strafe-project/fixed_wide/src/fixed.rs

use bnum::{BInt,cast::As};

#[derive(Clone,Copy,Debug,Default,Hash)]
/// A Fixed point number for which multiply operations widen the bits in the output. (when the wide-mul feature is enabled)
/// N is the number of u64s to use
/// F is the number of fractional bits (always N*32 lol)
pub struct Fixed<const N:usize,const F:usize>{
	pub(crate)bits:BInt<{N}>,
}

impl<const N:usize,const F:usize> Fixed<N,F>{
	pub const MAX:Self=Self::from_bits(BInt::<N>::MAX);
	pub const MIN:Self=Self::from_bits(BInt::<N>::MIN);
	pub const ZERO:Self=Self::from_bits(BInt::<N>::ZERO);
	pub const EPSILON:Self=Self::from_bits(BInt::<N>::ONE);
	pub const NEG_EPSILON:Self=Self::from_bits(BInt::<N>::NEG_ONE);
	pub const ONE:Self=Self::from_bits(BInt::<N>::ONE.shl(F as u32));
	pub const TWO:Self=Self::from_bits(BInt::<N>::TWO.shl(F as u32));
	pub const HALF:Self=Self::from_bits(BInt::<N>::ONE.shl(F as u32-1));
	pub const NEG_ONE:Self=Self::from_bits(BInt::<N>::NEG_ONE.shl(F as u32));
	pub const NEG_TWO:Self=Self::from_bits(BInt::<N>::NEG_TWO.shl(F as u32));
	pub const NEG_HALF:Self=Self::from_bits(BInt::<N>::NEG_ONE.shl(F as u32-1));
}
impl<const N:usize,const F:usize> Fixed<N,F>{
	#[inline]
	pub const fn from_bits(bits:BInt::<N>)->Self{
		Self{
			bits,
		}
	}
	#[inline]
	pub const fn to_bits(self)->BInt<N>{
		self.bits
	}
	#[inline]
	pub const fn raw_digit(value:i64)->Self{
		let mut digits=[0u64;N];
		digits[0]=value.abs() as u64;
		//sign bit
		digits[N-1]|=(value&i64::MIN) as u64;
		Self::from_bits(BInt::from_bits(bnum::BUint::from_digits(digits)))
	}
	#[inline]
	pub const fn is_zero(self)->bool{
		self.bits.is_zero()
	}
	#[inline]
	pub const fn is_negative(self)->bool{
		self.bits.is_negative()
	}
	#[inline]
	pub const fn is_positive(self)->bool{
		self.bits.is_positive()
	}
	#[inline]
	pub const fn abs(self)->Self{
		Self::from_bits(self.bits.abs())
	}
}
impl<const F:usize> Fixed<1,F>{
	/// My old code called this function everywhere so let's provide it
	#[inline]
	pub const fn raw(value:i64)->Self{
		Self::from_bits(BInt::from_bits(bnum::BUint::from_digit(value as u64)))
	}
	#[inline]
	pub const fn to_raw(self)->i64{
		let &[digit]=self.to_bits().to_bits().digits();
		digit as i64
	}
}

impl<const N:usize,const F:usize,T> From<T> for Fixed<N,F>
	where
		BInt<N>:From<T>
{
	#[inline]
	fn from(value:T)->Self{
		Self::from_bits(BInt::<{N}>::from(value)<<F as u32)
	}
}

impl<const N:usize,const F:usize> PartialEq for Fixed<N,F>{
	#[inline]
	fn eq(&self,other:&Self)->bool{
		self.bits.eq(&other.bits)
	}
}
impl<const N:usize,const F:usize,T> PartialEq<T> for Fixed<N,F>
where
		T:Copy,
		BInt::<N>:From<T>,
{
	#[inline]
	fn eq(&self,&other:&T)->bool{
		self.bits.eq(&other.into())
	}
}
impl<const N:usize,const F:usize> Eq for Fixed<N,F>{}

