319 lines
12 KiB
Rust
319 lines
12 KiB
Rust
use core::mem;
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use core::num::Wrapping;
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use float::Float;
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macro_rules! add {
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($intrinsic:ident: $ty:ty) => {
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/// Returns `a + b`
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#[allow(unused_parens)]
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#[cfg_attr(not(test), no_mangle)]
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pub extern fn $intrinsic(a: $ty, b: $ty) -> $ty {
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let one = Wrapping(1 as <$ty as Float>::Int);
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let zero = Wrapping(0 as <$ty as Float>::Int);
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let bits = Wrapping(<$ty>::bits() as <$ty as Float>::Int);
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let significand_bits = Wrapping(<$ty>::significand_bits() as <$ty as Float>::Int);
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let exponent_bits = bits - significand_bits - one;
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let max_exponent = (one << exponent_bits.0 as usize) - one;
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let implicit_bit = one << significand_bits.0 as usize;
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let significand_mask = implicit_bit - one;
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let sign_bit = one << (significand_bits + exponent_bits).0 as usize;
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let abs_mask = sign_bit - one;
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let exponent_mask = abs_mask ^ significand_mask;
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let inf_rep = exponent_mask;
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let quiet_bit = implicit_bit >> 1;
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let qnan_rep = exponent_mask | quiet_bit;
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let mut a_rep = Wrapping(a.repr());
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let mut b_rep = Wrapping(b.repr());
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let a_abs = a_rep & abs_mask;
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let b_abs = b_rep & abs_mask;
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// Detect if a or b is zero, infinity, or NaN.
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if a_abs - one >= inf_rep - one ||
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b_abs - one >= inf_rep - one {
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// NaN + anything = qNaN
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if a_abs > inf_rep {
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return (<$ty as Float>::from_repr((a_abs | quiet_bit).0));
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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 (<$ty as Float>::from_repr((b_abs | quiet_bit).0));
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}
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if a_abs == inf_rep {
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// +/-infinity + -/+infinity = qNaN
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if (a.repr() ^ b.repr()) == sign_bit.0 {
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return (<$ty as Float>::from_repr(qnan_rep.0));
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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 == 0 {
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// but we need to get the sign right for zero + zero
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if b_abs.0 == 0 {
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return (<$ty as Float>::from_repr(a.repr() & b.repr()));
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} else {
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return b;
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}
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}
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// anything + zero = anything
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if b_abs.0 == 0 {
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return a;
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}
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}
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// Swap a and b if necessary so that a has the larger absolute value.
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if b_abs > a_abs {
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mem::swap(&mut a_rep, &mut b_rep);
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}
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// Extract the exponent and significand from the (possibly swapped) a and b.
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let mut a_exponent = Wrapping((a_rep >> significand_bits.0 as usize & max_exponent).0 as i32);
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let mut b_exponent = Wrapping((b_rep >> significand_bits.0 as usize & max_exponent).0 as i32);
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let mut a_significand = a_rep & significand_mask;
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let mut b_significand = b_rep & significand_mask;
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// normalize any denormals, and adjust the exponent accordingly.
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if a_exponent.0 == 0 {
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let (exponent, significand) = <$ty>::normalize(a_significand.0);
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a_exponent = Wrapping(exponent);
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a_significand = Wrapping(significand);
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}
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if b_exponent.0 == 0 {
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let (exponent, significand) = <$ty>::normalize(b_significand.0);
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b_exponent = Wrapping(exponent);
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b_significand = Wrapping(significand);
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}
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// The sign of the result is the sign of the larger operand, a. If they
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// have opposite signs, we are performing a subtraction; otherwise addition.
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let result_sign = a_rep & sign_bit;
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let subtraction = ((a_rep ^ b_rep) & sign_bit) != zero;
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// Shift the significands to give us round, guard and sticky, and or in the
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// implicit significand bit. (If we fell through from the denormal path it
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// was already set by normalize(), but setting it twice won't hurt
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// anything.)
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a_significand = (a_significand | implicit_bit) << 3;
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b_significand = (b_significand | implicit_bit) << 3;
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// Shift the significand of b by the difference in exponents, with a sticky
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// bottom bit to get rounding correct.
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let align = Wrapping((a_exponent - b_exponent).0 as <$ty as Float>::Int);
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if align.0 != 0 {
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if align < bits {
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let sticky = ((b_significand << (bits - align).0 as usize).0 != 0) as <$ty as Float>::Int;
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b_significand = (b_significand >> align.0 as usize) | Wrapping(sticky);
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} else {
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b_significand = one; // sticky; b is known to be non-zero.
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}
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}
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if subtraction {
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a_significand -= b_significand;
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// If a == -b, return +zero.
