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, uint, i8, i16, i32, i64, int, f32, f64}`.
17 #![allow(missing_docs)]
19 #[cfg(test)] use cmp::PartialEq;
20 #[cfg(test)] use fmt::Show;
21 #[cfg(test)] use ops::{Add, Sub, Mul, Div, Rem};
22 #[cfg(test)] use kinds::Copy;
24 pub use core::num::{Num, div_rem, Zero, zero, One, one};
25 pub use core::num::{Unsigned, pow, Bounded};
26 pub use core::num::{Primitive, Int, SignedInt, UnsignedInt};
27 pub use core::num::{cast, FromPrimitive, NumCast, ToPrimitive};
28 pub use core::num::{next_power_of_two, is_power_of_two};
29 pub use core::num::{checked_next_power_of_two};
30 pub use core::num::{from_int, from_i8, from_i16, from_i32, from_i64};
31 pub use core::num::{from_uint, from_u8, from_u16, from_u32, from_u64};
32 pub use core::num::{from_f32, from_f64};
33 pub use core::num::{FromStrRadix, from_str_radix};
34 pub use core::num::{FpCategory, Float};
36 #[experimental = "may be removed or relocated"]
39 /// Mathematical operations on primitive floating point numbers.
40 #[unstable = "may be altered to inline the Float trait"]
41 pub trait FloatMath: Float {
42 /// Constructs a floating point number created by multiplying `x` by 2
43 /// raised to the power of `exp`.
44 fn ldexp(x: Self, exp: int) -> Self;
45 /// Breaks the number into a normalized fraction and a base-2 exponent,
48 /// * `self = x * pow(2, exp)`
50 /// * `0.5 <= abs(x) < 1.0`
51 fn frexp(self) -> (Self, int);
53 /// Returns the next representable floating-point value in the direction of
55 fn next_after(self, other: Self) -> Self;
57 /// Returns the maximum of the two numbers.
58 fn max(self, other: Self) -> Self;
59 /// Returns the minimum of the two numbers.
60 fn min(self, other: Self) -> Self;
62 /// The positive difference of two numbers. Returns `0.0` if the number is
63 /// less than or equal to `other`, otherwise the difference between`self`
64 /// and `other` is returned.
65 fn abs_sub(self, other: Self) -> Self;
67 /// Take the cubic root of a number.
68 fn cbrt(self) -> Self;
69 /// Calculate the length of the hypotenuse of a right-angle triangle given
70 /// legs of length `x` and `y`.
71 fn hypot(self, other: Self) -> Self;
73 /// Computes the sine of a number (in radians).
75 /// Computes the cosine of a number (in radians).
77 /// Computes the tangent of a number (in radians).
80 /// Computes the arcsine of a number. Return value is in radians in
81 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
83 fn asin(self) -> Self;
84 /// Computes the arccosine of a number. Return value is in radians in
85 /// the range [0, pi] or NaN if the number is outside the range
87 fn acos(self) -> Self;
88 /// Computes the arctangent of a number. Return value is in radians in the
89 /// range [-pi/2, pi/2];
90 fn atan(self) -> Self;
91 /// Computes the four quadrant arctangent of a number, `y`, and another
92 /// number `x`. Return value is in radians in the range [-pi, pi].
93 fn atan2(self, other: Self) -> Self;
94 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
95 /// `(sin(x), cos(x))`.
96 fn sin_cos(self) -> (Self, Self);
98 /// Returns the exponential of the number, minus 1, in a way that is
99 /// accurate even if the number is close to zero.
100 fn exp_m1(self) -> Self;
101 /// Returns the natural logarithm of the number plus 1 (`ln(1+n)`) more
102 /// accurately than if the operations were performed separately.
103 fn ln_1p(self) -> Self;
105 /// Hyperbolic sine function.
106 fn sinh(self) -> Self;
107 /// Hyperbolic cosine function.
108 fn cosh(self) -> Self;
109 /// Hyperbolic tangent function.
110 fn tanh(self) -> Self;
111 /// Inverse hyperbolic sine function.
112 fn asinh(self) -> Self;
113 /// Inverse hyperbolic cosine function.
114 fn acosh(self) -> Self;
115 /// Inverse hyperbolic tangent function.
