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
//! Fast lexical string-to-float conversion routines.
//!
//! The following benchmarks were run on an "Intel(R) Core(TM) i7-6560U
//! CPU @ 2.20GHz" CPU, on Fedora 28, Linux kernel version 4.18.16-200
//! (x86-64), using the lexical formatter or `x.parse()`,
//! avoiding any inefficiencies in Rust string parsing. The code was
//! compiled with LTO and at an optimization level of 3.
//!
//! The benchmarks with `std` were compiled using "rustc 1.29.2 (17a9dc751
//! 2018-10-05", and the `no_std` benchmarks were compiled using "rustc
//! 1.31.0-nightly (46880f41b 2018-10-15)".
//!
//! The benchmark code may be found `benches/atof.rs`.
//!
//! # Benchmarks
//!
//! | Type  |  lexical (ns/iter) | parse (ns/iter)       | Relative Increase |
//! |:-----:|:------------------:|:---------------------:|:-----------------:|
//! | f32   | 761,670            | 28,650,637            | 37.62x            |
//! | f64   | 1,083,162          | 123,675,824           | 114.18x           |
//!
//! # Raw Benchmarks
//!
//! ```text
//! test f32_lexical ... bench:     761,670 ns/iter (+/- 194,856)
//! test f32_parse   ... bench:  28,650,637 ns/iter (+/- 7,269,036)
//! test f64_lexical ... bench:   1,083,162 ns/iter (+/- 315,101)
//! test f64_parse   ... bench: 123,675,824 ns/iter (+/- 20,924,195)
//! ```
//!
//! Raw Benchmarks (`no_std`)
//!
//! ```text
//! test f32_lexical ... bench:     652,922 ns/iter (+/- 44,491)
//! test f32_parse   ... bench:  24,381,160 ns/iter (+/- 687,175)
//! test f64_lexical ... bench:     835,822 ns/iter (+/- 28,754)
//! test f64_parse   ... bench: 113,449,442 ns/iter (+/- 3,983,104)
//! ```

// Code the generate the benchmark plot:
//  import numpy as np
//  import pandas as pd
//  import matplotlib.pyplot as plt
//  plt.style.use('ggplot')
//  lexical = np.array([761670, 1083162]) / 1e6
//  parse = np.array([28650637, 123675824]) / 1e6
//  index = ["f32", "f64"]
//  df = pd.DataFrame({'lexical': lexical, 'parse': parse}, index = index)
//  ax = df.plot.bar(rot=0)
//  ax.set_ylabel("ms/iter")
//  ax.figure.tight_layout()
//  plt.show()

use sealed::mem;
use sealed::ptr;

use ftoa::exponent_notation_char;
use util::*;

// TRAITS

/// Compatibility trait to allow wrapping arithmetic with atoi.
/// Doesn't really wrap, uses IEE754 float semantics.
trait WrappingFloat: Sized {
    fn wrapping_add(self, rhs: Self) -> Self;
    fn wrapping_mul(self, rhs: Self) -> Self;
}

macro_rules! wrapping_float_impl {
    ($($t:ty)*) => ($(
        impl WrappingFloat for $t {
            #[inline(always)]
            fn wrapping_add(self, rhs: $t) -> $t { self + rhs }

            #[inline(always)]
            fn wrapping_mul(self, rhs: $t) -> $t { self * rhs }
        }
    )*)
}

wrapping_float_impl! { f32 f64 }

// ATOF
// ----

/// Stores temporary state over atof
#[repr(C)]
struct State {
    /// Absolute start position.
    first: *const u8,
    /// Absolute last position.
    last: *const u8,
    /// Current first position.
    curr_first: *const u8,
    /// Current last position.
    curr_last: *const u8,
}

impl State {
    #[inline(always)]
    fn new(first: *const u8, last: *const u8) -> State {
        State {
            first: first,
            last: last,
            curr_first: unsafe { mem::uninitialized() },
            curr_last: unsafe { mem::uninitialized() }
        }
    }
}

#[inline(always)]
unsafe extern "C" fn starts_with_nan(first: *const u8, length: usize)
    -> bool
{
    starts_with(first, length, NAN_STRING.as_ptr(), NAN_STRING.len())
}

