diff options
Diffstat (limited to 'vendor/num-integer/tests/roots.rs')
| -rw-r--r-- | vendor/num-integer/tests/roots.rs | 272 |
1 files changed, 272 insertions, 0 deletions
diff --git a/vendor/num-integer/tests/roots.rs b/vendor/num-integer/tests/roots.rs new file mode 100644 index 0000000..f85f9e0 --- /dev/null +++ b/vendor/num-integer/tests/roots.rs @@ -0,0 +1,272 @@ +extern crate num_integer; +extern crate num_traits; + +use num_integer::Roots; +use num_traits::checked_pow; +use num_traits::{AsPrimitive, PrimInt, Signed}; +use std::f64::MANTISSA_DIGITS; +use std::fmt::Debug; +use std::mem; + +trait TestInteger: Roots + PrimInt + Debug + AsPrimitive<f64> + 'static {} + +impl<T> TestInteger for T where T: Roots + PrimInt + Debug + AsPrimitive<f64> + 'static {} + +/// Check that each root is correct +/// +/// If `x` is positive, check `rⁿ ≤ x < (r+1)ⁿ`. +/// If `x` is negative, check `(r-1)ⁿ < x ≤ rⁿ`. +fn check<T>(v: &[T], n: u32) +where + T: TestInteger, +{ + for i in v { + let rt = i.nth_root(n); + // println!("nth_root({:?}, {}) = {:?}", i, n, rt); + if n == 2 { + assert_eq!(rt, i.sqrt()); + } else if n == 3 { + assert_eq!(rt, i.cbrt()); + } + if *i >= T::zero() { + let rt1 = rt + T::one(); + assert!(rt.pow(n) <= *i); + if let Some(x) = checked_pow(rt1, n as usize) { + assert!(*i < x); + } + } else { + let rt1 = rt - T::one(); + assert!(rt < T::zero()); + assert!(*i <= rt.pow(n)); + if let Some(x) = checked_pow(rt1, n as usize) { + assert!(x < *i); + } + }; + } +} + +/// Get the maximum value that will round down as `f64` (if any), +/// and its successor that will round up. +/// +/// Important because the `std` implementations cast to `f64` to +/// get a close approximation of the roots. +fn mantissa_max<T>() -> Option<(T, T)> +where + T: TestInteger, +{ + let bits = if T::min_value().is_zero() { + 8 * mem::size_of::<T>() + } else { + 8 * mem::size_of::<T>() - 1 + }; + if bits > MANTISSA_DIGITS as usize { + let rounding_bit = T::one() << (bits - MANTISSA_DIGITS as usize - 1); + let x = T::max_value() - rounding_bit; + + let x1 = x + T::one(); + let x2 = x1 + T::one(); + assert!(x.as_() < x1.as_()); + assert_eq!(x1.as_(), x2.as_()); + + Some((x, x1)) + } else { + None + } +} + +fn extend<T>(v: &mut Vec<T>, start: T, end: T) +where + T: TestInteger, +{ + let mut i = start; + while i < end { + v.push(i); + i = i + T::one(); + } + v.push(i); +} + +fn extend_shl<T>(v: &mut Vec<T>, start: T, end: T, mask: T) +where + T: TestInteger, +{ + let mut i = start; + while i != end { + v.push(i); + i = (i << 1) & mask; + } +} + +fn extend_shr<T>(v: &mut Vec<T>, start: T, end: T) +where + T: TestInteger, +{ + let mut i = start; + while i != end { + v.push(i); + i = i >> 1; + } +} + +fn pos<T>() -> Vec<T> +where + T: TestInteger, + i8: AsPrimitive<T>, +{ + let mut v: Vec<T> = vec![]; + if mem::size_of::<T>() == 1 { + extend(&mut v, T::zero(), T::max_value()); + } else { + extend(&mut v, T::zero(), i8::max_value().as_()); + extend( + &mut v, + T::max_value() - i8::max_value().as_(), + T::max_value(), + ); + if let Some((i, j)) = mantissa_max::<T>() { + v.push(i); + v.push(j); + } + extend_shl(&mut v, T::max_value(), T::zero(), !T::min_value()); + extend_shr(&mut v, T::max_value(), T::zero()); + } + v +} + +fn neg<T>() -> Vec<T> +where + T: TestInteger + Signed, + i8: AsPrimitive<T>, +{ + let mut v: Vec<T> = vec![]; + if mem::size_of::<T>() <= 1 { + extend(&mut v, T::min_value(), T::zero()); + } else { + extend(&mut v, i8::min_value().as_(), T::zero()); + extend( + &mut v, + T::min_value(), + T::min_value() - i8::min_value().as_(), + ); + if let Some((i, j)) = mantissa_max::<T>() { + v.push(-i); + v.push(-j); + } + extend_shl(&mut v, -T::one(), T::min_value(), !T::zero()); + extend_shr(&mut v, T::min_value(), -T::one()); + } + v +} + +macro_rules! test_roots { + ($I:ident, $U:ident) => { + mod $I { + use check; + use neg; + use num_integer::Roots; + use pos; + use std::mem; + + #[test] + #[should_panic] + fn zeroth_root() { + (123 as $I).nth_root(0); + } + + #[test] + fn sqrt() { + check(&pos::<$I>(), 2); + } + + #[test] + #[should_panic] + fn sqrt_neg() { + (-123 as $I).sqrt(); + } + + #[test] + fn cbrt() { + check(&pos::<$I>(), 3); + } + + #[test] + fn cbrt_neg() { + check(&neg::<$I>(), 3); + } + + #[test] + fn nth_root() { + let bits = 8 * mem::size_of::<$I>() as u32 - 1; + let pos = pos::<$I>(); + for n in 4..bits { + check(&pos, n); + } + } + + #[test] + fn nth_root_neg() { + let bits = 8 * mem::size_of::<$I>() as u32 - 1; + let neg = neg::<$I>(); + for n in 2..bits / 2 { + check(&neg, 2 * n + 1); + } + } + + #[test] + fn bit_size() { + let bits = 8 * mem::size_of::<$I>() as u32 - 1; + assert_eq!($I::max_value().nth_root(bits - 1), 2); + assert_eq!($I::max_value().nth_root(bits), 1); + assert_eq!($I::min_value().nth_root(bits), -2); + assert_eq!(($I::min_value() + 1).nth_root(bits), -1); + } + } + + mod $U { + use check; + use num_integer::Roots; + use pos; + use std::mem; + + #[test] + #[should_panic] + fn zeroth_root() { + (123 as $U).nth_root(0); + } + + #[test] + fn sqrt() { + check(&pos::<$U>(), 2); + } + + #[test] + fn cbrt() { + check(&pos::<$U>(), 3); + } + + #[test] + fn nth_root() { + let bits = 8 * mem::size_of::<$I>() as u32 - 1; + let pos = pos::<$I>(); + for n in 4..bits { + check(&pos, n); + } + } + + #[test] + fn bit_size() { + let bits = 8 * mem::size_of::<$U>() as u32; + assert_eq!($U::max_value().nth_root(bits - 1), 2); + assert_eq!($U::max_value().nth_root(bits), 1); + } + } + }; +} + +test_roots!(i8, u8); +test_roots!(i16, u16); +test_roots!(i32, u32); +test_roots!(i64, u64); +#[cfg(has_i128)] +test_roots!(i128, u128); +test_roots!(isize, usize); |