impl<const N:usize,const F:usize> PartialOrd for Fixed<N,F>{
	#[inline]
	fn partial_cmp(&self,other:&Self)->Option<std::cmp::Ordering>{
		self.bits.partial_cmp(&other.bits)
	}
}
impl<const N:usize,const F:usize,T> PartialOrd<T> for Fixed<N,F>
	where
		T:Copy,
		BInt::<N>:From<T>,
{
	#[inline]
	fn partial_cmp(&self,&other:&T)->Option<std::cmp::Ordering>{
		self.bits.partial_cmp(&other.into())
	}
}
impl<const N:usize,const F:usize> Ord for Fixed<N,F>{
	#[inline]
	fn cmp(&self,other:&Self)->std::cmp::Ordering{
		self.bits.cmp(&other.bits)
	}
}

impl<const N:usize,const F:usize> std::ops::Neg for Fixed<N,F>{
	type Output=Self;
	#[inline]
	fn neg(self)->Self{
		Self::from_bits(self.bits.neg())
	}
}
impl<const N:usize,const F:usize> std::iter::Sum for Fixed<N,F>{
	#[inline]
	fn sum<I:Iterator<Item=Self>>(iter:I)->Self{
		let mut sum=Self::ZERO;
		for elem in iter{
			sum+=elem;
		}
		sum
	}
}

const fn signed_shift(lhs:u64,rhs:i32)->u64{
	if rhs.is_negative(){
		lhs>>-rhs
	}else{
		lhs<<rhs
	}
}
macro_rules! impl_into_float {
	( $output: ty, $unsigned:ty, $exponent_bits:expr, $mantissa_bits:expr ) => {
		impl<const N:usize,const F:usize> Into<$output> for Fixed<N,F>{
			#[inline]
			fn into(self)->$output{
				const DIGIT_SHIFT:u32=6;//Log2[64]
				// SBBB BBBB
				// 1001 1110 0000 0000
				let sign=if self.bits.is_negative(){(1 as $unsigned)<<(<$unsigned>::BITS-1)}else{0};
				let unsigned=self.bits.unsigned_abs();
				let most_significant_bit=unsigned.bits();
				let exp=if unsigned.is_zero(){
					0
				}else{
					let msb=most_significant_bit as $unsigned;
					let _127=((1 as $unsigned)<<($exponent_bits-1))-1;
					let msb_offset=msb+_127-1-F as $unsigned;
					msb_offset<<($mantissa_bits-1)
				};
				let digits=unsigned.digits();
				let digit_index=most_significant_bit>>DIGIT_SHIFT;
				let digit=digits[digit_index as usize];
				//How many bits does the mantissa take from this digit
				let take_bits=most_significant_bit-(digit_index<<DIGIT_SHIFT);
				let rest_of_mantissa=$mantissa_bits as i32-(take_bits as i32);
				let mut unmasked_mant=signed_shift(digit,rest_of_mantissa) as $unsigned;
				if 0<rest_of_mantissa&&digit_index!=0{
					//take the next digit down and shove some of its bits onto the bottom of the mantissa
					let digit=digits[digit_index as usize-1];
					let take_bits=most_significant_bit-((digit_index-1)<<DIGIT_SHIFT);
					let rest_of_mantissa=$mantissa_bits as i32-(take_bits as i32);
					let unmasked_mant2=signed_shift(digit,rest_of_mantissa) as $unsigned;
					unmasked_mant|=unmasked_mant2;
				}
				let mant=unmasked_mant&((1 as $unsigned)<<($mantissa_bits-1))-1;
				let bits=sign|exp|mant;
				<$output>::from_bits(bits)
			}
		}
	}
}
impl_into_float!(f32,u32,8,24);
impl_into_float!(f64,u64,11,53);

impl<const N:usize,const F:usize> core::fmt::Display for Fixed<N,F>{
	#[inline]
	fn fmt(&self,f:&mut core::fmt::Formatter)->Result<(),core::fmt::Error>{
		let float:f32=(*self).into();
		core::write!(f,"{:.3}",float)
	}
}