#[inline(always)]
unsafe extern "C" fn starts_with_infinity(first: *const u8, length: usize)
    -> bool
{
    starts_with(first, length, INFINITY_STRING.as_ptr(), INFINITY_STRING.len())
}

#[inline(always)]
unsafe extern "C" fn is_zero(first: *const u8, length: usize)
    -> bool
{
    length == 3 && equal_to(first, "0.0".as_ptr(), 3)
}

// ALGORITHM

/// Use powi() iteratively.
///
/// * `value`   - Base value.
/// * `op`      - Operation {*, /}.
/// * `base`    - Floating-point base for exponent.
/// * `exp`     - Iteration exponent {+256, -256}.
/// * `count`   - Number of times to iterate.
/// * `rem`     - Remaining exponent after iteration.
macro_rules! stable_powi_impl {
    ($value:ident, $op:tt, $base:ident, $exp:expr, $count:ident, $rem:ident) => ({
        for _ in 0..$count {
            $value = $value $op powi($base, $exp);
        }
        if $rem != 0 {
            $value = $value $op powi($base, $rem)
        }
        $value
    })
}

/// Cached powers to get the desired exponent.
/// Make sure all values are < 1e300.
const POWI_EXPONENTS: [i32; 35] = [512, 512, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128];

/// Stable powi implementation, with a base value.
///
/// Although valid results will occur with an exponent or value of 0,
/// ideally, you should not pass any value as such to this function.
///
/// Use powi() with an integral exponent, both for speed and
/// stability. Don't go any an exponent of magnitude >1e300, for numerical
/// stability.
macro_rules! stable_powi {
    ($value:ident, $op:tt, $base:ident, $exponent:ident) => ({
        let base = $base as f64;
        let exp = unsafe { *POWI_EXPONENTS.get_unchecked($base as usize) };
        if $exponent < 0 {
            // negative exponent
            let count = $exponent / -exp;
            let rem = $exponent % exp;
            stable_powi_impl!($value, $op, base, -exp, count, rem)
        } else {
            // positive exponent
            let count = $exponent / exp;
            let rem = $exponent % exp;
            stable_powi_impl!($value, $op, base, exp, count, rem)
        }
    })
}

/// `powi` implementation that is more stable at extremely low powers.
///
/// Equivalent to `value * powi(base, exponent)`
pub(crate) fn stable_powi_multiplier(mut value: f64, base: u64, exponent: i32) -> f64 {
    stable_powi!(value, *, base, exponent)
}

/// `powi` implementation that is more stable at extremely low powers.
///
/// Equivalent to `value / powi(base, exponent)`
pub(crate) fn stable_powi_divisor(mut value: f64, base: u64, exponent: i32) -> f64 {
    stable_powi!(value, /, base, exponent)
}

// Calculate the integer portion.
// Use a float since for large numbers, this may even overflow an
// integer 64.
#[inline(always)]
unsafe extern "C" fn calculate_integer(s: &mut State, base: u64) -> f64 {
    let mut integer: f64 = 0.0;
    s.curr_last = atoi_pointer!(integer, s.first, s.last, base, f64);
    integer
}

// Calculate the fraction portion.
// Calculate separately from the integer portion, since the small
// values for each may be too small to change the integer components
// representation **immediately**.
// For numeric stability, use this early.
#[inline(always)]
unsafe extern "C" fn calculate_fraction(s: &mut State, base: u64, sig: usize) -> f64 {
    let mut fraction: f64 = 0.0;
    // Ensure if there's a decimal, there are trailing values, so
    // invalid floats like "0." lead to an error.
    if distance(s.curr_last, s.last) > 1 && *s.curr_last == b'.' {
        let mut digits: usize = 0;
        s.curr_last = s.curr_last.add(1);
        loop {
            // This would get better numerical precision using Horner's method,
            // but that would require.
            let mut value: u64 = 0;
            s.curr_first = s.curr_last;
            s.curr_last = minv!(s.last, s.curr_first.add(sig));
            s.curr_last = atoi_pointer!(value, s.curr_first, s.curr_last, base, u64);
            digits += distance(s.curr_first, s.curr_last);

            // Ignore leading 0s, just not we've passed them.
            if value != 0 {
                fraction += stable_powi_divisor(value as f64, base, digits as i32);
            }