116 fn atanh(self) -> Self;
121 #[deprecated = "Use `FloatMath::abs_sub`"]
122 pub fn abs_sub<T: FloatMath>(x: T, y: T) -> T {
126 /// Helper function for testing numeric operations
128 pub fn test_num<T>(ten: T, two: T) where
129 T: PartialEq + NumCast
130 + Add<Output=T> + Sub<Output=T>
131 + Mul<Output=T> + Div<Output=T>
132 + Rem<Output=T> + Show
135 assert_eq!(ten.add(two), cast(12i).unwrap());
136 assert_eq!(ten.sub(two), cast(8i).unwrap());
137 assert_eq!(ten.mul(two), cast(20i).unwrap());
138 assert_eq!(ten.div(two), cast(5i).unwrap());
139 assert_eq!(ten.rem(two), cast(0i).unwrap());
141 assert_eq!(ten.add(two), ten + two);
142 assert_eq!(ten.sub(two), ten - two);
143 assert_eq!(ten.mul(two), ten * two);
144 assert_eq!(ten.div(two), ten / two);
145 assert_eq!(ten.rem(two), ten % two);
163 macro_rules! test_cast_20 {
167 assert_eq!(20u, _20.to_uint().unwrap());
168 assert_eq!(20u8, _20.to_u8().unwrap());
169 assert_eq!(20u16, _20.to_u16().unwrap());
170 assert_eq!(20u32, _20.to_u32().unwrap());
171 assert_eq!(20u64, _20.to_u64().unwrap());
172 assert_eq!(20i, _20.to_int().unwrap());
173 assert_eq!(20i8, _20.to_i8().unwrap());
174 assert_eq!(20i16, _20.to_i16().unwrap());
175 assert_eq!(20i32, _20.to_i32().unwrap());
176 assert_eq!(20i64, _20.to_i64().unwrap());
177 assert_eq!(20f32, _20.to_f32().unwrap());
178 assert_eq!(20f64, _20.to_f64().unwrap());
180 assert_eq!(_20, NumCast::from(20u).unwrap());
181 assert_eq!(_20, NumCast::from(20u8).unwrap());
182 assert_eq!(_20, NumCast::from(20u16).unwrap());
183 assert_eq!(_20, NumCast::from(20u32).unwrap());
184 assert_eq!(_20, NumCast::from(20u64).unwrap());
185 assert_eq!(_20, NumCast::from(20i).unwrap());
186 assert_eq!(_20, NumCast::from(20i8).unwrap());
187 assert_eq!(_20, NumCast::from(20i16).unwrap());
188 assert_eq!(_20, NumCast::from(20i32).unwrap());
189 assert_eq!(_20, NumCast::from(20i64).unwrap());
190 assert_eq!(_20, NumCast::from(20f32).unwrap());
191 assert_eq!(_20, NumCast::from(20f64).unwrap());
193 assert_eq!(_20, cast(20u).unwrap());
194 assert_eq!(_20, cast(20u8).unwrap());
195 assert_eq!(_20, cast(20u16).unwrap());
196 assert_eq!(_20, cast(20u32).unwrap());
197 assert_eq!(_20, cast(20u64).unwrap());
198 assert_eq!(_20, cast(20i).unwrap());
199 assert_eq!(_20, cast(20i8).unwrap());
200 assert_eq!(_20, cast(20i16).unwrap());
201 assert_eq!(_20, cast(20i32).unwrap());
202 assert_eq!(_20, cast(20i64).unwrap());
203 assert_eq!(_20, cast(20f32).unwrap());
204 assert_eq!(_20, cast(20f64).unwrap());
208 #[test] fn test_u8_cast() { test_cast_20!(20u8) }
209 #[test] fn test_u16_cast() { test_cast_20!(20u16) }
210 #[test] fn test_u32_cast() { test_cast_20!(20u32) }
211 #[test] fn test_u64_cast() { test_cast_20!(20u64) }
212 #[test] fn test_uint_cast() { test_cast_20!(20u) }
213 #[test] fn test_i8_cast() { test_cast_20!(20i8) }
214 #[test] fn test_i16_cast() { test_cast_20!(20i16) }
215 #[test] fn test_i32_cast() { test_cast_20!(20i32) }
216 #[test] fn test_i64_cast() { test_cast_20!(20i64) }
217 #[test] fn test_int_cast() { test_cast_20!(20i) }
218 #[test] fn test_f32_cast() { test_cast_20!(20f32) }
219 #[test] fn test_f64_cast() { test_cast_20!(20f64) }
222 fn test_cast_range_int_min() {
223 assert_eq!(int::MIN.to_int(), Some(int::MIN as int));
