#![allow(missing_docs)]
use crate::scalar::{ComplexField, Field, RealField, SubsetOf};
use crate::simd::{PrimitiveSimdValue, SimdValue};
use fixed::types::extra::{
IsLessOrEqual, LeEqU16, LeEqU32, LeEqU64, LeEqU8, True, Unsigned, U13, U14, U16, U29, U30, U32,
U5, U6, U61, U62, U64, U8,
};
use num::{Bounded, FromPrimitive, Num, One, Signed, Zero};
use std::cmp::Ordering;
use std::ops::{
Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, SubAssign,
};
macro_rules! impl_fixed_type(
($($FixedI: ident, $Int: ident, $LeEqDim: ident, $LeEqDim1: ident, $LeEqDim2: ident, $LeEqDim3: ident;)*) => {$(
#[derive(Copy, Clone)]
pub struct $FixedI<Fract: $LeEqDim>(pub fixed::$FixedI<Fract>);
impl<Fract: $LeEqDim> PartialEq for $FixedI<Fract> {
#[inline(always)]
fn eq(&self, other: &Self) -> bool {
self.0 == other.0
}
}
impl<Fract: $LeEqDim> Eq for $FixedI<Fract> {}
impl<Fract: $LeEqDim> PartialOrd for $FixedI<Fract> {
#[inline(always)]
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
self.0.partial_cmp(&other.0)
}
}
#[cfg(feature = "rand")]
impl<Fract: $LeEqDim> rand::distributions::Distribution<$FixedI<Fract>> for rand::distributions::Standard {
#[inline]
fn sample<'a, G: rand::Rng + ?Sized>(&self, rng: &mut G) -> $FixedI<Fract> {
let bits = rng.gen();
$FixedI(fixed::$FixedI::from_bits(bits))
}
}
#[cfg(feature = "rand")]
impl<Fract: $LeEqDim> rand::distributions::Distribution<$FixedI<Fract>> for rand::distributions::OpenClosed01 {
#[inline]
fn sample<'a, G: rand::Rng + ?Sized>(&self, rng: &mut G) -> $FixedI<Fract> {
let val: f64 = rng.gen();
$FixedI(fixed::$FixedI::from_num(val))
}
}
impl<Fract: $LeEqDim> PrimitiveSimdValue for $FixedI<Fract> {}
impl<Fract: $LeEqDim> SimdValue for $FixedI<Fract> {
type Element = Self;
type SimdBool = bool;
#[inline(always)]
fn lanes() -> usize {
1
}
#[inline(always)]
fn splat(val: Self::Element) -> Self {
val
}
#[inline(always)]
fn extract(&self, _: usize) -> Self::Element {
*self
}
#[inline(always)]
unsafe fn extract_unchecked(&self, _: usize) -> Self::Element {
*self
}
#[inline(always)]
fn replace(&mut self, _: usize, val: Self::Element) {
*self = val
}
#[inline(always)]
unsafe fn replace_unchecked(&mut self, _: usize, val: Self::Element) {
*self = val
}
#[inline(always)]
fn select(self, cond: Self::SimdBool, other: Self) -> Self {
if cond {
self
} else {
other
}
}
}
impl<Fract: $LeEqDim> Mul for $FixedI<Fract> {
type Output = Self;
#[inline(always)]
fn mul(self, rhs: Self) -> Self {
Self(self.0 * rhs.0)
}
}
impl<Fract: $LeEqDim> Div for $FixedI<Fract> {
type Output = Self;
#[inline(always)]
fn div(self, rhs: Self) -> Self {
Self(self.0 / rhs.0)
}
}
impl<Fract: $LeEqDim> Rem for $FixedI<Fract> {
type Output = Self;
#[inline(always)]
fn rem(self, rhs: Self) -> Self {
Self(self.0 % rhs.0)
}
}
impl<Fract: $LeEqDim> Add for $FixedI<Fract> {
