32-Bit Vector Prepare Functions#

group vect_s32_prepare_api

Defines

vect_s32_add_scalar_prepare#

Obtain the output exponent and shifts required for a call to vect_s32_add_scalar().

The logic for computing the shifts and exponents of vect_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_s32_nmacc_prepare#

Obtain the output exponent and shifts required for a call to vect_s32_nmacc().

The logic for computing the shifts and exponents of vect_s32_nmacc() is identical to that for vect_s32_macc_prepare().

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

vect_s32_scale_prepare#

Obtain the output exponent and shifts required for a call to vect_s32_scale().

The logic for computing the shifts and exponents of vect_s32_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_s32_sub_prepare#

Obtain the output exponent and shifts required for a call to vect_s32_sub().

The logic for computing the shifts and exponents of vect_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_s32_add_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 to add or subtract two 16- or 32-bit BFP vectors.

The block floating-point functions in this library which add or subtract vectors are of the general form:

\( \bar{a} \cdot 2^{a\_exp} = \bar{b}\cdot 2^{b\_exp} \pm \bar{c}\cdot 2^{c\_exp} \) }

\(\bar b\) and \(\bar c\) are the input mantissa vectors with exponents \(b\_exp\) and \(c\_exp\), which are shared by each element of their respective vectors. \(\bar a\) is the output mantissa vector with exponent \(a\_exp\). Two additional properties, \(b\_hr\) and \(c\_hr\), which are the headroom of mantissa vectors \(\bar b\) and \(\bar c\) respectively, are required by this function.

In order to avoid any overflows in the output mantissas, the output exponent \(a\_exp\) must be chosen such that the largest (in the sense of absolute value) possible output mantissa will fit into the allotted space (e.g. 32 bits for vect_s32_add()). Once \(a\_exp\) is chosen, the input bit-shifts \(b\_shr\) and \(c\_shr\) are calculated to achieve that resulting exponent.

This function chooses \(a\_exp\) to be the minimum exponent known to avoid overflows, given the input exponents ( \(b\_exp\) and \(c\_exp\)) and input headroom ( \(b\_hr\) and \(c\_hr\)).

This function is used calculate the output exponent and input bit-shifts for each of the following functions:

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

If \(b\_hr\) or \(c\_hr\) are unknown, they can be calculated using the appropriate headroom function (e.g. vect_complex_s16_headroom() for complex 16-bit vectors) or the value 0 can always be safely used (but may result in reduced precision).

Parameters:

a_exp – [out] Output exponent associated with output mantissa vector \(\bar a\)
b_shr – [out] Signed arithmetic right-shift to be applied to elements of \(\bar b\). Used by the function which computes the output mantissas \(\bar a\)
c_shr – [out] Signed arithmetic right-shift to be applied to elements of \(\bar c\). Used by the function which computes the output mantissas \(\bar a\)
b_exp – [in] Exponent of BFP vector \(\bar b\)
c_exp – [in] Exponent of BFP vector \(\bar c\)
b_hr – [in] Headroom of BFP vector \(\bar b\)
c_hr – [in] Headroom of BFP vector \(\bar c\)

void vect_s32_clip_prepare(exponent_t *a_exp, right_shift_t *b_shr, int32_t *lower_bound, int32_t *upper_bound, const exponent_t b_exp, const exponent_t bound_exp, const headroom_t b_hr)#

Obtain the output exponent, input shift and modified bounds used by vect_s32_clip().

This function is used in conjunction with vect_s32_clip() to bound the elements of a 32-bit BFP vector to a specified range.

This function computes a_exp, b_shr, lower_bound and upper_bound.

a_exp is the exponent associated with the 32-bit mantissa vector \(\bar a\) computed by vect_s32_clip().

b_shr is the shift parameter required by vect_s32_clip() to achieve the output exponent a_exp.

lower_bound and upper_bound are the 32-bit mantissas which indicate the lower and upper clipping bounds respectively. The values are modified by this function, and the resulting values should be passed along to vect_s32_clip().

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

bound_exp is the exponent associated with the bound mantissas lower_bound and upper_bound respectively.

b_hr is the headroom of \(\bar b\). If unknown, it can be obtained using vect_s32_headroom(). Alternatively, the value 0 can always be safely used (but may result in reduced precision).

See also

vect_s32_clip

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_s32_clip()
lower_bound – [inout] Lower bound of clipping range
upper_bound – [inout] Upper bound of clipping range
b_exp – [in] Exponent associated with input mantissa vector \(\bar b\)
bound_exp – [in] Exponent associated with clipping bounds lower_bound and upper_bound
b_hr – [in] Headroom of input mantissa vector \(\bar b\)

void vect_s32_dot_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, const unsigned length)#

Obtain the output exponent and input shift used by vect_s32_dot().

