196 lines
7.5 KiB
Rust
196 lines
7.5 KiB
Rust
use int::Int;
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use float::Float;
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/// Returns `a + b`
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macro_rules! add {
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($a:expr, $b:expr, $ty:ty) => ({
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let a = $a;
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let b = $b;
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let one = <$ty as Float>::Int::ONE;
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let zero = <$ty as Float>::Int::ZERO;
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let bits = <$ty>::BITS as <$ty as Float>::Int;
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let significand_bits = <$ty>::SIGNIFICAND_BITS as <$ty as Float>::Int;
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let exponent_bits = <$ty>::EXPONENT_BITS as <$ty as Float>::Int;
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let max_exponent = (one << exponent_bits as usize) - one;
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let implicit_bit = one << significand_bits as usize;
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let significand_mask = implicit_bit - one;
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let sign_bit = <$ty>::SIGN_MASK as <$ty as Float>::Int;
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let abs_mask = sign_bit - one;
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let exponent_mask = abs_mask ^ significand_mask;
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let inf_rep = exponent_mask;
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let quiet_bit = implicit_bit >> 1;
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let qnan_rep = exponent_mask | quiet_bit;
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let mut a_rep = a.repr();
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let mut b_rep = b.repr();
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let a_abs = a_rep & abs_mask;
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let b_abs = b_rep & abs_mask;
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// Detect if a or b is zero, infinity, or NaN.
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if a_abs.wrapping_sub(one) >= inf_rep - one ||
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b_abs.wrapping_sub(one) >= inf_rep - one {
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// NaN + anything = qNaN
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if a_abs > inf_rep {
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return <$ty as Float>::from_repr(a_abs | quiet_bit);
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}
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// anything + NaN = qNaN
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if b_abs > inf_rep {
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return <$ty as Float>::from_repr(b_abs | quiet_bit);
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}
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if a_abs == inf_rep {
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// +/-infinity + -/+infinity = qNaN
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if (a.repr() ^ b.repr()) == sign_bit {
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return <$ty as Float>::from_repr(qnan_rep);
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} else {
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// +/-infinity + anything remaining = +/- infinity
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return a;
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}
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}
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// anything remaining + +/-infinity = +/-infinity
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if b_abs == inf_rep {
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return b;
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}
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// zero + anything = anything
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if a_abs == 0 {
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// but we need to get the sign right for zero + zero
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if b_abs == 0 {
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return <$ty as Float>::from_repr(a.repr() & b.repr());
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} else {
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return b;
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}
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}
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// anything + zero = anything
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if b_abs == 0 {
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return a;
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}
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}
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// Swap a and b if necessary so that a has the larger absolute value.
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if b_abs > a_abs {
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// Don't use mem::swap because it may generate references to memcpy in unoptimized code.
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let tmp = a_rep;
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a_rep = b_rep;
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b_rep = tmp;
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}
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// Extract the exponent and significand from the (possibly swapped) a and b.
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let mut a_exponent = ((a_rep >> significand_bits) & max_exponent) as i32;
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let mut b_exponent = ((b_rep >> significand_bits) & max_exponent) as i32;
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let mut a_significand = a_rep & significand_mask;
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let mut b_significand = b_rep & significand_mask;
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// normalize any denormals, and adjust the exponent accordingly.
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if a_exponent == 0 {
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let (exponent, significand) = <$ty>::normalize(a_significand);
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a_exponent = exponent;
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a_significand = significand;
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}
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if b_exponent == 0 {
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let (exponent, significand) = <$ty>::normalize(b_significand);
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b_exponent = exponent;
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b_significand = significand;
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}
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// The sign of the result is the sign of the larger operand, a. If they
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// have opposite signs, we are performing a subtraction; otherwise addition.
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let result_sign = a_rep & sign_bit;
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let subtraction = ((a_rep ^ b_rep) & sign_bit) != zero;
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// Shift the significands to give us round, guard and sticky, and or in the
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// implicit significand bit. (If we fell through from the denormal path it
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// was already set by normalize(), but setting it twice won't hurt
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// anything.)
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a_significand = (a_significand | implicit_bit) << 3;
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b_significand = (b_significand | implicit_bit) << 3;
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// Shift the significand of b by the difference in exponents, with a sticky
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// bottom bit to get rounding correct.
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let align = a_exponent.wrapping_sub(b_exponent) as <$ty as Float>::Int;
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if align != 0 {
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if align < bits {
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let sticky = (b_significand << (bits.wrapping_sub(align) as usize) != 0) as <$ty as Float>::Int;
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b_significand = (b_significand >> align as usize) | sticky;
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} else {
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b_significand = one; // sticky; b is known to be non-zero.
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}
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}
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if subtraction {
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a_significand = a_significand.wrapping_sub(b_significand);
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// If a == -b, return +zero.
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if a_significand == 0 {
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return <$ty as Float>::from_repr(0);
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}
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// If partial cancellation occured, we need to left-shift the result
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// and adjust the exponent:
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if a_significand < implicit_bit << 3 {
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let shift = a_significand.leading_zeros() as i32
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- (implicit_bit << 3).leading_zeros() as i32;
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a_significand <<= shift as usize;
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a_exponent -= shift;
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}
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} else /* addition */ {
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a_significand += b_significand;
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// If the addition carried up, we need to right-shift the result and
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// adjust the exponent:
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if a_significand & implicit_bit << 4 != 0 {
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let sticky = (a_significand & one != 0) as <$ty as Float>::Int;
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a_significand = a_significand >> 1 | sticky;
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a_exponent += 1;
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}
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}
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// If we have overflowed the type, return +/- infinity:
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if a_exponent >= max_exponent as i32 {
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return <$ty>::from_repr(inf_rep | result_sign);
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}
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if a_exponent <= 0 {
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// Result is denormal before rounding; the exponent is zero and we
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// need to shift the significand.
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let shift = (1 - a_exponent) as <$ty as Float>::Int;
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let sticky = ((a_significand << bits.wrapping_sub(shift) as usize) != 0) as <$ty as Float>::Int;
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a_significand = a_significand >> shift as usize | sticky;
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a_exponent = 0;
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}
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// Low three bits are round, guard, and sticky.
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let round_guard_sticky: i32 = (a_significand & 0x7) as i32;
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// Shift the significand into place, and mask off the implicit bit.
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let mut result = a_significand >> 3 & significand_mask;
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// Insert the exponent and sign.
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result |= (a_exponent as <$ty as Float>::Int) << (significand_bits as usize);
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result |= result_sign;
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// Final rounding. The result may overflow to infinity, but that is the
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// correct result in that case.
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if round_guard_sticky > 0x4 { result += one; }
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if round_guard_sticky == 0x4 { result += result & one; }
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<$ty>::from_repr(result)
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})
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}
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intrinsics! {
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#[aapcs_on_arm]
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#[arm_aeabi_alias = __aeabi_fadd]
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pub extern "C" fn __addsf3(a: f32, b: f32) -> f32 {
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add!(a, b, f32)
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}
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#[aapcs_on_arm]
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#[arm_aeabi_alias = __aeabi_dadd]
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pub extern "C" fn __adddf3(a: f64, b: f64) -> f64 {
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add!(a, b, f64)
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}
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}
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