type Output = Self;
#[inline(always)]
fn add(self, rhs: Self) -> Self {
Self(self.0 + rhs.0)
}
}
impl<Fract: $LeEqDim> Sub for $FixedI<Fract> {
type Output = Self;
#[inline(always)]
fn sub(self, rhs: Self) -> Self {
Self(self.0 - rhs.0)
}
}
impl<Fract: $LeEqDim> Neg for $FixedI<Fract> {
type Output = Self;
#[inline(always)]
fn neg(self) -> Self {
Self(-self.0)
}
}
impl<Fract: $LeEqDim> MulAssign for $FixedI<Fract> {
#[inline(always)]
fn mul_assign(&mut self, rhs: Self) {
self.0 *= rhs.0
}
}
impl<Fract: $LeEqDim> DivAssign for $FixedI<Fract> {
#[inline(always)]
fn div_assign(&mut self, rhs: Self) {
self.0 /= rhs.0
}
}
impl<Fract: $LeEqDim> RemAssign for $FixedI<Fract> {
#[inline(always)]
fn rem_assign(&mut self, rhs: Self) {
self.0 %= rhs.0
}
}
impl<Fract: $LeEqDim> AddAssign for $FixedI<Fract> {
#[inline(always)]
fn add_assign(&mut self, rhs: Self) {
self.0 += rhs.0
}
}
impl<Fract: $LeEqDim> SubAssign for $FixedI<Fract> {
#[inline(always)]
fn sub_assign(&mut self, rhs: Self) {
self.0 -= rhs.0
}
}
impl<Fract: $LeEqDim> Zero for $FixedI<Fract> {
#[inline(always)]
fn zero() -> Self {
Self(fixed::$FixedI::from_num(0))
}
#[inline(always)]
fn is_zero(&self) -> bool {
self.0 == Self::zero().0
}
}
impl<Fract: $LeEqDim> One for $FixedI<Fract> {
#[inline(always)]
fn one() -> Self {
Self(fixed::$FixedI::from_num(1))
}
}
impl<Fract: $LeEqDim> Num for $FixedI<Fract> {
type FromStrRadixErr = ();
fn from_str_radix(_str: &str, _radix: u32) -> Result<Self, Self::FromStrRadixErr> {
unimplemented!()
}
}
impl<Fract: $LeEqDim> Field for $FixedI<Fract> {}
impl<Fract: $LeEqDim> SubsetOf<$FixedI<Fract>> for f64 {
#[inline]
fn to_superset(&self) -> $FixedI<Fract> {
$FixedI(fixed::$FixedI::from_num(*self))
}
#[inline]
fn from_superset(element: &$FixedI<Fract>) -> Option<Self> {
Some(Self::from_superset_unchecked(element))
}
#[inline]
fn from_superset_unchecked(element: &$FixedI<Fract>) -> Self {
element.0.to_num::<f64>()
}
#[inline]
fn is_in_subset(_: &$FixedI<Fract>) -> bool {
true
}
}
impl<Fract: $LeEqDim> SubsetOf<$FixedI<Fract>> for $FixedI<Fract> {
#[inline]
fn to_superset(&self) -> $FixedI<Fract> {
*self
}
#[inline]
fn from_superset(element: &$FixedI<Fract>) -> Option<Self> {
Some(*element)
}
#[inline]
fn from_superset_unchecked(element: &$FixedI<Fract>) -> Self {
*element
}
#[inline]
fn is_in_subset(_: &$FixedI<Fract>) -> bool {
true
}
}
impl<Fract: $LeEqDim> approx::AbsDiffEq for $FixedI<Fract> {
type Epsilon = Self;
fn default_epsilon() -> Self::Epsilon {
Self(fixed::$FixedI::from_bits(0b01))
}
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
if self > other {
(*self - *other) <= epsilon
} else {
(*other - *self) <= epsilon
}
}
}
impl<Fract: $LeEqDim> approx::RelativeEq for $FixedI<Fract> {
fn default_max_relative() -> Self::Epsilon {
use approx::AbsDiffEq;
