use core::mem; use core::num::Wrapping; use float::Float; macro_rules! add { ($abi:tt, $intrinsic:ident: $ty:ty) => { /// Returns `a + b` #[allow(unused_parens)] #[cfg_attr(not(test), no_mangle)] pub extern $abi fn $intrinsic(a: $ty, b: $ty) -> $ty { let one = Wrapping(1 as <$ty as Float>::Int); let zero = Wrapping(0 as <$ty as Float>::Int); let bits = Wrapping(<$ty>::bits() as <$ty as Float>::Int); let significand_bits = Wrapping(<$ty>::significand_bits() as <$ty as Float>::Int); let exponent_bits = bits - significand_bits - one; let max_exponent = (one << exponent_bits.0 as usize) - one; let implicit_bit = one << significand_bits.0 as usize; let significand_mask = implicit_bit - one; let sign_bit = one << (significand_bits + exponent_bits).0 as usize; let abs_mask = sign_bit - one; let exponent_mask = abs_mask ^ significand_mask; let inf_rep = exponent_mask; let quiet_bit = implicit_bit >> 1; let qnan_rep = exponent_mask | quiet_bit; let mut a_rep = Wrapping(a.repr()); let mut b_rep = Wrapping(b.repr()); let a_abs = a_rep & abs_mask; let b_abs = b_rep & abs_mask; // Detect if a or b is zero, infinity, or NaN. if a_abs - one >= inf_rep - one || b_abs - one >= inf_rep - one { // NaN + anything = qNaN if a_abs > inf_rep { return (<$ty as Float>::from_repr((a_abs | quiet_bit).0)); } // anything + NaN = qNaN if b_abs > inf_rep { return (<$ty as Float>::from_repr((b_abs | quiet_bit).0)); } if a_abs == inf_rep { // +/-infinity + -/+infinity = qNaN if (a.repr() ^ b.repr()) == sign_bit.0 { return (<$ty as Float>::from_repr(qnan_rep.0)); } 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 == 0 { // but we need to get the sign right for zero + zero if b_abs.0 == 0 { return (<$ty as Float>::from_repr(a.repr() & b.repr())); } else { return b; } } // anything + zero = anything if b_abs.0 == 0 { return a; } } // Swap a and b if necessary so that a has the larger absolute value. if b_abs > a_abs { mem::swap(&mut a_rep, &mut b_rep); } // Extract the exponent and significand from the (possibly swapped) a and b. let mut a_exponent = Wrapping((a_rep >> significand_bits.0 as usize & max_exponent).0 as i32); let mut b_exponent = Wrapping((b_rep >> significand_bits.0 as usize & max_exponent).0 as i32); let mut a_significand = a_rep & significand_mask; let mut b_significand = b_rep & significand_mask; // normalize any denormals, and adjust the exponent accordingly. if a_exponent.0 == 0 { let (exponent, significand) = <$ty>::normalize(a_significand.0); a_exponent = Wrapping(exponent); a_significand = Wrapping(significand); } if b_exponent.0 == 0 { let (exponent, significand) = <$ty>::normalize(b_significand.0); b_exponent = Wrapping(exponent); b_significand = Wrapping(significand); } // The sign of the result is the sign of the larger operand, a. If they // have opposite signs, we are performing a subtraction; otherwise addition. let result_sign = a_rep & sign_bit; let subtraction = ((a_rep ^ b_rep) & sign_bit) != zero; // Shift the significands to give us round, guard and sticky, and or in the // implicit significand bit. (If we fell through from the denormal path it // was already set by normalize(), but setting it twice won't hurt // anything.) a_significand = (a_significand | implicit_bit) << 3; b_significand = (b_significand | implicit_bit) << 3; // Shift the significand of b by the difference in exponents, with a sticky // bottom bit to get rounding correct. let align = Wrapping((a_exponent - b_exponent).0 as <$ty as Float>::Int); if align.0 != 0 { if align < bits { let sticky = ((b_significand << (bits - align).0 as usize).0 != 0) as <$ty as Float>::Int; b_significand = (b_significand >> align.0 as usize) | Wrapping(sticky); } else { b_significand = one; // sticky; b is known to be non-zero. } } if subtraction { a_significand -= b_significand; // If a == -b, return +zero. if a_significand.0 == 0 { return (<$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.0.leading_zeros() as i32 - (implicit_bit << 3).0.leading_zeros() as i32; a_significand <<= shift as usize; a_exponent -= Wrapping(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 != 0 { let sticky = ((a_significand & one).0 != 0) as <$ty as Float>::Int; a_significand = a_significand >> 1 | Wrapping(sticky); a_exponent += Wrapping(1); } } // If we have overflowed the type, return +/- infinity: if a_exponent >= Wrapping(max_exponent.0 as i32) { return (<$ty>::from_repr((inf_rep | result_sign).0)); } if a_exponent.0 <= 0 { // Result is denormal before rounding; the exponent is zero and we // need to shift the significand. let shift = Wrapping((Wrapping(1) - a_exponent).0 as <$ty as Float>::Int); let sticky = ((a_significand << (bits - shift).0 as usize).0 != 0) as <$ty as Float>::Int; a_significand = a_significand >> shift.0 as usize | Wrapping(sticky); a_exponent = Wrapping(0); } // Low three bits are round, guard, and sticky. let round_guard_sticky: i32 = (a_significand.0 & 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 |= Wrapping(a_exponent.0 as <$ty as Float>::Int) << significand_bits.0 as usize; result |= result_sign; // Final rounding. The result may overflow to infinity, but that is the // correct result in that case. if round_guard_sticky > 0x4 { result += one; } if round_guard_sticky == 0x4 { result += result & one; } <$ty>::from_repr(result.0) } } } #[cfg(target_arch = "arm")] add!("aapcs", __addsf3: f32); #[cfg(not(target_arch = "arm"))] add!("C", __addsf3: f32); #[cfg(target_arch = "arm")] add!("aapcs", __adddf3: f64); #[cfg(not(target_arch = "arm"))] add!("C", __adddf3: f64);