-a\_shr} ) ) \\ & Im\{a_k\} \leftarrow round( sat_{16}( s_k \cdot 2^{-a\_shr} ) ) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

See also

vect_complex_s16_mul_prepare

Parameters:

a_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input vector \(\bar c\)
c_imag – [in] Imaginary part of complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\) , \(\bar b\) and \(\bar c\)
a_shr – [in] Right-shift applied to 32-bit intermediate results.

Throws ET_LOAD_STORE:

Raised if `a_real`, `a_imag`, `b_real`, `b_imag`, `c_real` or `c_imag` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s16_real_mul(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real[], const unsigned length, const right_shift_t a_shr)#

Multiply a complex 16-bit vector element-wise by a real 16-bit vector.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

c_real[] represents the real 16-bit input mantissa vector \(\bar c\) .

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[], b_imag[] and c_real[].

length is the number of elements in each of the vectors.

a_shr is the unsigned arithmetic right-shift applied to the 32-bit accumulators holding the penultimate results.

Operation Performed

\[\begin{split}\begin{aligned} & v_k = \leftarrow Re\{b_k\} \cdot c_k \\ & s_k = \leftarrow Im\{b_k\} \cdot c_k \\ & Re\{a_k\} \leftarrow round( sat_{16}( v_k \cdot 2^{-a\_shr} ) ) \\ & Im\{a_k\} \leftarrow round( sat_{16}( s_k \cdot 2^{-a\_shr} ) ) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If \(\bar b\) are the complex 16-bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) and \(c\) is the complex 16-bit mantissa of floating-point 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_s16_real_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

vect_complex_s16_real_mul_prepare

Parameters:

a_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\) , \(\bar b\) and \(\bar c\)
a_shr – [in] Right-shift applied to 32-bit intermediate results.

Throws ET_LOAD_STORE:

Raised if `a_real`, `a_imag`, `b_real`, `b_imag` or `c_real` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\) .

headroom_t vect_complex_s16_real_scale(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c, const unsigned length, const right_shift_t a_shr)#

Multiply a complex 16-bit vector by a real scalar.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[] and b_imag[].

c is the real 16-bit input mantissa \(c\) .

length is the number of elements in each of the vectors.

a_shr is an unsigned arithmetic right-shift applied to the 32-bit accumulators holding the penultimate results.

Operation Performed

\[\begin{split}\begin{aligned} & v_k = \leftarrow Re\{b_k\} \cdot c \\ & s_k = \leftarrow Im\{b_k\} \cdot c \\ & Re\{a_k\} \leftarrow round( sat_{16}( v_k \cdot 2^{-a\_shr} ) ) \\ & Im\{a_k\} \leftarrow round( sat_{16}( s_k \cdot 2^{-a\_shr} ) ) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If \(\bar b\) are the complex 16-bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) and \(c\) is the complex 16-bit mantissa of floating-point 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_s16_real_scale_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 \(c\_hr\) .

Parameters:

a_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c – [in] Real input scalar \(c\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
a_shr – [in] Right-shift applied to 32-bit intermediate results.

Throws ET_LOAD_STORE:

Raised if `a_real`, `a_imag`, `b_real`, `b_imag` or `c` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\) .

headroom_t vect_complex_s16_scale(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real, const int16_t c_imag, const unsigned length, const right_shift_t a_shr)#

Multiply a complex 16-bit vector by a complex 16-bit scalar.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[] and b_imag[].

c_real and c_imag are the real and imaginary parts of the complex 16-bit input mantissa \(c\) .

length is the number of elements in each of the vectors.

a_shr is the unsigned arithmetic right-shift applied to the 32-bit accumulators holding the penultimate results.

Operation Performed

\[\begin{split}\begin{aligned} & v_k = \leftarrow Re\{b_k\} \cdot Re\{c\} - Im\{b_k\} \cdot Im\{c\} \\ & s_k = \leftarrow Im\{b_k\} \cdot Re\{c\} + Re\{b_k\} \cdot Im\{c\} \\ & Re\{a_k\} \leftarrow round( sat_{16}( v_k \cdot 2^{-a\_shr} ) ) \\ & Im\{a_k\} \leftarrow round( sat_{16}( s_k \cdot 2^{-a\_shr} ) ) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If \(\bar b\) are the complex 16-bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) and \(c\) is the complex 16-bit mantissa of floating-point 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_s16_scale_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 \(c\_hr\) .

Parameters:

a_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input scalar \(c\)
c_imag – [in] Imaginary part of complex input scalar \(c\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
a_shr – [in] Right-shift applied to 32-bit intermediate results

Throws ET_LOAD_STORE:

Raised if `a_real`, `a_imag`, `b_real`, `b_imag`, `c_real` or `c_imag` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\) .

void vect_complex_s16_set(int16_t a_real[], int16_t a_imag[], const int16_t b_real, const int16_t b_imag, const unsigned length)#

Set each element of a complex 16-bit vector to a specified value.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k]. Each must begin at a word-aligned address.

b_real and b_imag are the real and imaginary parts of the complex 16-bit input mantissa \(b\) . Each a_real[k] will be set to b_real. Each a_imag[k] will be set to b_imag.

length is the number of elements in a_real[] and a_imag[].