macro_rules! impl_additive_operator {
	( $struct: ident, $trait: ident, $method: ident, $output: ty ) => {
		impl<const N:usize,const F:usize> $struct<N,F>{
			#[inline]
			pub const fn $method(self, other: Self) -> Self {
				Self::from_bits(self.bits.$method(other.bits))
			}
		}
		impl<const N:usize,const F:usize> core::ops::$trait for $struct<N,F>{
			type Output = $output;
			#[inline]
			fn $method(self, other: Self) -> Self::Output {
				self.$method(other)
			}
		}
		impl<const N:usize,const F:usize,U> core::ops::$trait<U> for $struct<N,F>
			where
				BInt::<N>:From<U>,
		{
			type Output = $output;
			#[inline]
			fn $method(self, other: U) -> Self::Output {
				Self::from_bits(self.bits.$method(BInt::<N>::from(other).shl(F as u32)))
			}
		}
	};
}
macro_rules! impl_additive_assign_operator {
	( $struct: ident, $trait: ident, $method: ident ) => {
		impl<const N:usize,const F:usize> core::ops::$trait for $struct<N,F>{
			#[inline]
			fn $method(&mut self, other: Self) {
				self.bits.$method(other.bits);
			}
		}
		impl<const N:usize,const F:usize,U> core::ops::$trait<U> for $struct<N,F>
		where
				BInt::<N>:From<U>,
		{
			#[inline]
			fn $method(&mut self, other: U) {
				self.bits.$method(BInt::<N>::from(other).shl(F as u32));
			}
		}
	};
}

// Impl arithmetic pperators
impl_additive_assign_operator!( Fixed, AddAssign, add_assign );
impl_additive_operator!( Fixed, Add, add, Self );
impl_additive_assign_operator!( Fixed, SubAssign, sub_assign );
impl_additive_operator!( Fixed, Sub, sub, Self );
impl_additive_assign_operator!( Fixed, RemAssign, rem_assign );
impl_additive_operator!( Fixed, Rem, rem, Self );

// Impl bitwise operators
impl_additive_assign_operator!( Fixed, BitAndAssign, bitand_assign );
impl_additive_operator!( Fixed, BitAnd, bitand, Self );
impl_additive_assign_operator!( Fixed, BitOrAssign, bitor_assign );
impl_additive_operator!( Fixed, BitOr, bitor, Self );
impl_additive_assign_operator!( Fixed, BitXorAssign, bitxor_assign );
impl_additive_operator!( Fixed, BitXor, bitxor, Self );

// non-wide operators.  The result is the same width as the inputs.

// This macro is not used in the default configuration.
#[allow(unused_macros)]
macro_rules! impl_multiplicative_operator_not_const_generic {
	( ($struct: ident, $trait: ident, $method: ident, $output: ty ), $width:expr ) => {
		impl<const F:usize> core::ops::$trait for $struct<$width,F>{
			type Output = $output;
			#[inline]
			fn $method(self, other: Self) -> Self::Output {
				paste::item!{
				self.[<fixed_ $method>](other)
				}
			}
		}
	};
}
macro_rules! impl_multiplicative_assign_operator_not_const_generic {
	( ($struct: ident, $trait: ident, $method: ident, $non_assign_method: ident ), $width:expr ) => {
		impl<const F:usize> core::ops::$trait for $struct<$width,F>{
			#[inline]
			fn $method(&mut self, other: Self) {
				paste::item!{
				*self=self.[<fixed_ $non_assign_method>](other);
				}
			}
		}
	};
}