Self::default_epsilon()
}
fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon,
) -> bool
{
let abs_diff = (*self - *other).abs();
if abs_diff <= epsilon {
return true;
}
let abs_self = self.abs();
let abs_other = other.abs();
let largest = if abs_other > abs_self {
abs_other
} else {
abs_self
};
abs_diff <= largest * max_relative
}
}
impl<Fract: $LeEqDim> approx::UlpsEq for $FixedI<Fract> {
fn default_max_ulps() -> u32 {
4
}
fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
use approx::AbsDiffEq;
if self.abs_diff_eq(other, epsilon) {
return true;
}
if self.signum() != other.signum() {
return false;
}
let bits1 = self.0.to_bits();
let bits2 = other.0.to_bits();
if bits1 > bits2 {
(bits1 - bits2) <= max_ulps as $Int
} else {
(bits2 - bits1) <= max_ulps as $Int
}
}
}
impl<Fract: $LeEqDim> std::fmt::Debug for $FixedI<Fract> {
fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
self.0.fmt(f)
}
}
impl<Fract: $LeEqDim> std::fmt::Display for $FixedI<Fract> {
fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
self.0.fmt(f)
}
}
impl<Fract: $LeEqDim> Bounded for $FixedI<Fract> {
#[inline]
fn min_value() -> Self {
Self(fixed::$FixedI::MIN)
}
#[inline]
fn max_value() -> Self {
Self(fixed::$FixedI::MAX)
}
}
impl<Fract: $LeEqDim> FromPrimitive for $FixedI<Fract> {
fn from_i64(_n: i64) -> Option<Self> {
unimplemented!()
}
fn from_u64(_n: u64) -> Option<Self> {
unimplemented!()
}
fn from_isize(_n: isize) -> Option<Self> {
unimplemented!()
}
fn from_i8(_n: i8) -> Option<Self> {
unimplemented!()
}
fn from_i16(_n: i16) -> Option<Self> {
unimplemented!()
}
fn from_i32(_n: i32) -> Option<Self> {
unimplemented!()
}
fn from_usize(_n: usize) -> Option<Self> {
unimplemented!()
}
fn from_u8(_n: u8) -> Option<Self> {
unimplemented!()
}
fn from_u16(_n: u16) -> Option<Self> {
unimplemented!()
}
fn from_u32(_n: u32) -> Option<Self> {
unimplemented!()
}
fn from_f32(_n: f32) -> Option<Self> {
unimplemented!()
}
fn from_f64(_n: f64) -> Option<Self> {
unimplemented!()
}
}
impl<Fract: $LeEqDim> Signed for $FixedI<Fract> {
fn abs(&self) -> Self {
Self(self.0.abs())
}
fn abs_sub(&self, other: &Self) -> Self {
self.abs() - *other
}
fn signum(&self) -> Self {
Self(self.0.signum())
}
fn is_positive(&self) -> bool {
self.0 >= Self::zero().0
}
fn is_negative(&self) -> bool {
self.0 <= Self::zero().0
}
}
impl<Fract: Send + Sync + 'static> ComplexField for $FixedI<Fract>
where Fract: Unsigned
+ IsLessOrEqual<$LeEqDim1, Output = True>
+ IsLessOrEqual<$LeEqDim2, Output = True>
+ IsLessOrEqual<$LeEqDim3, Output = True> {
type RealField = Self;
#[inline]
fn from_real(re: Self::RealField) -> Self {
re
}
#[inline]
fn real(self) -> Self::RealField {
self
}
#[inline]
fn imaginary(self) -> Self::RealField {
Self::zero()
}
#[inline]
fn norm1(self) -> Self::RealField {
self.abs()
}
#[inline]
