32-Bit Complex Vector Prepare Functions#

group vect_complex_s32_prepare_api

Defines

vect_complex_s32_add_prepare#

Obtain the output exponent and shifts required for a call to vect_complex_s32_add().

The logic for computing the shifts and exponents of vect_complex_s32_add() is identical to that for vect_s32_add().

This macro is provided as a convenience to developers and to make the code more coherent.

See also

vect_s32_add_prepare()

vect_complex_s32_add_scalar_prepare#

Obtain the output exponent and shifts required for a call to vect_complex_s32_add_scalar().

The logic for computing the shifts and exponents of vect_complex_s32_add_scalar() is identical to that for vect_s32_add().

This macro is provided as a convenience to developers and to make the code more readable.

See also

vect_s32_add_prepare()

vect_complex_s32_conj_mul_prepare#

Obtain the output exponent and shifts required for a call to vect_complex_s32_conj_mul().

The logic for computing the shifts and exponents of vect_complex_s32_conj_mul() is identical to that for vect_complex_s32_mul().

This macro is provided as a convenience to developers and to make the code more readable.

See also

vect_complex_s32_mul_prepare()

vect_complex_s32_nmacc_prepare#

Obtain the output exponent and shifts required for a call to vect_complex_s32_nmacc().

The logic for computing the shifts and exponents of vect_complex_s32_nmacc() is identical to that for vect_complex_s32_macc_prepare().

This macro is provided as a convenience to developers and to make the code more readable.

vect_complex_s32_conj_macc_prepare#

Obtain the output exponent and shifts required for a call to vect_complex_s32_conj_macc().

The logic for computing the shifts and exponents of vect_complex_s32_conj_macc() is identical to that for vect_complex_s32_macc_prepare().

This macro is provided as a convenience to developers and to make the code more readable.

vect_complex_s32_conj_nmacc_prepare#

Obtain the output exponent and shifts required for a call to vect_complex_s32_conj_nmacc().

The logic for computing the shifts and exponents of vect_complex_s32_conj_nmacc() is identical to that for vect_complex_s32_macc_prepare().

This macro is provided as a convenience to developers and to make the code more readable.

vect_complex_s32_real_scale_prepare#

Obtain the output exponent and shifts required for a call to vect_complex_s32_real_scale().

The logic for computing the shifts and exponents of vect_complex_s32_real_scale() is identical to that for vect_s32_mul().

This macro is provided as a convenience to developers and to make the code more readable.

See also

vect_s32_mul_prepare()

vect_complex_s32_sub_prepare#

Obtain the output exponent and shifts required for a call to vect_complex_s32_sub().

The logic for computing the shifts and exponents of vect_complex_s32_sub() is identical to that for vect_s32_add().

This macro is provided as a convenience to developers and to make the code more readable.

See also

vect_s32_add_prepare()

Functions

void vect_complex_s32_macc_prepare(exponent_t *new_acc_exp, right_shift_t *acc_shr, right_shift_t *b_shr, right_shift_t *c_shr, const exponent_t acc_exp, const exponent_t b_exp, const exponent_t c_exp, const exponent_t acc_hr, const headroom_t b_hr, const headroom_t c_hr)#

Obtain the output exponent and shifts needed by vect_complex_s32_macc().

This function is used in conjunction with vect_complex_s32_macc() to perform an element-wise multiply-accumlate of 32-bit BFP vectors.

This function computes new_acc_exp, acc_shr, b_shr and c_shr, which are selected to maximize precision in the resulting accumulator vector without causing saturation of final or intermediate values. Normally the caller will pass these outputs to their corresponding inputs of vect_complex_s32_macc().

acc_exp is the exponent associated with the accumulator mantissa vector \(\bar a\) prior to the operation, whereas new_acc_exp is the exponent corresponding to the updated accumulator vector.

b_exp and c_exp are the exponents associated with the complex input mantissa vectors \(\bar b\) and \(\bar c\) respectively.

acc_hr, b_hr and c_hr are the headrooms of \(\bar a\), \(\bar b\) and \(\bar c\) respectively. If the headroom of any of these vectors is unknown, it can be obtained by calling vect_complex_s32_headroom(). Alternatively, the value 0 can always be safely used (but may result in reduced precision).

Adjusting Output Exponents

If a specific output exponent desired_exp is needed for the result (e.g. for emulating fixed-point arithmetic), the acc_shr and bc_sat produced by this function can be adjusted according to the following:

// Presumed to be set somewhere
exponent_t acc_exp, b_exp, c_exp;
headroom_t acc_hr, b_hr, c_hr;
exponent_t desired_exp;

...

