1 // Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! Numeric traits and functions for generic mathematics
13 //! These are implemented for the primitive numeric types in `std::{u8, u16,
14 //! u32, u64, usize, i8, i16, i32, i64, isize, f32, f64}`.
16 #![stable(feature = "rust1", since = "1.0.0")]
17 #![allow(missing_docs)]
19 pub use core::num::{Zero, One};
20 pub use core::num::{FpCategory, ParseIntError, ParseFloatError};
21 pub use core::num::{wrapping, Wrapping};
23 #[cfg(test)] use cmp::PartialEq;
25 #[cfg(test)] use marker::Copy;
26 #[cfg(test)] use ops::{Add, Sub, Mul, Div, Rem};
28 /// Helper function for testing numeric operations
30 pub fn test_num<T>(ten: T, two: T) where
32 + Add<Output=T> + Sub<Output=T>
33 + Mul<Output=T> + Div<Output=T>
34 + Rem<Output=T> + fmt::Debug
37 assert_eq!(ten.add(two), ten + two);
38 assert_eq!(ten.sub(two), ten - two);
39 assert_eq!(ten.mul(two), ten * two);
40 assert_eq!(ten.div(two), ten / two);
41 assert_eq!(ten.rem(two), ten % two);
62 fn test_saturating_add_uint() {
64 assert_eq!(3_usize.saturating_add(5_usize), 8_usize);
65 assert_eq!(3_usize.saturating_add(MAX-1), MAX);
66 assert_eq!(MAX.saturating_add(MAX), MAX);
67 assert_eq!((MAX-2).saturating_add(1), MAX-1);
71 fn test_saturating_sub_uint() {
73 assert_eq!(5_usize.saturating_sub(3_usize), 2_usize);
74 assert_eq!(3_usize.saturating_sub(5_usize), 0_usize);
75 assert_eq!(0_usize.saturating_sub(1_usize), 0_usize);
76 assert_eq!((MAX-1).saturating_sub(MAX), 0);
80 fn test_saturating_add_int() {
82 assert_eq!(3i32.saturating_add(5), 8);
83 assert_eq!(3isize.saturating_add(MAX-1), MAX);
84 assert_eq!(MAX.saturating_add(MAX), MAX);
85 assert_eq!((MAX-2).saturating_add(1), MAX-1);
86 assert_eq!(3i32.saturating_add(-5), -2);
87 assert_eq!(MIN.saturating_add(-1), MIN);
88 assert_eq!((-2isize).saturating_add(-MAX), MIN);
92 fn test_saturating_sub_int() {
94 assert_eq!(3i32.saturating_sub(5), -2);
95 assert_eq!(MIN.saturating_sub(1), MIN);
96 assert_eq!((-2isize).saturating_sub(MAX), MIN);
97 assert_eq!(3i32.saturating_sub(-5), 8);
98 assert_eq!(3isize.saturating_sub(-(MAX-1)), MAX);
99 assert_eq!(MAX.saturating_sub(-MAX), MAX);
100 assert_eq!((MAX-2).saturating_sub(-1), MAX-1);
104 fn test_checked_add() {
105 let five_less = usize::MAX - 5;
106 assert_eq!(five_less.checked_add(0), Some(usize::MAX - 5));
107 assert_eq!(five_less.checked_add(1), Some(usize::MAX - 4));
108 assert_eq!(five_less.checked_add(2), Some(usize::MAX - 3));
109 assert_eq!(five_less.checked_add(3), Some(usize::MAX - 2));
110 assert_eq!(five_less.checked_add(4), Some(usize::MAX - 1));
111 assert_eq!(five_less.checked_add(5), Some(usize::MAX));
112 assert_eq!(five_less.checked_add(6), None);
113 assert_eq!(five_less.checked_add(7), None);
117 fn test_checked_sub() {
118 assert_eq!(5_usize.checked_sub(0), Some(5));
119 assert_eq!(5_usize.checked_sub(1), Some(4));
120 assert_eq!(5_usize.checked_sub(2), Some(3));
121 assert_eq!(5_usize.checked_sub(3), Some(2));
122 assert_eq!(5_usize.checked_sub(4), Some(1));
123 assert_eq!(5_usize.checked_sub(5), Some(0));
124 assert_eq!(5_usize.checked_sub(6), None);
125 assert_eq!(5_usize.checked_sub(7), None);
129 fn test_checked_mul() {
130 let third = usize::MAX / 3;
131 assert_eq!(third.checked_mul(0), Some(0));
132 assert_eq!(third.checked_mul(1), Some(third));
133 assert_eq!(third.checked_mul(2), Some(third * 2));
134 assert_eq!(third.checked_mul(3), Some(third * 3));
135 assert_eq!(third.checked_mul(4), None);
138 macro_rules! test_is_power_of_two {
139 ($test_name:ident, $T:ident) => (
142 assert_eq!((0 as $T).is_power_of_two(), false);
143 assert_eq!((1 as $T).is_power_of_two(), true);
144 assert_eq!((2 as $T).is_power_of_two(), true);
145 assert_eq!((3 as $T).is_power_of_two(), false);
146 assert_eq!((4 as $T).is_power_of_two(), true);
147 assert_eq!((5 as $T).is_power_of_two(), false);
148 assert_eq!(($T::MAX / 2 + 1).is_power_of_two(), true);
153 test_is_power_of_two!{ test_is_power_of_two_u8, u8 }
154 test_is_power_of_two!{ test_is_power_of_two_u16, u16 }
155 test_is_power_of_two!{ test_is_power_of_two_u32, u32 }
156 test_is_power_of_two!{ test_is_power_of_two_u64, u64 }
157 test_is_power_of_two!{ test_is_power_of_two_uint, usize }
