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// Copyright © 2018–2023 Trevor Spiteri
// This library is free software: you can redistribute it and/or modify it under
// the terms of either
//
// * the Apache License, Version 2.0 or
// * the MIT License
//
// at your option.
//
// You should have recieved copies of the Apache License and the MIT License
// along with the library. If not, see
// <https://www.apache.org/licenses/LICENSE-2.0> and
// <https://opensource.org/licenses/MIT>.
use crate::{
float_helper, int_helper,
traits::{Fixed, FixedBits, FixedEquiv, FromFixed, ToFixed},
FixedI128, FixedI16, FixedI32, FixedI64, FixedI8, FixedU128, FixedU16, FixedU32, FixedU64,
FixedU8, F128,
};
use az::{OverflowingAs, OverflowingCast, OverflowingCastFrom};
use bytemuck::TransparentWrapper;
use core::mem;
use half::{bf16, f16};
impl ToFixed for bool {
/// Converts a [`bool`] to a fixed-point number.
///
/// # Panics
///
/// When debug assertions are enabled, panics if the value does
/// not fit. When debug assertions are not enabled, the wrapped
/// value can be returned, but it is not considered a breaking
/// change if in the future it panics; if wrapping is required use
/// [`wrapping_to_fixed`] instead.
///
/// [`wrapping_to_fixed`]: ToFixed::wrapping_to_fixed
#[inline]
#[track_caller]
fn to_fixed<F: Fixed>(self) -> F {
ToFixed::to_fixed(u8::from(self))
}
/// Converts a [`bool`] to a fixed-point number if it fits, otherwise returns [`None`].
#[inline]
fn checked_to_fixed<F: Fixed>(self) -> Option<F> {
ToFixed::checked_to_fixed(u8::from(self))
}
/// Convert a [`bool`] to a fixed-point number, saturating if it does not fit.
#[inline]
fn saturating_to_fixed<F: Fixed>(self) -> F {
ToFixed::saturating_to_fixed(u8::from(self))
}
/// Converts a [`bool`] to a fixed-point number, wrapping if it does not fit.
#[inline]
fn wrapping_to_fixed<F: Fixed>(self) -> F {
ToFixed::wrapping_to_fixed(u8::from(self))
}
/// Converts a [`bool`] to a fixed-point number.
///
/// Returns a [tuple] of the fixed-point number and a [`bool`]
/// indicating whether an overflow has occurred. On overflow, the
/// wrapped value is returned.
#[inline]
fn overflowing_to_fixed<F: Fixed>(self) -> (F, bool) {
ToFixed::overflowing_to_fixed(u8::from(self))
}
/// Converts a [`bool`] to a fixed-point number, panicking if it
/// does not fit.
///
/// # Panics
///
/// Panics if the value does not fit, even when debug assertions
/// are not enabled.
#[inline]
#[track_caller]
fn unwrapped_to_fixed<F: Fixed>(self) -> F {
ToFixed::unwrapped_to_fixed(u8::from(self))
}
}
macro_rules! impl_int {
($Int:ident as $IntAs:ident, $AsEquiv:ident) => {
impl FromFixed for $Int {
/// Converts a fixed-point number to an integer.
///
/// Any fractional bits are discarded, which rounds towards −∞.
///
/// # Panics
///
/// When debug assertions are enabled, panics if the value
/// does not fit. When debug assertions are not enabled,
/// the wrapped value can be returned, but it is not
/// considered a breaking change if in the future it
/// panics; if wrapping is required use
/// [`wrapping_from_fixed`] instead.
///
/// [`wrapping_from_fixed`]: FromFixed::wrapping_from_fixed
#[inline]
#[track_caller]
fn from_fixed<F: Fixed>(src: F) -> Self {
$AsEquiv::<0>::from_fixed(src).to_bits() as $Int
}
/// Converts a fixed-point number to an integer if it fits, otherwise returns [`None`].
///
/// Any fractional bits are discarded, which rounds towards −∞.
#[inline]
fn checked_from_fixed<F: Fixed>(src: F) -> Option<Self> {
$AsEquiv::<0>::checked_from_fixed(src).map(|x| x.to_bits() as $Int)
}
/// Converts a fixed-point number to an integer, saturating if it does not fit.
///
/// Any fractional bits are discarded, which rounds towards −∞.
