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 the built-in numeric types.
13 #![stable(feature = "rust1", since = "1.0.0")]
14 #![allow(missing_docs)]
16 use self::wrapping::OverflowingOps;
19 use cmp::{Eq, PartialOrd};
24 use option::Option::{self, Some, None};
25 use result::Result::{self, Ok, Err};
26 use str::{FromStr, StrExt};
28 /// Provides intentionally-wrapped arithmetic on `T`.
30 /// Operations like `+` on `u32` values is intended to never overflow,
31 /// and in some debug configurations overflow is detected and results
32 /// in a panic. While most arithmetic falls into this category, some
33 /// code explicitly expects and relies upon modular arithmetic (e.g.,
36 /// Wrapping arithmetic can be achieved either through methods like
37 /// `wrapping_add`, or through the `Wrapping<T>` type, which says that
38 /// all standard arithmetic operations on the underlying value are
39 /// intended to have wrapping semantics.
40 #[stable(feature = "rust1", since = "1.0.0")]
41 #[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Copy, Debug)]
42 pub struct Wrapping<T>(#[stable(feature = "rust1", since = "1.0.0")] pub T);
44 #[unstable(feature = "core", reason = "may be removed or relocated")]
47 #[unstable(feature = "core", reason = "internal routines only exposed for testing")]
50 /// Types that have a "zero" value.
52 /// This trait is intended for use in conjunction with `Add`, as an identity:
53 /// `x + T::zero() == x`.
54 #[unstable(feature = "zero_one",
55 reason = "unsure of placement, wants to use associated constants")]
57 /// The "zero" (usually, additive identity) for this type.
61 /// Types that have a "one" value.
63 /// This trait is intended for use in conjunction with `Mul`, as an identity:
64 /// `x * T::one() == x`.
65 #[unstable(feature = "zero_one",
66 reason = "unsure of placement, wants to use associated constants")]
68 /// The "one" (usually, multiplicative identity) for this type.
72 macro_rules! zero_one_impl {
76 fn zero() -> Self { 0 }
80 fn one() -> Self { 1 }
84 zero_one_impl! { u8 u16 u32 u64 usize i8 i16 i32 i64 isize }
86 macro_rules! zero_one_impl_float {
90 fn zero() -> Self { 0.0 }
94 fn one() -> Self { 1.0 }
98 zero_one_impl_float! { f32 f64 }
100 macro_rules! checked_op {
101 ($U:ty, $op:path, $x:expr, $y:expr) => {{
102 let (result, overflowed) = unsafe { $op($x as $U, $y as $U) };
103 if overflowed { None } else { Some(result as Self) }
107 /// Swapping a single byte is a no-op. This is marked as `unsafe` for
108 /// consistency with the other `bswap` intrinsics.
109 unsafe fn bswap8(x: u8) -> u8 { x }
111 // `Int` + `SignedInt` implemented for signed integers
112 macro_rules! int_impl {
113 ($ActualT:ty, $UnsignedT:ty, $BITS:expr,
114 $add_with_overflow:path,
115 $sub_with_overflow:path,
116 $mul_with_overflow:path) => {
117 /// Returns the smallest value that can be represented by this integer type.
118 #[stable(feature = "rust1", since = "1.0.0")]
120 pub fn min_value() -> Self {
121 (-1 as Self) << ($BITS - 1)
124 /// Returns the largest value that can be represented by this integer type.
125 #[stable(feature = "rust1", since = "1.0.0")]
127 pub fn max_value() -> Self {
128 let min = Self::min_value(); !min
131 /// Converts a string slice in a given base to an integer.
133 /// Leading and trailing whitespace represent an error.
138 /// assert_eq!(u32::from_str_radix("A", 16), Ok(10));
140 #[stable(feature = "rust1", since = "1.0.0")]
142 pub fn from_str_radix(src: &str, radix: u32) -> Result<Self, ParseIntError> {
143 from_str_radix(src, radix)
146 /// Returns the number of ones in the binary representation of `self`.
151 /// let n = 0b01001100u8;
153 /// assert_eq!(n.count_ones(), 3);
155 #[stable(feature = "rust1", since = "1.0.0")]
157 pub fn count_ones(self) -> u32 { (self as $UnsignedT).count_ones() }
159 /// Returns the number of zeros in the binary representation of `self`.
164 /// let n = 0b01001100u8;
166 /// assert_eq!(n.count_zeros(), 5);
168 #[stable(feature = "rust1", since = "1.0.0")]
170 pub fn count_zeros(self) -> u32 {
174 /// Returns the number of leading zeros in the binary representation
180 /// let n = 0b0101000u16;
182 /// assert_eq!(n.leading_zeros(), 10);
184 #[stable(feature = "rust1", since = "1.0.0")]
186 pub fn leading_zeros(self) -> u32 {
187 (self as $UnsignedT).leading_zeros()
190 /// Returns the number of trailing zeros in the binary representation
196 /// let n = 0b0101000u16;
198 /// assert_eq!(n.trailing_zeros(), 3);
200 #[stable(feature = "rust1", since = "1.0.0")]
202 pub fn trailing_zeros(self) -> u32 {
203 (self as $UnsignedT).trailing_zeros()
206 /// Shifts the bits to the left by a specified amount, `n`,
207 /// wrapping the truncated bits to the end of the resulting integer.