224 assert_eq!(int::MIN.to_i8(), None);
225 assert_eq!(int::MIN.to_i16(), None);
226 // int::MIN.to_i32() is word-size specific
227 assert_eq!(int::MIN.to_i64(), Some(int::MIN as i64));
228 assert_eq!(int::MIN.to_uint(), None);
229 assert_eq!(int::MIN.to_u8(), None);
230 assert_eq!(int::MIN.to_u16(), None);
231 assert_eq!(int::MIN.to_u32(), None);
232 assert_eq!(int::MIN.to_u64(), None);
234 #[cfg(target_word_size = "32")]
235 fn check_word_size() {
236 assert_eq!(int::MIN.to_i32(), Some(int::MIN as i32));
239 #[cfg(target_word_size = "64")]
240 fn check_word_size() {
241 assert_eq!(int::MIN.to_i32(), None);
248 fn test_cast_range_i8_min() {
249 assert_eq!(i8::MIN.to_int(), Some(i8::MIN as int));
250 assert_eq!(i8::MIN.to_i8(), Some(i8::MIN as i8));
251 assert_eq!(i8::MIN.to_i16(), Some(i8::MIN as i16));
252 assert_eq!(i8::MIN.to_i32(), Some(i8::MIN as i32));
253 assert_eq!(i8::MIN.to_i64(), Some(i8::MIN as i64));
254 assert_eq!(i8::MIN.to_uint(), None);
255 assert_eq!(i8::MIN.to_u8(), None);
256 assert_eq!(i8::MIN.to_u16(), None);
257 assert_eq!(i8::MIN.to_u32(), None);
258 assert_eq!(i8::MIN.to_u64(), None);
262 fn test_cast_range_i16_min() {
263 assert_eq!(i16::MIN.to_int(), Some(i16::MIN as int));
264 assert_eq!(i16::MIN.to_i8(), None);
265 assert_eq!(i16::MIN.to_i16(), Some(i16::MIN as i16));
266 assert_eq!(i16::MIN.to_i32(), Some(i16::MIN as i32));
267 assert_eq!(i16::MIN.to_i64(), Some(i16::MIN as i64));
268 assert_eq!(i16::MIN.to_uint(), None);
269 assert_eq!(i16::MIN.to_u8(), None);
270 assert_eq!(i16::MIN.to_u16(), None);
271 assert_eq!(i16::MIN.to_u32(), None);
272 assert_eq!(i16::MIN.to_u64(), None);
276 fn test_cast_range_i32_min() {
277 assert_eq!(i32::MIN.to_int(), Some(i32::MIN as int));
278 assert_eq!(i32::MIN.to_i8(), None);
279 assert_eq!(i32::MIN.to_i16(), None);
280 assert_eq!(i32::MIN.to_i32(), Some(i32::MIN as i32));
281 assert_eq!(i32::MIN.to_i64(), Some(i32::MIN as i64));
282 assert_eq!(i32::MIN.to_uint(), None);
283 assert_eq!(i32::MIN.to_u8(), None);
284 assert_eq!(i32::MIN.to_u16(), None);
285 assert_eq!(i32::MIN.to_u32(), None);
286 assert_eq!(i32::MIN.to_u64(), None);
290 fn test_cast_range_i64_min() {
291 // i64::MIN.to_int() is word-size specific
292 assert_eq!(i64::MIN.to_i8(), None);
293 assert_eq!(i64::MIN.to_i16(), None);
294 assert_eq!(i64::MIN.to_i32(), None);
295 assert_eq!(i64::MIN.to_i64(), Some(i64::MIN as i64));
296 assert_eq!(i64::MIN.to_uint(), None);
297 assert_eq!(i64::MIN.to_u8(), None);
298 assert_eq!(i64::MIN.to_u16(), None);
299 assert_eq!(i64::MIN.to_u32(), None);
300 assert_eq!(i64::MIN.to_u64(), None);
302 #[cfg(target_word_size = "32")]
303 fn check_word_size() {
304 assert_eq!(i64::MIN.to_int(), None);
307 #[cfg(target_word_size = "64")]
308 fn check_word_size() {
309 assert_eq!(i64::MIN.to_int(), Some(i64::MIN as int));
316 fn test_cast_range_int_max() {
317 assert_eq!(int::MAX.to_int(), Some(int::MAX as int));
318 assert_eq!(int::MAX.to_i8(), None);
319 assert_eq!(int::MAX.to_i16(), None);
320 // int::MAX.to_i32() is word-size specific
321 assert_eq!(int::MAX.to_i64(), Some(int::MAX as i64));
322 assert_eq!(int::MAX.to_u8(), None);
323 assert_eq!(int::MAX.to_u16(), None);
324 // int::MAX.to_u32() is word-size specific