fn modulus(self) -> Self::RealField {
self.abs()
}
#[inline]
fn modulus_squared(self) -> Self::RealField {
self * self
}
#[inline]
fn argument(self) -> Self::RealField {
if self >= Self::zero() {
Self::zero()
} else {
Self::pi()
}
}
#[inline]
fn to_exp(self) -> (Self, Self) {
if self >= Self::zero() {
(self, Self::one())
} else {
(-self, -Self::one())
}
}
#[inline]
fn recip(self) -> Self {
Self::one() / self
}
#[inline]
fn conjugate(self) -> Self {
self
}
#[inline]
fn scale(self, factor: Self::RealField) -> Self {
self * factor
}
#[inline]
fn unscale(self, factor: Self::RealField) -> Self {
self / factor
}
#[inline]
fn floor(self) -> Self {
Self(self.0.floor())
}
#[inline]
fn ceil(self) -> Self {
Self(self.0.ceil())
}
#[inline]
fn round(self) -> Self {
Self(self.0.round())
}
#[inline]
fn trunc(self) -> Self {
unimplemented!()
}
#[inline]
fn fract(self) -> Self {
Self(self.0.frac())
}
#[inline]
fn abs(self) -> Self {
Self(self.0.abs())
}
#[inline]
fn signum(self) -> Self {
Self(self.0.signum())
}
#[inline]
fn mul_add(self, a: Self, b: Self) -> Self {
self * a + b
}
#[cfg(feature = "std")]
#[inline]
fn powi(self, _n: i32) -> Self {
unimplemented!()
}
#[cfg(not(feature = "std"))]
#[inline]
fn powi(self, n: i32) -> Self {
unimplemented!()
}
#[inline]
fn powf(self, _n: Self) -> Self {
unimplemented!()
}
#[inline]
fn powc(self, _n: Self) -> Self {
unimplemented!()
}
#[inline]
fn sqrt(self) -> Self {
Self(cordic::sqrt(self.0))
}
#[inline]
fn try_sqrt(self) -> Option<Self> {
if self >= Self::zero() {
Some(self.sqrt())
} else {
None
}
}
#[inline]
fn exp(self) -> Self {
Self(cordic::exp(self.0))
}
#[inline]
fn exp2(self) -> Self {
unimplemented!()
}
#[inline]
fn exp_m1(self) -> Self {
unimplemented!()
}
#[inline]
fn ln_1p(self) -> Self {
unimplemented!()
}
#[inline]
fn ln(self) -> Self {
unimplemented!()
}
#[inline]
fn log(self, _base: Self) -> Self {
unimplemented!()
}
#[inline]
fn log2(self) -> Self {
unimplemented!()
}
#[inline]
fn log10(self) -> Self {
unimplemented!()
}
#[inline]
fn cbrt(self) -> Self {
unimplemented!()
}
#[inline]
fn hypot(self, _other: Self) -> Self::RealField {
unimplemented!()
}
#[inline]
fn sin(self) -> Self {
Self(cordic::sin(self.0))
}
#[inline]
fn cos(self) -> Self {
Self(cordic::cos(self.0))
}
#[inline]
fn tan(self) -> Self {
Self(cordic::tan(self.0))
}
#[inline]
fn asin(self) -> Self {
Self(cordic::asin(self.0))
}
#[inline]
fn acos(self) -> Self {
Self(cordic::acos(self.0))
}
#[inline]
fn atan(self) -> Self {
Self(cordic::atan(self.0))
}
#[inline]
fn sin_cos(self) -> (Self, Self) {
let (sin, cos) = cordic::sin_cos(self.0);
(Self(sin), Self(cos))
}
#[inline]
fn sinh(self) -> Self {
unimplemented!()
}
#[inline]
fn cosh(self) -> Self {
unimplemented!()
}
#[inline]
fn tanh(self) -> Self {
unimplemented!()
}
#[inline]
fn asinh(self) -> Self {