#[inline]
fn saturating_from_fixed<F: Fixed>(src: F) -> Self {
$AsEquiv::<0>::saturating_from_fixed(src).to_bits() as $Int
}
/// Converts a fixed-point number to an integer, wrapping if it does not fit.
///
/// Any fractional bits are discarded, which rounds towards −∞.
#[inline]
fn wrapping_from_fixed<F: Fixed>(src: F) -> Self {
$AsEquiv::<0>::wrapping_from_fixed(src).to_bits() as $Int
}
/// Converts a fixed-point number to an integer.
///
/// Returns a [tuple] of the value and a [`bool`] indicating whether
/// an overflow has occurred. On overflow, the wrapped value is
/// returned.
///
/// Any fractional bits are discarded, which rounds towards −∞.
#[inline]
fn overflowing_from_fixed<F: Fixed>(src: F) -> (Self, bool) {
let (fixed, overflow) = $AsEquiv::<0>::overflowing_from_fixed(src);
(fixed.to_bits() as $Int, overflow)
}
/// Converts a fixed-point number to an integer, panicking if it does not fit.
///
/// Any fractional bits are discarded, which rounds towards −∞.
///
/// # Panics
///
/// Panics if the value
/// does not fit, even when debug assertions are not enabled.
#[inline]
#[track_caller]
fn unwrapped_from_fixed<F: Fixed>(src: F) -> Self {
$AsEquiv::<0>::unwrapped_from_fixed(src).to_bits() as $Int
}
}
impl ToFixed for $Int {
/// Converts an integer to a fixed-point number.
///
/// # Panics
///
/// When debug assertions are enabled, panics if the value
/// does not fit. When debug assertions are not enabled,
/// the wrapped value can be returned, but it is not
/// considered a breaking change if in the future it
/// panics; if wrapping is required use
/// [`wrapping_to_fixed`] instead.
///
/// [`wrapping_to_fixed`]: ToFixed::wrapping_to_fixed
#[inline]
#[track_caller]
fn to_fixed<F: Fixed>(self) -> F {
$AsEquiv::<0>::from_bits(self as $IntAs).to_fixed()
}
/// Converts an integer to a fixed-point number if it fits, otherwise returns [`None`].
#[inline]
fn checked_to_fixed<F: Fixed>(self) -> Option<F> {
$AsEquiv::<0>::from_bits(self as $IntAs).checked_to_fixed()
}
/// Converts an integer to a fixed-point number, saturating if it does not fit.
#[inline]
fn saturating_to_fixed<F: Fixed>(self) -> F {
$AsEquiv::<0>::from_bits(self as $IntAs).saturating_to_fixed()
}
/// Converts an integer to a fixed-point number, wrapping if it does not fit.
#[inline]
fn wrapping_to_fixed<F: Fixed>(self) -> F {
$AsEquiv::<0>::from_bits(self as $IntAs).wrapping_to_fixed()
}
/// Converts an integer to a fixed-point number.
///
/// Returns a [tuple] of the fixed-point number and a [`bool`]
/// indicating whether an overflow has occurred. On overflow, the
/// wrapped value is returned.
#[inline]
fn overflowing_to_fixed<F: Fixed>(self) -> (F, bool) {
$AsEquiv::<0>::from_bits(self as $IntAs).overflowing_to_fixed()
}
/// Converts an integer to a fixed-point number, panicking if it does not fit.
///
/// # Panics
///
/// Panics if the value does not fit, even when debug
/// assertions are not enabled.
