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
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
use core::ops::{Mul, MulAssign};
use dashu_base::Gcd;
use dashu_int::{IBig, UBig};
use crate::{
helper_macros::{impl_binop_assign_by_taking, impl_binop_with_int, impl_binop_with_macro},
rbig::{RBig, Relaxed},
repr::Repr,
};
impl Repr {
#[inline]
fn sqr(&self) -> Self {
Self {
numerator: self.numerator.sqr().into(),
denominator: self.denominator.sqr(),
}
}
#[inline]
fn cubic(&self) -> Self {
Self {
numerator: self.numerator.cubic(),
denominator: self.denominator.cubic(),
}
}
/// `self^n` for any `n` in `isize`.
///
/// For a negative exponent the value is reciprocated first: `x.pow(-n) ==
/// 1 / x.pow(n)` for a nonzero `x`. A zero base raised to a negative power is
/// a division by zero and panics, matching the rest of the rationals API.
#[inline]
fn pow(&self, n: isize) -> Self {
if n >= 0 {
Self {
numerator: self.numerator.pow(n as usize),
denominator: self.denominator.pow(n as usize),
}
} else {
// self^n = (denominator / numerator)^|n|. Strip the numerator's
// sign onto the new numerator so the denominator stays a positive
// UBig. `into_parts` yields (Positive, ZERO) for a zero numerator,
// which we reject before inverting it.
let exp = n.unsigned_abs();
let (sign, numerator_mag) = self.numerator.clone().into_parts();
if numerator_mag.is_zero() {
crate::error::panic_divide_by_0();
}
// sign^exp collapses to Positive for an even exponent.
let result_sign = if exp % 2 == 0 {
dashu_base::Sign::Positive
} else {
sign
};
Self {
numerator: result_sign * self.denominator.pow(exp),
denominator: numerator_mag.pow(exp),
}
}
}
}
impl RBig {
/// Compute the square of the number (`self * self`).
///
/// # Examples
///
/// ```
/// # use dashu_ratio::RBig;
/// let a = RBig::from_parts(2.into(), 3u8.into());
/// let a2 = RBig::from_parts(4.into(), 9u8.into());
/// assert_eq!(a.sqr(), a2);
/// ```
#[inline]
pub fn sqr(&self) -> Self {
Self(self.0.sqr())
}
/// Compute the cubic of the number (`self * self * self`).
///
/// # Examples
///
/// ```
/// # use dashu_ratio::RBig;
/// let a = RBig::from_parts(2.into(), 3u8.into());
/// let a3 = RBig::from_parts(8.into(), 27u8.into());
/// assert_eq!(a.cubic(), a3);
/// ```
#[inline]
pub fn cubic(&self) -> Self {
Self(self.0.cubic())
}
/// Raise this number to a power of `n`.
///
/// A negative exponent reciprocates first: `x.pow(-n) == 1 / x.pow(n)` for a
/// nonzero `x` (matching `powf` on the floats). A zero base raised to a
/// negative power is a division by zero and panics. Non-negative exponents
/// behave exactly as before.
///
/// # Examples
///
/// ```
/// # use dashu_ratio::RBig;
/// let a = RBig::from_parts(2.into(), 3u8.into());
/// let a5 = RBig::from_parts(32.into(), 243u8.into());
/// assert_eq!(a.pow(5), a5);
/// let a_inv = RBig::from_parts(3.into(), 2u8.into());
/// assert_eq!(a.pow(-1), a_inv);
/// ```
#[inline]
pub fn pow(&self, n: isize) -> Self {
Self(self.0.pow(n))
}
}
macro_rules! impl_mul_with_rbig {
(
$a:ident, $b:ident, $c:ident, $d:ident,
$ra:ident, $rb:ident, $rc:ident, $rd:ident, $method:ident
) => {{
// a/b * c/d = (ac)/gcd(a,d)/gcd(b,c)/(bd)
let g_ad = $ra.gcd($rd);
let g_bc = $rb.gcd($rc);
RBig(Repr {
numerator: ($a / &g_ad).$method($c / &g_bc),
denominator: ($b / g_bc).$method($d / g_ad),
})
}};
}
impl_binop_with_macro!(impl Mul, mul, impl_mul_with_rbig);
impl_binop_assign_by_taking!(impl MulAssign for RBig, mul_assign, mul);
impl Relaxed {
/// Compute the square of the number (`self * self`).
///
/// See [RBig::sqr] for details.
#[inline]
pub fn sqr(&self) -> Self {
Self(self.0.sqr())
}
/// Compute the cubic of the number (`self * self * self`).
///
/// See [RBig::cubic] for details.
#[inline]
pub fn cubic(&self) -> Self {
Self(self.0.cubic())
}
/// Raise this number to a power of `n`.
///
/// See [RBig::pow] for details.
