use std::mem;
use std::cmp::Ordering;
pub trait Ulps {
type U;
fn ulps(&self, other: &Self) -> <Self as Ulps>::U;
}
impl Ulps for f32 {
type U = i32;
fn ulps(&self, other: &f32) -> i32 {
let ai32: i32 = unsafe { mem::transmute(*self) };
let bi32: i32 = unsafe { mem::transmute(*other) };
ai32.wrapping_sub(bi32)
}
}
#[test]
fn f32_ulps_test1() {
let x: f32 = 1000000_f32;
let y: f32 = 1000000.1_f32;
println!("DIST IS {}",x.ulps(&y));
assert!(x.ulps(&y) == -2);
}
#[test]
fn f32_ulps_test2() {
let pzero: f32 = unsafe { mem::transmute(0x00000000_u32) };
let nzero: f32 = unsafe { mem::transmute(0x80000000_u32) };
println!("DIST IS {}",pzero.ulps(&nzero));
assert!(pzero.ulps(&nzero) == -2147483648);
}
#[test]
fn f32_ulps_test3() {
let pinf: f32 = unsafe { mem::transmute(0x7f800000_u32) };
let ninf: f32 = unsafe { mem::transmute(0xff800000_u32) };
println!("DIST IS {}",pinf.ulps(&ninf));
assert!(pinf.ulps(&ninf) == -2147483648);
}
#[test]
fn f32_ulps_test4() {
let x: f32 = unsafe { mem::transmute(0x63a7f026_u32) };
let y: f32 = unsafe { mem::transmute(0x63a7f023_u32) };
println!("DIST IS {}",x.ulps(&y));
assert!(x.ulps(&y) == 3);
}
impl Ulps for f64 {
type U = i64;
fn ulps(&self, other: &f64) -> i64 {
let ai64: i64 = unsafe { mem::transmute(*self) };
let bi64: i64 = unsafe { mem::transmute(*other) };
ai64.wrapping_sub(bi64)
}
}
#[test]
fn f64_ulps_test1() {
let x: f64 = 1000000_f64;
let y: f64 = 1000000.00000001_f64;
println!("DIST IS {}",x.ulps(&y));
assert!(x.ulps(&y) == -86);
}
#[test]
fn f64_ulps_test2() {
let pzero: f64 = unsafe { mem::transmute(0x0000000000000000_u64) };
let nzero: f64 = unsafe { mem::transmute(0x8000000000000000_u64) };
println!("DIST IS {}",pzero.ulps(&nzero));
assert!(pzero.ulps(&nzero) == -9223372036854775808i64);
}
#[test]
fn f64_ulps_test3() {
let pinf: f64 = unsafe { mem::transmute(0x7f80000000000000_u64) };
let ninf: f64 = unsafe { mem::transmute(0xff80000000000000_u64) };
println!("DIST IS {}",pinf.ulps(&ninf));
assert!(pinf.ulps(&ninf) == -9223372036854775808i64);
}
#[test]
fn f64_ulps_test4() {
let x: f64 = unsafe { mem::transmute(0xd017f6cc63a7f026_u64) };
let y: f64 = unsafe { mem::transmute(0xd017f6cc63a7f023_u64) };
println!("DIST IS {}",x.ulps(&y));
assert!(x.ulps(&y) == 3);
}
pub trait ApproxEq : Ulps {
fn approx_eq(&self, other: &Self, ulps: <Self as Ulps>::U) -> bool;
#[inline]
fn approx_ne(&self, other: &Self, ulps: <Self as Ulps>::U) -> bool {
!self.approx_eq(other, ulps)
}
}
impl ApproxEq for f32 {
fn approx_eq(&self, other: &f32, ulps: i32) -> bool {
if *self==*other { return true; }
if *self>0_f32 && *other<0_f32 { return false; }
if *self<0_f32 && *other>0_f32 { return false; }
let diff: i32 = self.ulps(other);
diff >= -ulps && diff <= ulps
}
}
#[test]
fn f32_approx_eq_test1() {
let f: f32 = 0.1_f32;
let mut sum: f32 = 0.0_f32;
for _ in (0_isize..10_isize) { sum += f; }
let product: f32 = f * 10.0_f32;
assert!(sum != product); println!("Ulps Difference: {}",sum.ulps(&product));
assert!(sum.approx_eq(&product,1) == true); assert!(sum.approx_eq(&product,0) == false);
}
#[test]
fn f32_approx_eq_test2() {
let x: f32 = 1000000_f32;
let y: f32 = 1000000.1_f32;
assert!(x != y); println!("Ulps Difference: {}",x.ulps(&y));
assert!(x.approx_eq(&y,2) == true);
assert!(x.approx_eq(&y,1) == false);
}
#[test]
fn f32_approx_eq_test_zeroes() {
let x: f32 = 0.0_f32;
let y: f32 = -0.0_f32;
assert!(x.approx_eq(&y,0) == true);
}
impl ApproxEq for f64 {
fn approx_eq(&self, other: &f64, ulps: i64) -> bool {
if *self==*other { return true; }
if *self>0_f64 && *other<0_f64 { return false; }
if *self<0_f64 && *other>0_f64 { return false; }
let diff: i64 = self.ulps(other);
diff >= -ulps && diff <= ulps
}
}
#[test]
fn f64_approx_eq_test1() {
let f: f64 = 0.1_f64;
let mut sum: f64 = 0.0_f64;
