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
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! Numeric traits for generic mathematics
//!
//! ## Compatibility
//!
//! The `num-traits` crate is tested for rustc 1.8 and greater.

#![doc(html_root_url = "https://docs.rs/num-traits/0.2")]
#![deny(unconditional_recursion)]
#![cfg_attr(all(target_env = "sgx", target_vendor = "mesalock"), feature(rustc_private))]

#![no_std]
#[cfg(all(feature = "std", feature = "mesalock_sgx", not(target_env = "sgx")))]
#[macro_use]
extern crate sgx_tstd as std;
#[cfg(all(feature = "std", feature = "mesalock_sgx", target_env = "sgx"))]
extern crate std;

// Only `no_std` builds actually use `libm`.
#[cfg(all(not(feature = "std"), feature = "libm"))]
extern crate libm;

use core::fmt;
use core::num::Wrapping;
use core::ops::{Add, Div, Mul, Rem, Sub};
use core::ops::{AddAssign, DivAssign, MulAssign, RemAssign, SubAssign};

pub use bounds::Bounded;
#[cfg(any(feature = "std", feature = "libm"))]
pub use float::Float;
pub use float::FloatConst;
// pub use real::{FloatCore, Real}; // NOTE: Don't do this, it breaks `use num_traits::*;`.
pub use cast::{cast, AsPrimitive, FromPrimitive, NumCast, ToPrimitive};
pub use identities::{one, zero, One, Zero};
pub use int::PrimInt;
pub use ops::checked::{
    CheckedAdd, CheckedDiv, CheckedMul, CheckedNeg, CheckedRem, CheckedShl, CheckedShr, CheckedSub,
};
pub use ops::inv::Inv;
pub use ops::mul_add::{MulAdd, MulAddAssign};
pub use ops::saturating::Saturating;
pub use ops::wrapping::{WrappingAdd, WrappingMul, WrappingShl, WrappingShr, WrappingSub};
pub use pow::{checked_pow, pow, Pow};
pub use sign::{abs, abs_sub, signum, Signed, Unsigned};

#[macro_use]
mod macros;

pub mod bounds;
pub mod cast;
pub mod float;
pub mod identities;
pub mod int;
pub mod ops;
pub mod pow;
pub mod real;
pub mod sign;

/// The base trait for numeric types, covering `0` and `1` values,
/// comparisons, basic numeric operations, and string conversion.
pub trait Num: PartialEq + Zero + One + NumOps {
    type FromStrRadixErr;

    /// Convert from a string and radix <= 36.
    ///
    /// # Examples
    ///
    /// ```rust
    /// use num_traits::Num;
    ///
    /// let result = <i32 as Num>::from_str_radix("27", 10);
    /// assert_eq!(result, Ok(27));
    ///
    /// let result = <i32 as Num>::from_str_radix("foo", 10);
    /// assert!(result.is_err());
    /// ```
    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>;
}

/// The trait for types implementing basic numeric operations
///
/// This is automatically implemented for types which implement the operators.
pub trait NumOps<Rhs = Self, Output = Self>:
    Add<Rhs, Output = Output>
    + Sub<Rhs, Output = Output>
    + Mul<Rhs, Output = Output>
    + Div<Rhs, Output = Output>
    + Rem<Rhs, Output = Output>
{
}

impl<T, Rhs, Output> NumOps<Rhs, Output> for T where
    T: Add<Rhs, Output = Output>
        + Sub<Rhs, Output = Output>
        + Mul<Rhs, Output = Output>
        + Div<Rhs, Output = Output>
        + Rem<Rhs, Output = Output>
{
}

/// The trait for `Num` types which also implement numeric operations taking
/// the second operand by reference.
///
/// This is automatically implemented for types which implement the operators.
pub trait NumRef: Num + for<'r> NumOps<&'r Self> {}
impl<T> NumRef for T where T: Num + for<'r> NumOps<&'r T> {}

/// The trait for references which implement numeric operations, taking the
/// second operand either by value or by reference.
///
/// This is automatically implemented for types which implement the operators.
pub trait RefNum<Base>: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}
impl<T, Base> RefNum<Base> for T where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base> {}

/// The trait for types implementing numeric assignment operators (like `+=`).
///
/// This is automatically implemented for types which implement the operators.
pub trait NumAssignOps<Rhs = Self>:
    AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
{
}

impl<T, Rhs> NumAssignOps<Rhs> for T where
    T: AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>
{
}

/// The trait for `Num` types which also implement assignment operators.
///
/// This is automatically implemented for types which implement the operators.
pub trait NumAssign: Num + NumAssignOps {}
impl<T> NumAssign for T where T: Num + NumAssignOps {}

