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Convert add! to a function

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est31 2017-09-14 17:33:44 +02:00
parent 482d98318f
commit 3efae7f7d9
2 changed files with 159 additions and 157 deletions
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315
src/float/add.rs
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@ -1,195 +1,196 @@
use int::Int;
use int::{Int, CastInto};
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 = <$ty as Float>::Int::ZERO;
fn add<F: Float>(a: F, b: F) -> F where
u32: CastInto<F::Int>,
F::Int: CastInto<u32>,
i32: CastInto<F::Int>,
F::Int: CastInto<i32>,
{
let one = F::Int::ONE;
let zero = F::Int::ZERO;
let bits = <$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 <$ty as Float>::Int;
let max_exponent = (one << exponent_bits as usize) - one;
let bits = F::BITS.cast();
let significand_bits = F::SIGNIFICAND_BITS;
let max_exponent = F::EXPONENT_MAX;
let implicit_bit = one << significand_bits as usize;
let significand_mask = implicit_bit - one;
let sign_bit = <$ty>::SIGN_MASK as <$ty as Float>::Int;
let abs_mask = sign_bit - one;
let exponent_mask = abs_mask ^ significand_mask;
let inf_rep = exponent_mask;
let quiet_bit = implicit_bit >> 1;
let qnan_rep = exponent_mask | quiet_bit;
let implicit_bit = F::IMPLICIT_BIT;
let significand_mask = F::SIGNIFICAND_MASK;
let sign_bit = F::SIGN_MASK as F::Int;
let abs_mask = sign_bit - one;
let exponent_mask = F::EXPONENT_MASK;
let inf_rep = exponent_mask;
let quiet_bit = implicit_bit >> 1;
let qnan_rep = exponent_mask | quiet_bit;
let mut a_rep = a.repr();
let mut b_rep = b.repr();
let a_abs = a_rep & abs_mask;
let b_abs = b_rep & abs_mask;
let mut a_rep = a.repr();
let mut b_rep = b.repr();
let a_abs = a_rep & abs_mask;
let b_abs = b_rep & abs_mask;
// Detect if a or b is zero, infinity, or NaN.
if a_abs.wrapping_sub(one) >= inf_rep - one ||
b_abs.wrapping_sub(one) >= inf_rep - one {
// NaN + anything = qNaN
if a_abs > inf_rep {
return <$ty as Float>::from_repr(a_abs | quiet_bit);
}
// anything + NaN = qNaN
if b_abs > inf_rep {
return <$ty as Float>::from_repr(b_abs | quiet_bit);
// Detect if a or b is zero, infinity, or NaN.
if a_abs.wrapping_sub(one) >= inf_rep - one ||
b_abs.wrapping_sub(one) >= inf_rep - one {
// NaN + anything = qNaN
if a_abs > inf_rep {
return F::from_repr(a_abs | quiet_bit);
}
// anything + NaN = qNaN
if b_abs > inf_rep {
return F::from_repr(b_abs | quiet_bit);
}
if a_abs == inf_rep {
// +/-infinity + -/+infinity = qNaN
if (a.repr() ^ b.repr()) == sign_bit {
return F::from_repr(qnan_rep);
} else {
// +/-infinity + anything remaining = +/- infinity
return a;
}
}
if a_abs == inf_rep {
// +/-infinity + -/+infinity = qNaN
if (a.repr() ^ b.repr()) == sign_bit {
return <$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;
}
// anything remaining + +/-infinity = +/-infinity
if b_abs == inf_rep {
// zero + anything = anything
if a_abs == Int::ZERO {
// but we need to get the sign right for zero + zero
if b_abs == Int::ZERO {
return F::from_repr(a.repr() & b.repr());
} else {
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;
// anything + zero = anything
if b_abs == Int::ZERO {
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).cast();
let mut b_exponent: i32 = ((b_rep & exponent_mask) >> significand_bits).cast();
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).cast();
if align != Int::ZERO {
if align < bits {
let sticky = F::Int::from_bool(b_significand << bits.wrapping_sub(align).cast() != Int::ZERO);
b_significand = (b_significand >> align.cast()) | 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 == Int::ZERO {
return F::from_repr(Int::ZERO);
}
// 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 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;
}
if b_exponent == 0 {
let (exponent, significand) = <$ty>::normalize(b_significand);
b_exponent = exponent;
b_significand = significand;
} else /* addition */ {
a_significand += b_significand;
// If the addition carried up, we need to right-shift the result and
// adjust the exponent:
if a_significand & implicit_bit << 4 != Int::ZERO {
let sticky = F::Int::from_bool(a_significand & one != Int::ZERO);
a_significand = a_significand >> 1 | sticky;
a_exponent += 1;
}
}
// The sign of the result is the sign of the larger operand, a. If they
// have opposite signs, we are performing a subtraction; otherwise addition.
let result_sign = a_rep & sign_bit;
let subtraction = ((a_rep ^ b_rep) & sign_bit) != zero;
// If we have overflowed the type, return +/- infinity:
if a_exponent >= max_exponent as i32 {
return F::from_repr(inf_rep | result_sign);
}
// Shift the significands to give us round, guard and sticky, and or in the
// implicit significand bit. (If we fell through from the denormal path it
// was already set by normalize(), but setting it twice won't hurt
// anything.)
a_significand = (a_significand | implicit_bit) << 3;
b_significand = (b_significand | implicit_bit) << 3;
if a_exponent <= 0 {
// Result is denormal before rounding; the exponent is zero and we
// need to shift the significand.
let shift = (1 - a_exponent).cast();
let sticky = F::Int::from_bool((a_significand << bits.wrapping_sub(shift).cast()) != Int::ZERO);
a_significand = a_significand >> shift.cast() | sticky;
a_exponent = 0;
}
// Shift the significand of b by the difference in exponents, with a sticky
// bottom bit to get rounding correct.
let align = a_exponent.wrapping_sub(b_exponent) as <$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);
}
// Low three bits are round, guard, and sticky.
let a_significand_i32: i32 = a_significand.cast();
let round_guard_sticky: i32 = a_significand_i32 & 0x7;
// 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;
// Shift the significand into place, and mask off the implicit bit.
let mut result = a_significand >> 3 & significand_mask;
// 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 <$ty as Float>::Int;
a_significand = a_significand >> 1 | sticky;
a_exponent += 1;
}
}
// Insert the exponent and sign.
result |= a_exponent.cast() << significand_bits;
result |= result_sign;
// If we have overflowed the type, return +/- infinity:
if a_exponent >= max_exponent as i32 {
return <$ty>::from_repr(inf_rep | 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; }
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)
})
F::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)
add(a, b)
}
#[aapcs_on_arm]
#[arm_aeabi_alias = __aeabi_dadd]
pub extern "C" fn __adddf3(a: f64, b: f64) -> f64 {
add!(a, b, f64)
add(a, b)
}
}

1
src/int/mod.rs
View File

@ -25,6 +25,7 @@ pub trait Int:
ops::AddAssign +
ops::BitAndAssign +
ops::BitOrAssign +
ops::ShlAssign<i32> +
ops::ShrAssign<u32> +
ops::Add<Output = Self> +
ops::Sub<Output = Self> +