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if a_significand.0 == 0 {
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return (<$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.0.leading_zeros() as i32
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- (implicit_bit << 3).0.leading_zeros() as i32;
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a_significand <<= shift as usize;
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a_exponent -= Wrapping(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 != 0 {
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let sticky = ((a_significand & one).0 != 0) as <$ty as Float>::Int;
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a_significand = a_significand >> 1 | Wrapping(sticky);
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a_exponent += Wrapping(1);
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}
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}
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// If we have overflowed the type, return +/- infinity:
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if a_exponent >= Wrapping(max_exponent.0 as i32) {
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return (<$ty>::from_repr((inf_rep | result_sign).0));
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}
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if a_exponent.0 <= 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 = Wrapping((Wrapping(1) - a_exponent).0 as <$ty as Float>::Int);
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let sticky = ((a_significand << (bits - shift).0 as usize).0 != 0) as <$ty as Float>::Int;
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a_significand = a_significand >> shift.0 as usize | Wrapping(sticky);
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a_exponent = Wrapping(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.0 & 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 |= Wrapping(a_exponent.0 as <$ty as Float>::Int) << significand_bits.0 as usize;
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result |= result_sign;
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// Final rounding. The result may overflow to infinity, but that is the
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// correct result in that case.
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if round_guard_sticky > 0x4 { result += one; }
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if round_guard_sticky == 0x4 { result += result & one; }
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return (<$ty>::from_repr(result.0));
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}
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}
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}
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add!(__addsf3: f32);
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add!(__adddf3: f64);
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#[cfg(test)]
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mod tests {
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use core::{f32, f64};
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use float::Float;
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use qc::{U32, U64};
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// NOTE The tests below have special handing for NaN values.
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// Because NaN != NaN, the floating-point representations must be used
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// Because there are many diffferent values of NaN, and the implementation
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// doesn't care about calculating the 'correct' one, if both values are NaN
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// the values are considered equivalent.
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struct FRepr<F>(F);
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impl<F: Float> PartialEq for FRepr<F> {
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fn eq(&self, other: &FRepr<F>) -> bool {
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// NOTE(cfg) for some reason, on hard float targets, our implementation doesn't
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// match the output of its gcc_s counterpart. Until we investigate further, we'll
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// just avoid testing against gcc_s on those targets. Do note that our
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// implementation matches the output of the FPU instruction on *hard* float targets
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// and matches its gcc_s counterpart on *soft* float targets.
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if cfg!(gnueabihf) {
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return true
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}
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self.0.eq_repr(other.0)
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}
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}
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// TODO: Add F32/F64 to qc so that they print the right values (at the very least)
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check! {
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fn __addsf3(f: extern fn(f32, f32) -> f32,
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a: U32,
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b: U32)
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-> Option<FRepr<f32> > {
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let (a, b) = (f32::from_repr(a.0), f32::from_repr(b.0));
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Some(FRepr(f(a, b)))
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}
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fn __adddf3(f: extern fn(f64, f64) -> f64,
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a: U64,
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b: U64) -> Option<FRepr<f64> > {
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let (a, b) = (f64::from_repr(a.0), f64::from_repr(b.0));
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Some(FRepr(f(a, b)))
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}
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}
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// More tests for special float values
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#[test]
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fn test_float_tiny_plus_tiny() {
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let tiny = f32::from_repr(1);
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let r = super::__addsf3(tiny, tiny);
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assert!(r.eq_repr(tiny + tiny));
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}
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#[test]
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fn test_double_tiny_plus_tiny() {
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let tiny = f64::from_repr(1);
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let r = super::__adddf3(tiny, tiny);
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assert!(r.eq_repr(tiny + tiny));
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}
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#[test]
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fn test_float_small_plus_small() {
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let a = f32::from_repr(327);
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let b = f32::from_repr(256);
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let r = super::__addsf3(a, b);
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assert!(r.eq_repr(a + b));
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}
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#[test]
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fn test_double_small_plus_small() {
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let a = f64::from_repr(327);
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let b = f64::from_repr(256);
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let r = super::__adddf3(a, b);
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assert!(r.eq_repr(a + b));
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}
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#[test]
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fn test_float_one_plus_one() {
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let r = super::__addsf3(1f32, 1f32);
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assert!(r.eq_repr(1f32 + 1f32));
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}
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#[test]
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fn test_double_one_plus_one() {
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let r = super::__adddf3(1f64, 1f64);
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assert!(r.eq_repr(1f64 + 1f64));
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}
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#[test]
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fn test_float_different_nan() {
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let a = f32::from_repr(1);
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let b = f32::from_repr(0b11111111100100010001001010101010);
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let x = super::__addsf3(a, b);
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let y = a + b;
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assert!(x.eq_repr(y));
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}
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#[test]
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fn test_double_different_nan() {
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let a = f64::from_repr(1);
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let b = f64::from_repr(0b1111111111110010001000100101010101001000101010000110100011101011);
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let x = super::__adddf3(a, b);
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let y = a + b;
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assert!(x.eq_repr(y));
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}
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#[test]
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fn test_float_nan() {
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let r = super::__addsf3(f32::NAN, 1.23);
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assert_eq!(r.repr(), f32::NAN.repr());
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}
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#[test]
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fn test_double_nan() {
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let r = super::__adddf3(f64::NAN, 1.23);
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assert_eq!(r.repr(), f64::NAN.repr());
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}
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#[test]
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fn test_float_inf() {
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let r = super::__addsf3(f32::INFINITY, -123.4);
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assert_eq!(r, f32::INFINITY);
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}
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#[test]
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fn test_double_inf() {
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let r = super::__adddf3(f64::INFINITY, -123.4);
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assert_eq!(r, f64::INFINITY);
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}
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}
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