325 assert_eq!(int::MAX.to_u64(), Some(int::MAX as u64));
327 #[cfg(target_word_size = "32")]
328 fn check_word_size() {
329 assert_eq!(int::MAX.to_i32(), Some(int::MAX as i32));
330 assert_eq!(int::MAX.to_u32(), Some(int::MAX as u32));
333 #[cfg(target_word_size = "64")]
334 fn check_word_size() {
335 assert_eq!(int::MAX.to_i32(), None);
336 assert_eq!(int::MAX.to_u32(), None);
343 fn test_cast_range_i8_max() {
344 assert_eq!(i8::MAX.to_int(), Some(i8::MAX as int));
345 assert_eq!(i8::MAX.to_i8(), Some(i8::MAX as i8));
346 assert_eq!(i8::MAX.to_i16(), Some(i8::MAX as i16));
347 assert_eq!(i8::MAX.to_i32(), Some(i8::MAX as i32));
348 assert_eq!(i8::MAX.to_i64(), Some(i8::MAX as i64));
349 assert_eq!(i8::MAX.to_uint(), Some(i8::MAX as uint));
350 assert_eq!(i8::MAX.to_u8(), Some(i8::MAX as u8));
351 assert_eq!(i8::MAX.to_u16(), Some(i8::MAX as u16));
352 assert_eq!(i8::MAX.to_u32(), Some(i8::MAX as u32));
353 assert_eq!(i8::MAX.to_u64(), Some(i8::MAX as u64));
357 fn test_cast_range_i16_max() {
358 assert_eq!(i16::MAX.to_int(), Some(i16::MAX as int));
359 assert_eq!(i16::MAX.to_i8(), None);
360 assert_eq!(i16::MAX.to_i16(), Some(i16::MAX as i16));
361 assert_eq!(i16::MAX.to_i32(), Some(i16::MAX as i32));
362 assert_eq!(i16::MAX.to_i64(), Some(i16::MAX as i64));
363 assert_eq!(i16::MAX.to_uint(), Some(i16::MAX as uint));
364 assert_eq!(i16::MAX.to_u8(), None);
365 assert_eq!(i16::MAX.to_u16(), Some(i16::MAX as u16));
366 assert_eq!(i16::MAX.to_u32(), Some(i16::MAX as u32));
367 assert_eq!(i16::MAX.to_u64(), Some(i16::MAX as u64));
371 fn test_cast_range_i32_max() {
372 assert_eq!(i32::MAX.to_int(), Some(i32::MAX as int));
373 assert_eq!(i32::MAX.to_i8(), None);
374 assert_eq!(i32::MAX.to_i16(), None);
375 assert_eq!(i32::MAX.to_i32(), Some(i32::MAX as i32));
376 assert_eq!(i32::MAX.to_i64(), Some(i32::MAX as i64));
377 assert_eq!(i32::MAX.to_uint(), Some(i32::MAX as uint));
378 assert_eq!(i32::MAX.to_u8(), None);
379 assert_eq!(i32::MAX.to_u16(), None);
380 assert_eq!(i32::MAX.to_u32(), Some(i32::MAX as u32));
381 assert_eq!(i32::MAX.to_u64(), Some(i32::MAX as u64));
385 fn test_cast_range_i64_max() {
386 // i64::MAX.to_int() is word-size specific
387 assert_eq!(i64::MAX.to_i8(), None);
388 assert_eq!(i64::MAX.to_i16(), None);
389 assert_eq!(i64::MAX.to_i32(), None);
390 assert_eq!(i64::MAX.to_i64(), Some(i64::MAX as i64));
391 // i64::MAX.to_uint() is word-size specific
392 assert_eq!(i64::MAX.to_u8(), None);
393 assert_eq!(i64::MAX.to_u16(), None);
394 assert_eq!(i64::MAX.to_u32(), None);
395 assert_eq!(i64::MAX.to_u64(), Some(i64::MAX as u64));
397 #[cfg(target_word_size = "32")]
398 fn check_word_size() {
399 assert_eq!(i64::MAX.to_int(), None);
400 assert_eq!(i64::MAX.to_uint(), None);
403 #[cfg(target_word_size = "64")]
404 fn check_word_size() {
405 assert_eq!(i64::MAX.to_int(), Some(i64::MAX as int));
406 assert_eq!(i64::MAX.to_uint(), Some(i64::MAX as uint));
413 fn test_cast_range_uint_min() {
414 assert_eq!(uint::MIN.to_int(), Some(uint::MIN as int));
415 assert_eq!(uint::MIN.to_i8(), Some(uint::MIN as i8));
416 assert_eq!(uint::MIN.to_i16(), Some(uint::MIN as i16));
417 assert_eq!(uint::MIN.to_i32(), Some(uint::MIN as i32));
418 assert_eq!(uint::MIN.to_i64(), Some(uint::MIN as i64));
