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# 16-bit scalar API

group scalar_s16_api

  Functions

  int32_t s16_to_s32(exponent_t *a_exp, const int16_t b, const exponent_t b_exp, const unsigned remove_hr)

    Convert a 16-bit floating-point scalar to a 32-bit floating-point scalar.

    Converts a 16-bit floating-point scalar, represented by the 16-bit mantissa `b` and exponent `b_exp`, into a 32-bit floating-point scalar, represented by the 32-bit returned mantissa and output exponent `a_exp`.

    `remove_hr`, if nonzero, indicates that the output mantissa should have no headroom. Otherwise, the output mantissa will be the same as the input mantissa.

    Parameters:

      - a_exp – [out] Output exponent

      - b – [in] 16-bit input mantissa

      - b_exp – [in] Input exponent

      - remove_hr – [in] Whether to remove headroom in output

    Returns:

      32-bit output mantissa

  int16_t s16_inverse(exponent_t *a_exp, const int16_t b)

    Compute the inverse of a 16-bit integer.

    `b` represents the integer \(b\) . `a` and `a_exp` together represent the result \(a \cdot 2^{a\_exp}\) .

    Operation Performed

      \[\begin{aligned} a \cdot 2^{a\_exp} \leftarrow \frac{1}{b} \end{aligned}\]
    Parameters:

      - a_exp – [out] Output exponent \(a\_exp\)

      - b – [in] Input integer \(b\)

    Returns:

      Output mantissa \(a\)

  int16_t s16_mul(exponent_t *a_exp, const int16_t b, const int16_t c, const exponent_t b_exp, const exponent_t c_exp)

    Compute the product of two 16-bit floating-point scalars.

    `a` and `a_exp` together represent the result \(a \cdot 2^{a\_exp}\) .

    `b` and `b_exp` together represent the result \(b \cdot 2^{b\_exp}\) .

    `c` and `c_exp` together represent the result \(c \cdot 2^{c\_exp}\) .

    Operation Performed

      \[\begin{aligned} a \cdot 2^{a\_exp} \leftarrow \left( b\cdot 2^{b\_exp} \right) \cdot \left( c\cdot 2^{c\_exp} \right) \end{aligned}\]
    Parameters:

      - a_exp – [out] Output exponent \(a\_exp\)

      - b – [in] First input mantissa \(b\)

      - c – [in] Second input mantissa \(c\)

      - b_exp – [in] First input exponent \(b\_exp\)

      - c_exp – [in] Second input exponent \(c\_exp\)

    Returns:

      Output mantissa \(a\)