/// The trait for `NumAssign` types which also implement assignment operations
/// taking the second operand by reference.
///
/// This is automatically implemented for types which implement the operators.
pub trait NumAssignRef: NumAssign + for<'r> NumAssignOps<&'r Self> {}
impl<T> NumAssignRef for T where T: NumAssign + for<'r> NumAssignOps<&'r T> {}

macro_rules! int_trait_impl {
    ($name:ident for $($t:ty)*) => ($(
        impl $name for $t {
            type FromStrRadixErr = ::core::num::ParseIntError;
            #[inline]
            fn from_str_radix(s: &str, radix: u32)
                              -> Result<Self, ::core::num::ParseIntError>
            {
                <$t>::from_str_radix(s, radix)
            }
        }
    )*)
}
int_trait_impl!(Num for usize u8 u16 u32 u64 isize i8 i16 i32 i64);
#[cfg(has_i128)]
int_trait_impl!(Num for u128 i128);

impl<T: Num> Num for Wrapping<T>
where
    Wrapping<T>: Add<Output = Wrapping<T>>
        + Sub<Output = Wrapping<T>>
        + Mul<Output = Wrapping<T>>
        + Div<Output = Wrapping<T>>
        + Rem<Output = Wrapping<T>>,
{
    type FromStrRadixErr = T::FromStrRadixErr;
    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
        T::from_str_radix(str, radix).map(Wrapping)
    }
}

#[derive(Debug)]
pub enum FloatErrorKind {
    Empty,
    Invalid,
}
// FIXME: core::num::ParseFloatError is stable in 1.0, but opaque to us,
// so there's not really any way for us to reuse it.
#[derive(Debug)]
pub struct ParseFloatError {
    pub kind: FloatErrorKind,
}

impl fmt::Display for ParseFloatError {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        let description = match self.kind {
            FloatErrorKind::Empty => "cannot parse float from empty string",
            FloatErrorKind::Invalid => "invalid float literal",
        };

        description.fmt(f)
    }
}

// FIXME: The standard library from_str_radix on floats was deprecated, so we're stuck
// with this implementation ourselves until we want to make a breaking change.
// (would have to drop it from `Num` though)
macro_rules! float_trait_impl {
    ($name:ident for $($t:ident)*) => ($(
        impl $name for $t {
            type FromStrRadixErr = ParseFloatError;

            fn from_str_radix(src: &str, radix: u32)
                              -> Result<Self, Self::FromStrRadixErr>
            {
                use self::FloatErrorKind::*;
                use self::ParseFloatError as PFE;

                // Special values
                match src {
                    "inf"   => return Ok(core::$t::INFINITY),
                    "-inf"  => return Ok(core::$t::NEG_INFINITY),
                    "NaN"   => return Ok(core::$t::NAN),
                    _       => {},
                }

                fn slice_shift_char(src: &str) -> Option<(char, &str)> {
                    let mut chars = src.chars();
                    if let Some(ch) = chars.next() {
                        Some((ch, chars.as_str()))
                    } else {
                        None
                    }
                }

                let (is_positive, src) =  match slice_shift_char(src) {
                    None             => return Err(PFE { kind: Empty }),
                    Some(('-', ""))  => return Err(PFE { kind: Empty }),
                    Some(('-', src)) => (false, src),
                    Some((_, _))     => (true,  src),
                };

                // The significand to accumulate
                let mut sig = if is_positive { 0.0 } else { -0.0 };
                // Necessary to detect overflow
                let mut prev_sig = sig;
                let mut cs = src.chars().enumerate();
                // Exponent prefix and exponent index offset
                let mut exp_info = None::<(char, usize)>;

                // Parse the integer part of the significand
                for (i, c) in cs.by_ref() {
                    match c.to_digit(radix) {
                        Some(digit) => {
                            // shift significand one digit left
                            sig = sig * (radix as $t);

                            // add/subtract current digit depending on sign
                            if is_positive {
                                sig = sig + ((digit as isize) as $t);
                            } else {
                                sig = sig - ((digit as isize) as $t);
                            }

                            // Detect overflow by comparing to last value, except
                            // if we've not seen any non-zero digits.
                            if prev_sig != 0.0 {
                                if is_positive && sig <= prev_sig
                                    { return Ok(core::$t::INFINITY); }
                                if !is_positive && sig >= prev_sig
                                    { return Ok(core::$t::NEG_INFINITY); }