212 /// let n = 0x0123456789ABCDEFu64;
213 /// let m = 0x3456789ABCDEF012u64;
215 /// assert_eq!(n.rotate_left(12), m);
217 #[stable(feature = "rust1", since = "1.0.0")]
219 pub fn rotate_left(self, n: u32) -> Self {
220 (self as $UnsignedT).rotate_left(n) as Self
223 /// Shifts the bits to the right by a specified amount, `n`,
224 /// wrapping the truncated bits to the beginning of the resulting
230 /// let n = 0x0123456789ABCDEFu64;
231 /// let m = 0xDEF0123456789ABCu64;
233 /// assert_eq!(n.rotate_right(12), m);
235 #[stable(feature = "rust1", since = "1.0.0")]
237 pub fn rotate_right(self, n: u32) -> Self {
238 (self as $UnsignedT).rotate_right(n) as Self
241 /// Reverses the byte order of the integer.
246 /// let n = 0x0123456789ABCDEFu64;
247 /// let m = 0xEFCDAB8967452301u64;
249 /// assert_eq!(n.swap_bytes(), m);
251 #[stable(feature = "rust1", since = "1.0.0")]
253 pub fn swap_bytes(self) -> Self {
254 (self as $UnsignedT).swap_bytes() as Self
257 /// Converts an integer from big endian to the target's endianness.
259 /// On big endian this is a no-op. On little endian the bytes are
265 /// let n = 0x0123456789ABCDEFu64;
267 /// if cfg!(target_endian = "big") {
268 /// assert_eq!(u64::from_be(n), n)
270 /// assert_eq!(u64::from_be(n), n.swap_bytes())
273 #[stable(feature = "rust1", since = "1.0.0")]
275 pub fn from_be(x: Self) -> Self {
276 if cfg!(target_endian = "big") { x } else { x.swap_bytes() }
279 /// Converts an integer from little endian to the target's endianness.
281 /// On little endian this is a no-op. On big endian the bytes are
287 /// let n = 0x0123456789ABCDEFu64;
289 /// if cfg!(target_endian = "little") {
290 /// assert_eq!(u64::from_le(n), n)
292 /// assert_eq!(u64::from_le(n), n.swap_bytes())
295 #[stable(feature = "rust1", since = "1.0.0")]
297 pub fn from_le(x: Self) -> Self {
298 if cfg!(target_endian = "little") { x } else { x.swap_bytes() }
301 /// Converts `self` to big endian from the target's endianness.
303 /// On big endian this is a no-op. On little endian the bytes are
309 /// let n = 0x0123456789ABCDEFu64;
311 /// if cfg!(target_endian = "big") {
312 /// assert_eq!(n.to_be(), n)
314 /// assert_eq!(n.to_be(), n.swap_bytes())
317 #[stable(feature = "rust1", since = "1.0.0")]
319 pub fn to_be(self) -> Self { // or not to be?
320 if cfg!(target_endian = "big") { self } else { self.swap_bytes() }
323 /// Converts `self` to little endian from the target's endianness.
325 /// On little endian this is a no-op. On big endian the bytes are
331 /// let n = 0x0123456789ABCDEFu64;
333 /// if cfg!(target_endian = "little") {
334 /// assert_eq!(n.to_le(), n)
336 /// assert_eq!(n.to_le(), n.swap_bytes())
339 #[stable(feature = "rust1", since = "1.0.0")]
341 pub fn to_le(self) -> Self {
342 if cfg!(target_endian = "little") { self } else { self.swap_bytes() }
345 /// Checked integer addition. Computes `self + other`, returning `None`
346 /// if overflow occurred.
351 /// assert_eq!(5u16.checked_add(65530), Some(65535));
352 /// assert_eq!(6u16.checked_add(65530), None);
354 #[stable(feature = "rust1", since = "1.0.0")]
356 pub fn checked_add(self, other: Self) -> Option<Self> {
357 checked_op!($ActualT, $add_with_overflow, self, other)
360 /// Checked integer subtraction. Computes `self - other`, returning
361 /// `None` if underflow occurred.
366 /// assert_eq!((-127i8).checked_sub(1), Some(-128));
367 /// assert_eq!((-128i8).checked_sub(1), None);
369 #[stable(feature = "rust1", since = "1.0.0")]
371 pub fn checked_sub(self, other: Self) -> Option<Self> {
372 checked_op!($ActualT, $sub_with_overflow, self, other)
375 /// Checked integer multiplication. Computes `self * other`, returning
376 /// `None` if underflow or overflow occurred.
381 /// assert_eq!(5u8.checked_mul(51), Some(255));
382 /// assert_eq!(5u8.checked_mul(52), None);
384 #[stable(feature = "rust1", since = "1.0.0")]
386 pub fn checked_mul(self, other: Self) -> Option<Self> {
387 checked_op!($ActualT, $mul_with_overflow, self, other)
390 /// Checked integer division. Computes `self / other`, returning `None`
391 /// if `other == 0` or the operation results in underflow or overflow.
396 /// assert_eq!((-127i8).checked_div(-1), Some(127));
397 /// assert_eq!((-128i8).checked_div(-1), None);
398 /// assert_eq!((1i8).checked_div(0), None);
400 #[stable(feature = "rust1", since = "1.0.0")]
402 pub fn checked_div(self, v: Self) -> Option<Self> {
405 -1 if self == Self::min_value()
411 /// Saturating integer addition. Computes `self + other`, saturating at
412 /// the numeric bounds instead of overflowing.
413 #[stable(feature = "rust1", since = "1.0.0")]
415 pub fn saturating_add(self, other: Self) -> Self {
416 match self.checked_add(other) {
418 None if other >= Self::zero() => Self::max_value(),
419 None => Self::min_value(),
423 /// Saturating integer subtraction. Computes `self - other`, saturating
424 /// at the numeric bounds instead of overflowing.