for _ in (0_isize..10_isize) { sum += f; }
let product: f64 = f * 10.0_f64;
assert!(sum != product); println!("Ulps Difference: {}",sum.ulps(&product));
assert!(sum.approx_eq(&product,1) == true); assert!(sum.approx_eq(&product,0) == false);
}
#[test]
fn f64_approx_eq_test2() {
let x: f64 = 1000000_f64;
let y: f64 = 1000000.0000000003_f64;
assert!(x != y); println!("Ulps Difference: {}",x.ulps(&y));
assert!(x.approx_eq(&y,3) == true);
assert!(x.approx_eq(&y,2) == false);
}
#[test]
fn f64_approx_eq_test_zeroes() {
let x: f64 = 0.0_f64;
let y: f64 = -0.0_f64;
assert!(x.approx_eq(&y,0) == true);
}
pub trait ApproxOrd: ApproxEq + Ulps {
fn approx_cmp(&self, other: &Self, ulps: <Self as Ulps>::U) -> Ordering;
#[inline]
fn approx_lt(&self, other: &Self, ulps: <Self as Ulps>::U) -> bool {
match self.approx_cmp(other, ulps) {
Ordering::Less => true,
_ => false,
}
}
#[inline]
fn approx_le(&self, other: &Self, ulps: <Self as Ulps>::U) -> bool {
match self.approx_cmp(other, ulps) {
Ordering::Less | Ordering::Equal => true,
_ => false,
}
}
#[inline]
fn approx_gt(&self, other: &Self, ulps: <Self as Ulps>::U) -> bool {
match self.approx_cmp(other, ulps) {
Ordering::Greater => true,
_ => false,
}
}
#[inline]
fn approx_ge(&self, other: &Self, ulps: <Self as Ulps>::U) -> bool {
match self.approx_cmp(other, ulps) {
Ordering::Greater | Ordering::Equal => true,
_ => false,
}
}
}
impl ApproxOrd for f32 {
fn approx_cmp(&self, other: &f32, ulps: <Self as Ulps>::U) -> Ordering {
if self==other { return Ordering::Equal; }
if *self>0_f32 && *other<0_f32 { return Ordering::Greater; }
if *self<0_f32 && *other>0_f32 { return Ordering::Less }
let diff: i32 = self.ulps(other);
match diff {
x if x > 0 && x <= ulps => Ordering::Equal,
x if x > 0 => Ordering::Greater,
x if x < 0 && x >= -ulps => Ordering::Equal,
x if x < 0 => Ordering::Less,
_ => Ordering::Equal
}
}
}
#[test]
fn f32_approx_cmp_test1() {
let f: f32 = 0.1_f32;
let mut sum: f32 = 0.0_f32;
for _ in (0_isize..10_isize) { sum += f; }
let product: f32 = f * 10.0_f32;
assert!(sum != product); println!("Ulps Difference: {}",sum.ulps(&product));
assert!(sum.approx_cmp(&product,1) == Ordering::Equal); assert!(sum.approx_cmp(&product,0) != Ordering::Equal);
assert!(product.approx_cmp(&sum,0) != Ordering::Equal);
}
#[test]
fn f32_approx_cmp_test2() {
let x: f32 = 1000000_f32;
let y: f32 = 1000000.1_f32;
assert!(x != y); println!("Ulps Difference: {}",x.ulps(&y));
assert!(x.approx_cmp(&y,2) == Ordering::Equal);
assert!(x.approx_cmp(&y,1) == Ordering::Less);
assert!(y.approx_cmp(&x,1) == Ordering::Greater);
}
impl ApproxOrd for f64 {
fn approx_cmp(&self, other: &f64, ulps: <Self as Ulps>::U) -> Ordering {
if self==other { return Ordering::Equal; }
if *self>0_f64 && *other<0_f64 { return Ordering::Greater; }
if *self<0_f64 && *other>0_f64 { return Ordering::Less }
let diff: i64 = self.ulps(other);
match diff {
x if x > 0 && x <= ulps => Ordering::Equal,
x if x > 0 => Ordering::Greater,
x if x < 0 && x >= -ulps => Ordering::Equal,
x if x < 0 => Ordering::Less,
_ => Ordering::Equal
}
}
}
#[test]
fn f64_approx_cmp_test1() {
let f: f64 = 0.000000001_f64;
let mut sum: f64 = 0.0_f64;
for _ in (0_isize..10_isize) { sum += f; }
let product: f64 = f * 10.0_f64;
assert!(sum != product); println!("Ulps Difference: {}",sum.ulps(&product));
assert!(sum.approx_cmp(&product,1) == Ordering::Equal); assert!(sum.approx_cmp(&product,0) != Ordering::Equal);
assert!(product.approx_cmp(&sum,0) != Ordering::Equal);
}
#[test]
fn f64_approx_cmp_test2() {
let x: f64 = 1000000_f64;
let y: f64 = 1000000.0000000003_f64;
assert!(x != y); println!("Ulps Difference: {}",x.ulps(&y));
assert!(x.approx_cmp(&y,3) == Ordering::Equal);
assert!(x.approx_cmp(&y,2) == Ordering::Less);
assert!(y.approx_cmp(&x,2) == Ordering::Greater);
}