// Call prepare
right_shift_t acc_shr, b_shr, c_shr;
vect_complex_s32_macc_prepare(&acc_exp, &acc_shr, &b_shr, &c_shr, 
                                  acc_exp, b_exp, c_exp,
                                  acc_hr, b_hr, c_hr);

// Modify results
right_shift_t mant_shr = desired_exp - acc_exp;
acc_exp += mant_shr;
acc_shr += mant_shr;
b_shr  += mant_shr;
c_shr  += mant_shr;

// acc_shr, b_shr and c_shr may now be used in a call to vect_complex_s32_macc() 

When applying the above adjustment, the following conditions should be maintained:

acc_shr > -acc_hr (Shifting any further left may cause saturation)
b_shr => -b_hr (Shifting any further left may cause saturation)
c_shr => -c_hr (Shifting any further left may cause saturation)

It is up to the user to ensure any such modification does not result in saturation or unacceptable loss of precision.

See also

vect_complex_s32_macc

Parameters:

new_acc_exp – [out] Exponent associated with output mantissa vector \(\bar a\) (after macc)
acc_shr – [out] Signed arithmetic right-shift used for \(\bar a\) in vect_complex_s32_macc()
b_shr – [out] Signed arithmetic right-shift used for \(\bar b\) in vect_complex_s32_macc()
c_shr – [out] Signed arithmetic right-shift used for \(\bar c\) in vect_complex_s32_macc()
acc_exp – [in] Exponent associated with input mantissa vector \(\bar a\) (before macc)
b_exp – [in] Exponent associated with input mantissa vector \(\bar b\)
c_exp – [in] Exponent associated with input mantissa vector \(\bar c\)
acc_hr – [in] Headroom of input mantissa vector \(\bar a\) (before macc)
b_hr – [in] Headroom of input mantissa vector \(\bar b\)
c_hr – [in] Headroom of input mantissa vector \(\bar c\)

void vect_complex_s32_mag_prepare(exponent_t *a_exp, right_shift_t *b_shr, const exponent_t b_exp, const headroom_t b_hr)#

Obtain the output exponent and input shift used by vect_complex_s32_mag() and vect_complex_s16_mag().

This function is used in conjunction with vect_complex_s32_mag() to compute the magnitude of each element of a complex 32-bit BFP vector.

This function computes a_exp and b_shr.

a_exp is the exponent associated with mantissa vector \(\bar a\), and is be chosen to maximize precision when elements of \(\bar a\) are computed. The a_exp chosen by this function is derived from the exponent and headroom associated with the input vector.

b_shr is the shift parameter required by vect_complex_s32_mag() to achieve the chosen output exponent a_exp.

b_exp is the exponent associated with the input mantissa vector \(\bar b\).

b_hr is the headroom of \(\bar b\). If the headroom of \(\bar b\) is unknown it can be calculated using vect_complex_s32_headroom(). Alternatively, the value 0 can always be safely used (but may result in reduced precision).

Adjusting Output Exponents

If a specific output exponent desired_exp is needed for the result (e.g. for emulating fixed-point arithmetic), the b_shr produced by this function can be adjusted according to the following:

exponent_t desired_exp = ...; // Value known a priori
right_shift_t new_b_shr = b_shr + (desired_exp - a_exp);

When applying the above adjustment, the following condition should be maintained:

b_hr + b_shr >= 0

Using larger values than strictly necessary for b_shr may result in unnecessary underflows or loss of precision.

See also

vect_complex_s32_mag()

Parameters:

a_exp – [out] Output exponent associated with output mantissa vector \(\bar a\)
b_shr – [out] Signed arithmetic right-shift for \(\bar b\) used by vect_complex_s32_mag()
b_exp – [in] Exponent associated with input mantissa vector \(\bar b\)
b_hr – [in] Headroom of input mantissa vector \(\bar b\)

void vect_complex_s32_mul_prepare(exponent_t *a_exp, right_shift_t *b_shr, right_shift_t *c_shr, const exponent_t b_exp, const exponent_t c_exp, const headroom_t b_hr, const headroom_t c_hr)#

Obtain the output exponent and input shifts used by vect_complex_s32_mul() and vect_complex_s32_conj_mul().

This function is used in conjunction with vect_complex_s32_mul() to perform a complex element-wise multiplication of two complex 32-bit BFP vectors.

This function computes a_exp, b_shr and c_shr.

a_exp is the exponent associated with mantissa vector \(\bar a\), and must be chosen to be large enough to avoid overflow when elements of \(\bar a\) are computed. To maximize precision, this function chooses a_exp to be the smallest exponent known to avoid saturation (see exception below). The a_exp chosen by this function is derived from the exponents and headrooms of associated with the input vectors.

b_shr and c_shr are the shift parameters required by vect_complex_s32_mul() to achieve the chosen output exponent a_exp.

b_exp and c_exp are the exponents associated with the input mantissa vectors \(\bar b\) and \(\bar c\) respectively.

b_hr and c_hr are the headroom of \(\bar b\) and \(\bar c\) respectively. If the headroom of \(\bar b\) or \(\bar c\) is unknown, they can be obtained by calling vect_complex_s32_headroom(). Alternatively, the value 0 can always be safely used (but may result in reduced precision).