macro_rules! impl_multiply_operator_not_const_generic {
	( ($struct: ident, $trait: ident, $method: ident, $output: ty ), $width:expr ) => {
		impl<const F:usize> $struct<$width,F>{
			paste::item!{
			#[inline]
			pub fn [<fixed_ $method>](self, rhs: Self) -> Self {
				let (low,high)=self.bits.unsigned_abs().widening_mul(rhs.bits.unsigned_abs());
				let out:BInt::<{$width*2}>=unsafe{core::mem::transmute([low,high])};
				if self.is_negative()==rhs.is_negative(){
					Self::from_bits(out.shr(F as u32).as_())
				}else{
					-Self::from_bits(out.shr(F as u32).as_())
				}
			}
			}
		}
		#[cfg(not(feature="wide-mul"))]
		impl_multiplicative_operator_not_const_generic!(($struct, $trait, $method, $output ), $width);
		#[cfg(feature="deferred-division")]
		impl ratio_ops::ratio::Divide<i64> for Fixed<$width,{$width*32}>{
			type Output=Self;
			#[inline]
			fn divide(self, other: i64)->Self::Output{
				Self::from_bits(self.bits/BInt::from(other))
			}
		}
	}
}
macro_rules! impl_divide_operator_not_const_generic {
	( ($struct: ident, $trait: ident, $method: ident, $output: ty ), $width:expr ) => {
		impl<const F:usize> $struct<$width,F>{
			paste::item!{
			#[inline]
			pub fn [<fixed_ $method>](self, other: Self) -> Self {
				//this only needs to be $width+F as u32/64+1 but MUH CONST GENERICS!!!!!
				let lhs=self.bits.as_::<BInt::<{$width*2}>>().shl(F as u32);
				let rhs=other.bits.as_::<BInt::<{$width*2}>>();
				Self::from_bits(lhs.div(rhs).as_())
			}
			}
		}
		#[cfg(all(not(feature="wide-mul"),not(feature="deferred-division")))]
		impl_multiplicative_operator_not_const_generic!(($struct, $trait, $method, $output ), $width);
		#[cfg(all(not(feature="wide-mul"),feature="deferred-division"))]
		impl<const F:usize> ratio_ops::ratio::Divide for $struct<$width,F>{
			type Output = $output;
			#[inline]
			fn divide(self, other: Self) -> Self::Output {
				paste::item!{
				self.[<fixed_ $method>](other)
				}
			}
		}
	};
}

macro_rules! impl_multiplicative_operator {
	( $struct: ident, $trait: ident, $method: ident, $output: ty ) => {
		impl<const N:usize,const F:usize,U> core::ops::$trait<U> for $struct<N,F>
			where
				BInt::<N>:From<U>+core::ops::$trait,
		{
			type Output = $output;
			#[inline]
			fn $method(self, other: U) -> Self::Output {
				Self::from_bits(self.bits.$method(BInt::<N>::from(other)))
			}
		}
	};
}
macro_rules! impl_multiplicative_assign_operator {
	( $struct: ident, $trait: ident, $method: ident ) => {
		impl<const N:usize,const F:usize,U> core::ops::$trait<U> for $struct<N,F>
			where
				BInt::<N>:From<U>+core::ops::$trait,
		{
			#[inline]
			fn $method(&mut self, other: U) {
				self.bits.$method(BInt::<N>::from(other));
			}
		}
	};
}

macro_rules! macro_repeated{
	(
		$macro:ident,
		$any:tt,
		$($repeated:tt),*
	)=>{
		$(
			$macro!($any, $repeated);
		)*
	};
}

macro_rules! macro_16 {
	( $macro: ident, $any:tt ) => {
		macro_repeated!($macro,$any,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);
	}
}

