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use crate::{Category, ExpInt, Float, FloatConvert, Round, ParseError, Status, StatusAnd};
use crate::ieee;
use std::cmp::Ordering;
use std::fmt;
use std::ops::Neg;
#[must_use]
#[derive(Copy, Clone, PartialEq, PartialOrd, Debug)]
pub struct DoubleFloat<F>(F, F);
pub type DoubleDouble = DoubleFloat<ieee::Double>;
// These are legacy semantics for the Fallback, inaccurate implementation of
// IBM double-double, if the accurate DoubleDouble doesn't handle the
// operation. It's equivalent to having an IEEE number with consecutive 106
// bits of mantissa and 11 bits of exponent.
//
// It's not equivalent to IBM double-double. For example, a legit IBM
// double-double, 1 + epsilon:
//
// 1 + epsilon = 1 + (1 >> 1076)
//
// is not representable by a consecutive 106 bits of mantissa.
//
// Currently, these semantics are used in the following way:
//
// DoubleDouble -> (Double, Double) ->
// DoubleDouble's Fallback -> IEEE operations
//
// FIXME: Implement all operations in DoubleDouble, and delete these
// semantics.
// FIXME(eddyb) This shouldn't need to be `pub`, it's only used in bounds.
pub struct FallbackS<F>(F);
type Fallback<F> = ieee::IeeeFloat<FallbackS<F>>;
impl<F: Float> ieee::Semantics for FallbackS<F> {
// Forbid any conversion to/from bits.
const BITS: usize = 0;
const PRECISION: usize = F::PRECISION * 2;
const MAX_EXP: ExpInt = F::MAX_EXP as ExpInt;
const MIN_EXP: ExpInt = F::MIN_EXP as ExpInt + F::PRECISION as ExpInt;
}
// Convert number to F. To avoid spurious underflows, we re-
// normalize against the F exponent range first, and only *then*
// truncate the mantissa. The result of that second conversion
// may be inexact, but should never underflow.
// FIXME(eddyb) This shouldn't need to be `pub`, it's only used in bounds.
pub struct FallbackExtendedS<F>(F);
type FallbackExtended<F> = ieee::IeeeFloat<FallbackExtendedS<F>>;
impl<F: Float> ieee::Semantics for FallbackExtendedS<F> {
// Forbid any conversion to/from bits.
const BITS: usize = 0;
const PRECISION: usize = Fallback::<F>::PRECISION;
const MAX_EXP: ExpInt = F::MAX_EXP as ExpInt;
}
impl<F: Float> From<Fallback<F>> for DoubleFloat<F>
where
F: FloatConvert<FallbackExtended<F>>,
FallbackExtended<F>: FloatConvert<F>,
{
fn from(x: Fallback<F>) -> Self {
let mut status;
let mut loses_info = false;
let extended: FallbackExtended<F> = unpack!(status=, x.convert(&mut loses_info));
assert_eq!((status, loses_info), (Status::OK, false));
let a = unpack!(status=, extended.convert(&mut loses_info));
assert_eq!(status - Status::INEXACT, Status::OK);
// If conversion was exact or resulted in a special case, we're done;
// just set the second double to zero. Otherwise, re-convert back to
// the extended format and compute the difference. This now should
// convert exactly to double.
let b = if a.is_finite_non_zero() && loses_info {
let u: FallbackExtended<F> = unpack!(status=, a.convert(&mut loses_info));
assert_eq!((status, loses_info), (Status::OK, false));
let v = unpack!(status=, extended - u);
assert_eq!(status, Status::OK);
let v = unpack!(status=, v.convert(&mut loses_info));
assert_eq!((status, loses_info), (Status::OK, false));
v
} else {
F::ZERO
};
DoubleFloat(a, b)
}
}
impl<F: FloatConvert<Self>> From<DoubleFloat<F>> for Fallback<F> {
fn from(DoubleFloat(a, b): DoubleFloat<F>) -> Self {
let mut status;
let mut loses_info = false;
// Get the first F and convert to our format.
