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