#[inline]
#[track_caller]
fn unwrapped_to_fixed<F: Fixed>(self) -> F {
$AsEquiv::<0>::from_bits(self as $IntAs).unwrapped_to_fixed()
}
}
};
}
impl_int! { i8 as i8, FixedI8 }
impl_int! { i16 as i16, FixedI16 }
impl_int! { i32 as i32, FixedI32 }
impl_int! { i64 as i64, FixedI64 }
impl_int! { i128 as i128, FixedI128 }
#[cfg(target_pointer_width = "16")]
impl_int! { isize as i16, FixedI16 }
#[cfg(target_pointer_width = "32")]
impl_int! { isize as i32, FixedI32 }
#[cfg(target_pointer_width = "64")]
impl_int! { isize as i64, FixedI64 }
impl_int! { u8 as u8, FixedU8 }
impl_int! { u16 as u16, FixedU16 }
impl_int! { u32 as u32, FixedU32 }
impl_int! { u64 as u64, FixedU64 }
impl_int! { u128 as u128, FixedU128 }
#[cfg(target_pointer_width = "16")]
impl_int! { usize as u16, FixedU16 }
#[cfg(target_pointer_width = "32")]
impl_int! { usize as u32, FixedU32 }
#[cfg(target_pointer_width = "64")]
impl_int! { usize as u64, FixedU64 }
macro_rules! impl_int_equiv {
($Int:ident, $Equiv:ident) => {
impl FixedEquiv for $Int {
type Equiv = $Equiv<0>;
#[inline]
fn to_fixed_equiv(self) -> $Equiv<0> {
$Equiv::from_bits(self)
}
#[inline]
fn as_fixed_equiv(&self) -> &$Equiv<0> {
$Equiv::wrap_ref(self)
}
#[inline]
fn as_fixed_equiv_mut(&mut self) -> &mut $Equiv<0> {
$Equiv::wrap_mut(self)
}
#[inline]
fn from_fixed_equiv(f: $Equiv<0>) -> $Int {
f.to_bits()
}
#[inline]
fn ref_from_fixed_equiv(f: &$Equiv<0>) -> &$Int {
&f.bits
}
#[inline]
fn mut_from_fixed_equiv(f: &mut $Equiv<0>) -> &mut $Int {
&mut f.bits
}
}
};
}
impl_int_equiv! { i8, FixedI8 }
impl_int_equiv! { i16, FixedI16 }
impl_int_equiv! { i32, FixedI32 }
impl_int_equiv! { i64, FixedI64 }
impl_int_equiv! { i128, FixedI128 }
impl_int_equiv! { u8, FixedU8 }
impl_int_equiv! { u16, FixedU16 }
impl_int_equiv! { u32, FixedU32 }
impl_int_equiv! { u64, FixedU64 }
impl_int_equiv! { u128, FixedU128 }
#[inline]
fn leading_ones<Bits: FixedBits>(bits: Bits) -> u32 {
let neg_overflows = Bits::overflowing_cast_from(-1i8).1;
let is_signed = !neg_overflows;
match (is_signed, mem::size_of::<Bits>()) {
(false, 1) => bits.overflowing_as::<u8>().0.leading_ones(),
(false, 2) => bits.overflowing_as::<u16>().0.leading_ones(),
(false, 4) => bits.overflowing_as::<u32>().0.leading_ones(),
(false, 8) => bits.overflowing_as::<u64>().0.leading_ones(),
(false, 16) => bits.overflowing_as::<u128>().0.leading_ones(),
(true, 1) => bits.overflowing_as::<i8>().0.leading_ones(),
(true, 2) => bits.overflowing_as::<i16>().0.leading_ones(),
(true, 4) => bits.overflowing_as::<i32>().0.leading_ones(),
(true, 8) => bits.overflowing_as::<i64>().0.leading_ones(),
(true, 16) => bits.overflowing_as::<i128>().0.leading_ones(),
_ => unreachable!(),
}
}
#[inline]
fn leading_zeros<Bits: FixedBits>(bits: Bits) -> u32 {
let neg_overflows = Bits::overflowing_cast_from(-1i8).1;
let is_signed = !neg_overflows;
match (is_signed, mem::size_of::<Bits>()) {
(false, 1) => bits.overflowing_as::<u8>().0.leading_zeros(),
(false, 2) => bits.overflowing_as::<u16>().0.leading_zeros(),
(false, 4) => bits.overflowing_as::<u32>().0.leading_zeros(),
(false, 8) => bits.overflowing_as::<u64>().0.leading_zeros(),
(false, 16) => bits.overflowing_as::<u128>().0.leading_zeros(),
(true, 1) => bits.overflowing_as::<i8>().0.leading_zeros(),
(true, 2) => bits.overflowing_as::<i16>().0.leading_zeros(),
(true, 4) => bits.overflowing_as::<i32>().0.leading_zeros(),
(true, 8) => bits.overflowing_as::<i64>().0.leading_zeros(),
(true, 16) => bits.overflowing_as::<i128>().0.leading_zeros(),
_ => unreachable!(),
}
}
macro_rules! impl_float {
($Float:ident, $FloatI:ident, $FloatU:ident) => {
impl FromFixed for $Float {
/// Converts a fixed-point number to a floating-point number.