            // do/while condition
            if s.curr_last == s.last || char_to_digit!(*s.curr_last) as u64 >= base {
                break;
            }
        }
    }

    fraction
}

// Calculate the exponential portion, if
// we have an `e[+-]?\d+`.
// We don't care about the pointer after this, so just use `atoi_value`.
#[inline(always)]
unsafe extern "C" fn calculate_exponent(s: &mut State, base: u64) -> i32 {
    let dist = distance(s.curr_last, s.last);
    if dist > 1 && (*s.curr_last).to_ascii_lowercase() == exponent_notation_char(base) {
        s.curr_last = s.curr_last.add(1);
        s.curr_first = s.curr_last;
        s.curr_last = s.last;
        let (value, p) = atoi_signed!(s.curr_first, s.curr_last, base, i32);
        s.curr_last = p;
        value
    } else {
        0
    }
}

/// Calculate value from pieces.
#[inline(always)]
unsafe extern "C" fn calculate_value(integer: f64, fraction: f64, exponent: i32, base: u64)
    -> f64
{
    let mut value = integer + fraction;
    if exponent != 0 && value != 0.0 {
        value = stable_powi_multiplier(value, base, exponent);
    }
    value
}

// ATOF

/// Implied atof for non-special (no NaN or Infinity) numbers.
///
/// Allows a custom quad type (if enabled) to be passed for higher-precision
/// calculations.
macro_rules! atof_finite {
    ($first:expr, $last:expr, $base:expr, $sig:expr) => ({
        let mut s = State::new($first, $last);
        let integer = calculate_integer(&mut s, $base);
        let fraction = calculate_fraction(&mut s, $base, $sig);
        let exponent = calculate_exponent(&mut s, $base);
        let value = calculate_value(integer, fraction, exponent, $base);
        (value, s.curr_last)
    })
}

/// Convert string to float (must be called within an unsafe block).
macro_rules! atof_value {
    ($first:expr, $last:expr, $base:expr, $sig:expr, $nan:ident, $inf:ident) => ({
        // special case checks
        let length = distance($first, $last);
        if starts_with_nan($first, length) {
            return ($nan, $first.add(NAN_STRING.len()));
        } else if starts_with_infinity($first, length) {
            return ($inf, $first.add(INFINITY_STRING.len()));
        } else if is_zero($first, length) {
            return (0.0, $first.add(3));
        }

        atof_finite!($first, $last, $base, $sig)
    })
}

/// Sanitizer for string to float (must be called within an unsafe block).
macro_rules! atof {
    ($first:expr, $last:expr, $base:expr, $sig:expr, $nan:ident, $inf:ident) => ({
        if $first == $last {
            (0.0, ptr::null())
        } else if *$first == b'-' {
            let(value, p) = atof_value!($first.add(1), $last, $base, $sig, $nan, $inf);
            (-value, p)
        } else if *$first == b'+' {
            atof_value!($first.add(1), $last, $base, $sig, $nan, $inf)
        } else {
            atof_value!($first, $last, $base, $sig, $nan, $inf)
        }
    })
}

// UNSAFE API

/// Generate the unsafe public wrappers.
///
/// * `func`        Function name.
/// * `sig`         Significand step for exponent.
/// * `f`           Float type.
/// * `nan`         NaN literal.
/// * `inf`         Infinity literal.
macro_rules! unsafe_impl {
    ($func:ident, $sig:expr, $f:ty, $nan:ident, $inf:ident) => (
        /// Unsafe, C-like importer for signed numbers.
        #[inline]
        pub unsafe extern "C" fn $func(
            first: *const u8,
            last: *const u8,
            base: u8
        )
            -> ($f, *const u8)
        {
            let (value, p) = atof!(first, last, base as u64, $sig, $nan, $inf);
            (value as $f, p)
        }
    )
}

unsafe_impl!(atof32_unsafe, 6, f32, F32_NAN, F32_INFINITY);
unsafe_impl!(atof64_unsafe, 12, f64, F64_NAN, F64_INFINITY);