425 #[stable(feature = "rust1", since = "1.0.0")]
427 pub fn saturating_sub(self, other: Self) -> Self {
428 match self.checked_sub(other) {
430 None if other >= Self::zero() => Self::min_value(),
431 None => Self::max_value(),
435 /// Wrapping (modular) addition. Computes `self + other`,
436 /// wrapping around at the boundary of the type.
437 #[stable(feature = "rust1", since = "1.0.0")]
439 pub fn wrapping_add(self, rhs: Self) -> Self {
441 intrinsics::overflowing_add(self, rhs)
445 /// Wrapping (modular) subtraction. Computes `self - other`,
446 /// wrapping around at the boundary of the type.
447 #[stable(feature = "rust1", since = "1.0.0")]
449 pub fn wrapping_sub(self, rhs: Self) -> Self {
451 intrinsics::overflowing_sub(self, rhs)
455 /// Wrapping (modular) multiplication. Computes `self *
456 /// other`, wrapping around at the boundary of the type.
457 #[stable(feature = "rust1", since = "1.0.0")]
459 pub fn wrapping_mul(self, rhs: Self) -> Self {
461 intrinsics::overflowing_mul(self, rhs)
465 /// Wrapping (modular) division. Computes `floor(self / other)`,
466 /// wrapping around at the boundary of the type.
468 /// The only case where such wrapping can occur is when one
469 /// divides `MIN / -1` on a signed type (where `MIN` is the
470 /// negative minimal value for the type); this is equivalent
471 /// to `-MIN`, a positive value that is too large to represent
472 /// in the type. In such a case, this function returns `MIN`
474 #[unstable(feature = "core", since = "1.0.0")]
476 pub fn wrapping_div(self, rhs: Self) -> Self {
477 self.overflowing_div(rhs).0
480 /// Wrapping (modular) remainder. Computes `self % other`,
481 /// wrapping around at the boundary of the type.
483 /// Such wrap-around never actually occurs mathematically;
484 /// implementation artifacts make `x % y` illegal for `MIN /
485 /// -1` on a signed type illegal (where `MIN` is the negative
486 /// minimal value). In such a case, this function returns `0`.
487 #[unstable(feature = "core", since = "1.0.0")]
489 pub fn wrapping_rem(self, rhs: Self) -> Self {
490 self.overflowing_rem(rhs).0
493 /// Wrapping (modular) negation. Computes `-self`,
494 /// wrapping around at the boundary of the type.
496 /// The only case where such wrapping can occur is when one
497 /// negates `MIN` on a signed type (where `MIN` is the
498 /// negative minimal value for the type); this is a positive
499 /// value that is too large to represent in the type. In such
500 /// a case, this function returns `MIN` itself.
501 #[unstable(feature = "core", since = "1.0.0")]
503 pub fn wrapping_neg(self) -> Self {
504 self.overflowing_neg().0
507 /// Panic-free bitwise shift-left; yields `self << mask(rhs)`,
508 /// where `mask` removes any high-order bits of `rhs` that
509 /// would cause the shift to exceed the bitwidth of the type.
510 #[unstable(feature = "core", since = "1.0.0")]
512 pub fn wrapping_shl(self, rhs: u32) -> Self {
513 self.overflowing_shl(rhs).0
516 /// Panic-free bitwise shift-left; yields `self >> mask(rhs)`,
517 /// where `mask` removes any high-order bits of `rhs` that
518 /// would cause the shift to exceed the bitwidth of the type.
519 #[unstable(feature = "core", since = "1.0.0")]
521 pub fn wrapping_shr(self, rhs: u32) -> Self {
522 self.overflowing_shr(rhs).0
525 /// Raises self to the power of `exp`, using exponentiation by squaring.
530 /// let x: i32 = 2; // or any other integer type
532 /// assert_eq!(x.pow(4), 16);
534 #[stable(feature = "rust1", since = "1.0.0")]
536 pub fn pow(self, mut exp: u32) -> Self {
538 let mut acc = Self::one();
540 let mut prev_base = self;
541 let mut base_oflo = false;
545 // ensure overflow occurs in the same manner it
546 // would have otherwise (i.e. signal any exception
547 // it would have otherwise).
548 acc = acc * (prev_base * prev_base);
554 let (new_base, new_base_oflo) = base.overflowing_mul(base);
556 base_oflo = new_base_oflo;
562 /// Computes the absolute value of `self`.
564 /// # Overflow behavior
566 /// The absolute value of `i32::min_value()` cannot be represented as an
567 /// `i32`, and attempting to calculate it will cause an overflow. This
568 /// means that code in debug mode will trigger a panic on this case and
569 /// optimized code will return `i32::min_value()` without a panic.
570 #[stable(feature = "rust1", since = "1.0.0")]
572 pub fn abs(self) -> Self {
573 if self.is_negative() {
574 // Note that the #[inline] above means that the overflow
575 // semantics of this negation depend on the crate we're being
583 /// Returns a number representing sign of `self`.
585 /// - `0` if the number is zero
586 /// - `1` if the number is positive
587 /// - `-1` if the number is negative
588 #[stable(feature = "rust1", since = "1.0.0")]
590 pub fn signum(self) -> Self {
598 /// Returns `true` if `self` is positive and `false` if the number
599 /// is zero or negative.
600 #[stable(feature = "rust1", since = "1.0.0")]
602 pub fn is_positive(self) -> bool { self > 0 }
604 /// Returns `true` if `self` is negative and `false` if the number
605 /// is zero or positive.