#[inline]
pub fn pow(&self, n: isize) -> Self {
Self(self.0.pow(n))
}
}
macro_rules! impl_mul_with_relaxed {
(
$a:ident, $b:ident, $c:ident, $d:ident,
$ra:ident, $rb:ident, $rc:ident, $rd:ident, $method:ident
) => {{
let _unused = ($ra, $rb, $rc, $rd);
Relaxed::from_parts($a.$method($c), $b.$method($d))
}};
}
impl_binop_with_macro!(impl Mul for Relaxed, mul, impl_mul_with_relaxed);
impl_binop_assign_by_taking!(impl MulAssign for Relaxed, mul_assign, mul);
macro_rules! impl_mul_int_with_rbig {
(
$a:ident, $b:ident, $i:ident,
$ra:ident, $rb:ident, $ri:ident, $method:ident
) => {{
let _unused = ($ra, $rb, $ri);
let g = $rb.gcd($ri);
RBig(Repr {
numerator: $a.$method($i / &g),
denominator: $b / g,
})
}};
}
impl_binop_with_int!(impl Mul<UBig>, mul, impl_mul_int_with_rbig);
impl_binop_with_int!(impl Mul<IBig>, mul, impl_mul_int_with_rbig);
impl_binop_with_int!(impl Mul for UBig, mul, impl_mul_int_with_rbig);
impl_binop_with_int!(impl Mul for IBig, mul, impl_mul_int_with_rbig);
macro_rules! impl_mul_int_with_relaxed {
(
$a:ident, $b:ident, $i:ident,
$ra:ident, $rb:ident, $ri:ident, $method:ident
) => {{
let _unused = ($ra, $rb, $ri);
Relaxed::from_parts($a.$method($i), $b)
}};
}
impl_binop_with_int!(impl Mul<UBig>, mul, Relaxed, impl_mul_int_with_relaxed);
impl_binop_with_int!(impl Mul<IBig>, mul, Relaxed, impl_mul_int_with_relaxed);
impl_binop_with_int!(impl Mul for UBig, mul, Relaxed, impl_mul_int_with_relaxed);
impl_binop_with_int!(impl Mul for IBig, mul, Relaxed, impl_mul_int_with_relaxed);
#[cfg(test)]
mod tests {
use super::*;
fn r(n: i64, d: u64) -> RBig {
RBig::from_parts(IBig::from(n), UBig::from(d))
}
#[test]
fn pow_non_negative() {
let a = r(2, 3);
assert_eq!(a.pow(0), RBig::ONE);
assert_eq!(a.pow(1), a);
assert_eq!(a.pow(5), r(32, 243));
// zero base with a non-negative exponent is well defined.
assert_eq!(RBig::ZERO.pow(0), RBig::ONE);
assert_eq!(RBig::ZERO.pow(5), RBig::ZERO);
}
#[test]
fn pow_negative_positive_base() {
// (2/3)^-1 = 3/2, (2/3)^-3 = 27/8
let a = r(2, 3);
assert_eq!(a.pow(-1), r(3, 2));
assert_eq!(a.pow(-3), r(27, 8));
// integer-valued base: 5^-1 = 1/5, 5^-2 = 1/25
let five = r(5, 1);
assert_eq!(five.pow(-1), r(1, 5));
assert_eq!(five.pow(-2), r(1, 25));
}
#[test]
fn pow_negative_base() {
let a = r(-2, 3);
// odd exponents keep the sign: (-2/3)^-1 = -3/2, (-2/3)^-3 = -27/8
assert_eq!(a.pow(-1), r(-3, 2));
assert_eq!(a.pow(-3), r(-27, 8));
// even exponents collapse to positive: (-2/3)^-2 = 9/4
assert_eq!(a.pow(-2), r(9, 4));
// reciprocal of an even unsigned power: (-6/35)^-2 = 1225/36, ^-4 = 1500625/1296
let b = r(-6, 35);
assert_eq!(b.pow(-2), r(1225, 36));
assert_eq!(b.pow(-4), r(1_500_625, 1296));
}
#[test]
fn pow_relaxed_matches_rbig() {
let a = r(-2, 3);
for n in [-3isize, -2, -1, 0, 1, 2, 3] {
assert_eq!(a.clone().relax().pow(n).canonicalize(), a.pow(n));
}
// a non-canonical Relaxed (common factor 3) still yields the same value
// after canonicalization.
let relaxed = Relaxed::from_parts(IBig::from(6), UBig::from(9u8));
assert_eq!(relaxed.pow(-1).canonicalize(), r(3, 2));
}
#[test]
#[should_panic(expected = "Divisor or denominator must not be zero")]
fn pow_zero_base_negative_panics() {
let _ = RBig::ZERO.pow(-1);
}
#[test]
#[should_panic(expected = "Divisor or denominator must not be zero")]
fn pow_zero_base_negative_even_panics() {
let _ = RBig::ZERO.pow(-2);
}
}