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use crate::soft_f32::F32;
type F = F32;
type FInt = u32;
pub(crate) const fn add(a: F, b: F) -> F {
let one: FInt = 1;
let zero: FInt = 0;
let bits = F::BITS as FInt;
let significand_bits = F::SIGNIFICAND_BITS;
let max_exponent = F::EXPONENT_MAX;
let implicit_bit = F::IMPLICIT_BIT;
let significand_mask = F::SIGNIFICAND_MASK;
let sign_bit = F::SIGN_MASK as FInt;
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 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 F::from_repr(a_abs | quiet_bit);
}
// anything + NaN = qNaN
if b_abs > inf_rep {
return F::from_repr(b_abs | quiet_bit);
}
if a_abs == inf_rep {
// +/-infinity + -/+infinity = qNaN
if (a.repr() ^ b.repr()) == sign_bit {
return F::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 F::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: i32 = ((a_rep & exponent_mask) >> significand_bits) as _;
let mut b_exponent: i32 = ((b_rep & exponent_mask) >> significand_bits) as _;
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) = F::normalize(a_significand);
a_exponent = exponent;
a_significand = significand;
}
if b_exponent == 0 {
let (exponent, significand) = F::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 _;
if align != 0 {
if align < bits {
let sticky = (b_significand << bits.wrapping_sub(align) != 0) as FInt;
b_significand = (b_significand >> align) | 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 F::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;
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 FInt;
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 F::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 _;
let sticky = ((a_significand << bits.wrapping_sub(shift)) != 0) as FInt;
a_significand = a_significand >> shift | sticky;
a_exponent = 0;
}
// Low three bits are round, guard, and sticky.
let a_significand_i32: i32 = a_significand as _;
let round_guard_sticky: i32 = a_significand_i32 & 0x7;
// 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 FInt) << significand_bits;
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;
}
F::from_repr(result)
}
#[cfg(test)]
mod test {
#[test]
fn sanity_check() {
assert_eq!(f32!(1.0).add(f32!(1.0)), f32!(2.0))
}
}