unimplemented!()
}
#[inline]
fn acosh(self) -> Self {
unimplemented!()
}
#[inline]
fn atanh(self) -> Self {
unimplemented!()
}
#[inline]
fn is_finite(&self) -> bool {
unimplemented!()
}
}
impl<Fract: Send + Sync + 'static> RealField for $FixedI<Fract>
where Fract: Unsigned
+ IsLessOrEqual<$LeEqDim1, Output = True>
+ IsLessOrEqual<$LeEqDim2, Output = True>
+ IsLessOrEqual<$LeEqDim3, Output = True> {
#[inline]
fn is_sign_positive(self) -> bool {
unimplemented!()
}
#[inline]
fn is_sign_negative(self) -> bool {
unimplemented!()
}
#[inline]
fn max(self, other: Self) -> Self {
if self >= other {
self
} else {
other
}
}
#[inline]
fn min(self, other: Self) -> Self {
if self < other {
self
} else {
other
}
}
#[inline]
fn clamp(self, min: Self, max: Self) -> Self {
if self < min {
min
} else if self > max {
max
} else {
self
}
}
#[inline]
fn atan2(self, other: Self) -> Self {
Self(cordic::atan2(self.0, other.0))
}
#[inline]
fn pi() -> Self {
Self(fixed::$FixedI::PI)
}
#[inline]
fn two_pi() -> Self {
Self::pi() + Self::pi()
}
#[inline]
fn frac_pi_2() -> Self {
Self(fixed::$FixedI::FRAC_PI_2)
}
#[inline]
fn frac_pi_3() -> Self {
Self(fixed::$FixedI::FRAC_PI_3)
}
#[inline]
fn frac_pi_4() -> Self {
unimplemented!()
}
#[inline]
fn frac_pi_6() -> Self {
unimplemented!()
}
#[inline]
fn frac_pi_8() -> Self {
Self(fixed::$FixedI::FRAC_PI_8)
}
#[inline]
fn frac_1_pi() -> Self {
Self(fixed::$FixedI::FRAC_1_PI)
}
#[inline]
fn frac_2_pi() -> Self {
unimplemented!()
}
#[inline]
fn frac_2_sqrt_pi() -> Self {
unimplemented!()
}
#[inline]
fn e() -> Self {
unimplemented!()
}
#[inline]
fn log2_e() -> Self {
unimplemented!()
}
#[inline]
fn log10_e() -> Self {
unimplemented!()
}
#[inline]
fn ln_2() -> Self {
unimplemented!()
}
#[inline]
fn ln_10() -> Self {
unimplemented!()
}
}
)*}
);
impl_fixed_type!(
FixedI8, i8, LeEqU8, U8, U6, U5;
FixedI16, i16, LeEqU16, U16, U14, U13;
FixedI32, i32, LeEqU32, U32, U30, U29;
FixedI64, i64, LeEqU64, U64, U62, U61;
);
pub type FixedI8F0 = FixedI8<fixed::types::extra::U0>;
pub type FixedI7F1 = FixedI8<fixed::types::extra::U1>;
pub type FixedI6F2 = FixedI8<fixed::types::extra::U2>;
pub type FixedI5F3 = FixedI8<fixed::types::extra::U3>;
pub type FixedI4F4 = FixedI8<fixed::types::extra::U4>;
pub type FixedI3F5 = FixedI8<fixed::types::extra::U5>;
pub type FixedI16F0 = FixedI16<fixed::types::extra::U0>;
pub type FixedI15F1 = FixedI16<fixed::types::extra::U1>;
pub type FixedI14F2 = FixedI16<fixed::types::extra::U2>;
pub type FixedI13F3 = FixedI16<fixed::types::extra::U3>;
pub type FixedI12F4 = FixedI16<fixed::types::extra::U4>;
pub type FixedI11F5 = FixedI16<fixed::types::extra::U5>;
pub type FixedI10F6 = FixedI16<fixed::types::extra::U6>;
pub type FixedI9F7 = FixedI16<fixed::types::extra::U7>;
pub type FixedI8F8 = FixedI16<fixed::types::extra::U8>;