Adjusting Output Exponents

If a specific output exponent desired_exp is needed for the result (e.g. for emulating fixed-point arithmetic), the b_shr and c_shr produced by this function can be adjusted according to the following:

exponent_t desired_exp = ...; // Value known a priori
right_shift_t new_b_shr = b_shr + (desired_exp - a_exp);
right_shift_t new_c_shr = c_shr + (desired_exp - a_exp);

When applying the above adjustment, the following conditions should be maintained:

b_hr + b_shr >= 0
c_hr + c_shr >= 0

Be aware that using smaller values than strictly necessary for b_shr and c_shr can result in saturation, and using larger values may result in unnecessary underflows or loss of precision.

Notes

Using the outputs of this function, an output mantissa which would otherwise be INT32_MIN will instead saturate to -INT32_MAX. This is due to the symmetric saturation logic employed by the VPU and is a hardware feature. This is a corner case which is usually unlikely and results in 1 LSb of error when it occurs.

Parameters:

a_exp – [out] Exponent associated with output mantissa vector \(\bar a\)
b_shr – [out] Signed arithmetic right-shift for \(\bar b\) used by vect_complex_s32_mul()
c_shr – [out] Signed arithmetic right-shift for \(\bar c\) used by vect_complex_s32_mul()
b_exp – [in] Exponent associated with input mantissa vector \(\bar b\)
c_exp – [in] Exponent associated with input mantissa vector \(\bar c\)
b_hr – [in] Headroom of input mantissa vector \(\bar b\)
c_hr – [in] Headroom of input mantissa vector \(\bar c\)

void vect_complex_s32_real_mul_prepare(exponent_t *a_exp, right_shift_t *b_shr, right_shift_t *c_shr, const exponent_t b_exp, const exponent_t c_exp, const headroom_t b_hr, const headroom_t c_hr)#

Obtain the output exponent and input shifts used by vect_complex_s32_real_mul().

This function is used in conjunction with vect_complex_s32_real_mul() to perform a the element-wise multiplication of complex 32-bit BFP vector by a real 32-bit BFP vector.

This function computes a_exp, b_shr and c_shr.

b_shr and c_shr are the shift parameters required by vect_complex_s32_mul() to achieve the chosen output exponent a_exp.

b_exp and c_exp are the exponents associated with the input mantissa vectors \(\bar b\) and \(\bar c\) respectively.

Adjusting Output Exponents

exponent_t desired_exp = ...; // Value known a priori
right_shift_t new_b_shr = b_shr + (desired_exp - a_exp);
right_shift_t new_c_shr = c_shr + (desired_exp - a_exp);

When applying the above adjustment, the following conditions should be maintained:

b_hr + b_shr >= 0
c_hr + c_shr >= 0

Be aware that using smaller values than strictly necessary for b_shr and c_shr can result in saturation, and using larger values may result in unnecessary underflows or loss of precision.

Notes

Using the outputs of this function, an output mantissa which would otherwise be INT32_MIN will instead saturate to -INT32_MAX. This is due to the symmetric saturation logic employed by the VPU and is a hardware feature. This is a corner case which is usually unlikely and results in 1 LSb of error when it occurs.

See also

vect_complex_s32_real_mul

Parameters:

a_exp – [out] Output exponent associated with \(\bar a\)
b_shr – [out] Signed arithmetic right-shift for \(\bar b\) used by vect_complex_s32_real_mul()
c_shr – [out] Signed arithmetic right-shift for \(\bar c\) used by vect_complex_s32_real_mul()
b_exp – [in] Exponent associated with \(\bar b\)
c_exp – [in] Exponent associated with \(\bar c\)
b_hr – [in] Headroom of mantissa vector \(\bar b\)
c_hr – [in] Headroom of mantissa vector \(\bar c\)

void vect_complex_s32_scale_prepare(exponent_t *a_exp, right_shift_t *b_shr, right_shift_t *c_shr, const exponent_t b_exp, const exponent_t c_exp, const headroom_t b_hr, const headroom_t c_hr)#

Obtain the output exponent and input shifts used by vect_complex_s32_scale().

This function is used in conjunction with vect_complex_s32_scale() to perform a complex multiplication of a complex 32-bit BFP vector by a complex 32-bit scalar.

This function computes a_exp, b_shr and c_shr.

b_shr and c_shr are the shift parameters required by vect_complex_s32_mul() to achieve the chosen output exponent a_exp.

b_exp and c_exp are the exponents associated with the input mantissa vectors \(\bar b\) and \(\bar c\) respectively.

