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Don't use the Wrapping wrapper in float addition 

Inspired by a patch by mattico.
This commit is contained in:
est31 2017-09-14 02:08:28 +02:00
parent 72ed4c8bce
commit a272d753f5
1 changed files with 52 additions and 54 deletions
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106
src/float/add.rs
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@ -1,5 +1,3 @@
use core::num::Wrapping;
use int::Int;
use float::Float;
@ -8,44 +6,44 @@ macro_rules! add {
($a:expr, $b:expr, $ty:ty) => ({
let a = $a;
let b = $b;
let one = Wrapping(<$ty as Float>::Int::ONE);
let zero = Wrapping(<$ty as Float>::Int::ZERO);
let one = <$ty as Float>::Int::ONE;
let zero = <$ty as Float>::Int::ZERO;
let bits = Wrapping(<$ty>::BITS as <$ty as Float>::Int);
let significand_bits = Wrapping(<$ty>::SIGNIFICAND_BITS as <$ty as Float>::Int);
let exponent_bits = bits - significand_bits - one;
let max_exponent = (one << exponent_bits.0 as usize) - one;
let bits = <$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 <$ty as Float>::Int;
let max_exponent = (one << exponent_bits as usize) - one;
let implicit_bit = one << significand_bits.0 as usize;
let implicit_bit = one << significand_bits as usize;
let significand_mask = implicit_bit - one;
let sign_bit = one << (significand_bits + exponent_bits).0 as usize;
let sign_bit = <$ty>::SIGN_MASK as <$ty as Float>::Int;
let abs_mask = sign_bit - one;
let exponent_mask = abs_mask ^ significand_mask;
let inf_rep = exponent_mask;
let quiet_bit = implicit_bit >> 1;
let qnan_rep = exponent_mask | quiet_bit;
let mut a_rep = Wrapping(a.repr());
let mut b_rep = Wrapping(b.repr());
let mut a_rep = a.repr();
let mut b_rep = b.repr();
let a_abs = a_rep & abs_mask;
let b_abs = b_rep & abs_mask;
// Detect if a or b is zero, infinity, or NaN.
if a_abs - one >= inf_rep - one ||
b_abs - one >= inf_rep - one {
if a_abs.wrapping_sub(one) >= inf_rep - one ||
b_abs.wrapping_sub(one) >= inf_rep - one {
// NaN + anything = qNaN
if a_abs > inf_rep {
return <$ty as Float>::from_repr((a_abs | quiet_bit).0);
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).0);
return <$ty as Float>::from_repr(b_abs | quiet_bit);
}
if a_abs == inf_rep {
// +/-infinity + -/+infinity = qNaN
if (a.repr() ^ b.repr()) == sign_bit.0 {
return <$ty as Float>::from_repr(qnan_rep.0);
if (a.repr() ^ b.repr()) == sign_bit {
return <$ty as Float>::from_repr(qnan_rep);
} else {
// +/-infinity + anything remaining = +/- infinity
return a;
@ -58,9 +56,9 @@ macro_rules! add {
}
// zero + anything = anything
if a_abs.0 == 0 {
if a_abs == 0 {
// but we need to get the sign right for zero + zero
if b_abs.0 == 0 {
if b_abs == 0 {
return <$ty as Float>::from_repr(a.repr() & b.repr());
} else {
return b;
@ -68,7 +66,7 @@ macro_rules! add {
}
// anything + zero = anything
if b_abs.0 == 0 {
if b_abs == 0 {
return a;
}
}
@ -82,21 +80,21 @@ macro_rules! add {
}
// 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_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 == 0 {
let (exponent, significand) = <$ty>::normalize(a_significand.0);
a_exponent = Wrapping(exponent);
a_significand = Wrapping(significand);
if a_exponent == 0 {
let (exponent, significand) = <$ty>::normalize(a_significand);
a_exponent = exponent;
a_significand = significand;
}
if b_exponent.0 == 0 {
let (exponent, significand) = <$ty>::normalize(b_significand.0);
b_exponent = Wrapping(exponent);
b_significand = Wrapping(significand);
if b_exponent == 0 {
let (exponent, significand) = <$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
@ -113,64 +111,64 @@ macro_rules! add {
// 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 <$ty as Float>::Int);
if align.0 != 0 {
let align = a_exponent.wrapping_sub(b_exponent) as <$ty as Float>::Int;
if align != 0 {
if align < bits {
let sticky = ((b_significand << (bits - align).0 as usize).0 != 0) as <$ty as Float>::Int;
b_significand = (b_significand >> align.0 as usize) | Wrapping(sticky);
let sticky = (b_significand << (bits.wrapping_sub(align) as usize) != 0) as <$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 -= b_significand;
a_significand = a_significand.wrapping_sub(b_significand);
// If a == -b, return +zero.
