1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
use crate::convert::UncheckedFrom;
// todo: const trait implementations
// todo: maybe default implementations should not require `Self` traits
/// Provides a base implementation for what a `NonStandardInteger` needs.
pub trait NonStandardInteger<T, const BITS: u32>
where
T: PartialOrd + Copy,
Self: UncheckedFrom<T>,
{
// TODO: find a better name for this.
/// The underlying representation of the integer.
type Repr = T;
/// The size of this integer type in bits.
const BITS: u32 = BITS;
/// The smallest value that can be represented by this integer type.
const MIN: T;
/// The largest value that can be represented by this integer type.
const MAX: T;
/// Returns the smallest value that can be represented by this integer type.
fn min_value() -> Self;
/// Returns the largest value that can be represented by this integer type.
fn max_value() -> Self;
}
/// Provides integer methods.
pub trait NonStandardIntegerCommon<T: PartialOrd + Copy, const BITS: u32>
where
Self: NonStandardInteger<T, BITS>,
{
/// Checked integer addition. Computes `self + rhs`, returning [`None`]
/// if overflow occurred.
fn checked_add(self, rhs: Self) -> Option<Self>;
/// Checked integer subtraction. Computes `self - rhs`, returning [`None`]
/// if overflow occurred.
fn checked_sub(self, rhs: Self) -> Option<Self>;
/// Checked integer multiplication. Computes `self * rhs`, returning [`None`]
/// if overflow occurred.
fn checked_mul(self, rhs: Self) -> Option<Self>;
/// Checked integer division. Computes `self / rhs`, returning [`None`]
/// if `rhs == 0`.
fn checked_div(self, rhs: Self) -> Option<Self>;
/// Checked integer remainder. Computes `self % rhs`, returning [`None`]
/// if `rhs == 0`.
fn checked_rem(self, rhs: Self) -> Option<Self>;
/// Checked shift left. Computes `self << rhs`, returning [`None`]
/// if `rhs` is larger than or equal to the number of bits in `self`.
fn checked_shl(self, rhs: u32) -> Option<Self>;
/// Checked shift right. Computes `self >> rhs`, returning [`None`]
/// if `rhs` is larger than or equal to the number of bits in `self`.
fn checked_shr(self, rhs: u32) -> Option<Self>;
// fn checked_pow(self, rhs: u32) -> Self;
/// Saturating integer addition. Computes `self + rhs`, saturating at the numeric bounds instead of overflowing.
fn saturating_add(self, rhs: Self) -> Self;
/// Saturating integer subtraction. Computes `self - rhs`, saturating at the numeric bounds instead of overflowing.
fn saturating_sub(self, rhs: Self) -> Self;
/// Saturating integer multiplication. Computes `self * rhs`, saturating at the numeric bounds instead of overflowing.
fn saturating_mul(self, rhs: Self) -> Self;
/// Saturating integer exponentiation. Computes `self.pow(exp)`, saturating at the numeric bounds instead of overflowing.
fn saturating_pow(self, exp: u32) -> Self;
/// Wrapping (modular) addition. Computes `self + rhs`, wrapping around at the
/// boundary of the type.
fn wrapping_add(self, rhs: Self) -> Self;
/// Wrapping (modular) subtraction. Computes `self - rhs`, wrapping around at the
/// boundary of the type.
fn wrapping_sub(self, rhs: Self) -> Self;
/// Wrapping (modular) multiplication. Computes `self * rhs`, wrapping around at
/// the boundary of the type.
fn wrapping_mul(self, rhs: Self) -> Self;
/// Wrapping (modular) division. Computes `self / rhs`, wrapping around at the
/// boundary of the type.
///
/// The only case where such wrapping can occur is when one divides `MIN / -1` on a signed type (where
/// [`MIN`](NonStandardInteger::MIN) is the negative minimal value for the type); this is equivalent to `-MIN`, a positive value
/// that is too large to represent in the type. In such a case, this function returns [`MIN`](NonStandardInteger::MIN) itself.
///
/// # Panics
///
/// This function will panic if `rhs` is 0.
fn wrapping_div(self, rhs: Self) -> Self;
/// Wrapping (modular) remainder. Computes `self % rhs`, wrapping around at the
/// boundary of the type.
///
/// Such wrap-around never actually occurs mathematically;
/// implementation artifacts make `x % y` invalid for `MIN / -1` on a signed type (where [`MIN`](NonStandardInteger::MIN) is the negative minimal value).
/// In such a case, this function returns `0`.
///
/// # Panics
///
/// This function will panic if `rhs` is 0.
fn wrapping_rem(self, rhs: Self) -> Self;
/// Panic-free bitwise shift-left; yields `self << mask(rhs)`,
/// where `mask` removes any high-order bits of `rhs` that
/// would cause the shift to exceed the bitwidth of the type.
fn wrapping_shl(self, rhs: u32) -> Self;
/// Panic-free bitwise shift-right; yields `self >> mask(rhs)`,
/// where `mask` removes any high-order bits of `rhs` that
/// would cause the shift to exceed the bitwidth of the type.
fn wrapping_shr(self, rhs: u32) -> Self;
// fn wrapping_pow(self, exp: u32) -> Self;
/// Calculates `self` + `rhs`
///
/// Returns a tuple of the addition along with a boolean indicating whether an arithmetic overflow would
/// occur. If an overflow would have occurred then the wrapped value is returned.
fn overflowing_add(self, rhs: Self) -> (Self, bool);
/// Calculates `self` - `rhs`
///
/// Returns a tuple of the subtraction along with a boolean indicating whether an arithmetic overflow
/// would occur. If an overflow would have occurred then the wrapped value is returned.
fn overflowing_sub(self, rhs: Self) -> (Self, bool);
/// Calculates the multiplication of `self` and `rhs`.