let a = unpack!(status=, a.convert(&mut loses_info));
assert_eq!((status, loses_info), (Status::OK, false));
// Unless we have a special case, add in second F.
if a.is_finite_non_zero() {
let b = unpack!(status=, b.convert(&mut loses_info));
assert_eq!((status, loses_info), (Status::OK, false));
(a + b).value
} else {
a
}
}
}
float_common_impls!(DoubleFloat<F>);
impl<F: Float> Neg for DoubleFloat<F> {
type Output = Self;
fn neg(self) -> Self {
if self.1.is_finite_non_zero() {
DoubleFloat(-self.0, -self.1)
} else {
DoubleFloat(-self.0, self.1)
}
}
}
impl<F: FloatConvert<Fallback<F>>> fmt::Display for DoubleFloat<F> {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
fmt::Display::fmt(&Fallback::from(*self), f)
}
}
impl<F: FloatConvert<Fallback<F>>> Float for DoubleFloat<F>
where
Self: From<Fallback<F>>,
{
const BITS: usize = F::BITS * 2;
const PRECISION: usize = Fallback::<F>::PRECISION;
const MAX_EXP: ExpInt = Fallback::<F>::MAX_EXP;
const MIN_EXP: ExpInt = Fallback::<F>::MIN_EXP;
const ZERO: Self = DoubleFloat(F::ZERO, F::ZERO);
const INFINITY: Self = DoubleFloat(F::INFINITY, F::ZERO);
// FIXME(eddyb) remove when qnan becomes const fn.
const NAN: Self = DoubleFloat(F::NAN, F::ZERO);
fn qnan(payload: Option<u128>) -> Self {
DoubleFloat(F::qnan(payload), F::ZERO)
}
fn snan(payload: Option<u128>) -> Self {
DoubleFloat(F::snan(payload), F::ZERO)
}
fn largest() -> Self {
let status;
let mut r = DoubleFloat(F::largest(), F::largest());
r.1 = r.1.scalbn(-(F::PRECISION as ExpInt + 1));
r.1 = unpack!(status=, r.1.next_down());
assert_eq!(status, Status::OK);
r
}
const SMALLEST: Self = DoubleFloat(F::SMALLEST, F::ZERO);
fn smallest_normalized() -> Self {
DoubleFloat(
F::smallest_normalized().scalbn(F::PRECISION as ExpInt),
F::ZERO,
)
}
// Implement addition, subtraction, multiplication and division based on:
// "Software for Doubled-Precision Floating-Point Computations",
// by Seppo Linnainmaa, ACM TOMS vol 7 no 3, September 1981, pages 272-283.
fn add_r(mut self, rhs: Self, round: Round) -> StatusAnd<Self> {
match (self.category(), rhs.category()) {
(Category::Infinity, Category::Infinity) => {
if self.is_negative() != rhs.is_negative() {
Status::INVALID_OP.and(Self::NAN.copy_sign(self))
} else {
Status::OK.and(self)
}
}
(_, Category::Zero) |
(Category::NaN, _) |
(Category::Infinity, Category::Normal) => Status::OK.and(self),
(Category::Zero, _) |
(_, Category::NaN) |
(_, Category::Infinity) => Status::OK.and(rhs),
(Category::Normal, Category::Normal) => {
let mut status = Status::OK;
let (a, aa, c, cc) = (self.0, self.1, rhs.0, rhs.1);
let mut z = a;
z = unpack!(status|=, z.add_r(c, round));
if !z.is_finite() {
if !z.is_infinite() {
return status.and(DoubleFloat(z, F::ZERO));
}
status = Status::OK;
let a_cmp_c = a.cmp_abs_normal(c);
z = cc;
