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use crate::soft_f64::{u64_widen_mul, F64};
type F = F64;
type FInt = u64;
const fn widen_mul(a: FInt, b: FInt) -> (FInt, FInt) {
u64_widen_mul(a, b)
}
pub(crate) const fn mul(a: F, b: F) -> F {
let one: FInt = 1;
let zero: FInt = 0;
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 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 exponent_bits = F::EXPONENT_BITS;
let a_rep = a.repr();
let b_rep = b.repr();
let a_exponent = (a_rep >> significand_bits) & max_exponent as FInt;
let b_exponent = (b_rep >> significand_bits) & max_exponent as FInt;
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) as FInt
|| b_exponent.wrapping_sub(one) >= (max_exponent - 1) as FInt
{
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_low, mut product_high) =
widen_mul(a_significand, b_significand << exponent_bits);
let a_exponent_i32: i32 = a_exponent as _;
let b_exponent_i32: i32 = b_exponent as _;
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 {
product_high = (product_high << 1) | (product_low >> (bits - 1));
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 as FInt) as u32;
if shift >= bits {
return F::from_repr(product_sign);
}
// Otherwise, shift the significand of the result so that the round
// bit is the high bit of productLo.
if shift < bits {
let sticky = product_low << (bits - shift);
product_low = product_high << (bits - shift) | product_low >> shift | sticky;
product_high >>= shift;
} else if shift < (2 * bits) {
let sticky = product_high << (2 * bits - shift) | product_low;
product_low = product_high >> (shift - bits) | sticky;
product_high = zero;
} else {
product_high = zero;
}
} else {
// Result is normal before rounding; insert the exponent.
product_high &= significand_mask;
product_high |= (product_exponent as FInt) << 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;
}
F::from_repr(product_high)
}
#[cfg(test)]
mod test {
#[test]
fn sanity_check() {
assert_eq!(f64!(2.0).mul(f64!(2.0)), f64!(4.0))
}
}