                                // Detect overflow by reversing the shift-and-add process
                                if is_positive && (prev_sig != (sig - digit as $t) / radix as $t)
                                    { return Ok(core::$t::INFINITY); }
                                if !is_positive && (prev_sig != (sig + digit as $t) / radix as $t)
                                    { return Ok(core::$t::NEG_INFINITY); }
                            }
                            prev_sig = sig;
                        },
                        None => match c {
                            'e' | 'E' | 'p' | 'P' => {
                                exp_info = Some((c, i + 1));
                                break;  // start of exponent
                            },
                            '.' => {
                                break;  // start of fractional part
                            },
                            _ => {
                                return Err(PFE { kind: Invalid });
                            },
                        },
                    }
                }

                // If we are not yet at the exponent parse the fractional
                // part of the significand
                if exp_info.is_none() {
                    let mut power = 1.0;
                    for (i, c) in cs.by_ref() {
                        match c.to_digit(radix) {
                            Some(digit) => {
                                // Decrease power one order of magnitude
                                power = power / (radix as $t);
                                // add/subtract current digit depending on sign
                                sig = if is_positive {
                                    sig + (digit as $t) * power
                                } else {
                                    sig - (digit as $t) * power
                                };
                                // Detect overflow by comparing to last value
                                if is_positive && sig < prev_sig
                                    { return Ok(core::$t::INFINITY); }
                                if !is_positive && sig > prev_sig
                                    { return Ok(core::$t::NEG_INFINITY); }
                                prev_sig = sig;
                            },
                            None => match c {
                                'e' | 'E' | 'p' | 'P' => {
                                    exp_info = Some((c, i + 1));
                                    break; // start of exponent
                                },
                                _ => {
                                    return Err(PFE { kind: Invalid });
                                },
                            },
                        }
                    }
                }

                // Parse and calculate the exponent
                let exp = match exp_info {
                    Some((c, offset)) => {
                        let base = match c {
                            'E' | 'e' if radix == 10 => 10.0,
                            'P' | 'p' if radix == 16 => 2.0,
                            _ => return Err(PFE { kind: Invalid }),
                        };

                        // Parse the exponent as decimal integer
                        let src = &src[offset..];
                        let (is_positive, exp) = match slice_shift_char(src) {
                            Some(('-', src)) => (false, src.parse::<usize>()),
                            Some(('+', src)) => (true,  src.parse::<usize>()),
                            Some((_, _))     => (true,  src.parse::<usize>()),
                            None             => return Err(PFE { kind: Invalid }),
                        };

                        #[cfg(feature = "std")]
                        fn pow(base: $t, exp: usize) -> $t {
                            Float::powi(base, exp as i32)
                        }
                        // otherwise uses the generic `pow` from the root

                        match (is_positive, exp) {
                            (true,  Ok(exp)) => pow(base, exp),
                            (false, Ok(exp)) => 1.0 / pow(base, exp),
                            (_, Err(_))      => return Err(PFE { kind: Invalid }),
                        }
                    },
                    None => 1.0, // no exponent
                };

                Ok(sig * exp)
            }
        }
    )*)
}
float_trait_impl!(Num for f32 f64);

/// A value bounded by a minimum and a maximum
///
///  If input is less than min then this returns min.
///  If input is greater than max then this returns max.
///  Otherwise this returns input.
///
/// **Panics** in debug mode if `!(min <= max)`.
#[inline]
pub fn clamp<T: PartialOrd>(input: T, min: T, max: T) -> T {
    debug_assert!(min <= max, "min must be less than or equal to max");
    if input < min {
        min
    } else if input > max {
        max
    } else {
        input
    }
}

/// A value bounded by a minimum value
///
///  If input is less than min then this returns min.
///  Otherwise this returns input.
///  `clamp_min(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::min(std::f32::NAN, 1.0)`.
///
/// **Panics** in debug mode if `!(min == min)`. (This occurs if `min` is `NAN`.)
#[inline]
pub fn clamp_min<T: PartialOrd>(input: T, min: T) -> T {
    debug_assert!(min == min, "min must not be NAN");
    if input < min {
        min
    } else {
        input
    }
}

/// A value bounded by a maximum value
///
///  If input is greater than max then this returns max.
///  Otherwise this returns input.
///  `clamp_max(std::f32::NAN, 1.0)` preserves `NAN` different from `f32::max(std::f32::NAN, 1.0)`.
///
/// **Panics** in debug mode if `!(max == max)`. (This occurs if `max` is `NAN`.)
#[inline]
pub fn clamp_max<T: PartialOrd>(input: T, max: T) -> T {
    debug_assert!(max == max, "max must not be NAN");
    if input > max {
        max
    } else {
        input
    }
}