macro_16!( impl_multiplicative_assign_operator_not_const_generic, (Fixed, MulAssign, mul_assign, mul) );
macro_16!( impl_multiply_operator_not_const_generic, (Fixed, Mul, mul, Self) );
macro_16!( impl_multiplicative_assign_operator_not_const_generic, (Fixed, DivAssign, div_assign, div) );
macro_16!( impl_divide_operator_not_const_generic, (Fixed, Div, div, Self) );
impl_multiplicative_assign_operator!( Fixed, MulAssign, mul_assign );
impl_multiplicative_operator!( Fixed, Mul, mul, Self );
impl_multiplicative_assign_operator!( Fixed, DivAssign, div_assign );
impl_multiplicative_operator!( Fixed, Div, div, Self );
#[cfg(feature="deferred-division")]
impl<const LHS_N:usize,const LHS_F:usize,const RHS_N:usize,const RHS_F:usize> core::ops::Div<Fixed<RHS_N,RHS_F>> for Fixed<LHS_N,LHS_F>{
	type Output=ratio_ops::ratio::Ratio<Fixed<LHS_N,LHS_F>,Fixed<RHS_N,RHS_F>>;
	#[inline]
	fn div(self, other: Fixed<RHS_N,RHS_F>)->Self::Output{
		ratio_ops::ratio::Ratio::new(self,other)
	}
}
#[cfg(feature="deferred-division")]
impl<const N:usize,const F:usize> ratio_ops::ratio::Parity for Fixed<N,F>{
	fn parity(&self)->bool{
		self.is_negative()
	}
}
macro_rules! impl_shift_operator {
	( $struct: ident, $trait: ident, $method: ident, $output: ty ) => {
		impl<const N:usize,const F:usize> core::ops::$trait<u32> for $struct<N,F>{
			type Output = $output;
			#[inline]
			fn $method(self, other: u32) -> Self::Output {
				Self::from_bits(self.bits.$method(other))
			}
		}
	};
}
macro_rules! impl_shift_assign_operator {
	( $struct: ident, $trait: ident, $method: ident ) => {
		impl<const N:usize,const F:usize> core::ops::$trait<u32> for $struct<N,F>{
			#[inline]
			fn $method(&mut self, other: u32) {
				self.bits.$method(other);
			}
		}
	};
}
impl_shift_assign_operator!( Fixed, ShlAssign, shl_assign );
impl_shift_operator!( Fixed, Shl, shl, Self );
impl_shift_assign_operator!( Fixed, ShrAssign, shr_assign );
impl_shift_operator!( Fixed, Shr, shr, Self );

// wide operators.  The result width is the sum of the input widths, i.e. none of the multiplication

#[allow(unused_macros)]
macro_rules! impl_wide_operators{
	($lhs:expr,$rhs:expr)=>{
		impl core::ops::Mul<Fixed<$rhs,{$rhs*32}>> for Fixed<$lhs,{$lhs*32}>{
			type Output=Fixed<{$lhs+$rhs},{($lhs+$rhs)*32}>;
			#[inline]
			fn mul(self, other: Fixed<$rhs,{$rhs*32}>)->Self::Output{
				paste::item!{
				self.[<wide_mul_ $lhs _ $rhs>](other)
				}
			}
		}
		#[cfg(not(feature="deferred-division"))]
		impl core::ops::Div<Fixed<$rhs,{$rhs*32}>> for Fixed<$lhs,{$lhs*32}>{
			type Output=Fixed<{$lhs+$rhs},{($lhs+$rhs)*32}>;
			#[inline]
			fn div(self, other: Fixed<$rhs,{$rhs*32}>)->Self::Output{
				paste::item!{
				self.[<wide_div_ $lhs _ $rhs>](other)
				}
			}
		}
		#[cfg(feature="deferred-division")]
		impl ratio_ops::ratio::Divide<Fixed<$rhs,{$rhs*32}>> for Fixed<$lhs,{$lhs*32}>{
			type Output=Fixed<{$lhs+$rhs},{($lhs+$rhs)*32}>;
			#[inline]
			fn divide(self, other: Fixed<$rhs,{$rhs*32}>)->Self::Output{
				paste::item!{
				self.[<wide_div_ $lhs _ $rhs>](other)
				}
			}
		}
	}
}