z = unpack!(status|=, z.add_r(aa, round));
if a_cmp_c == Ordering::Greater {
// z = cc + aa + c + a;
z = unpack!(status|=, z.add_r(c, round));
z = unpack!(status|=, z.add_r(a, round));
} else {
// z = cc + aa + a + c;
z = unpack!(status|=, z.add_r(a, round));
z = unpack!(status|=, z.add_r(c, round));
}
if !z.is_finite() {
return status.and(DoubleFloat(z, F::ZERO));
}
self.0 = z;
let mut zz = aa;
zz = unpack!(status|=, zz.add_r(cc, round));
if a_cmp_c == Ordering::Greater {
// self.1 = a - z + c + zz;
self.1 = a;
self.1 = unpack!(status|=, self.1.sub_r(z, round));
self.1 = unpack!(status|=, self.1.add_r(c, round));
self.1 = unpack!(status|=, self.1.add_r(zz, round));
} else {
// self.1 = c - z + a + zz;
self.1 = c;
self.1 = unpack!(status|=, self.1.sub_r(z, round));
self.1 = unpack!(status|=, self.1.add_r(a, round));
self.1 = unpack!(status|=, self.1.add_r(zz, round));
}
} else {
// q = a - z;
let mut q = a;
q = unpack!(status|=, q.sub_r(z, round));
// zz = q + c + (a - (q + z)) + aa + cc;
// Compute a - (q + z) as -((q + z) - a) to avoid temporary copies.
let mut zz = q;
zz = unpack!(status|=, zz.add_r(c, round));
q = unpack!(status|=, q.add_r(z, round));
q = unpack!(status|=, q.sub_r(a, round));
q = -q;
zz = unpack!(status|=, zz.add_r(q, round));
zz = unpack!(status|=, zz.add_r(aa, round));
zz = unpack!(status|=, zz.add_r(cc, round));
if zz.is_zero() && !zz.is_negative() {
return Status::OK.and(DoubleFloat(z, F::ZERO));
}
self.0 = z;
self.0 = unpack!(status|=, self.0.add_r(zz, round));
if !self.0.is_finite() {
self.1 = F::ZERO;
return status.and(self);
}
self.1 = z;
self.1 = unpack!(status|=, self.1.sub_r(self.0, round));
self.1 = unpack!(status|=, self.1.add_r(zz, round));
}
status.and(self)
}
}
}
fn mul_r(mut self, rhs: Self, round: Round) -> StatusAnd<Self> {
// Interesting observation: For special categories, finding the lowest
// common ancestor of the following layered graph gives the correct
// return category:
//
// NaN
// / \
// Zero Inf
// \ /
// Normal
//
// e.g., NaN * NaN = NaN
// Zero * Inf = NaN
// Normal * Zero = Zero
// Normal * Inf = Inf
match (self.category(), rhs.category()) {
(Category::NaN, _) => Status::OK.and(self),
(_, Category::NaN) => Status::OK.and(rhs),
(Category::Zero, Category::Infinity) |
(Category::Infinity, Category::Zero) => Status::OK.and(Self::NAN),
(Category::Zero, _) |
(Category::Infinity, _) => Status::OK.and(self),
(_, Category::Zero) |
(_, Category::Infinity) => Status::OK.and(rhs),
(Category::Normal, Category::Normal) => {
let mut status = Status::OK;
let (a, b, c, d) = (self.0, self.1, rhs.0, rhs.1);
// t = a * c
let mut t = a;
t = unpack!(status|=, t.mul_r(c, round));
if !t.is_finite_non_zero() {
return status.and(DoubleFloat(t, F::ZERO));
}
// tau = fmsub(a, c, t), that is -fmadd(-a, c, t).