Adjusting Output Exponents

exponent_t desired_exp = ...; // Value known a priori
right_shift_t new_b_shr = b_shr + (desired_exp - a_exp);
right_shift_t new_c_shr = c_shr + (desired_exp - a_exp);

When applying the above adjustment, the following conditions should be maintained:

b_hr + b_shr >= 0
c_hr + c_shr >= 0

Be aware that using smaller values than strictly necessary for b_shr and c_shr can result in saturation, and using larger values may result in unnecessary underflows or loss of precision.

Notes

Using the outputs of this function, an output mantissa which would otherwise be INT32_MIN will instead saturate to -INT32_MAX. This is due to the symmetric saturation logic employed by the VPU and is a hardware feature. This is a corner case which is usually unlikely and results in 1 LSb of error when it occurs.

See also

vect_complex_s32_scale

Parameters:

a_exp – [out] Exponent associated with output mantissa vector \(\bar a\)
b_shr – [out] Signed arithmetic right-shift for \(\bar b\) used by vect_complex_s32_scale()
c_shr – [out] Signed arithmetic right-shift for \(\bar c\) used by vect_complex_s32_scale()
b_exp – [in] Exponent associated with input mantissa vector \(\bar b\)
c_exp – [in] Exponent associated with input mantissa vector \(\bar c\)
b_hr – [in] Headroom of input mantissa vector \(\bar b\)
c_hr – [in] Headroom of input mantissa vector \(\bar c\)

void vect_complex_s32_squared_mag_prepare(exponent_t *a_exp, right_shift_t *b_shr, const exponent_t b_exp, const headroom_t b_hr)#

Obtain the output exponent and input shift used by vect_complex_s32_squared_mag().

This function is used in conjunction with vect_complex_s32_squared_mag() to compute the squared magnitude of each element of a complex 32-bit BFP vector.

This function computes a_exp and b_shr.

b_shr is the shift parameter required by vect_complex_s32_mag() to achieve the chosen output exponent a_exp.

b_exp is the exponent associated with the input mantissa vector \(\bar b\).

Adjusting Output Exponents

If a specific output exponent desired_exp is needed for the result (e.g. for emulating fixed-point arithmetic), the b_shr produced by this function can be adjusted according to the following:

exponent_t desired_exp = ...; // Value known a priori
right_shift_t new_b_shr = b_shr + (desired_exp - a_exp);

When applying the above adjustment, the following condition should be maintained:

b_hr + b_shr >= 0

Using larger values than strictly necessary for b_shr may result in unnecessary underflows or loss of precision.

See also

vect_complex_s32_squared_mag()

Parameters:

a_exp – [out] Output exponent associated with output mantissa vector \(\bar a\)
b_shr – [out] Signed arithmetic right-shift for \(\bar b\) used by vect_complex_s32_squared_mag()
b_exp – [in] Exponent associated with input mantissa vector \(\bar b\)
b_hr – [in] Headroom of input mantissa vector \(\bar b\)

void vect_complex_s32_sum_prepare(exponent_t *a_exp, right_shift_t *b_shr, const exponent_t b_exp, const headroom_t b_hr, const unsigned length)#

Obtain the output exponent and input shift used by vect_complex_s32_sum().

This function is used in conjunction with vect_complex_s32_sum() to compute the sum of elements of a complex 32-bit BFP vector.

This function computes a_exp and b_shr.

a_exp is the exponent associated with the 64-bit mantissa \(a\) returned by vect_complex_s32_sum(), and must be chosen to be large enough to avoid saturation when \(a\) is computed. To maximize precision, this function chooses a_exp to be the smallest exponent known to avoid saturation (see exception below). The a_exp chosen by this function is derived from the exponents and headrooms associated with the input vector.

b_shr is the shift parameter required by vect_complex_s32_sum() to achieve the chosen output exponent a_exp.

b_exp is the exponent associated with the input mantissa vector \(\bar b\).

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

Adjusting Output Exponents

If a specific output exponent desired_exp is needed for the result (e.g. for emulating fixed-point arithmetic), the b_shr produced by this function can be adjusted according to the following:

exponent_t desired_exp = ...; // Value known a priori
right_shift_t new_b_shr = b_shr + (desired_exp - a_exp);

When applying the above adjustment, the following conditions should be maintained:

b_hr + b_shr >= 0

Be aware that using smaller values than strictly necessary for b_shr can result in saturation, and using larger values may result in unnecessary underflows or loss of precision.

See also

vect_complex_s32_sum

Parameters:

a_exp – [out] Exponent associated with output mantissa \(a\)
b_shr – [out] Signed arithmetic right-shift for \(\bar b\) used by vect_complex_s32_sum()
b_exp – [in] Exponent associated with input mantissa vector \(\bar b\)
b_hr – [in] Headroom of input mantissa vector \(\bar b\)
length – [in] Number of elements in \(\bar b\)