419 assert_eq!(uint::MIN.to_uint(), Some(uint::MIN as uint));
420 assert_eq!(uint::MIN.to_u8(), Some(uint::MIN as u8));
421 assert_eq!(uint::MIN.to_u16(), Some(uint::MIN as u16));
422 assert_eq!(uint::MIN.to_u32(), Some(uint::MIN as u32));
423 assert_eq!(uint::MIN.to_u64(), Some(uint::MIN as u64));
427 fn test_cast_range_u8_min() {
428 assert_eq!(u8::MIN.to_int(), Some(u8::MIN as int));
429 assert_eq!(u8::MIN.to_i8(), Some(u8::MIN as i8));
430 assert_eq!(u8::MIN.to_i16(), Some(u8::MIN as i16));
431 assert_eq!(u8::MIN.to_i32(), Some(u8::MIN as i32));
432 assert_eq!(u8::MIN.to_i64(), Some(u8::MIN as i64));
433 assert_eq!(u8::MIN.to_uint(), Some(u8::MIN as uint));
434 assert_eq!(u8::MIN.to_u8(), Some(u8::MIN as u8));
435 assert_eq!(u8::MIN.to_u16(), Some(u8::MIN as u16));
436 assert_eq!(u8::MIN.to_u32(), Some(u8::MIN as u32));
437 assert_eq!(u8::MIN.to_u64(), Some(u8::MIN as u64));
441 fn test_cast_range_u16_min() {
442 assert_eq!(u16::MIN.to_int(), Some(u16::MIN as int));
443 assert_eq!(u16::MIN.to_i8(), Some(u16::MIN as i8));
444 assert_eq!(u16::MIN.to_i16(), Some(u16::MIN as i16));
445 assert_eq!(u16::MIN.to_i32(), Some(u16::MIN as i32));
446 assert_eq!(u16::MIN.to_i64(), Some(u16::MIN as i64));
447 assert_eq!(u16::MIN.to_uint(), Some(u16::MIN as uint));
448 assert_eq!(u16::MIN.to_u8(), Some(u16::MIN as u8));
449 assert_eq!(u16::MIN.to_u16(), Some(u16::MIN as u16));
450 assert_eq!(u16::MIN.to_u32(), Some(u16::MIN as u32));
451 assert_eq!(u16::MIN.to_u64(), Some(u16::MIN as u64));
455 fn test_cast_range_u32_min() {
456 assert_eq!(u32::MIN.to_int(), Some(u32::MIN as int));
457 assert_eq!(u32::MIN.to_i8(), Some(u32::MIN as i8));
458 assert_eq!(u32::MIN.to_i16(), Some(u32::MIN as i16));
459 assert_eq!(u32::MIN.to_i32(), Some(u32::MIN as i32));
460 assert_eq!(u32::MIN.to_i64(), Some(u32::MIN as i64));
461 assert_eq!(u32::MIN.to_uint(), Some(u32::MIN as uint));
462 assert_eq!(u32::MIN.to_u8(), Some(u32::MIN as u8));
463 assert_eq!(u32::MIN.to_u16(), Some(u32::MIN as u16));
464 assert_eq!(u32::MIN.to_u32(), Some(u32::MIN as u32));
465 assert_eq!(u32::MIN.to_u64(), Some(u32::MIN as u64));
469 fn test_cast_range_u64_min() {
470 assert_eq!(u64::MIN.to_int(), Some(u64::MIN as int));
471 assert_eq!(u64::MIN.to_i8(), Some(u64::MIN as i8));
472 assert_eq!(u64::MIN.to_i16(), Some(u64::MIN as i16));
473 assert_eq!(u64::MIN.to_i32(), Some(u64::MIN as i32));
474 assert_eq!(u64::MIN.to_i64(), Some(u64::MIN as i64));
475 assert_eq!(u64::MIN.to_uint(), Some(u64::MIN as uint));
476 assert_eq!(u64::MIN.to_u8(), Some(u64::MIN as u8));
477 assert_eq!(u64::MIN.to_u16(), Some(u64::MIN as u16));
478 assert_eq!(u64::MIN.to_u32(), Some(u64::MIN as u32));
479 assert_eq!(u64::MIN.to_u64(), Some(u64::MIN as u64));
483 fn test_cast_range_uint_max() {
484 assert_eq!(uint::MAX.to_int(), None);
485 assert_eq!(uint::MAX.to_i8(), None);
486 assert_eq!(uint::MAX.to_i16(), None);
487 assert_eq!(uint::MAX.to_i32(), None);
488 // uint::MAX.to_i64() is word-size specific
489 assert_eq!(uint::MAX.to_u8(), None);
490 assert_eq!(uint::MAX.to_u16(), None);
491 // uint::MAX.to_u32() is word-size specific
492 assert_eq!(uint::MAX.to_u64(), Some(uint::MAX as u64));
494 #[cfg(target_word_size = "32")]
495 fn check_word_size() {