// LOW-LEVEL API

bytes_impl!(atof32_bytes, f32, atof32_unsafe);
bytes_impl!(atof64_bytes, f64, atof64_unsafe);
try_bytes_impl!(try_atof32_bytes, f32, atof32_unsafe);
try_bytes_impl!(try_atof64_bytes, f64, atof64_unsafe);

// TESTS
// -----

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn atof32_base10_test() {
        // integer test
        assert_relative_eq!(0.0, atof32_bytes(b"0", 10), epsilon=1e-20);
        assert_relative_eq!(1.0, atof32_bytes(b"1", 10), epsilon=1e-20);
        assert_relative_eq!(12.0, atof32_bytes(b"12", 10), epsilon=1e-20);
        assert_relative_eq!(123.0, atof32_bytes(b"123", 10), epsilon=1e-20);
        assert_relative_eq!(1234.0, atof32_bytes(b"1234", 10), epsilon=1e-20);
        assert_relative_eq!(12345.0, atof32_bytes(b"12345", 10), epsilon=1e-20);
        assert_relative_eq!(123456.0, atof32_bytes(b"123456", 10), epsilon=1e-20);
        assert_relative_eq!(1234567.0, atof32_bytes(b"1234567", 10), epsilon=1e-20);
        assert_relative_eq!(12345678.0, atof32_bytes(b"12345678", 10), epsilon=1e-20);

        // decimal test
        assert_relative_eq!(123.1, atof32_bytes(b"123.1", 10), epsilon=1e-20);
        assert_relative_eq!(123.12, atof32_bytes(b"123.12", 10), epsilon=1e-20);
        assert_relative_eq!(123.123, atof32_bytes(b"123.123", 10), epsilon=1e-20);
        assert_relative_eq!(123.1234, atof32_bytes(b"123.1234", 10), epsilon=1e-20);
        assert_relative_eq!(123.12345, atof32_bytes(b"123.12345", 10), epsilon=1e-20);

        // rounding test
        assert_relative_eq!(123456790.0, atof32_bytes(b"123456789", 10), epsilon=1e-20);
        assert_relative_eq!(123456790.0, atof32_bytes(b"123456789.1", 10), epsilon=1e-20);
        assert_relative_eq!(123456790.0, atof32_bytes(b"123456789.12", 10), epsilon=1e-20);
        assert_relative_eq!(123456790.0, atof32_bytes(b"123456789.123", 10), epsilon=1e-20);
        assert_relative_eq!(123456790.0, atof32_bytes(b"123456789.1234", 10), epsilon=1e-20);
        assert_relative_eq!(123456790.0, atof32_bytes(b"123456789.12345", 10), epsilon=1e-20);

        // exponent test
        assert_relative_eq!(123456789.12345, atof32_bytes(b"1.2345678912345e8", 10), epsilon=1e-20);
        assert_relative_eq!(123450000.0, atof32_bytes(b"1.2345e+8", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e+11, atof32_bytes(b"1.2345e+11", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e+11, atof32_bytes(b"123450000000", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e+38, atof32_bytes(b"1.2345e+38", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e+38, atof32_bytes(b"123450000000000000000000000000000000000", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e-8, atof32_bytes(b"1.2345e-8", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e-8, atof32_bytes(b"0.000000012345", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e-38, atof32_bytes(b"1.2345e-38", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e-38, atof32_bytes(b"0.000000000000000000000000000000000000012345", 10), epsilon=1e-20);

        #[cfg(feature = "std")]
        assert!(atof32_bytes(b"NaN", 10).is_nan());
        assert!(atof32_bytes(b"inf", 10).is_infinite());
        assert!(atof32_bytes(b"+inf", 10).is_infinite());
        assert!(atof32_bytes(b"-inf", 10).is_infinite());
    }

    #[test]
    fn atof32_basen_test() {
        assert_relative_eq!(1234.0, atof32_bytes(b"YA", 36));
    }