///
/// Returns a tuple of the multiplication along with a boolean indicating whether an arithmetic overflow
/// would occur. If an overflow would have occurred then the wrapped value is returned.
fn overflowing_mul(self, rhs: Self) -> (Self, bool);
/// Calculates the divisor when `self` is divided by `rhs`.
///
/// Returns a tuple of the divisor along with a boolean indicating whether an arithmetic overflow would
/// occur. If an overflow would occur then self is returned.
///
/// # Panics
///
/// This function will panic if `rhs` is 0.
fn overflowing_div(self, rhs: Self) -> (Self, bool);
/// Calculates the remainder when `self` is divided by `rhs`.
///
/// Returns a tuple of the remainder after dividing along with a boolean indicating whether an
/// arithmetic overflow would occur. If an overflow would occur then 0 is returned.
///
/// # Panics
///
/// This function will panic if `rhs` is 0.
fn overflowing_rem(self, rhs: Self) -> (Self, bool);
/// Shifts self left by `rhs` bits.
///
/// Returns a tuple of the shifted version of self along with a boolean
/// indicating whether the shift value was larger than or equal to the
/// number of bits. If the shift value is too large, then value is
/// masked `(BITS - 1)` where N is the number of bits, and this value is then
/// used to perform the shift.
fn overflowing_shl(self, rhs: u32) -> (Self, bool);
/// Shifts self right by `rhs` bits.
///
/// Returns a tuple of the shifted version of self along with a boolean
/// indicating whether the shift value was larger than or equal to the
/// number of bits. If the shift value is too large, then value is
/// masked `(BITS - 1)`, and this value is then
/// used to perform the shift.
fn overflowing_shr(self, rhs: u32) -> (Self, bool);
// fn overflowing_pow(self, exp: u32) -> Self;
}
/// Provides integer methods that only make sense with signed integers.
pub trait NonStandardIntegerSigned<T: PartialOrd + Copy, const BITS: u32>
where
Self: NonStandardInteger<T, BITS>,
{
/// Computes the absolute value of `self`.
///
/// # Overflow behavior
///
/// The absolute value of [`MIN`](NonStandardInteger::MIN) cannot be represented as a value in signed integers.
///
/// Attempting to calculate it will cause an overflow. This means
/// that code in debug mode will trigger a panic on this case and
/// optimized code will return [`MIN`](NonStandardInteger::MIN) without a panic.
fn abs(self) -> Self;
/// Returns `true` if `self` is negative and `false` if the number is zero or
/// positive.
fn is_negative(self) -> bool;
/// Saturating integer negation. Computes `-self`, returning [`MAX`](NonStandardInteger::MAX)
/// if `self == MIN` instead of overflowing.
fn saturating_neg(self) -> Self;
/// Saturating absolute value. Computes [`self.abs()`](Self::abs), returning [`MAX`](NonStandardInteger::MAX)
/// if `self == MIN` instead of overflowing.
fn saturating_abs(self) -> Self;
/// Negates self, overflowing if this is equal to the minimum value.
///
/// Returns a tuple of the negated version of self along with a boolean indicating whether an overflow
/// happened. If `self` is the minimum value [`MIN`](NonStandardInteger::MIN), then the
/// minimum value will be returned again and [`true`] will be returned for an overflow happening.
fn overflowing_neg(self) -> (Self, bool);
/// Computes the absolute value of `self`.
///
/// Returns a tuple of the absolute version of self along with a boolean indicating whether an overflow
/// happened. If self is the minimum value [`MIN`](NonStandardInteger::MIN) then the value will be returned
/// again and [`true`] will be returned for an overflow happening.
fn overflowing_abs(self) -> (Self, bool);
/// Checked negation. Computes `-self`, returning [`None`] if `self == MIN`.
fn checked_neg(self) -> Option<Self>;
/// Checked absolute value. Computes [`self.abs()`](Self::abs), returning [`None`] if
/// `self == MIN`
fn checked_abs(self) -> Option<Self>;
/// Wrapping (modular) negation. Computes `-self`, wrapping around at the boundary
/// of the type.
///
/// The only case where such wrapping can occur is when one negates[`MIN`](NonStandardInteger::MIN) on a signed type (where [`MIN`](NonStandardInteger::MIN)
/// is the negative minimal value for the type); this is a positive value that is too large to represent
/// in the type. In such a case, this function returns [`MIN`](NonStandardInteger::MIN) itself.
fn wrapping_neg(self) -> Self;
/// Wrapping (modular) absolute value. Computes [`self.abs()`](Self::abs), wrapping around at
/// the boundary of the type.
///
/// The only case where such wrapping can occur is when one takes the absolute value of the negative
/// minimal value for the type; this is a positive value that is too large to represent in the type. In
/// such a case, this function returns [`MIN`](NonStandardInteger::MIN) itself.
fn wrapping_abs(self) -> Self;
}