606 #[stable(feature = "rust1", since = "1.0.0")]
608 pub fn is_negative(self) -> bool { self < 0 }
614 int_impl! { i8, u8, 8,
615 intrinsics::i8_add_with_overflow,
616 intrinsics::i8_sub_with_overflow,
617 intrinsics::i8_mul_with_overflow }
622 int_impl! { i16, u16, 16,
623 intrinsics::i16_add_with_overflow,
624 intrinsics::i16_sub_with_overflow,
625 intrinsics::i16_mul_with_overflow }
630 int_impl! { i32, u32, 32,
631 intrinsics::i32_add_with_overflow,
632 intrinsics::i32_sub_with_overflow,
633 intrinsics::i32_mul_with_overflow }
638 int_impl! { i64, u64, 64,
639 intrinsics::i64_add_with_overflow,
640 intrinsics::i64_sub_with_overflow,
641 intrinsics::i64_mul_with_overflow }
644 #[cfg(target_pointer_width = "32")]
647 int_impl! { i32, u32, 32,
648 intrinsics::i32_add_with_overflow,
649 intrinsics::i32_sub_with_overflow,
650 intrinsics::i32_mul_with_overflow }
653 #[cfg(target_pointer_width = "64")]
656 int_impl! { i64, u64, 64,
657 intrinsics::i64_add_with_overflow,
658 intrinsics::i64_sub_with_overflow,
659 intrinsics::i64_mul_with_overflow }
662 // `Int` + `UnsignedInt` implemented for signed integers
663 macro_rules! uint_impl {
664 ($ActualT:ty, $BITS:expr,
669 $add_with_overflow:path,
670 $sub_with_overflow:path,
671 $mul_with_overflow:path) => {
672 /// Returns the smallest value that can be represented by this integer type.
673 #[stable(feature = "rust1", since = "1.0.0")]
674 pub fn min_value() -> Self { 0 }
676 /// Returns the largest value that can be represented by this integer type.
677 #[stable(feature = "rust1", since = "1.0.0")]
678 pub fn max_value() -> Self { !0 }
680 /// Converts a string slice in a given base to an integer.
682 /// Leading and trailing whitespace represent an error.
686 /// * src - A string slice
687 /// * radix - The base to use. Must lie in the range [2 .. 36]
691 /// `Err(ParseIntError)` if the string did not represent a valid number.
692 /// Otherwise, `Ok(n)` where `n` is the integer represented by `src`.
693 #[stable(feature = "rust1", since = "1.0.0")]
695 pub fn from_str_radix(src: &str, radix: u32) -> Result<Self, ParseIntError> {
696 from_str_radix(src, radix)
699 /// Returns the number of ones in the binary representation of `self`.
704 /// let n = 0b01001100u8;
706 /// assert_eq!(n.count_ones(), 3);
708 #[stable(feature = "rust1", since = "1.0.0")]
710 pub fn count_ones(self) -> u32 {
711 unsafe { $ctpop(self as $ActualT) as u32 }
714 /// Returns the number of zeros in the binary representation of `self`.
719 /// let n = 0b01001100u8;
721 /// assert_eq!(n.count_zeros(), 5);
723 #[stable(feature = "rust1", since = "1.0.0")]
725 pub fn count_zeros(self) -> u32 {
729 /// Returns the number of leading zeros in the binary representation
735 /// let n = 0b0101000u16;
737 /// assert_eq!(n.leading_zeros(), 10);
739 #[stable(feature = "rust1", since = "1.0.0")]
741 pub fn leading_zeros(self) -> u32 {
742 unsafe { $ctlz(self as $ActualT) as u32 }
745 /// Returns the number of trailing zeros in the binary representation
751 /// let n = 0b0101000u16;
753 /// assert_eq!(n.trailing_zeros(), 3);
755 #[stable(feature = "rust1", since = "1.0.0")]
757 pub fn trailing_zeros(self) -> u32 {
758 // As of LLVM 3.6 the codegen for the zero-safe cttz8 intrinsic
759 // emits two conditional moves on x86_64. By promoting the value to
760 // u16 and setting bit 8, we get better code without any conditional
762 // FIXME: There's a LLVM patch (http://reviews.llvm.org/D9284)
763 // pending, remove this workaround once LLVM generates better code
767 intrinsics::cttz16(self as u16 | 0x100) as u32
769 $cttz(self as $ActualT) as u32
774 /// Shifts the bits to the left by a specified amount, `n`,
775 /// wrapping the truncated bits to the end of the resulting integer.
780 /// let n = 0x0123456789ABCDEFu64;
781 /// let m = 0x3456789ABCDEF012u64;
783 /// assert_eq!(n.rotate_left(12), m);
785 #[stable(feature = "rust1", since = "1.0.0")]
787 pub fn rotate_left(self, n: u32) -> Self {
788 // Protect against undefined behaviour for over-long bit shifts
790 (self << n) | (self >> (($BITS - n) % $BITS))
793 /// Shifts the bits to the right by a specified amount, `n`,
794 /// wrapping the truncated bits to the beginning of the resulting
800 /// let n = 0x0123456789ABCDEFu64;
801 /// let m = 0xDEF0123456789ABCu64;
803 /// assert_eq!(n.rotate_right(12), m);
805 #[stable(feature = "rust1", since = "1.0.0")]
807 pub fn rotate_right(self, n: u32) -> Self {
808 // Protect against undefined behaviour for over-long bit shifts
810 (self >> n) | (self << (($BITS - n) % $BITS))
813 /// Reverses the byte order of the integer.
818 /// let n = 0x0123456789ABCDEFu64;
819 /// let m = 0xEFCDAB8967452301u64;
821 /// assert_eq!(n.swap_bytes(), m);
823 #[stable(feature = "rust1", since = "1.0.0")]
825 pub fn swap_bytes(self) -> Self {
826 unsafe { $bswap(self as $ActualT) as Self }
829 /// Converts an integer from big endian to the target's endianness.