let mut tau = a;
tau = unpack!(status|=, tau.mul_add_r(c, -t, round));
// v = a * d
let mut v = a;
v = unpack!(status|=, v.mul_r(d, round));
// w = b * c
let mut w = b;
w = unpack!(status|=, w.mul_r(c, round));
v = unpack!(status|=, v.add_r(w, round));
// tau += v + w
tau = unpack!(status|=, tau.add_r(v, round));
// u = t + tau
let mut u = t;
u = unpack!(status|=, u.add_r(tau, round));
self.0 = u;
if !u.is_finite() {
self.1 = F::ZERO;
} else {
// self.1 = (t - u) + tau
t = unpack!(status|=, t.sub_r(u, round));
t = unpack!(status|=, t.add_r(tau, round));
self.1 = t;
}
status.and(self)
}
}
}
fn mul_add_r(self, multiplicand: Self, addend: Self, round: Round) -> StatusAnd<Self> {
Fallback::from(self)
.mul_add_r(Fallback::from(multiplicand), Fallback::from(addend), round)
.map(Self::from)
}
fn div_r(self, rhs: Self, round: Round) -> StatusAnd<Self> {
Fallback::from(self).div_r(Fallback::from(rhs), round).map(
Self::from,
)
}
fn c_fmod(self, rhs: Self) -> StatusAnd<Self> {
Fallback::from(self).c_fmod(Fallback::from(rhs)).map(
Self::from,
)
}
fn round_to_integral(self, round: Round) -> StatusAnd<Self> {
Fallback::from(self).round_to_integral(round).map(
Self::from,
)
}
fn next_up(self) -> StatusAnd<Self> {
Fallback::from(self).next_up().map(Self::from)
}
fn from_bits(input: u128) -> Self {
let (a, b) = (input, input >> F::BITS);
DoubleFloat(
F::from_bits(a & ((1 << F::BITS) - 1)),
F::from_bits(b & ((1 << F::BITS) - 1)),
)
}
fn from_u128_r(input: u128, round: Round) -> StatusAnd<Self> {
Fallback::from_u128_r(input, round).map(Self::from)
}
fn from_str_r(s: &str, round: Round) -> Result<StatusAnd<Self>, ParseError> {
Fallback::from_str_r(s, round).map(|r| r.map(Self::from))
}
fn to_bits(self) -> u128 {
self.0.to_bits() | (self.1.to_bits() << F::BITS)
}
fn to_u128_r(self, width: usize, round: Round, is_exact: &mut bool) -> StatusAnd<u128> {
Fallback::from(self).to_u128_r(width, round, is_exact)
}
fn cmp_abs_normal(self, rhs: Self) -> Ordering {
self.0.cmp_abs_normal(rhs.0).then_with(|| {
let result = self.1.cmp_abs_normal(rhs.1);
if result != Ordering::Equal {
let against = self.0.is_negative() ^ self.1.is_negative();
let rhs_against = rhs.0.is_negative() ^ rhs.1.is_negative();
(!against).cmp(&!rhs_against).then_with(|| if against {
result.reverse()
} else {
result
})
} else {
result
}
})
}
fn bitwise_eq(self, rhs: Self) -> bool {
self.0.bitwise_eq(rhs.0) && self.1.bitwise_eq(rhs.1)
}
fn is_negative(self) -> bool {
self.0.is_negative()
}
fn is_denormal(self) -> bool {
self.category() == Category::Normal &&
(self.0.is_denormal() || self.0.is_denormal() ||
// (double)(Hi + Lo) == Hi defines a normal number.
!(self.0 + self.1).value.bitwise_eq(self.0))
}
fn is_signaling(self) -> bool {
self.0.is_signaling()
}
fn category(self) -> Category {
self.0.category()
}
fn get_exact_inverse(self) -> Option<Self> {
Fallback::from(self).get_exact_inverse().map(Self::from)
}
fn ilogb(self) -> ExpInt {
self.0.ilogb()
}
fn scalbn_r(self, exp: ExpInt, round: Round) -> Self {
DoubleFloat(self.0.scalbn_r(exp, round), self.1.scalbn_r(exp, round))
}
fn frexp_r(self, exp: &mut ExpInt, round: Round) -> Self {
let a = self.0.frexp_r(exp, round);
let mut b = self.1;
if self.category() == Category::Normal {
b = b.scalbn_r(-*exp, round);
}
DoubleFloat(a, b)
}
}
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