///
/// Rounding is to the nearest, with ties rounded to even.
///
/// # Panics
///
/// When debug assertions are enabled, panics if the value
/// does not fit. When debug assertions are not enabled,
/// the wrapped value can be returned, but it is not
/// considered a breaking change if in the future it
/// panics; if wrapping is required use
/// [`wrapping_from_fixed`] instead.
///
/// [`wrapping_from_fixed`]: FromFixed::wrapping_from_fixed
#[inline]
#[track_caller]
fn from_fixed<F: Fixed>(src: F) -> Self {
let zero = F::Bits::overflowing_cast_from(0u8).0;
let src = src.to_bits();
// handle zero early so that we can assume bits != 0
if src == zero {
return Self::from_bits(0);
}
let src_neg_overflows = F::Bits::overflowing_cast_from(-1i8).1;
let src_is_signed = !src_neg_overflows;
let src_bits = mem::size_of::<F>() as u32 * 8;
let (neg, abs, excess_shift) = if $FloatU::BITS >= src_bits {
if src_is_signed {
let (widened, overflow): ($FloatI, bool) = src.overflowing_cast();
debug_assert!(!overflow);
let (neg, abs) = int_helper::$FloatI::neg_abs(widened);
let shift = abs.leading_zeros();
(neg, abs << shift, shift as i32)
} else {
let (widened, overflow): ($FloatU, bool) = src.overflowing_cast();
debug_assert!(!overflow);
let shift = widened.leading_zeros();
(false, widened << shift, shift as i32)
}
} else {
// We need to narrow the source. First we push the bits to
// the left so that we don't crop off bits we'd need.
let lossless_shift = if !src_is_signed {
leading_zeros(src)
} else if src < zero {
leading_ones(src) - 1
} else {
leading_zeros(src) - 1
};
let src = src << lossless_shift;
let narrow_by = src_bits - $FloatU::BITS;
let narrowed = src >> narrow_by;
let sig_lower_bits = narrowed << narrow_by != src;
if src_is_signed {
let (narrowed, overflow) = narrowed.overflowing_as::<$FloatI>();
debug_assert!(!overflow);
let (neg, mut abs) = int_helper::$FloatI::neg_abs(narrowed);
let shift = abs.leading_zeros();
abs <<= shift;
if sig_lower_bits {
abs |= 1;
}
(neg, abs, (shift + lossless_shift) as i32 - narrow_by as i32)
} else {
let (mut narrowed, overflow) = narrowed.overflowing_as::<$FloatU>();
debug_assert!(!overflow);
debug_assert!(narrowed.leading_zeros() == 0);
if sig_lower_bits {
narrowed |= 1;
}
(false, narrowed, lossless_shift as i32 - narrow_by as i32)
}
};
// excess_shift is how much we have shifted the bits to the left.
// So eventually we need to divide if excess_shift is positive.
// Similarly we need to divide if F::FRAC_BITS is positive.
// That means that we can add excess_shift and F::FRAC_BITS.
let frac = F::FRAC_BITS.saturating_add(excess_shift);
float_helper::$Float::from_neg_abs(neg, abs, frac)
}
/// Converts a fixed-point number to a floating-point
/// number if it fits, otherwise returns [`None`].
///
/// Rounding is to the nearest, with ties rounded to even.
#[inline]
fn checked_from_fixed<F: Fixed>(src: F) -> Option<Self> {
Some(FromFixed::from_fixed(src))
}
/// Converts a fixed-point number to a floating-point
/// number, saturating if it does not fit.
///
/// Rounding is to the nearest, with ties rounded to even.
#[inline]
fn saturating_from_fixed<F: Fixed>(src: F) -> Self {
FromFixed::from_fixed(src)
}
/// Converts a fixed-point number to a floating-point
/// number, wrapping if it does not fit.
///
/// Rounding is to the nearest, with ties rounded to even.
#[inline]
fn wrapping_from_fixed<F: Fixed>(src: F) -> Self {
FromFixed::from_fixed(src)
}
/// Converts a fixed-point number to a floating-point number.
///
/// Returns a [tuple] of the value and a [`bool`]
/// indicating whether an overflow has occurred. On
/// overflow, the wrapped value is returned.
///
/// Rounding is to the nearest, with ties rounded to even.