831 /// On big endian this is a no-op. On little endian the bytes are
837 /// let n = 0x0123456789ABCDEFu64;
839 /// if cfg!(target_endian = "big") {
840 /// assert_eq!(u64::from_be(n), n)
842 /// assert_eq!(u64::from_be(n), n.swap_bytes())
845 #[stable(feature = "rust1", since = "1.0.0")]
847 pub fn from_be(x: Self) -> Self {
848 if cfg!(target_endian = "big") { x } else { x.swap_bytes() }
851 /// Converts an integer from little endian to the target's endianness.
853 /// On little endian this is a no-op. On big endian the bytes are
859 /// let n = 0x0123456789ABCDEFu64;
861 /// if cfg!(target_endian = "little") {
862 /// assert_eq!(u64::from_le(n), n)
864 /// assert_eq!(u64::from_le(n), n.swap_bytes())
867 #[stable(feature = "rust1", since = "1.0.0")]
869 pub fn from_le(x: Self) -> Self {
870 if cfg!(target_endian = "little") { x } else { x.swap_bytes() }
873 /// Converts `self` to big endian from the target's endianness.
875 /// On big endian this is a no-op. On little endian the bytes are
881 /// let n = 0x0123456789ABCDEFu64;
883 /// if cfg!(target_endian = "big") {
884 /// assert_eq!(n.to_be(), n)
886 /// assert_eq!(n.to_be(), n.swap_bytes())
889 #[stable(feature = "rust1", since = "1.0.0")]
891 pub fn to_be(self) -> Self { // or not to be?
892 if cfg!(target_endian = "big") { self } else { self.swap_bytes() }
895 /// Converts `self` to little endian from the target's endianness.
897 /// On little endian this is a no-op. On big endian the bytes are
903 /// let n = 0x0123456789ABCDEFu64;
905 /// if cfg!(target_endian = "little") {
906 /// assert_eq!(n.to_le(), n)
908 /// assert_eq!(n.to_le(), n.swap_bytes())
911 #[stable(feature = "rust1", since = "1.0.0")]
913 pub fn to_le(self) -> Self {
914 if cfg!(target_endian = "little") { self } else { self.swap_bytes() }
917 /// Checked integer addition. Computes `self + other`, returning `None`
918 /// if overflow occurred.
923 /// assert_eq!(5u16.checked_add(65530), Some(65535));
924 /// assert_eq!(6u16.checked_add(65530), None);
926 #[stable(feature = "rust1", since = "1.0.0")]
928 pub fn checked_add(self, other: Self) -> Option<Self> {
929 checked_op!($ActualT, $add_with_overflow, self, other)
932 /// Checked integer subtraction. Computes `self - other`, returning
933 /// `None` if underflow occurred.
938 /// assert_eq!((-127i8).checked_sub(1), Some(-128));
939 /// assert_eq!((-128i8).checked_sub(1), None);
941 #[stable(feature = "rust1", since = "1.0.0")]
943 pub fn checked_sub(self, other: Self) -> Option<Self> {
944 checked_op!($ActualT, $sub_with_overflow, self, other)
947 /// Checked integer multiplication. Computes `self * other`, returning
948 /// `None` if underflow or overflow occurred.
953 /// assert_eq!(5u8.checked_mul(51), Some(255));
954 /// assert_eq!(5u8.checked_mul(52), None);
956 #[stable(feature = "rust1", since = "1.0.0")]
958 pub fn checked_mul(self, other: Self) -> Option<Self> {
959 checked_op!($ActualT, $mul_with_overflow, self, other)
962 /// Checked integer division. Computes `self / other`, returning `None`
963 /// if `other == 0` or the operation results in underflow or overflow.
968 /// assert_eq!((-127i8).checked_div(-1), Some(127));
969 /// assert_eq!((-128i8).checked_div(-1), None);
970 /// assert_eq!((1i8).checked_div(0), None);
972 #[stable(feature = "rust1", since = "1.0.0")]
974 pub fn checked_div(self, v: Self) -> Option<Self> {
981 /// Saturating integer addition. Computes `self + other`, saturating at
982 /// the numeric bounds instead of overflowing.
983 #[stable(feature = "rust1", since = "1.0.0")]
985 pub fn saturating_add(self, other: Self) -> Self {
986 match self.checked_add(other) {
988 None if other >= Self::zero() => Self::max_value(),
989 None => Self::min_value(),
993 /// Saturating integer subtraction. Computes `self - other`, saturating
994 /// at the numeric bounds instead of overflowing.
995 #[stable(feature = "rust1", since = "1.0.0")]
997 pub fn saturating_sub(self, other: Self) -> Self {
998 match self.checked_sub(other) {
1000 None if other >= Self::zero() => Self::min_value(),
1001 None => Self::max_value(),
1005 /// Wrapping (modular) addition. Computes `self + other`,
1006 /// wrapping around at the boundary of the type.
1007 #[stable(feature = "rust1", since = "1.0.0")]
1009 pub fn wrapping_add(self, rhs: Self) -> Self {
1011 intrinsics::overflowing_add(self, rhs)
1015 /// Wrapping (modular) subtraction. Computes `self - other`,
1016 /// wrapping around at the boundary of the type.
1017 #[stable(feature = "rust1", since = "1.0.0")]
1019 pub fn wrapping_sub(self, rhs: Self) -> Self {
1021 intrinsics::overflowing_sub(self, rhs)
1025 /// Wrapping (modular) multiplication. Computes `self *
1026 /// other`, wrapping around at the boundary of the type.