This function is used in conjunction with vect_s32_dot() to compute the inner product of two 32-bit BFP vectors.

This function computes a_exp, b_shr and c_shr.

a_exp is the exponent associated with the 64-bit mantissa \(a\) returned by vect_s32_dot(), 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 vectors.

b_shr and c_shr are the shift parameters required by vect_s32_dot() 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 either is unknown, they can be obtained using vect_s32_headroom(). Alternatively, the value 0 can always be safely used (but may result in reduced precision).

length is the number of elements in the input mantissa vectors \(\bar b\) and \(\bar c\).

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 or c_shr can result in saturation, and using larger values may result in unnecessary underflows or loss of precision.

See also

vect_s32_dot

Parameters:

a_exp – [out] Exponent associated with output mantissa \(a\)
b_shr – [out] Signed arithmetic right-shift for \(\bar b\) used by vect_s32_dot()
c_shr – [out] Signed arithmetic right-shift for \(\bar c\) used by vect_s32_dot()
b_exp – [in] Exponent associated with input mantissa vector \(\bar b\)
c_exp – [in] Exponent associated with input mantissa vector \(\bar b\)
b_hr – [in] Headroom of input mantissa vector \(\bar b\)
c_hr – [in] Headroom of input mantissa vector \(\bar b\)
length – [in] Number of elements in vectors \(\bar b\) and \(\bar c\)

void vect_s32_energy_prepare(exponent_t *a_exp, right_shift_t *b_shr, const unsigned length, const exponent_t b_exp, const headroom_t b_hr)#

Obtain the output exponent and input shift used by vect_s32_energy().

This function is used in conjunction with vect_s32_energy() to compute the inner product of a 32-bit BFP vector with itself.

This function computes a_exp and b_shr.

a_exp is the exponent associated with the 64-bit mantissa \(a\) returned by vect_s32_energy(), 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 exponent and headroom associated with the input vector.

b_shr is the shift parameter required by vect_s32_energy() 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 it is unknown, it can be obtained using vect_s32_headroom(). Alternatively, the value 0 can always be safely used (but may result in reduced precision).

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 condition 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_s32_energy

Parameters:

a_exp – [out] Exponent of outputs of vect_s32_energy()
b_shr – [out] Right-shift to be applied to elements of \(\bar b\)
length – [in] Number of elements in vector \(\bar b\)
b_exp – [in] Exponent of vector{b}
b_hr – [in] Headroom of vector{b}

void vect_s32_inverse_prepare(exponent_t *a_exp, unsigned *scale, const int32_t b[], const exponent_t b_exp, const unsigned length)#

Obtain the output exponent and scale used by vect_s32_inverse().

This function is used in conjunction with vect_s32_inverse() to compute the inverse of elements of a 32-bit BFP vector.

This function computes a_exp and scale.

a_exp is the exponent associated with output mantissa vector \(\bar a\), and must be chosen to avoid overflow in the smallest element of the input vector, which when inverted becomes the largest output element. To maximize precision, this function chooses a_exp to be the smallest exponent known to avoid saturation. The a_exp chosen by this function is derived from the exponent and smallest element of the input vector.

scale is a scaling parameter used by vect_s32_inverse() to achieve the chosen output exponent.

b[] is the input mantissa vector \(\bar b\).

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

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

See also

vect_s32_inverse

Parameters:

a_exp – [out] Exponent of output vector \(\bar a\)
scale – [out] Scale factor to be applied when computing inverse
b – [in] Input vector \(\bar b\)
b_exp – [in] Exponent of \(\bar b\)
length – [in] Number of elements in vector \(\bar b\)

void vect_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 headroom_t acc_hr, const headroom_t b_hr, const headroom_t c_hr)#

Obtain the output exponent and shifts needed by vect_s32_macc().

This function is used in conjunction with vect_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_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_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_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_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_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_s32_macc()
b_shr – [out] Signed arithmetic right-shift used for \(\bar b\) in vect_s32_macc()
c_shr – [out] Signed arithmetic right-shift used for \(\bar c\) in vect_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_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_s32_mul().

This function is used in conjunction with vect_s32_mul() to perform an element-wise multiplication of two 32-bit BFP vectors.

This function computes a_exp, b_shr, 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_s32_headroom(). Alternatively, the value 0 can always be safely used (but may result in reduced precision).