// WIDE MUL: multiply into a wider type
// let a = I32F32::ONE;
// let b:I64F64 = a.wide_mul(a);
macro_rules! impl_wide_not_const_generic{
	(
		(),
		($lhs:expr,$rhs:expr)
	)=>{
		impl Fixed<$lhs,{$lhs*32}>
		{
			paste::item!{
				#[inline]
				pub fn [<wide_mul_ $lhs _ $rhs>](self,rhs:Fixed<$rhs,{$rhs*32}>)->Fixed<{$lhs+$rhs},{($lhs+$rhs)*32}>{
					let lhs=self.bits.as_::<BInt<{$lhs+$rhs}>>();
					let rhs=rhs.bits.as_::<BInt<{$lhs+$rhs}>>();
					Fixed::from_bits(lhs*rhs)
				}
				/// This operation cannot represent the fraction exactly,
				/// but it shapes the output to have precision for the
				/// largest and smallest possible fractions.
				#[inline]
				pub fn [<wide_div_ $lhs _ $rhs>](self,rhs:Fixed<$rhs,{$rhs*32}>)->Fixed<{$lhs+$rhs},{($lhs+$rhs)*32}>{
					// (lhs/2^LHS_FRAC)/(rhs/2^RHS_FRAC)
					let lhs=self.bits.as_::<BInt<{$lhs+$rhs}>>().shl($rhs*64);
					let rhs=rhs.bits.as_::<BInt<{$lhs+$rhs}>>();
					Fixed::from_bits(lhs/rhs)
				}
			}
		}
		#[cfg(feature="wide-mul")]
		impl_wide_operators!($lhs,$rhs);
	};
}
macro_rules! impl_wide_same_size_not_const_generic{
	(
		(),
		$width:expr
	)=>{
		impl Fixed<$width,{$width*32}>
		{
			paste::item!{
				#[inline]
				pub fn [<wide_mul_ $width _ $width>](self,rhs:Fixed<$width,{$width*32}>)->Fixed<{$width*2},{$width*2*32}>{
					let (low,high)=self.bits.unsigned_abs().widening_mul(rhs.bits.unsigned_abs());
					let out:BInt::<{$width*2}>=unsafe{core::mem::transmute([low,high])};
					if self.is_negative()==rhs.is_negative(){
						Fixed::from_bits(out)
					}else{
						// Normal neg is the cheapest negation operation
						// And the inputs cannot reach the point where it matters
						Fixed::from_bits(out.neg())
					}
				}
				/// This operation cannot represent the fraction exactly,
				/// but it shapes the output to have precision for the
				/// largest and smallest possible fractions.
				#[inline]
				pub fn [<wide_div_ $width _ $width>](self,rhs:Fixed<$width,{$width*32}>)->Fixed<{$width*2},{$width*2*32}>{
					// (lhs/2^LHS_FRAC)/(rhs/2^RHS_FRAC)
					let lhs=self.bits.as_::<BInt<{$width*2}>>().shl($width*64);
					let rhs=rhs.bits.as_::<BInt<{$width*2}>>();
					Fixed::from_bits(lhs/rhs)
				}
			}
		}
		#[cfg(feature="wide-mul")]
		impl_wide_operators!($width,$width);
	};
}

//const generics sidestepped wahoo
macro_repeated!(
	impl_wide_not_const_generic,(),
	      (2,1),(3,1),(4,1),(5,1),(6,1),(7,1),(8,1),(9,1),(10,1),(11,1),(12,1),(13,1),(14,1),(15,1),
	(1,2),      (3,2),(4,2),(5,2),(6,2),(7,2),(8,2),(9,2),(10,2),(11,2),(12,2),(13,2),(14,2),
	(1,3),(2,3),      (4,3),(5,3),(6,3),(7,3),(8,3),(9,3),(10,3),(11,3),(12,3),(13,3),
	(1,4),(2,4),(3,4),      (5,4),(6,4),(7,4),(8,4),(9,4),(10,4),(11,4),(12,4),
	(1,5),(2,5),(3,5),(4,5),      (6,5),(7,5),(8,5),(9,5),(10,5),(11,5),
	(1,6),(2,6),(3,6),(4,6),(5,6),      (7,6),(8,6),(9,6),(10,6),
	(1,7),(2,7),(3,7),(4,7),(5,7),(6,7),      (8,7),(9,7),
	(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8),      (9,8),
	(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),
	(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),
	(1,11),(2,11),(3,11),(4,11),(5,11),
	(1,12),(2,12),(3,12),(4,12),
	(1,13),(2,13),(3,13),
	(1,14),(2,14),
	(1,15)
);
macro_repeated!(
	impl_wide_same_size_not_const_generic,(),
	1,2,3,4,5,6,7,8
);