#[inline]
fn overflowing_from_fixed<F: Fixed>(src: F) -> (Self, bool) {
(FromFixed::from_fixed(src), false)
}
/// Converts a fixed-point number to a floating-point
/// number, panicking if it does not fit.
///
/// Rounding is to the nearest, with ties rounded to even.
///
/// # Panics
///
/// Panics if the value does not fit, even when debug
/// assertions are not enabled.
#[inline]
#[track_caller]
fn unwrapped_from_fixed<F: Fixed>(src: F) -> Self {
FromFixed::from_fixed(src)
}
}
impl ToFixed for $Float {
comment! {
"Converts a floating-point number to a fixed-point number.
Rounding is to the nearest, with ties rounded to even.
# Panics
Panics if `self` is not [finite].
When debug assertions are enabled, also panics if the value does not
fit. When debug assertions are not enabled, the wrapped value can be
returned, but it is not considered a breaking change if in the future
it panics; if wrapping is required use [`wrapping_to_fixed`] instead.
[`wrapping_to_fixed`]: ToFixed::wrapping_to_fixed
[finite]: ", stringify!($Float), "::is_finite
";
#[inline]
#[track_caller]
#[allow(clippy::redundant_closure_call)]
fn to_fixed<F: Fixed>(self) -> F {
let (wrapped, overflow) = ToFixed::overflowing_to_fixed(self);
debug_assert!(!overflow, "overflow");
wrapped
}
}
/// Converts a floating-point number to a fixed-point
/// number if it fits, otherwise returns [`None`].
///
/// Rounding is to the nearest, with ties rounded to even.
#[inline]
fn checked_to_fixed<F: Fixed>(self) -> Option<F> {
if !self.is_finite() {
return None;
}
match ToFixed::overflowing_to_fixed(self) {
(wrapped, false) => Some(wrapped),
(_, true) => None,
}
}
comment! {
"Converts a floating-point number to a fixed-point
number, saturating if it does not fit.
Rounding is to the nearest, with ties rounded to even.
# Panics
Panics if `self` is [NaN].
[NaN]: ", stringify!($Float), "::is_nan
";
#[inline]
#[track_caller]
fn saturating_to_fixed<F: Fixed>(self) -> F {
if self.is_nan() {
panic!("NaN");
}
if self.is_finite() {
let (wrapped, overflow) = ToFixed::overflowing_to_fixed(self);
if !overflow {
return wrapped;
}
}
// either self is infinite, or overflow flag returned is true
if self.is_sign_negative() {
F::MIN
} else {
F::MAX
}
}
}
comment! {
"Converts a floating-point number to a fixed-point
number, wrapping if it does not fit.
Rounding is to the nearest, with ties rounded to even.
# Panics
Panics if `self` is not [finite].
[finite]: ", stringify!($Float), "::is_finite
";
#[inline]
#[track_caller]
fn wrapping_to_fixed<F: Fixed>(self) -> F {
let (wrapped, _) = ToFixed::overflowing_to_fixed(self);
wrapped
}
}
comment! {
"Converts a floating-point number to a fixed-point number.
Returns a [tuple] of the fixed-point number and a [`bool`] indicating
whether an overflow has occurred. On overflow, the wrapped value is
returned.
Rounding is to the nearest, with ties rounded to even.
# Panics
Panics if `self` is not [finite].
[finite]: ", stringify!($Float), "::is_finite
";
#[inline]
#[track_caller]
fn overflowing_to_fixed<F: Fixed>(self) -> (F, bool) {
float_helper::$Float::overflowing_to_fixed(self)
}
}
comment! {
"Converts a floating-point number to a fixed-point
number, panicking if it does not fit.
Rounding is to the nearest, with ties rounded to even.
# Panics
Panics if `self` is not [finite] or if the value does not fit, even
when debug assertions are not enabled.
[finite]: ", stringify!($Float), "::is_finite
";
#[inline]
#[track_caller]
fn unwrapped_to_fixed<F: Fixed>(self) -> F {
match ToFixed::overflowing_to_fixed(self) {
(val, false) => val,
(_, true) => panic!("overflow"),
}
}
}
}
};
}
impl_float! { f16, i16, u16 }
impl_float! { bf16, i16, u16 }
impl_float! { f32, i32, u32 }
impl_float! { f64, i64, u64 }
impl_float! { F128, i128, u128 }