pub type FixedI7F9 = FixedI16<fixed::types::extra::U9>;
pub type FixedI6F10 = FixedI16<fixed::types::extra::U10>;
pub type FixedI5F11 = FixedI16<fixed::types::extra::U11>;
pub type FixedI4F12 = FixedI16<fixed::types::extra::U12>;
pub type FixedI3F13 = FixedI16<fixed::types::extra::U13>;
pub type FixedI32F0 = FixedI32<fixed::types::extra::U0>;
pub type FixedI31F1 = FixedI32<fixed::types::extra::U1>;
pub type FixedI30F2 = FixedI32<fixed::types::extra::U2>;
pub type FixedI29F3 = FixedI32<fixed::types::extra::U3>;
pub type FixedI28F4 = FixedI32<fixed::types::extra::U4>;
pub type FixedI27F5 = FixedI32<fixed::types::extra::U5>;
pub type FixedI26F6 = FixedI32<fixed::types::extra::U6>;
pub type FixedI25F7 = FixedI32<fixed::types::extra::U7>;
pub type FixedI24F8 = FixedI32<fixed::types::extra::U8>;
pub type FixedI23F9 = FixedI32<fixed::types::extra::U9>;
pub type FixedI22F10 = FixedI32<fixed::types::extra::U10>;
pub type FixedI21F11 = FixedI32<fixed::types::extra::U11>;
pub type FixedI20F12 = FixedI32<fixed::types::extra::U12>;
pub type FixedI19F13 = FixedI32<fixed::types::extra::U13>;
pub type FixedI18F14 = FixedI32<fixed::types::extra::U14>;
pub type FixedI17F15 = FixedI32<fixed::types::extra::U15>;
pub type FixedI16F16 = FixedI32<fixed::types::extra::U16>;
pub type FixedI15F17 = FixedI32<fixed::types::extra::U17>;
pub type FixedI14F18 = FixedI32<fixed::types::extra::U18>;
pub type FixedI13F19 = FixedI32<fixed::types::extra::U19>;
pub type FixedI12F20 = FixedI32<fixed::types::extra::U20>;
pub type FixedI11F21 = FixedI32<fixed::types::extra::U21>;
pub type FixedI10F22 = FixedI32<fixed::types::extra::U22>;
pub type FixedI9F23 = FixedI32<fixed::types::extra::U23>;
pub type FixedI8F24 = FixedI32<fixed::types::extra::U24>;
pub type FixedI7F25 = FixedI32<fixed::types::extra::U25>;
pub type FixedI6F26 = FixedI32<fixed::types::extra::U26>;
pub type FixedI5F27 = FixedI32<fixed::types::extra::U27>;
pub type FixedI4F28 = FixedI32<fixed::types::extra::U28>;
pub type FixedI3F29 = FixedI32<fixed::types::extra::U29>;
pub type FixedI64F0 = FixedI64<fixed::types::extra::U0>;
pub type FixedI63F1 = FixedI64<fixed::types::extra::U1>;
pub type FixedI62F2 = FixedI64<fixed::types::extra::U2>;
pub type FixedI61F3 = FixedI64<fixed::types::extra::U3>;
pub type FixedI60F4 = FixedI64<fixed::types::extra::U4>;
pub type FixedI59F5 = FixedI64<fixed::types::extra::U5>;
pub type FixedI58F6 = FixedI64<fixed::types::extra::U6>;
pub type FixedI57F7 = FixedI64<fixed::types::extra::U7>;
pub type FixedI56F8 = FixedI64<fixed::types::extra::U8>;
pub type FixedI55F9 = FixedI64<fixed::types::extra::U9>;
pub type FixedI54F10 = FixedI64<fixed::types::extra::U10>;
pub type FixedI53F11 = FixedI64<fixed::types::extra::U11>;
pub type FixedI52F12 = FixedI64<fixed::types::extra::U12>;