pub trait Fix<Out>{
	fn fix(self)->Out;
}

macro_rules! impl_fix_rhs_lt_lhs_not_const_generic{
	(
		(),
		($lhs:expr,$rhs:expr)
	)=>{
		impl Fixed<$lhs,{$lhs*32}>
		{
			paste::item!{
				#[inline]
				pub fn [<fix_ $rhs>](self)->Fixed<$rhs,{$rhs*32}>{
					Fixed::from_bits(bnum::cast::As::as_::<BInt::<$rhs>>(self.bits.shr(($lhs-$rhs)*32)))
				}
			}
		}
		impl Fix<Fixed<$rhs,{$rhs*32}>> for Fixed<$lhs,{$lhs*32}>{
			fn fix(self)->Fixed<$rhs,{$rhs*32}>{
				paste::item!{
				self.[<fix_ $rhs>]()
				}
			}
		}
	}
}
macro_rules! impl_fix_lhs_lt_rhs_not_const_generic{
	(
		(),
		($lhs:expr,$rhs:expr)
	)=>{
		impl Fixed<$lhs,{$lhs*32}>
		{
			paste::item!{
				#[inline]
				pub fn [<fix_ $rhs>](self)->Fixed<$rhs,{$rhs*32}>{
					Fixed::from_bits(bnum::cast::As::as_::<BInt::<$rhs>>(self.bits).shl(($rhs-$lhs)*32))
				}
			}
		}
		impl Fix<Fixed<$rhs,{$rhs*32}>> for Fixed<$lhs,{$lhs*32}>{
			fn fix(self)->Fixed<$rhs,{$rhs*32}>{
				paste::item!{
				self.[<fix_ $rhs>]()
				}
			}
		}
	}
}
macro_rules! impl_fix_lhs_eq_rhs_not_const_generic{
	(
		(),
		($lhs:expr,$rhs:expr)
	)=>{
		impl Fixed<$lhs,{$lhs*32}>
		{
			paste::item!{
				#[inline]
				pub fn [<fix_ $rhs>](self)->Fixed<$rhs,{$rhs*32}>{
					self
				}
			}
		}
		impl Fix<Fixed<$rhs,{$rhs*32}>> for Fixed<$lhs,{$lhs*32}>{
			fn fix(self)->Fixed<$rhs,{$rhs*32}>{
				paste::item!{
				self.[<fix_ $rhs>]()
				}
			}
		}
	}
}