1027 #[stable(feature = "rust1", since = "1.0.0")]
1029 pub fn wrapping_mul(self, rhs: Self) -> Self {
1031 intrinsics::overflowing_mul(self, rhs)
1035 /// Wrapping (modular) division. Computes `floor(self / other)`,
1036 /// wrapping around at the boundary of the type.
1038 /// The only case where such wrapping can occur is when one
1039 /// divides `MIN / -1` on a signed type (where `MIN` is the
1040 /// negative minimal value for the type); this is equivalent
1041 /// to `-MIN`, a positive value that is too large to represent
1042 /// in the type. In such a case, this function returns `MIN`
1044 #[unstable(feature = "core", since = "1.0.0")]
1046 pub fn wrapping_div(self, rhs: Self) -> Self {
1047 self.overflowing_div(rhs).0
1050 /// Wrapping (modular) remainder. Computes `self % other`,
1051 /// wrapping around at the boundary of the type.
1053 /// Such wrap-around never actually occurs mathematically;
1054 /// implementation artifacts make `x % y` illegal for `MIN /
1055 /// -1` on a signed type illegal (where `MIN` is the negative
1056 /// minimal value). In such a case, this function returns `0`.
1057 #[unstable(feature = "core", since = "1.0.0")]
1059 pub fn wrapping_rem(self, rhs: Self) -> Self {
1060 self.overflowing_rem(rhs).0
1063 /// Wrapping (modular) negation. Computes `-self`,
1064 /// wrapping around at the boundary of the type.
1066 /// The only case where such wrapping can occur is when one
1067 /// negates `MIN` on a signed type (where `MIN` is the
1068 /// negative minimal value for the type); this is a positive
1069 /// value that is too large to represent in the type. In such
1070 /// a case, this function returns `MIN` itself.
1071 #[unstable(feature = "core", since = "1.0.0")]
1073 pub fn wrapping_neg(self) -> Self {
1074 self.overflowing_neg().0
1077 /// Panic-free bitwise shift-left; yields `self << mask(rhs)`,
1078 /// where `mask` removes any high-order bits of `rhs` that
1079 /// would cause the shift to exceed the bitwidth of the type.
1080 #[unstable(feature = "core", since = "1.0.0")]
1082 pub fn wrapping_shl(self, rhs: u32) -> Self {
1083 self.overflowing_shl(rhs).0
1086 /// Panic-free bitwise shift-left; yields `self >> mask(rhs)`,
1087 /// where `mask` removes any high-order bits of `rhs` that
1088 /// would cause the shift to exceed the bitwidth of the type.
1089 #[unstable(feature = "core", since = "1.0.0")]
1091 pub fn wrapping_shr(self, rhs: u32) -> Self {
1092 self.overflowing_shr(rhs).0
1095 /// Raises self to the power of `exp`, using exponentiation by squaring.
1100 /// assert_eq!(2i32.pow(4), 16);
1102 #[stable(feature = "rust1", since = "1.0.0")]
1104 pub fn pow(self, mut exp: u32) -> Self {
1105 let mut base = self;
1106 let mut acc = Self::one();
1108 let mut prev_base = self;
1109 let mut base_oflo = false;
1113 // ensure overflow occurs in the same manner it
1114 // would have otherwise (i.e. signal any exception
1115 // it would have otherwise).
1116 acc = acc * (prev_base * prev_base);
1122 let (new_base, new_base_oflo) = base.overflowing_mul(base);
1124 base_oflo = new_base_oflo;
1130 /// Returns `true` iff `self == 2^k` for some `k`.
1131 #[stable(feature = "rust1", since = "1.0.0")]
1133 pub fn is_power_of_two(self) -> bool {
1134 (self.wrapping_sub(Self::one())) & self == Self::zero() &&
1135 !(self == Self::zero())
1138 /// Returns the smallest power of two greater than or equal to `self`.
1139 /// Unspecified behavior on overflow.
1140 #[stable(feature = "rust1", since = "1.0.0")]
1142 pub fn next_power_of_two(self) -> Self {
1143 let bits = size_of::<Self>() * 8;
1144 let one: Self = Self::one();
1145 one << ((bits - self.wrapping_sub(one).leading_zeros() as usize) % bits)
1148 /// Returns the smallest power of two greater than or equal to `n`. If
1149 /// the next power of two is greater than the type's maximum value,
1150 /// `None` is returned, otherwise the power of two is wrapped in `Some`.