496 assert_eq!(uint::MAX.to_u32(), Some(uint::MAX as u32));
497 assert_eq!(uint::MAX.to_i64(), Some(uint::MAX as i64));
500 #[cfg(target_word_size = "64")]
501 fn check_word_size() {
502 assert_eq!(uint::MAX.to_u32(), None);
503 assert_eq!(uint::MAX.to_i64(), None);
510 fn test_cast_range_u8_max() {
511 assert_eq!(u8::MAX.to_int(), Some(u8::MAX as int));
512 assert_eq!(u8::MAX.to_i8(), None);
513 assert_eq!(u8::MAX.to_i16(), Some(u8::MAX as i16));
514 assert_eq!(u8::MAX.to_i32(), Some(u8::MAX as i32));
515 assert_eq!(u8::MAX.to_i64(), Some(u8::MAX as i64));
516 assert_eq!(u8::MAX.to_uint(), Some(u8::MAX as uint));
517 assert_eq!(u8::MAX.to_u8(), Some(u8::MAX as u8));
518 assert_eq!(u8::MAX.to_u16(), Some(u8::MAX as u16));
519 assert_eq!(u8::MAX.to_u32(), Some(u8::MAX as u32));
520 assert_eq!(u8::MAX.to_u64(), Some(u8::MAX as u64));
524 fn test_cast_range_u16_max() {
525 assert_eq!(u16::MAX.to_int(), Some(u16::MAX as int));
526 assert_eq!(u16::MAX.to_i8(), None);
527 assert_eq!(u16::MAX.to_i16(), None);
528 assert_eq!(u16::MAX.to_i32(), Some(u16::MAX as i32));
529 assert_eq!(u16::MAX.to_i64(), Some(u16::MAX as i64));
530 assert_eq!(u16::MAX.to_uint(), Some(u16::MAX as uint));
531 assert_eq!(u16::MAX.to_u8(), None);
532 assert_eq!(u16::MAX.to_u16(), Some(u16::MAX as u16));
533 assert_eq!(u16::MAX.to_u32(), Some(u16::MAX as u32));
534 assert_eq!(u16::MAX.to_u64(), Some(u16::MAX as u64));
538 fn test_cast_range_u32_max() {
539 // u32::MAX.to_int() is word-size specific
540 assert_eq!(u32::MAX.to_i8(), None);
541 assert_eq!(u32::MAX.to_i16(), None);
542 assert_eq!(u32::MAX.to_i32(), None);
543 assert_eq!(u32::MAX.to_i64(), Some(u32::MAX as i64));
544 assert_eq!(u32::MAX.to_uint(), Some(u32::MAX as uint));
545 assert_eq!(u32::MAX.to_u8(), None);
546 assert_eq!(u32::MAX.to_u16(), None);
547 assert_eq!(u32::MAX.to_u32(), Some(u32::MAX as u32));
548 assert_eq!(u32::MAX.to_u64(), Some(u32::MAX as u64));
550 #[cfg(target_word_size = "32")]
551 fn check_word_size() {
552 assert_eq!(u32::MAX.to_int(), None);
555 #[cfg(target_word_size = "64")]
556 fn check_word_size() {
557 assert_eq!(u32::MAX.to_int(), Some(u32::MAX as int));
564 fn test_cast_range_u64_max() {
565 assert_eq!(u64::MAX.to_int(), None);
566 assert_eq!(u64::MAX.to_i8(), None);
567 assert_eq!(u64::MAX.to_i16(), None);
568 assert_eq!(u64::MAX.to_i32(), None);
569 assert_eq!(u64::MAX.to_i64(), None);
570 // u64::MAX.to_uint() is word-size specific
571 assert_eq!(u64::MAX.to_u8(), None);
572 assert_eq!(u64::MAX.to_u16(), None);
573 assert_eq!(u64::MAX.to_u32(), None);
574 assert_eq!(u64::MAX.to_u64(), Some(u64::MAX as u64));
576 #[cfg(target_word_size = "32")]
577 fn check_word_size() {
578 assert_eq!(u64::MAX.to_uint(), None);
581 #[cfg(target_word_size = "64")]
582 fn check_word_size() {
583 assert_eq!(u64::MAX.to_uint(), Some(u64::MAX as uint));
590 fn test_saturating_add_uint() {
592 assert_eq!(3u.saturating_add(5u), 8u);
593 assert_eq!(3u.saturating_add(MAX-1), MAX);
594 assert_eq!(MAX.saturating_add(MAX), MAX);
595 assert_eq!((MAX-2).saturating_add(1), MAX-1);
599 fn test_saturating_sub_uint() {
601 assert_eq!(5u.saturating_sub(3u), 2u);
602 assert_eq!(3u.saturating_sub(5u), 0u);
603 assert_eq!(0u.saturating_sub(1u), 0u);
604 assert_eq!((MAX-1).saturating_sub(MAX), 0);