// I LOVE NOT BEING ABLE TO USE CONST GENERICS

macro_repeated!(
	impl_fix_rhs_lt_lhs_not_const_generic,(),
	(2,1),(3,1),(4,1),(5,1),(6,1),(7,1),(8,1),(9,1),(10,1),(11,1),(12,1),(13,1),(14,1),(15,1),(16,1),(17,1),
	(3,2),(4,2),(5,2),(6,2),(7,2),(8,2),(9,2),(10,2),(11,2),(12,2),(13,2),(14,2),(15,2),(16,2),
	(4,3),(5,3),(6,3),(7,3),(8,3),(9,3),(10,3),(11,3),(12,3),(13,3),(14,3),(15,3),(16,3),
	(5,4),(6,4),(7,4),(8,4),(9,4),(10,4),(11,4),(12,4),(13,4),(14,4),(15,4),(16,4),
	(6,5),(7,5),(8,5),(9,5),(10,5),(11,5),(12,5),(13,5),(14,5),(15,5),(16,5),
	(7,6),(8,6),(9,6),(10,6),(11,6),(12,6),(13,6),(14,6),(15,6),(16,6),
	(8,7),(9,7),(10,7),(11,7),(12,7),(13,7),(14,7),(15,7),(16,7),
	(9,8),(10,8),(11,8),(12,8),(13,8),(14,8),(15,8),(16,8),
	(10,9),(11,9),(12,9),(13,9),(14,9),(15,9),(16,9),
	(11,10),(12,10),(13,10),(14,10),(15,10),(16,10),
	(12,11),(13,11),(14,11),(15,11),(16,11),
	(13,12),(14,12),(15,12),(16,12),
	(14,13),(15,13),(16,13),
	(15,14),(16,14),
	(16,15)
);
macro_repeated!(
	impl_fix_lhs_lt_rhs_not_const_generic,(),
	(1,2),
	(1,3),(2,3),
	(1,4),(2,4),(3,4),
	(1,5),(2,5),(3,5),(4,5),
	(1,6),(2,6),(3,6),(4,6),(5,6),
	(1,7),(2,7),(3,7),(4,7),(5,7),(6,7),
	(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8),
	(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9),
	(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10),
	(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11),
	(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12),
	(1,13),(2,13),(3,13),(4,13),(5,13),(6,13),(7,13),(8,13),(9,13),(10,13),(11,13),(12,13),
	(1,14),(2,14),(3,14),(4,14),(5,14),(6,14),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14),
	(1,15),(2,15),(3,15),(4,15),(5,15),(6,15),(7,15),(8,15),(9,15),(10,15),(11,15),(12,15),(13,15),(14,15),
	(1,16),(2,16),(3,16),(4,16),(5,16),(6,16),(7,16),(8,16),(9,16),(10,16),(11,16),(12,16),(13,16),(14,16),(15,16)
);
macro_repeated!(
	impl_fix_lhs_eq_rhs_not_const_generic,(),
	(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7),(8,8),(9,9),(10,10),(11,11),(12,12),(13,13),(14,14),(15,15),(16,16)
);

macro_rules! impl_not_const_generic{
	($n:expr,$_2n:expr)=>{
		impl Fixed<$n,{$n*32}>{
			paste::item!{
			#[inline]
			pub fn sqrt_unchecked(self)->Self{
				//1<<max_shift must be the minimum power of two which when squared is greater than self
				//calculating max_shift:
				//1. count "used" bits to the left of the decimal, not including the sign bit (so -1)
				//2. divide by 2 via >>1 (sqrt-ish)
				//3. add on fractional offset
				//Voila
				let used_bits=self.bits.bits() as i32-1-($n*32) as i32;
				let max_shift=((used_bits>>1)+($n*32) as i32) as u32;
				let mut result=Self::ZERO;

				//resize self to match the wide mul output
				let wide_self=self.[<fix_ $_2n>]();
				//descend down the bits and check if flipping each bit would push the square over the input value
				for shift in (0..=max_shift).rev(){
					let new_result={
						let mut bits=result.to_bits().to_bits();
						bits.set_bit(shift,true);
						Self::from_bits(BInt::from_bits(bits))
					};
					if new_result.[<wide_mul_ $n _ $n>](new_result)<=wide_self{
						result=new_result;
					}
				}
				result
			}
			}
			#[inline]
			pub fn sqrt(self)->Self{
				if self<Self::ZERO{
					panic!("Square root less than zero")
				}else{
					self.sqrt_unchecked()
				}
			}
			#[inline]
			pub fn sqrt_checked(self)->Option<Self>{
				if self<Self::ZERO{
					None
				}else{
					Some(self.sqrt_unchecked())
				}
			}
		}
	}
}
impl_not_const_generic!(1,2);
impl_not_const_generic!(2,4);
impl_not_const_generic!(3,6);
impl_not_const_generic!(4,8);
impl_not_const_generic!(5,10);
impl_not_const_generic!(6,12);
impl_not_const_generic!(7,14);
impl_not_const_generic!(8,16);