compiler-builtins-zynq/src/float/mul.rs

use int::{CastInto, Int, WideInt};
use float::Float;

fn mul<F: Float>(a: F, b: F) -> F
where
    u32: CastInto<F::Int>,
    F::Int: CastInto<u32>,
    i32: CastInto<F::Int>,
    F::Int: CastInto<i32>,
    F::Int: WideInt,
{
    let one = F::Int::ONE;
    let zero = F::Int::ZERO;

    let bits = F::BITS;
    let significand_bits = F::SIGNIFICAND_BITS;
    let max_exponent = F::EXPONENT_MAX;

    let exponent_bias = F::EXPONENT_BIAS;

    let implicit_bit = F::IMPLICIT_BIT;
    let significand_mask = F::SIGNIFICAND_MASK;
    let sign_bit = F::SIGN_MASK as F::Int;
    let abs_mask = sign_bit - one;
    let exponent_mask = F::EXPONENT_MASK;
    let inf_rep = exponent_mask;
    let quiet_bit = implicit_bit >> 1;
    let qnan_rep = exponent_mask | quiet_bit;
    let exponent_bits = F::EXPONENT_BITS;

    let a_rep = a.repr();
    let b_rep = b.repr();

    let a_exponent = (a_rep >> significand_bits) & max_exponent.cast();
    let b_exponent = (b_rep >> significand_bits) & max_exponent.cast();
    let product_sign = (a_rep ^ b_rep) & sign_bit;

    let mut a_significand = a_rep & significand_mask;
    let mut b_significand = b_rep & significand_mask;
    let mut scale = 0;

    // Detect if a or b is zero, denormal, infinity, or NaN.
    if a_exponent.wrapping_sub(one) >= (max_exponent - 1).cast()
        || b_exponent.wrapping_sub(one) >= (max_exponent - 1).cast()
    {
        let a_abs = a_rep & abs_mask;
        let b_abs = b_rep & abs_mask;

        // NaN + anything = qNaN
        if a_abs > inf_rep {
            return F::from_repr(a_rep | quiet_bit);
        }
        // anything + NaN = qNaN
        if b_abs > inf_rep {
            return F::from_repr(b_rep | quiet_bit);
        }

        if a_abs == inf_rep {
            if b_abs != zero {
                // infinity * non-zero = +/- infinity
                return F::from_repr(a_abs | product_sign);
            } else {
                // infinity * zero = NaN
                return F::from_repr(qnan_rep);
            }
        }

        if b_abs == inf_rep {
            if a_abs != zero {
                // infinity * non-zero = +/- infinity
                return F::from_repr(b_abs | product_sign);
            } else {
                // infinity * zero = NaN
                return F::from_repr(qnan_rep);
            }
        }

        // zero * anything = +/- zero
        if a_abs == zero {
            return F::from_repr(product_sign);
        }

        // anything * zero = +/- zero
        if b_abs == zero {
            return F::from_repr(product_sign);
        }

        // one or both of a or b is denormal, the other (if applicable) is a
        // normal number.  Renormalize one or both of a and b, and set scale to
        // include the necessary exponent adjustment.
        if a_abs < implicit_bit {
            let (exponent, significand) = F::normalize(a_significand);
            scale += exponent;
            a_significand = significand;
        }

        if b_abs < implicit_bit {
            let (exponent, significand) = F::normalize(b_significand);
            scale += exponent;
            b_significand = significand;
        }
    }

    // Or in the implicit significand bit.  (If we fell through from the
    // denormal path it was already set by normalize( ), but setting it twice
    // won't hurt anything.)
    a_significand |= implicit_bit;
    b_significand |= implicit_bit;

    // Get the significand of a*b.  Before multiplying the significands, shift
    // one of them left to left-align it in the field.  Thus, the product will
    // have (exponentBits + 2) integral digits, all but two of which must be
    // zero.  Normalizing this result is just a conditional left-shift by one
    // and bumping the exponent accordingly.
    let (mut product_high, mut product_low) =
        <F::Int as WideInt>::wide_mul(a_significand, b_significand << exponent_bits);

    let a_exponent_i32: i32 = a_exponent.cast();
    let b_exponent_i32: i32 = b_exponent.cast();
    let mut product_exponent: i32 = a_exponent_i32
        .wrapping_add(b_exponent_i32)
        .wrapping_add(scale)
        .wrapping_sub(exponent_bias as i32);

    // Normalize the significand, adjust exponent if needed.
    if (product_high & implicit_bit) != zero {
        product_exponent = product_exponent.wrapping_add(1);
    } else {
        <F::Int as WideInt>::wide_shift_left(&mut product_high, &mut product_low, 1);
    }

    // If we have overflowed the type, return +/- infinity.
    if product_exponent >= max_exponent as i32 {
        return F::from_repr(inf_rep | product_sign);
    }

    if product_exponent <= 0 {
        // Result is denormal before rounding
        //
        // If the result is so small that it just underflows to zero, return
        // a zero of the appropriate sign.  Mathematically there is no need to
        // handle this case separately, but we make it a special case to
        // simplify the shift logic.
        let shift = one.wrapping_sub(product_exponent.cast()).cast();
        if shift >= bits as i32 {
            return F::from_repr(product_sign);
        }

        // Otherwise, shift the significand of the result so that the round
        // bit is the high bit of productLo.
        <F::Int as WideInt>::wide_shift_right_with_sticky(
            &mut product_high,
            &mut product_low,
            shift,
        )
    } else {
        // Result is normal before rounding; insert the exponent.
        product_high &= significand_mask;
        product_high |= product_exponent.cast() << significand_bits;
    }

    // Insert the sign of the result:
    product_high |= product_sign;

    // Final rounding.  The final result may overflow to infinity, or underflow
    // to zero, but those are the correct results in those cases.  We use the
    // default IEEE-754 round-to-nearest, ties-to-even rounding mode.
    if product_low > sign_bit {
        product_high += one;
    }

    if product_low == sign_bit {
        product_high += product_high & one;
    }

    return F::from_repr(product_high);
}

intrinsics! {
    #[aapcs_on_arm]
    #[arm_aeabi_alias = __aeabi_fmul]
    pub extern "C" fn __mulsf3(a: f32, b: f32) -> f32 {
        mul(a, b)
    }

    #[aapcs_on_arm]
    #[arm_aeabi_alias = __aeabi_dmul]
    pub extern "C" fn __muldf3(a: f64, b: f64) -> f64 {
        mul(a, b)
    }

    pub extern "C" fn __mulsf3vfp(a: f32, b: f32) -> f32 {
        a * b
    }

    pub extern "C" fn __muldf3vfp(a: f64, b: f64) -> f64 {
        a * b
    }
}