608 fn test_saturating_add_int() {
610 assert_eq!(3i.saturating_add(5i), 8i);
611 assert_eq!(3i.saturating_add(MAX-1), MAX);
612 assert_eq!(MAX.saturating_add(MAX), MAX);
613 assert_eq!((MAX-2).saturating_add(1), MAX-1);
614 assert_eq!(3i.saturating_add(-5i), -2i);
615 assert_eq!(MIN.saturating_add(-1i), MIN);
616 assert_eq!((-2i).saturating_add(-MAX), MIN);
620 fn test_saturating_sub_int() {
622 assert_eq!(3i.saturating_sub(5i), -2i);
623 assert_eq!(MIN.saturating_sub(1i), MIN);
624 assert_eq!((-2i).saturating_sub(MAX), MIN);
625 assert_eq!(3i.saturating_sub(-5i), 8i);
626 assert_eq!(3i.saturating_sub(-(MAX-1)), MAX);
627 assert_eq!(MAX.saturating_sub(-MAX), MAX);
628 assert_eq!((MAX-2).saturating_sub(-1), MAX-1);
632 fn test_checked_add() {
633 let five_less = uint::MAX - 5;
634 assert_eq!(five_less.checked_add(0), Some(uint::MAX - 5));
635 assert_eq!(five_less.checked_add(1), Some(uint::MAX - 4));
636 assert_eq!(five_less.checked_add(2), Some(uint::MAX - 3));
637 assert_eq!(five_less.checked_add(3), Some(uint::MAX - 2));
638 assert_eq!(five_less.checked_add(4), Some(uint::MAX - 1));
639 assert_eq!(five_less.checked_add(5), Some(uint::MAX));
640 assert_eq!(five_less.checked_add(6), None);
641 assert_eq!(five_less.checked_add(7), None);
645 fn test_checked_sub() {
646 assert_eq!(5u.checked_sub(0), Some(5));
647 assert_eq!(5u.checked_sub(1), Some(4));
648 assert_eq!(5u.checked_sub(2), Some(3));
649 assert_eq!(5u.checked_sub(3), Some(2));
650 assert_eq!(5u.checked_sub(4), Some(1));
651 assert_eq!(5u.checked_sub(5), Some(0));
652 assert_eq!(5u.checked_sub(6), None);
653 assert_eq!(5u.checked_sub(7), None);
657 fn test_checked_mul() {
658 let third = uint::MAX / 3;
659 assert_eq!(third.checked_mul(0), Some(0));
660 assert_eq!(third.checked_mul(1), Some(third));
661 assert_eq!(third.checked_mul(2), Some(third * 2));
662 assert_eq!(third.checked_mul(3), Some(third * 3));
663 assert_eq!(third.checked_mul(4), None);
666 macro_rules! test_is_power_of_two {
667 ($test_name:ident, $T:ident) => (
670 assert_eq!((0 as $T).is_power_of_two(), false);
671 assert_eq!((1 as $T).is_power_of_two(), true);
672 assert_eq!((2 as $T).is_power_of_two(), true);
673 assert_eq!((3 as $T).is_power_of_two(), false);
674 assert_eq!((4 as $T).is_power_of_two(), true);
675 assert_eq!((5 as $T).is_power_of_two(), false);
676 assert!(($T::MAX / 2 + 1).is_power_of_two(), true);
681 test_is_power_of_two!{ test_is_power_of_two_u8, u8 }
682 test_is_power_of_two!{ test_is_power_of_two_u16, u16 }
683 test_is_power_of_two!{ test_is_power_of_two_u32, u32 }
684 test_is_power_of_two!{ test_is_power_of_two_u64, u64 }
685 test_is_power_of_two!{ test_is_power_of_two_uint, uint }
687 macro_rules! test_next_power_of_two {
688 ($test_name:ident, $T:ident) => (
691 assert_eq!((0 as $T).next_power_of_two(), 1);
692 let mut next_power = 1;
693 for i in range::<$T>(1, 40) {
694 assert_eq!(i.next_power_of_two(), next_power);
695 if i == next_power { next_power *= 2 }
701 test_next_power_of_two! { test_next_power_of_two_u8, u8 }
702 test_next_power_of_two! { test_next_power_of_two_u16, u16 }
703 test_next_power_of_two! { test_next_power_of_two_u32, u32 }
704 test_next_power_of_two! { test_next_power_of_two_u64, u64 }
