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use std::fmt;
use std::ops;
use rand::distributions::uniform::SampleUniform;
pub trait FloatExt:
SampleUniform
+ Copy
+ fmt::Debug
+ Default
+ PartialOrd<Self>
+ ops::Add<Self, Output = Self>
+ ops::Sub<Self, Output = Self>
+ ops::Mul<Self, Output = Self>
+ ops::Div<Self, Output = Self>
{
fn nextup(self) -> Self;
fn nextdown(self) -> Self;
fn decompose(self) -> (Self, i32);
fn floats_between(self, other: Self) -> u64;
#[doc(hidden)]
fn abs(self) -> Self;
#[doc(hidden)]
fn sqrt(self) -> Self;
#[doc(hidden)]
fn round(self) -> Self;
#[doc(hidden)]
fn modulo(self, m: i64) -> i64;
#[doc(hidden)]
fn zero() -> Self;
#[doc(hidden)]
fn one() -> Self;
#[doc(hidden)]
fn eps() -> Self;
}
macro_rules! nextup {
($value:expr, $float:ty) => {{
debug_assert!($value.is_finite());
let value = if $value == -0.0 { 0.0 } else { $value };
let bits = value.to_bits();
let bits = if value >= 0.0 { bits + 1 } else { bits - 1 };
<$float>::from_bits(bits)
}};
}
macro_rules! nextdown {
($value:expr, $float:ty) => {{
debug_assert!($value.is_finite());
-(-$value).nextup()
}};
}
macro_rules! decompose {
($value:expr, $float:tt, $uint:ty) => {{
let xbits = $value.to_bits();
let fbits = xbits & !consts::$float::EXP_MASK;
let fbits = fbits | (consts::$float::EXP_BIAS as $uint) << consts::$float::MANTISSA_DIGITS;
let nbits = xbits & consts::$float::EXP_MASK;
let nbits = (nbits >> consts::$float::MANTISSA_DIGITS) as i32 - consts::$float::EXP_BIAS;
(<$float>::from_bits(fbits), nbits)
}};
}
macro_rules! floats_between {
($low:expr, $high:expr, $float:tt) => {{
let low = $low;
let high = $high;
if low == high {
return 1;
}
assert!(low < high);
let low_positive = low >= 0.0;
let high_positive = high >= 0.0;
let (low, high) = if low_positive != high_positive {
return low.floats_between(0.0.nextdown()) + 0.0.floats_between(high);
} else if !low_positive {
(-high, -low)
} else {
(low, high)
};
let (f_low, n_low) = low.decompose();
let (f_high, n_high) = high.decompose();
let f_high = (f_high.to_bits() & consts::$float::MANTISSA_MASK) as u64;
let f_low = (f_low.to_bits() & consts::$float::MANTISSA_MASK) as u64;
let floats_per_exponent = 1u64 << consts::$float::MANTISSA_DIGITS;
let (f_high, n_high) = if f_low > f_high {
(f_high + floats_per_exponent, n_high - 1)
} else {
(f_high, n_high)
};
let floats = (n_low..n_high).fold(0, |acc, _| acc + floats_per_exponent);
floats + f_high - f_low + 1
}};
}
mod consts {
pub mod f32 {
pub const EXP_MASK: u32 = 0x7f800000;
pub const EXP_BIAS: i32 = 127;
pub const MANTISSA_MASK: u32 = 0x007fffff;
pub const MANTISSA_DIGITS: u32 = 23;
}
pub mod f64 {
pub const EXP_MASK: u64 = 0x7ff0000000000000;
pub const EXP_BIAS: i32 = 1023;
pub const MANTISSA_MASK: u64 = 0x000fffffffffffff;
pub const MANTISSA_DIGITS: u64 = 52;
}
}
impl FloatExt for f32 {
fn nextup(self) -> Self {
nextup!(self, f32)
}
fn nextdown(self) -> Self {
nextdown!(self, f32)
}
fn decompose(self) -> (Self, i32) {
decompose!(self, f32, u32)
}
fn floats_between(self, other: Self) -> u64 {
floats_between!(self, other, f32)
}
fn abs(self) -> Self {
self.abs()
}
fn sqrt(self) -> Self {
self.sqrt()
}
fn round(self) -> Self {
self.round()
}
fn modulo(self, m: i64) -> i64 {
(self.round() as i64) % m
}
fn zero() -> Self {
0.0
}
fn one() -> Self {
1.0
}
fn eps() -> Self {
std::f32::EPSILON
}
}
impl FloatExt for f64 {
fn nextup(self) -> Self {
nextup!(self, f64)
}
fn nextdown(self) -> Self {
nextdown!(self, f64)
}
fn decompose(self) -> (Self, i32) {
decompose!(self, f64, u64)
}
fn floats_between(self, other: Self) -> u64 {
floats_between!(self, other, f64)
}
fn abs(self) -> Self {
self.abs()
}
fn sqrt(self) -> Self {
self.sqrt()
}
fn round(self) -> Self {
self.round()
}
fn modulo(self, m: i64) -> i64 {
(self.round() as i64) % m
}
fn zero() -> Self {
0.0
}
fn one() -> Self {
1.0
}
fn eps() -> Self {
std::f64::EPSILON
}
}
#[cfg(test)]
mod tests {
use super::consts::f32::{EXP_BIAS, MANTISSA_DIGITS};
use super::*;
use proptest::prelude::*;
proptest! {
#[test]
fn next(x: f32) {
if x.is_finite() {
assert_eq!(x.nextup().nextdown(), x);
}
}
}
#[test]
fn next_special() {
assert!(0.0f32.nextup() > 0.0);
assert!(0.0f32.nextdown() < 0.0);
assert!(0.0f32.nextdown().nextup().nextup() > 0.0);
}
#[test]
fn floats_between() {
let floats_per_exponent = (1 << MANTISSA_DIGITS) as u64;
let bias = EXP_BIAS as u64;
assert_eq!(1.0f32.floats_between(2.0), floats_per_exponent + 1);
assert_eq!(1.0f32.floats_between(2.0.nextdown()), floats_per_exponent);
assert_eq!((-2.0f32).floats_between(-1.0), floats_per_exponent + 1);
assert_eq!(3.14f32.floats_between(3.14.nextup()), 2);
assert_eq!(0.0f32.floats_between(1.0), bias * floats_per_exponent + 1);
assert_eq!(
(-1.0f32).floats_between(0.0),
bias * floats_per_exponent + 1
);
}
}