1151 #[stable(feature = "rust1", since = "1.0.0")]
1152 pub fn checked_next_power_of_two(self) -> Option<Self> {
1153 let npot = self.next_power_of_two();
1170 intrinsics::u8_add_with_overflow,
1171 intrinsics::u8_sub_with_overflow,
1172 intrinsics::u8_mul_with_overflow }
1177 uint_impl! { u16, 16,
1178 intrinsics::ctpop16,
1181 intrinsics::bswap16,
1182 intrinsics::u16_add_with_overflow,
1183 intrinsics::u16_sub_with_overflow,
1184 intrinsics::u16_mul_with_overflow }
1189 uint_impl! { u32, 32,
1190 intrinsics::ctpop32,
1193 intrinsics::bswap32,
1194 intrinsics::u32_add_with_overflow,
1195 intrinsics::u32_sub_with_overflow,
1196 intrinsics::u32_mul_with_overflow }
1202 uint_impl! { u64, 64,
1203 intrinsics::ctpop64,
1206 intrinsics::bswap64,
1207 intrinsics::u64_add_with_overflow,
1208 intrinsics::u64_sub_with_overflow,
1209 intrinsics::u64_mul_with_overflow }
1212 #[cfg(target_pointer_width = "32")]
1215 uint_impl! { u32, 32,
1216 intrinsics::ctpop32,
1219 intrinsics::bswap32,
1220 intrinsics::u32_add_with_overflow,
1221 intrinsics::u32_sub_with_overflow,
1222 intrinsics::u32_mul_with_overflow }
1225 #[cfg(target_pointer_width = "64")]
1228 uint_impl! { u64, 64,
1229 intrinsics::ctpop64,
1232 intrinsics::bswap64,
1233 intrinsics::u64_add_with_overflow,
1234 intrinsics::u64_sub_with_overflow,
1235 intrinsics::u64_mul_with_overflow }
1238 /// Used for representing the classification of floating point numbers
1239 #[derive(Copy, Clone, PartialEq, Debug)]
1240 #[stable(feature = "rust1", since = "1.0.0")]
1241 pub enum FpCategory {
1242 /// "Not a Number", often obtained by dividing by zero
1243 #[stable(feature = "rust1", since = "1.0.0")]
1246 /// Positive or negative infinity
1247 #[stable(feature = "rust1", since = "1.0.0")]
1250 /// Positive or negative zero
1251 #[stable(feature = "rust1", since = "1.0.0")]
1254 /// De-normalized floating point representation (less precise than `Normal`)
1255 #[stable(feature = "rust1", since = "1.0.0")]
1258 /// A regular floating point number
1259 #[stable(feature = "rust1", since = "1.0.0")]
1263 /// A built-in floating point number.
1266 /// Returns the NaN value.
1268 /// Returns the infinite value.
1269 fn infinity() -> Self;
1270 /// Returns the negative infinite value.
1271 fn neg_infinity() -> Self;
1273 fn neg_zero() -> Self;
1278 /// Parses the string `s` with the radix `r` as a float.
1279 fn from_str_radix(s: &str, r: u32) -> Result<Self, ParseFloatError>;
1281 /// Returns true if this value is NaN and false otherwise.
1282 fn is_nan(self) -> bool;
1283 /// Returns true if this value is positive infinity or negative infinity and
1284 /// false otherwise.
1285 fn is_infinite(self) -> bool;
1286 /// Returns true if this number is neither infinite nor NaN.
1287 fn is_finite(self) -> bool;
1288 /// Returns true if this number is neither zero, infinite, denormal, or NaN.
1289 fn is_normal(self) -> bool;
1290 /// Returns the category that this number falls into.
1291 fn classify(self) -> FpCategory;
1293 /// Returns the mantissa, exponent and sign as integers, respectively.
1294 fn integer_decode(self) -> (u64, i16, i8);
1296 /// Return the largest integer less than or equal to a number.
1297 fn floor(self) -> Self;
1298 /// Return the smallest integer greater than or equal to a number.
1299 fn ceil(self) -> Self;
1300 /// Return the nearest integer to a number. Round half-way cases away from
1302 fn round(self) -> Self;
1303 /// Return the integer part of a number.
1304 fn trunc(self) -> Self;
1305 /// Return the fractional part of a number.
1306 fn fract(self) -> Self;
1308 /// Computes the absolute value of `self`. Returns `Float::nan()` if the
1309 /// number is `Float::nan()`.
1310 fn abs(self) -> Self;
1311 /// Returns a number that represents the sign of `self`.
1313 /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
1314 /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
1315 /// - `Float::nan()` if the number is `Float::nan()`
1316 fn signum(self) -> Self;
1317 /// Returns `true` if `self` is positive, including `+0.0` and
1318 /// `Float::infinity()`.
1319 fn is_positive(self) -> bool;
1320 /// Returns `true` if `self` is negative, including `-0.0` and
1321 /// `Float::neg_infinity()`.
1322 fn is_negative(self) -> bool;
1324 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
1325 /// error. This produces a more accurate result with better performance than
1326 /// a separate multiplication operation followed by an add.
1327 fn mul_add(self, a: Self, b: Self) -> Self;
1328 /// Take the reciprocal (inverse) of a number, `1/x`.
1329 fn recip(self) -> Self;
1331 /// Raise a number to an integer power.
1333 /// Using this function is generally faster than using `powf`
1334 fn powi(self, n: i32) -> Self;
1335 /// Raise a number to a floating point power.
1336 fn powf(self, n: Self) -> Self;
1338 /// Take the square root of a number.
1340 /// Returns NaN if `self` is a negative number.
1341 fn sqrt(self) -> Self;
1342 /// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
1343 fn rsqrt(self) -> Self;
1345 /// Returns `e^(self)`, (the exponential function).
1346 fn exp(self) -> Self;
1347 /// Returns 2 raised to the power of the number, `2^(self)`.
1348 fn exp2(self) -> Self;
1349 /// Returns the natural logarithm of the number.
1350 fn ln(self) -> Self;
1351 /// Returns the logarithm of the number with respect to an arbitrary base.
1352 fn log(self, base: Self) -> Self;
1353 /// Returns the base 2 logarithm of the number.
1354 fn log2(self) -> Self;
1355 /// Returns the base 10 logarithm of the number.
1356 fn log10(self) -> Self;
1358 /// Convert radians to degrees.
1359 fn to_degrees(self) -> Self;
1360 /// Convert degrees to radians.
1361 fn to_radians(self) -> Self;
1364 macro_rules! from_str_float_impl {
1366 #[stable(feature = "rust1", since = "1.0.0")]
1367 impl FromStr for $t {
1368 type Err = ParseFloatError;
1370 /// Converts a string in base 10 to a float.
1371 /// Accepts an optional decimal exponent.