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_s32_mul

Parameters:

a_exp – [out] Exponent of output elements of vect_s32_mul()
b_shr – [out] Right-shift to be applied to elements of \(\bar b\)
c_shr – [out] Right-shift to be applied to elemetns of \(\bar c\)
b_exp – [in] Exponent of \(\bar b\)
c_exp – [in] Exponent of \(\bar c\)
b_hr – [in] Headroom of \(\bar b\)
c_hr – [in] Headroom of \(\bar c\)

void vect_s32_sqrt_prepare(exponent_t *a_exp, right_shift_t *b_shr, const exponent_t b_exp, const right_shift_t b_hr)#

Obtain the output exponent and shift parameter used by vect_s32_sqrt().

This function is used in conjunction withx vect_s32_sqrt() to compute the square root of elements of a 32-bit BFP vector.

This function computes a_exp and b_shr.

a_exp is the exponent associated with output mantissa vector \(\bar a\), and should be chosen to maximize the precision of the results. To that end, this function chooses a_exp to be the smallest exponent known to avoid saturation of the resulting mantissa vector \(\bar a\). It is derived from the exponent and headroom of the input BFP vector.

b_shr is the shift parameter required by vect_s32_sqrt() 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 it is unknown, it can be obtained using vect_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 a_exp;
right_shift_t b_shr;
vect_s16_mul_prepare(&a_exp, &b_shr, b_exp, c_exp, b_hr, c_hr);
exponent_t desired_exp = ...; // Value known a priori
b_shr = b_shr + (desired_exp - a_exp);
a_exp = desired_exp;

When applying the above adjustment, the following condition 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.

Also, if a larger exponent is used than necessary, a larger depth parameter (see vect_s32_sqrt()) will be required to achieve the same precision, as the results are computed bit by bit, starting with the most significant bit.

See also

vect_s32_sqrt

Parameters:

a_exp – [out] Exponent of outputs of vect_s32_sqrt()
b_shr – [out] Right-shift to be applied to elements of \(\bar b\)
b_exp – [in] Exponent of vector{b}
b_hr – [in] Headroom of vector{b}

void vect_2vec_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, const headroom_t extra_operand_hr)#

Obtain the output exponent and input shifts required to perform a binary add-like operation.

This function computes the output exponent and input shifts required for BFP operations which take two vectors as input, where the operation is “add-like”.

Here, “add-like” operations are loosely defined as those which require input vectors to share an exponent before their mantissas can be meaningfully used to perform that operation.

For example, consider adding \( 3 \cdot 2^{x} + 4 \cdot 2^{y} \). If \(x = y\), then the mantissas can be added directly to get a meaningful result \( (3+4) \cdot 2^{x} \). If \(x \ne y\) however, adding the mantissas together is meaningless. Before the mantissas can be added in this case, one or both of the input mantissas must be shifted so that the representations correspond to the same exponent. Likewise, similar logic applies to binary comparisons.

This is in contrast to a “multiply-like” operation, which does not have this same requirement (e.g. \(a \cdot 2^x \cdot b \cdot 2^y = ab \cdot 2^{x+y}\), regardless of whether \(x=y\)).

For a general operation like:

\( \bar{a} \cdot 2^{a\_exp} = \bar{b}\cdot 2^{b\_exp} \oplus \bar{c}\cdot 2^{c\_exp} \)

In addition to \(a\_exp\), this function computes \(b\_shr\) and \(c\_shr\), signed arithmetic right-shifts applied to the mantissa vectors \(\bar b\) and \(\bar c\) so that the add-like \(\oplus\) operation can be applied.

This function chooses \(a\_exp\) to be the minimum exponent which can be used to express both \(\bar B\) and \(\bar C\) without saturation of their mantissas, and which leaves both \(\bar b\) and \(\bar c\) with at least extra_operand_hr bits of headroom. The shifts \(b\_shr\) and \(c\_shr\) are derived from \(a\_exp\) using \(b\_exp\) and \(c\_exp\).

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

If \(b\_hr\) or \(c\_hr\) are unknown, they can be calculated using the appropriate headroom function (e.g. vect_complex_s16_headroom() for complex 16-bit vectors) or the value 0 can always be safely used (but may result in reduced precision).

Parameters:

a_exp – [out] Output exponent associated with output mantissa vector \(\bar a\)
b_shr – [out] Signed arithmetic right-shift to be applied to elements of \(\bar b\). Used by the function which computes the output mantissas \(\bar a\)
c_shr – [out] Signed arithmetic right-shift to be applied to elements of \(\bar c\). Used by the function which computes the output mantissas \(\bar a\)
b_exp – [in] Exponent of BFP vector \(\bar b\)
c_exp – [in] Exponent of BFP vector \(\bar c\)
b_hr – [in] Headroom of BFP vector \(\bar b\)
c_hr – [in] Headroom of BFP vector \(\bar c\)
extra_operand_hr – [in] The minimum amount of headroom that will be left in the mantissa vectors following the arithmetic right-shift, as required by some operations.