Operation Performed

\[\begin{split}\begin{aligned} & Re\{a_k\} \leftarrow Re\{b\} \\ & Im\{a_k\} \leftarrow Im\{b\} \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If \(b\) is the mantissa of floating-point 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_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input scalar \(b\)
b_imag – [in] Imaginary part of complex input scalar \(b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)

Throws ET_LOAD_STORE:

Raised if `a_real` or `a_imag` is not word-aligned (See Note: Vector Alignment)

headroom_t vect_complex_s16_shl(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const unsigned length, const left_shift_t b_shl)#

Left-shift each element of a complex 16-bit vector by a specified number of bits.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[] and b_imag[].

length is the number of elements in \(\bar a\) and \(\bar b\) .

b_shl is the signed arithmetic left-shift applied to each element of \(\bar b\) .

Operation Performed

\[\begin{split}\begin{aligned} & Re\{a_k\} \leftarrow sat_{16}(\lfloor Re\{b_k\} \cdot 2^{b\_shl} \rfloor) \\ & Im\{a_k\} \leftarrow sat_{16}(\lfloor Im\{b_k\} \cdot 2^{b\_shl} \rfloor) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If \(\bar b\) are the complex 16-bit mantissas of a BFP vector \( \bar{b} \cdot 2^{b\_exp} \) , then the resulting vector \(\bar a\) are the complex 16-bit 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_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shl – [in] Left-shift applied to \(\bar b\)

Throws ET_LOAD_STORE:

Raised if `a_real`, `a_imag`, `b_real` or `b_imag` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s16_shr(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const unsigned length, const right_shift_t b_shr)#

Right-shift each element of a complex 16-bit vector by a specified number of bits.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[] and b_imag[].

length is the number of elements in \(\bar a\) and \(\bar b\) .

b_shr is the signed arithmetic right-shift applied to each element of \(\bar b\) .

Operation Performed

\[\begin{split}\begin{aligned} & Re\{a_k\} \leftarrow sat_{16}(\lfloor Re\{b_k\} \cdot 2^{-b\_shr} \rfloor) \\ & Im\{a_k\} \leftarrow sat_{16}(\lfloor Im\{b_k\} \cdot 2^{-b\_shr} \rfloor) \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

Parameters:

a_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
b_shr – [in] Right-shift applied to \(\bar b\)

Throws ET_LOAD_STORE:

Raised if `a_real`, `a_imag`, `b_real` or `b_imag` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of the output vector \(\bar a\)

headroom_t vect_complex_s16_squared_mag(int16_t a[], const int16_t b_real[], const int16_t b_imag[], const unsigned length, const right_shift_t a_shr)#

Get the squared magnitudes of elements of a complex 16-bit vector.

a[] represents the real 16-bit output mantissa vector \(\bar a\) .

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

Each of the input vectors must begin at a word-aligned address.

length is the number of elements in each of the vectors.

a_shr is the unsigned arithmetic right-shift applied to the 32-bit accumulators holding the penultimate results.

Operation Performed

\[\begin{split}\begin{aligned} & a_k \leftarrow ((Re\{b_k'\})^2 + (Im\{b_k'\})^2)\cdot 2^{-a\_shr} \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

The function vect_complex_s16_squared_mag_prepare() can be used to obtain values for \(a\_exp\) and \(a\_shr\) based on the input exponent \(b\_exp\) and headroom \(b\_hr\) .

See also

vect_complex_s16_squared_mag_prepare

Parameters:

a – [out] Real output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)
a_shr – [in] Right-shift appled to 32-bit intermediate results

Throws ET_LOAD_STORE:

Raised if `a`, `b_real` or `b_imag` is not word-aligned (See Note: Vector Alignment)

headroom_t vect_complex_s16_sub(int16_t a_real[], int16_t a_imag[], const int16_t b_real[], const int16_t b_imag[], const int16_t c_real[], const int16_t c_imag[], const unsigned length, const right_shift_t b_shr, const right_shift_t c_shr)#

Subtract one complex 16-bit vector from another.

a_real[] and a_imag[] together represent the complex 16-bit output mantissa vector \(\bar a\) . Each \(Re\{a_k\}\) is a_real[k], and each \(Im\{a_k\}\) is a_imag[k].

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

c_real[] and c_imag[] together represent the complex 16-bit input mantissa vector \(\bar c\) . Each \(Re\{c_k\}\) is c_real[k], and each \(Im\{c_k\}\) is c_imag[k].