if a_significand.0 == 0 {
if a_significand == 0 {
return <$ty as Float>::from_repr(0);
}
// If partial cancellation occured, we need to left-shift the result
// and adjust the exponent:
if a_significand < implicit_bit << 3 {
let shift = a_significand.0.leading_zeros() as i32
- (implicit_bit << 3).0.leading_zeros() as i32;
let shift = a_significand.leading_zeros() as i32
- (implicit_bit << 3).leading_zeros() as i32;
a_significand <<= shift as usize;
a_exponent -= Wrapping(shift);
a_exponent -= shift;
}
} else /* addition */ {
a_significand += b_significand;
// If the addition carried up, we need to right-shift the result and
// adjust the exponent:
if (a_significand & implicit_bit << 4).0 != 0 {
let sticky = ((a_significand & one).0 != 0) as <$ty as Float>::Int;
a_significand = a_significand >> 1 | Wrapping(sticky);
a_exponent += Wrapping(1);
if a_significand & implicit_bit << 4 != 0 {
let sticky = (a_significand & one != 0) as <$ty as Float>::Int;
a_significand = a_significand >> 1 | sticky;
a_exponent += 1;
}
}
// If we have overflowed the type, return +/- infinity:
if a_exponent >= Wrapping(max_exponent.0 as i32) {
return <$ty>::from_repr((inf_rep | result_sign).0);
if a_exponent >= max_exponent as i32 {
return <$ty>::from_repr(inf_rep | result_sign);
}
if a_exponent.0 <= 0 {
if a_exponent <= 0 {
// Result is denormal before rounding; the exponent is zero and we
// need to shift the significand.
let shift = Wrapping((Wrapping(1) - a_exponent).0 as <$ty as Float>::Int);
let sticky = ((a_significand << (bits - shift).0 as usize).0 != 0) as <$ty as Float>::Int;
a_significand = a_significand >> shift.0 as usize | Wrapping(sticky);
a_exponent = Wrapping(0);
let shift = (1 - a_exponent) as <$ty as Float>::Int;
let sticky = ((a_significand << bits.wrapping_sub(shift) as usize) != 0) as <$ty as Float>::Int;
a_significand = a_significand >> shift as usize | sticky;
a_exponent = 0;
}
// Low three bits are round, guard, and sticky.
let round_guard_sticky: i32 = (a_significand.0 & 0x7) as i32;
let round_guard_sticky: i32 = (a_significand & 0x7) as i32;
// Shift the significand into place, and mask off the implicit bit.
let mut result = a_significand >> 3 & significand_mask;
// Insert the exponent and sign.
result |= Wrapping(a_exponent.0 as <$ty as Float>::Int) << significand_bits.0 as usize;
result |= (a_exponent as <$ty as Float>::Int) << (significand_bits as usize);
result |= result_sign;
// Final rounding. The result may overflow to infinity, but that is the
@ -178,7 +176,7 @@ macro_rules! add {
if round_guard_sticky > 0x4 { result += one; }
if round_guard_sticky == 0x4 { result += result & one; }
<$ty>::from_repr(result.0)
<$ty>::from_repr(result)
})
}