pub type FixedI51F13 = FixedI64<fixed::types::extra::U13>;
pub type FixedI50F14 = FixedI64<fixed::types::extra::U14>;
pub type FixedI49F15 = FixedI64<fixed::types::extra::U15>;
pub type FixedI48F16 = FixedI64<fixed::types::extra::U16>;
pub type FixedI47F17 = FixedI64<fixed::types::extra::U17>;
pub type FixedI46F18 = FixedI64<fixed::types::extra::U18>;
pub type FixedI45F19 = FixedI64<fixed::types::extra::U19>;
pub type FixedI44F20 = FixedI64<fixed::types::extra::U20>;
pub type FixedI43F21 = FixedI64<fixed::types::extra::U21>;
pub type FixedI42F22 = FixedI64<fixed::types::extra::U22>;
pub type FixedI41F23 = FixedI64<fixed::types::extra::U23>;
pub type FixedI40F24 = FixedI64<fixed::types::extra::U24>;
pub type FixedI39F25 = FixedI64<fixed::types::extra::U25>;
pub type FixedI38F26 = FixedI64<fixed::types::extra::U26>;
pub type FixedI37F27 = FixedI64<fixed::types::extra::U27>;
pub type FixedI36F28 = FixedI64<fixed::types::extra::U28>;
pub type FixedI35F29 = FixedI64<fixed::types::extra::U29>;
pub type FixedI34F30 = FixedI64<fixed::types::extra::U30>;
pub type FixedI33F31 = FixedI64<fixed::types::extra::U31>;
pub type FixedI32F32 = FixedI64<fixed::types::extra::U32>;
pub type FixedI31F33 = FixedI64<fixed::types::extra::U33>;
pub type FixedI30F34 = FixedI64<fixed::types::extra::U34>;
pub type FixedI29F35 = FixedI64<fixed::types::extra::U35>;
pub type FixedI28F36 = FixedI64<fixed::types::extra::U36>;
pub type FixedI27F37 = FixedI64<fixed::types::extra::U37>;
pub type FixedI26F38 = FixedI64<fixed::types::extra::U38>;
pub type FixedI25F39 = FixedI64<fixed::types::extra::U39>;
pub type FixedI24F40 = FixedI64<fixed::types::extra::U40>;
pub type FixedI23F41 = FixedI64<fixed::types::extra::U41>;
pub type FixedI22F42 = FixedI64<fixed::types::extra::U42>;
pub type FixedI21F43 = FixedI64<fixed::types::extra::U43>;
pub type FixedI20F44 = FixedI64<fixed::types::extra::U44>;
pub type FixedI19F45 = FixedI64<fixed::types::extra::U45>;
pub type FixedI18F46 = FixedI64<fixed::types::extra::U46>;
pub type FixedI17F47 = FixedI64<fixed::types::extra::U47>;
pub type FixedI16F48 = FixedI64<fixed::types::extra::U48>;
pub type FixedI15F49 = FixedI64<fixed::types::extra::U49>;
pub type FixedI14F50 = FixedI64<fixed::types::extra::U50>;
pub type FixedI13F51 = FixedI64<fixed::types::extra::U51>;
pub type FixedI12F52 = FixedI64<fixed::types::extra::U52>;
pub type FixedI11F53 = FixedI64<fixed::types::extra::U53>;
pub type FixedI10F54 = FixedI64<fixed::types::extra::U54>;
pub type FixedI9F55 = FixedI64<fixed::types::extra::U55>;
pub type FixedI8F56 = FixedI64<fixed::types::extra::U56>;
pub type FixedI7F57 = FixedI64<fixed::types::extra::U57>;
pub type FixedI6F58 = FixedI64<fixed::types::extra::U58>;
pub type FixedI5F59 = FixedI64<fixed::types::extra::U59>;
pub type FixedI4F60 = FixedI64<fixed::types::extra::U60>;