Each of the input vectors must begin at a word-aligned address. This operation can be performed safely in-place on inputs b_real[], b_imag[], c_real[] and c_imag[].

length is the number of elements in each of the vectors.

b_shr and c_shr are the signed arithmetic right-shifts applied to each element of \(\bar b\) and \(\bar c\) respectively.

Operation Performed

\[\begin{split}\begin{aligned} & b_k' \leftarrow sat_{16}(\lfloor b_k \cdot 2^{-b\_shr} \rfloor) \\ & c_k' \leftarrow sat_{16}(\lfloor c_k \cdot 2^{-c\_shr} \rfloor) \\ & Re\{a_k\} \leftarrow Re\{b_k'\} - Re\{c_k'\} \\ & Im\{a_k\} \leftarrow Im\{b_k'\} - Im\{c_k'\} \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

The function vect_complex_s16_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

vect_complex_s16_sub_prepare

Parameters:

a_real – [out] Real part of complex output vector \(\bar a\)
a_imag – [out] Imaginary aprt of complex output vector \(\bar a\)
b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
c_real – [in] Real part of complex input vector \(\bar c\)
c_imag – [in] Imaginary part of complex input vector \(\bar c\)
length – [in] Number of elements in vectors \(\bar a\) , \(\bar b\) and \(\bar c\)
b_shr – [in] Right-shift applied to \(\bar b\)
c_shr – [in] Right-shift applied to \(\bar c\)

Throws ET_LOAD_STORE:

Raised if `a_real`, `a_imag`, `b_real`, `b_imag`, `c_real` or `c_imag` is not word-aligned (See Note: Vector Alignment)

Returns:

Headroom of output vector \(\bar a\) .

complex_s32_t vect_complex_s16_sum(const int16_t b_real[], const int16_t b_imag[], const unsigned length)#

Get the sum of elements of a complex 16-bit vector.

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) , and must both begin at a word-aligned address. Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

length is the number of elements in \(\bar b\) .

Operation Performed

\[\begin{split}\begin{aligned} & Re\{a\} \leftarrow \sum_{k=0}^{length-1} \left( Re\{b_k\} \right) \\ & Im\{a\} \leftarrow \sum_{k=0}^{length-1} \left( Im\{b_k\} \right) \end{aligned}\end{split}\]

Block Floating-Point

If \(\bar b\) are the mantissas of BFP vector \(\bar{b} \cdot 2^{b\_exp}\) , then the returned value \(a\) is the complex 32-bit mantissa of floating-point value \(a \cdot 2^{a\_exp}\) , where \(a\_exp = b\_exp\) .

Parameters:

b_real – [in] Real part of complex input vector \(\bar b\)
b_imag – [in] Imaginary part of complex input vector \(\bar b\)
length – [in] Number of elements in vector \(\bar b\) .

Throws ET_LOAD_STORE:

Raised if `b_real` or `b_imag` is not word-aligned (See Note: Vector Alignment)

Returns:

\(a\) , the 32-bit complex sum of elements in \(\bar b\) .

void vect_complex_s16_to_vect_complex_s32(complex_s32_t a[], const int16_t b_real[], const int16_t b_imag[], const unsigned length)#

Convert a complex 16-bit vector into a complex 32-bit vector.

a[] represents the complex 32-bit output vector \(\bar a\) . It must begin at a double word (8-byte) aligned address.

b_real[] and b_imag[] together represent the complex 16-bit input mantissa vector \(\bar b\) . Each \(Re\{b_k\}\) is b_real[k], and each \(Im\{b_k\}\) is b_imag[k].

The parameter length is the number of elements in each of the vectors.

length is the number of elements in each of the vectors.

Operation Performed

\[\begin{split}\begin{aligned} & Re\{a_k\} \leftarrow Re\{b_k\} \\ & Im\{a_k\} \leftarrow Im\{b_k\} \\ & \qquad\text{ for }k\in 0\ ...\ (length-1) \end{aligned}\end{split}\]

Block Floating-Point

If \(\bar b\) are the complex 16-bit mantissas of a BFP vector \(\bar{b} \cdot 2^{b\_exp}\) , then the resulting vector \(\bar a\) are the complex 32-bit mantissas of BFP vector \(\bar{a} \cdot 2^{a\_exp}\) , where \(a\_exp = b\_exp\) .

Notes

The headroom of output vector \(\bar a\) is not returned by this function. The headroom of the output is always 16 bits greater than the headroom of the input.

Parameters:

a – [out] Complex output vector \(\bar a\) .
b_real – [in] Real part of complex input vector \(\bar b\) .
b_imag – [in] Imaginary part of complex input vector \(\bar b\) .
length – [in] Number of elements in vectors \(\bar a\) and \(\bar b\)

Throws ET_LOAD_STORE:

Raised if `a` is not double-word-aligned (See Note: Vector Alignment)