705 test_next_power_of_two! { test_next_power_of_two_uint, uint }
707 macro_rules! test_checked_next_power_of_two {
708 ($test_name:ident, $T:ident) => (
711 assert_eq!((0 as $T).checked_next_power_of_two(), Some(1));
712 assert!(($T::MAX / 2).checked_next_power_of_two().is_some());
713 assert_eq!(($T::MAX - 1).checked_next_power_of_two(), None);
714 assert_eq!($T::MAX.checked_next_power_of_two(), None);
715 let mut next_power = 1;
716 for i in range::<$T>(1, 40) {
717 assert_eq!(i.checked_next_power_of_two(), Some(next_power));
718 if i == next_power { next_power *= 2 }
724 test_checked_next_power_of_two! { test_checked_next_power_of_two_u8, u8 }
725 test_checked_next_power_of_two! { test_checked_next_power_of_two_u16, u16 }
726 test_checked_next_power_of_two! { test_checked_next_power_of_two_u32, u32 }
727 test_checked_next_power_of_two! { test_checked_next_power_of_two_u64, u64 }
728 test_checked_next_power_of_two! { test_checked_next_power_of_two_uint, uint }
730 #[deriving(PartialEq, Show)]
731 struct Value { x: int }
733 impl ToPrimitive for Value {
734 fn to_i64(&self) -> Option<i64> { self.x.to_i64() }
735 fn to_u64(&self) -> Option<u64> { self.x.to_u64() }
738 impl FromPrimitive for Value {
739 fn from_i64(n: i64) -> Option<Value> { Some(Value { x: n as int }) }
740 fn from_u64(n: u64) -> Option<Value> { Some(Value { x: n as int }) }
744 fn test_to_primitive() {
745 let value = Value { x: 5 };
746 assert_eq!(value.to_int(), Some(5));
747 assert_eq!(value.to_i8(), Some(5));
748 assert_eq!(value.to_i16(), Some(5));
749 assert_eq!(value.to_i32(), Some(5));
750 assert_eq!(value.to_i64(), Some(5));
751 assert_eq!(value.to_uint(), Some(5));
752 assert_eq!(value.to_u8(), Some(5));
753 assert_eq!(value.to_u16(), Some(5));
754 assert_eq!(value.to_u32(), Some(5));
755 assert_eq!(value.to_u64(), Some(5));
756 assert_eq!(value.to_f32(), Some(5f32));
757 assert_eq!(value.to_f64(), Some(5f64));
761 fn test_from_primitive() {
762 assert_eq!(from_int(5), Some(Value { x: 5 }));
763 assert_eq!(from_i8(5), Some(Value { x: 5 }));
764 assert_eq!(from_i16(5), Some(Value { x: 5 }));
765 assert_eq!(from_i32(5), Some(Value { x: 5 }));
766 assert_eq!(from_i64(5), Some(Value { x: 5 }));
767 assert_eq!(from_uint(5), Some(Value { x: 5 }));
768 assert_eq!(from_u8(5), Some(Value { x: 5 }));
769 assert_eq!(from_u16(5), Some(Value { x: 5 }));
770 assert_eq!(from_u32(5), Some(Value { x: 5 }));
771 assert_eq!(from_u64(5), Some(Value { x: 5 }));
772 assert_eq!(from_f32(5f32), Some(Value { x: 5 }));
773 assert_eq!(from_f64(5f64), Some(Value { x: 5 }));
778 fn naive_pow<T: Int>(base: T, exp: uint) -> T {
779 let one: T = Int::one();
780 range(0, exp).fold(one, |acc, _| acc * base)
782 macro_rules! assert_pow {
783 (($num:expr, $exp:expr) => $expected:expr) => {{
784 let result = $num.pow($exp);
785 assert_eq!(result, $expected);
786 assert_eq!(result, naive_pow($num, $exp));
789 assert_pow!((3i, 0 ) => 1);
790 assert_pow!((5i, 1 ) => 5);
791 assert_pow!((-4i, 2 ) => 16);
792 assert_pow!((8i, 3 ) => 512);
793 assert_pow!((2u64, 50) => 1125899906842624);
801 use self::test::Bencher;
806 fn bench_pow_function(b: &mut Bencher) {
807 let v = Vec::from_fn(1024u, |n| n);
808 b.iter(|| {v.iter().fold(0u, |old, new| old.pow(*new));});