1373 /// This function accepts strings such as
1376 /// * '+3.14', equivalent to '3.14'
1378 /// * '2.5E10', or equivalently, '2.5e10'
1380 /// * '.' (understood as 0)
1382 /// * '.5', or, equivalently, '0.5'
1383 /// * '+inf', 'inf', '-inf', 'NaN'
1385 /// Leading and trailing whitespace represent an error.
1389 /// * src - A string
1393 /// `Err(ParseFloatError)` if the string did not represent a valid
1394 /// number. Otherwise, `Ok(n)` where `n` is the floating-point
1395 /// number represented by `src`.
1397 #[allow(deprecated)]
1398 fn from_str(src: &str) -> Result<Self, ParseFloatError> {
1399 Self::from_str_radix(src, 10)
1404 from_str_float_impl!(f32);
1405 from_str_float_impl!(f64);
1407 macro_rules! from_str_radix_int_impl {
1409 #[stable(feature = "rust1", since = "1.0.0")]
1410 #[allow(deprecated)]
1411 impl FromStr for $t {
1412 type Err = ParseIntError;
1413 fn from_str(src: &str) -> Result<Self, ParseIntError> {
1414 from_str_radix(src, 10)
1419 from_str_radix_int_impl! { isize i8 i16 i32 i64 usize u8 u16 u32 u64 }
1422 trait FromStrRadixHelper: PartialOrd + Copy {
1423 fn min_value() -> Self;
1424 fn from_u32(u: u32) -> Self;
1425 fn checked_mul(&self, other: u32) -> Option<Self>;
1426 fn checked_sub(&self, other: u32) -> Option<Self>;
1427 fn checked_add(&self, other: u32) -> Option<Self>;
1431 ($($t:ty)*) => ($(impl FromStrRadixHelper for $t {
1432 fn min_value() -> Self { Self::min_value() }
1433 fn from_u32(u: u32) -> Self { u as Self }
1434 fn checked_mul(&self, other: u32) -> Option<Self> {
1435 Self::checked_mul(*self, other as Self)
1437 fn checked_sub(&self, other: u32) -> Option<Self> {
1438 Self::checked_sub(*self, other as Self)
1440 fn checked_add(&self, other: u32) -> Option<Self> {
1441 Self::checked_add(*self, other as Self)
1445 doit! { i8 i16 i32 i64 isize u8 u16 u32 u64 usize }
1447 fn from_str_radix<T: FromStrRadixHelper>(src: &str, radix: u32)
1448 -> Result<T, ParseIntError> {
1449 use self::IntErrorKind::*;
1450 use self::ParseIntError as PIE;
1451 assert!(radix >= 2 && radix <= 36,
1452 "from_str_radix_int: must lie in the range `[2, 36]` - found {}",
1455 let is_signed_ty = T::from_u32(0) > T::min_value();
1457 match src.slice_shift_char() {
1458 Some(('-', "")) => Err(PIE { kind: Empty }),
1459 Some(('-', src)) if is_signed_ty => {
1460 // The number is negative
1461 let mut result = T::from_u32(0);
1462 for c in src.chars() {
1463 let x = match c.to_digit(radix) {
1465 None => return Err(PIE { kind: InvalidDigit }),
1467 result = match result.checked_mul(radix) {
1468 Some(result) => result,
1469 None => return Err(PIE { kind: Underflow }),
1471 result = match result.checked_sub(x) {
1472 Some(result) => result,
1473 None => return Err(PIE { kind: Underflow }),
1479 // The number is signed
1480 let mut result = T::from_u32(0);
1481 for c in src.chars() {
1482 let x = match c.to_digit(radix) {
1484 None => return Err(PIE { kind: InvalidDigit }),
1486 result = match result.checked_mul(radix) {
1487 Some(result) => result,
1488 None => return Err(PIE { kind: Overflow }),
1490 result = match result.checked_add(x) {
1491 Some(result) => result,
1492 None => return Err(PIE { kind: Overflow }),
1497 None => Err(ParseIntError { kind: Empty }),
1501 /// An error which can be returned when parsing an integer.
1502 #[derive(Debug, Clone, PartialEq)]
1503 #[stable(feature = "rust1", since = "1.0.0")]
1504 pub struct ParseIntError { kind: IntErrorKind }
1506 #[derive(Debug, Clone, PartialEq)]
1514 impl ParseIntError {
1515 #[unstable(feature = "core", reason = "available through Error trait")]
1516 pub fn description(&self) -> &str {
1518 IntErrorKind::Empty => "cannot parse integer from empty string",
1519 IntErrorKind::InvalidDigit => "invalid digit found in string",
1520 IntErrorKind::Overflow => "number too large to fit in target type",
1521 IntErrorKind::Underflow => "number too small to fit in target type",
1526 #[stable(feature = "rust1", since = "1.0.0")]
1527 impl fmt::Display for ParseIntError {
1528 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
1529 self.description().fmt(f)
1533 /// An error which can be returned when parsing a float.
1534 #[derive(Debug, Clone, PartialEq)]
1535 #[stable(feature = "rust1", since = "1.0.0")]
1536 pub struct ParseFloatError {
1538 pub __kind: FloatErrorKind
1541 #[derive(Debug, Clone, PartialEq)]
1542 pub enum FloatErrorKind {
1547 impl ParseFloatError {
1549 pub fn __description(&self) -> &str {
1551 FloatErrorKind::Empty => "cannot parse float from empty string",
1552 FloatErrorKind::Invalid => "invalid float literal",
1557 #[stable(feature = "rust1", since = "1.0.0")]
1558 impl fmt::Display for ParseFloatError {
1559 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
1560 self.__description().fmt(f)