159 macro_rules! test_next_power_of_two {
160 ($test_name:ident, $T:ident) => (
163 assert_eq!((0 as $T).next_power_of_two(), 1);
164 let mut next_power = 1;
165 for i in 1 as $T..40 {
166 assert_eq!(i.next_power_of_two(), next_power);
167 if i == next_power { next_power *= 2 }
173 test_next_power_of_two! { test_next_power_of_two_u8, u8 }
174 test_next_power_of_two! { test_next_power_of_two_u16, u16 }
175 test_next_power_of_two! { test_next_power_of_two_u32, u32 }
176 test_next_power_of_two! { test_next_power_of_two_u64, u64 }
177 test_next_power_of_two! { test_next_power_of_two_uint, usize }
179 macro_rules! test_checked_next_power_of_two {
180 ($test_name:ident, $T:ident) => (
183 assert_eq!((0 as $T).checked_next_power_of_two(), Some(1));
184 assert!(($T::MAX / 2).checked_next_power_of_two().is_some());
185 assert_eq!(($T::MAX - 1).checked_next_power_of_two(), None);
186 assert_eq!($T::MAX.checked_next_power_of_two(), None);
187 let mut next_power = 1;
188 for i in 1 as $T..40 {
189 assert_eq!(i.checked_next_power_of_two(), Some(next_power));
190 if i == next_power { next_power *= 2 }
196 test_checked_next_power_of_two! { test_checked_next_power_of_two_u8, u8 }
197 test_checked_next_power_of_two! { test_checked_next_power_of_two_u16, u16 }
198 test_checked_next_power_of_two! { test_checked_next_power_of_two_u32, u32 }
199 test_checked_next_power_of_two! { test_checked_next_power_of_two_u64, u64 }
200 test_checked_next_power_of_two! { test_checked_next_power_of_two_uint, usize }
204 fn naive_pow<T: Mul<Output=T> + One + Copy>(base: T, exp: usize) -> T {
205 let one: T = T::one();
206 (0..exp).fold(one, |acc, _| acc * base)
208 macro_rules! assert_pow {
209 (($num:expr, $exp:expr) => $expected:expr) => {{
210 let result = $num.pow($exp);
211 assert_eq!(result, $expected);
212 assert_eq!(result, naive_pow($num, $exp));
215 assert_pow!((3u32, 0 ) => 1);
216 assert_pow!((5u32, 1 ) => 5);
217 assert_pow!((-4i32, 2 ) => 16);
218 assert_pow!((8u32, 3 ) => 512);
219 assert_pow!((2u64, 50) => 1125899906842624);
223 fn test_uint_to_str_overflow() {
224 let mut u8_val: u8 = 255;
225 assert_eq!(u8_val.to_string(), "255");
227 u8_val = u8_val.wrapping_add(1);
228 assert_eq!(u8_val.to_string(), "0");
230 let mut u16_val: u16 = 65_535;
231 assert_eq!(u16_val.to_string(), "65535");
233 u16_val = u16_val.wrapping_add(1);
234 assert_eq!(u16_val.to_string(), "0");
236 let mut u32_val: u32 = 4_294_967_295;
237 assert_eq!(u32_val.to_string(), "4294967295");
239 u32_val = u32_val.wrapping_add(1);
240 assert_eq!(u32_val.to_string(), "0");
242 let mut u64_val: u64 = 18_446_744_073_709_551_615;
243 assert_eq!(u64_val.to_string(), "18446744073709551615");
245 u64_val = u64_val.wrapping_add(1);
246 assert_eq!(u64_val.to_string(), "0");
249 fn from_str<T: ::str::FromStr>(t: &str) -> Option<T> {
250 ::str::FromStr::from_str(t).ok()
254 fn test_uint_from_str_overflow() {
255 let mut u8_val: u8 = 255;
256 assert_eq!(from_str::<u8>("255"), Some(u8_val));
257 assert_eq!(from_str::<u8>("256"), None);
259 u8_val = u8_val.wrapping_add(1);
260 assert_eq!(from_str::<u8>("0"), Some(u8_val));
261 assert_eq!(from_str::<u8>("-1"), None);
263 let mut u16_val: u16 = 65_535;
264 assert_eq!(from_str::<u16>("65535"), Some(u16_val));
265 assert_eq!(from_str::<u16>("65536"), None);
267 u16_val = u16_val.wrapping_add(1);
268 assert_eq!(from_str::<u16>("0"), Some(u16_val));
269 assert_eq!(from_str::<u16>("-1"), None);
271 let mut u32_val: u32 = 4_294_967_295;
272 assert_eq!(from_str::<u32>("4294967295"), Some(u32_val));
273 assert_eq!(from_str::<u32>("4294967296"), None);
275 u32_val = u32_val.wrapping_add(1);
276 assert_eq!(from_str::<u32>("0"), Some(u32_val));
277 assert_eq!(from_str::<u32>("-1"), None);
279 let mut u64_val: u64 = 18_446_744_073_709_551_615;
280 assert_eq!(from_str::<u64>("18446744073709551615"), Some(u64_val));
281 assert_eq!(from_str::<u64>("18446744073709551616"), None);
283 u64_val = u64_val.wrapping_add(1);
284 assert_eq!(from_str::<u64>("0"), Some(u64_val));
285 assert_eq!(from_str::<u64>("-1"), None);
293 use self::test::Bencher;
297 fn bench_pow_function(b: &mut Bencher) {
298 let v = (0..1024).collect::<Vec<u32>>();
299 b.iter(|| {v.iter().fold(0u32, |old, new| old.pow(*new as u32));});