#[test]
fn clamp_test() {
    // Int test
    assert_eq!(1, clamp(1, -1, 2));
    assert_eq!(-1, clamp(-2, -1, 2));
    assert_eq!(2, clamp(3, -1, 2));
    assert_eq!(1, clamp_min(1, -1));
    assert_eq!(-1, clamp_min(-2, -1));
    assert_eq!(-1, clamp_max(1, -1));
    assert_eq!(-2, clamp_max(-2, -1));

    // Float test
    assert_eq!(1.0, clamp(1.0, -1.0, 2.0));
    assert_eq!(-1.0, clamp(-2.0, -1.0, 2.0));
    assert_eq!(2.0, clamp(3.0, -1.0, 2.0));
    assert_eq!(1.0, clamp_min(1.0, -1.0));
    assert_eq!(-1.0, clamp_min(-2.0, -1.0));
    assert_eq!(-1.0, clamp_max(1.0, -1.0));
    assert_eq!(-2.0, clamp_max(-2.0, -1.0));
    assert!(clamp(::core::f32::NAN, -1.0, 1.0).is_nan());
    assert!(clamp_min(::core::f32::NAN, 1.0).is_nan());
    assert!(clamp_max(::core::f32::NAN, 1.0).is_nan());
}

#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_nan_min() {
    clamp(0., ::core::f32::NAN, 1.);
}

#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_nan_max() {
    clamp(0., -1., ::core::f32::NAN);
}

#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_nan_min_max() {
    clamp(0., ::core::f32::NAN, ::core::f32::NAN);
}

#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_min_nan_min() {
    clamp_min(0., ::core::f32::NAN);
}

#[test]
#[should_panic]
#[cfg(debug_assertions)]
fn clamp_max_nan_max() {
    clamp_max(0., ::core::f32::NAN);
}

#[test]
fn from_str_radix_unwrap() {
    // The Result error must impl Debug to allow unwrap()

    let i: i32 = Num::from_str_radix("0", 10).unwrap();
    assert_eq!(i, 0);

    let f: f32 = Num::from_str_radix("0.0", 10).unwrap();
    assert_eq!(f, 0.0);
}

#[test]
fn from_str_radix_multi_byte_fail() {
    // Ensure parsing doesn't panic, even on invalid sign characters
    assert!(f32::from_str_radix("™0.2", 10).is_err());

    // Even when parsing the exponent sign
    assert!(f32::from_str_radix("0.2E™1", 10).is_err());
}

#[test]
fn wrapping_is_num() {
    fn require_num<T: Num>(_: &T) {}
    require_num(&Wrapping(42_u32));
    require_num(&Wrapping(-42));
}

#[test]
fn wrapping_from_str_radix() {
    macro_rules! test_wrapping_from_str_radix {
        ($($t:ty)+) => {
            $(
                for &(s, r) in &[("42", 10), ("42", 2), ("-13.0", 10), ("foo", 10)] {
                    let w = Wrapping::<$t>::from_str_radix(s, r).map(|w| w.0);
                    assert_eq!(w, <$t as Num>::from_str_radix(s, r));
                }
            )+
        };
    }

    test_wrapping_from_str_radix!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
}

#[test]
fn check_num_ops() {
    fn compute<T: Num + Copy>(x: T, y: T) -> T {
        x * y / y % y + y - y
    }
    assert_eq!(compute(1, 2), 1)
}

#[test]
fn check_numref_ops() {
    fn compute<T: NumRef>(x: T, y: &T) -> T {
        x * y / y % y + y - y
    }
    assert_eq!(compute(1, &2), 1)
}

#[test]
fn check_refnum_ops() {
    fn compute<T: Copy>(x: &T, y: T) -> T
    where
        for<'a> &'a T: RefNum<T>,
    {
        &(&(&(&(x * y) / y) % y) + y) - y
    }
    assert_eq!(compute(&1, 2), 1)
}

#[test]
fn check_refref_ops() {
    fn compute<T>(x: &T, y: &T) -> T
    where
        for<'a> &'a T: RefNum<T>,
    {
        &(&(&(&(x * y) / y) % y) + y) - y
    }
    assert_eq!(compute(&1, &2), 1)
}

#[test]
fn check_numassign_ops() {
    fn compute<T: NumAssign + Copy>(mut x: T, y: T) -> T {
        x *= y;
        x /= y;
        x %= y;
        x += y;
        x -= y;
        x
    }
    assert_eq!(compute(1, 2), 1)
}

// TODO test `NumAssignRef`, but even the standard numeric types don't
// implement this yet. (see rust pr41336)