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# 16-bit vector prepare functions

group vect_s16_prepare_api

  Defines

  vect_s16_add_prepare

    Obtain the output exponent and shifts required for a call to `vect_s16_add()`.

    The logic for computing the shifts and exponents of `vect_s16_add()` 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_s16_add_scalar_prepare

    Obtain the output exponent and shifts required for a call to `vect_s16_add_scalar()`.

    The logic for computing the shifts and exponents of `vect_s16_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_s16_nmacc_prepare

    Obtain the output exponent and shifts required for a call to vect_s16_nmacc().

    The logic for computing the shifts and exponents of `vect_s16_nmacc()` is identical to that for `vect_s16_macc_prepare()`.

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

    See also

    vect_s16_macc_prepare(), vect_s16_nmacc()

  vect_s16_sub_prepare

    Obtain the output exponent and shifts required for a call to `vect_s16_sub()`.

    The logic for computing the shifts and exponents of `vect_s16_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_s16_clip_prepare(exponent_t *a_exp, right_shift_t *b_shr, int16_t *lower_bound, int16_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_s16_clip().

    This function is used in conjunction with vect_s16_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 16-bit mantissa vector \(\bar a\) computed by vect_s32_clip().

    `b_shr` is the shift parameter required by vect_s16_clip() to achieve the output exponent `a_exp`.

    `lower_bound` and `upper_bound` are the 16-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_s16_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_s16_headroom(). Alternatively, the value `0` can always be safely used (but may result in reduced precision).

    See also

    vect_s16_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_s16_inverse_prepare(exponent_t *a_exp, unsigned *scale, const int16_t b[], const exponent_t b_exp, const unsigned length)

    Obtain the output exponent and scaling parameter used by vect_s16_inverse().

    This function is used in conjunction with vect_s16_inverse() to compute the inverse of elements of a 16-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_s16_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_s16_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_s16_macc_prepare(exponent_t *new_acc_exp, right_shift_t *acc_shr, right_shift_t *bc_sat, 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_s16_macc().

    This function is used in conjunction with vect_s16_macc() to perform an element-wise multiply-accumlate of 16-bit BFP vectors.

    This function computes `new_acc_exp` and `acc_shr` and `bc_sat`, 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_s16_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_s16_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, bc_sat;
          vect_s16_macc_prepare(&acc_exp, &acc_shr, &bc_sat,
                                    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;
          bc_sat  += mant_shr;

          // acc_shr and bc_sat may now be used in a call to vect_s16_macc()

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

      - `bc_sat >= 0` (`bc_sat` is an unsigned right-shift)

      - `acc_shr > -acc_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_s16_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_s16_macc()

      - bc_sat – [out] Unsigned arithmetic right-shift applied to the product of elements \(b_k\) and \(c_k\) in vect_s16_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_s16_mul_prepare(exponent_t *a_exp, right_shift_t *a_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 output shift used by vect_s16_mul().

    This function is used in conjunction with vect_s16_mul() to perform an element-wise multiplication of two 16-bit BFP vectors.

    This function computes `a_exp` and `a_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.

    `a_shr` is an arithmetic right-shift applied by vect_complex_s16_mul() to the 32-bit products of input elements 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_s16_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 `a_shr` produced by this function can be adjusted according to the following:

          exponent_t a_exp;
          right_shift_t a_shr;
          vect_s16_mul_prepare(&a_exp, &a_shr, b_exp, c_exp, b_hr, c_hr);
          exponent_t desired_exp = ...; // Value known a priori
          a_shr = a_shr + (desired_exp - a_exp);
          a_exp = desired_exp;

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

      - `a_shr >= 0`

      Be aware that using a smaller value than strictly necessary for `a_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 `INT16_MIN` will instead saturate to `-INT16_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_s16_mul

    Parameters:

      - a_exp – [out] Exponent of output elements of vect_s16_mul()

      - a_shr – [out] Right-shift supplied to vect_s16_mul()

      - b_exp – [in] Exponent associated with \(\bar b\)

      - c_exp – [in] Exponent associated with \(\bar c\)

      - b_hr – [in] Headroom of \(\bar b\)

      - c_hr – [in] Headroom of \(\bar c\)

  void vect_s16_scale_prepare(exponent_t *a_exp, right_shift_t *a_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 output shift used by vect_s16_scale().

    This function is used in conjunction with vect_s16_scale() to perform multiplication of a 16-bit BFP vector \(\bar{b} \cdot 2^{b\_exp}\) by a 16-bit scalar \(c \cdot 2^{c\_exp}\). The result is another 16-bit BFP vector \(\bar{a} \cdot 2^{a\_exp}\).

    This function computes `a_exp` and `a_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 inputs.

    `a_shr` is an arithmetic right-shift applied by vect_complex_s16_scale() to the 32-bit products of input elements to achieve the chosen output exponent `a_exp`.

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

    `b_hr` and `c_hr` are the headroom of \(\bar b\) and \(c\) respectively. If the headroom of \(\bar b\) or \(c\) are unknown, they can be obtained by calling vect_s16_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 `a_shr` produced by this function can be adjusted according to the following:

          exponent_t a_exp;
          right_shift_t a_shr;
          vect_s16_scale_prepare(&a_exp, &a_shr, b_exp, c_exp, b_hr, c_hr);
          exponent_t desired_exp = ...; // Value known a priori
          a_shr = a_shr + (desired_exp - a_exp);
          a_exp = desired_exp;

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

      - `a_shr >= 0`

      Be aware that using a smaller value than strictly necessary for `a_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 `INT16_MIN` will instead saturate to `-INT16_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_s16_scale

    Parameters:

      - a_exp – [out] Exponent of output elements of vect_s16_scale()

      - a_shr – [out] Right-shift supplied to vect_s16_scale()

      - b_exp – [in] Exponent associated with \(\bar b\)

      - c_exp – [in] Exponent associated with \(\bar c\)

      - b_hr – [in] Headroom of \(\bar b\)

      - c_hr – [in] Headroom of \(\bar c\)

  void vect_s16_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_s16_sqrt().

    This function is used in conjunction withx vect_s16_sqrt() to compute the square root of elements of a 16-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_s16_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_s16_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_s16_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_s16_sqrt

    Parameters:

      - a_exp – [out] Exponent of outputs of vect_s16_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}