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

use int::Int;
use float::Float;

/// Returns `a + b`
macro_rules! add {
    ($a:expr, $b:expr, $ty:ty) => ({
        let a = $a;
        let b = $b;
        let one = <$ty as Float>::Int::ONE;
        let zero = <$ty as Float>::Int::ZERO;

        let bits =             <$ty>::BITS as <$ty as Float>::Int;
        let significand_bits = <$ty>::SIGNIFICAND_BITS as <$ty as Float>::Int;
        let exponent_bits =    <$ty>::EXPONENT_BITS as <$ty as Float>::Int;
        let max_exponent =     (one << exponent_bits as usize) - one;

        let implicit_bit =     one << significand_bits as usize;
        let significand_mask = implicit_bit - one;
        let sign_bit =         <$ty>::SIGN_MASK as <$ty as Float>::Int;
        let abs_mask =         sign_bit - one;
        let exponent_mask =    abs_mask ^ significand_mask;
        let inf_rep =          exponent_mask;
        let quiet_bit =        implicit_bit >> 1;
        let qnan_rep =         exponent_mask | quiet_bit;

        let mut a_rep = a.repr();
        let mut b_rep = b.repr();
        let a_abs = a_rep & abs_mask;
        let b_abs = b_rep & abs_mask;

        // Detect if a or b is zero, infinity, or NaN.
        if a_abs.wrapping_sub(one) >= inf_rep - one ||
            b_abs.wrapping_sub(one) >= inf_rep - one {
            // NaN + anything = qNaN
            if a_abs > inf_rep {
                return <$ty as Float>::from_repr(a_abs | quiet_bit);
            }
            // anything + NaN = qNaN
            if b_abs > inf_rep {
                return <$ty as Float>::from_repr(b_abs | quiet_bit);
            }

            if a_abs == inf_rep {
                // +/-infinity + -/+infinity = qNaN
                if (a.repr() ^ b.repr()) == sign_bit {
                    return <$ty as Float>::from_repr(qnan_rep);
                } else {
                    // +/-infinity + anything remaining = +/- infinity
                    return a;
                }
            }

            // anything remaining + +/-infinity = +/-infinity
            if b_abs == inf_rep {
                return b;
            }

            // zero + anything = anything
            if a_abs == 0 {
                // but we need to get the sign right for zero + zero
                if b_abs == 0 {
                    return <$ty as Float>::from_repr(a.repr() & b.repr());
                } else {
                    return b;
                }
            }

            // anything + zero = anything
            if b_abs == 0 {
                 return a;
            }
        }

        // Swap a and b if necessary so that a has the larger absolute value.
        if b_abs > a_abs {
            // Don't use mem::swap because it may generate references to memcpy in unoptimized code.
            let tmp = a_rep;
            a_rep = b_rep;
            b_rep = tmp;
        }

        // Extract the exponent and significand from the (possibly swapped) a and b.
        let mut a_exponent = ((a_rep >> significand_bits) & max_exponent) as i32;
        let mut b_exponent = ((b_rep >> significand_bits) & max_exponent) as i32;
        let mut a_significand = a_rep & significand_mask;
        let mut b_significand = b_rep & significand_mask;

        // normalize any denormals, and adjust the exponent accordingly.
        if a_exponent == 0 {
            let (exponent, significand) = <$ty>::normalize(a_significand);
            a_exponent = exponent;
            a_significand = significand;
        }
        if b_exponent == 0 {
            let (exponent, significand) = <$ty>::normalize(b_significand);
            b_exponent = exponent;
            b_significand = significand;
        }

        // The sign of the result is the sign of the larger operand, a.  If they
        // have opposite signs, we are performing a subtraction; otherwise addition.
        let result_sign = a_rep & sign_bit;
        let subtraction = ((a_rep ^ b_rep) & sign_bit) != zero;

        // Shift the significands to give us round, guard and sticky, and 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 = (a_significand | implicit_bit) << 3;
        b_significand = (b_significand | implicit_bit) << 3;

        // Shift the significand of b by the difference in exponents, with a sticky
        // bottom bit to get rounding correct.
        let align = a_exponent.wrapping_sub(b_exponent) as <$ty as Float>::Int;
        if align != 0 {
            if align < bits {
                let sticky = (b_significand << (bits.wrapping_sub(align) as usize) != 0) as <$ty as Float>::Int;
                b_significand = (b_significand >> align as usize) | sticky;
            } else {
                b_significand = one; // sticky; b is known to be non-zero.
            }
        }
        if subtraction {
            a_significand = a_significand.wrapping_sub(b_significand);
            // If a == -b, return +zero.
            if a_significand == 0 {
                return <$ty as Float>::from_repr(0);
            }

            // If partial cancellation occured, we need to left-shift the result
            // and adjust the exponent:
            if a_significand < implicit_bit << 3 {
                let shift = a_significand.leading_zeros() as i32
                    - (implicit_bit << 3).leading_zeros() as i32;
                a_significand <<= shift as usize;
                a_exponent -= shift;
            }
        } else /* addition */ {
            a_significand += b_significand;

            // If the addition carried up, we need to right-shift the result and
            // adjust the exponent:
            if a_significand & implicit_bit << 4 != 0 {
                let sticky = (a_significand & one != 0) as <$ty as Float>::Int;
                a_significand = a_significand >> 1 | sticky;
                a_exponent += 1;
            }
        }

        // If we have overflowed the type, return +/- infinity:
        if a_exponent >= max_exponent as i32 {
            return <$ty>::from_repr(inf_rep | result_sign);
        }

        if a_exponent <= 0 {
            // Result is denormal before rounding; the exponent is zero and we
            // need to shift the significand.
            let shift = (1 - a_exponent) as <$ty as Float>::Int;
            let sticky = ((a_significand << bits.wrapping_sub(shift) as usize) != 0) as <$ty as Float>::Int;
            a_significand = a_significand >> shift as usize | sticky;
            a_exponent = 0;
        }

        // Low three bits are round, guard, and sticky.
        let round_guard_sticky: i32 = (a_significand & 0x7) as i32;

        // Shift the significand into place, and mask off the implicit bit.
        let mut result = a_significand >> 3 & significand_mask;

        // Insert the exponent and sign.
        result |= (a_exponent as <$ty as Float>::Int) << (significand_bits as usize);
        result |= result_sign;

        // Final rounding.  The result may overflow to infinity, but that is the
        // correct result in that case.
        if round_guard_sticky > 0x4 { result += one; }
        if round_guard_sticky == 0x4 { result += result & one; }

        <$ty>::from_repr(result)
    })
}

intrinsics! {
    #[aapcs_on_arm]
    #[arm_aeabi_alias = __aeabi_fadd]
    pub extern "C" fn __addsf3(a: f32, b: f32) -> f32 {
        add!(a, b, f32)
    }

    #[aapcs_on_arm]
    #[arm_aeabi_alias = __aeabi_dadd]
    pub extern "C" fn __adddf3(a: f64, b: f64) -> f64 {
        add!(a, b, f64)
    }
}