    #[test]
    fn atof64_base10_test() {
        // integer test
        assert_relative_eq!(0.0, atof64_bytes(b"0", 10), epsilon=1e-20);
        assert_relative_eq!(1.0, atof64_bytes(b"1", 10), epsilon=1e-20);
        assert_relative_eq!(12.0, atof64_bytes(b"12", 10), epsilon=1e-20);
        assert_relative_eq!(123.0, atof64_bytes(b"123", 10), epsilon=1e-20);
        assert_relative_eq!(1234.0, atof64_bytes(b"1234", 10), epsilon=1e-20);
        assert_relative_eq!(12345.0, atof64_bytes(b"12345", 10), epsilon=1e-20);
        assert_relative_eq!(123456.0, atof64_bytes(b"123456", 10), epsilon=1e-20);
        assert_relative_eq!(1234567.0, atof64_bytes(b"1234567", 10), epsilon=1e-20);
        assert_relative_eq!(12345678.0, atof64_bytes(b"12345678", 10), epsilon=1e-20);

        // decimal test
        assert_relative_eq!(123456789.0, atof64_bytes(b"123456789", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.1, atof64_bytes(b"123456789.1", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.12, atof64_bytes(b"123456789.12", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.123, atof64_bytes(b"123456789.123", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.1234, atof64_bytes(b"123456789.1234", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.12345, atof64_bytes(b"123456789.12345", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.123456, atof64_bytes(b"123456789.123456", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.1234567, atof64_bytes(b"123456789.1234567", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.12345678, atof64_bytes(b"123456789.12345678", 10), epsilon=1e-20);

        // rounding test
        assert_relative_eq!(123456789.12345679, atof64_bytes(b"123456789.123456789", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.12345679, atof64_bytes(b"123456789.1234567890", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.12345679, atof64_bytes(b"123456789.123456789012", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.12345679, atof64_bytes(b"123456789.1234567890123", 10), epsilon=1e-20);
        assert_relative_eq!(123456789.12345679, atof64_bytes(b"123456789.12345678901234", 10), epsilon=1e-20);

        // exponent test
        assert_relative_eq!(123456789.12345, atof64_bytes(b"1.2345678912345e8", 10), epsilon=1e-20);
        assert_relative_eq!(123450000.0, atof64_bytes(b"1.2345e+8", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e+11, atof64_bytes(b"123450000000", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e+11, atof64_bytes(b"1.2345e+11", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e+38, atof64_bytes(b"1.2345e+38", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e+38, atof64_bytes(b"123450000000000000000000000000000000000", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e+308, atof64_bytes(b"1.2345e+308", 10), max_relative=1e-12);
        assert_relative_eq!(1.2345e+308, atof64_bytes(b"123450000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", 10), max_relative=1e-12);
        assert_relative_eq!(0.000000012345, atof64_bytes(b"1.2345e-8", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e-8, atof64_bytes(b"0.000000012345", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e-38, atof64_bytes(b"1.2345e-38", 10), epsilon=1e-20);
        assert_relative_eq!(1.2345e-38, atof64_bytes(b"0.000000000000000000000000000000000000012345", 10), epsilon=1e-20);

        // denormalized (try extremely low values)
        assert_relative_eq!(1.2345e-308, atof64_bytes(b"1.2345e-308", 10), epsilon=1e-20);
        assert_eq!(5e-322, atof64_bytes(b"5e-322", 10));
        assert_eq!(5e-323, atof64_bytes(b"5e-323", 10));
        assert_eq!(5e-324, atof64_bytes(b"5e-324", 10));
        // due to issues in how the data is parsed, manually extracting
        // non-exponents of 1.<e-299 is prone to error
        // test the limit of our ability
        // We tend to get relative errors of 1e-16, even at super low values.
        assert_relative_eq!(1.2345e-299, atof64_bytes(b"0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012345", 10), epsilon=1e-314);

        // Keep pushing from -300 to -324
        assert_relative_eq!(1.2345e-300, atof64_bytes(b"0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012345", 10), epsilon=1e-315);
        assert_relative_eq!(1.2345e-310, atof64_bytes(b"0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012345", 10), epsilon=5e-324);
        assert_relative_eq!(1.2345e-320, atof64_bytes(b"0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012345", 10), epsilon=5e-324);
        assert_relative_eq!(1.2345e-321, atof64_bytes(b"0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012345", 10), epsilon=5e-324);
        assert_relative_eq!(1.24e-322, atof64_bytes(b"0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000124", 10), epsilon=5e-324);
        assert_eq!(1e-323, atof64_bytes(b"0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", 10));
        assert_eq!(5e-324, atof64_bytes(b"0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000005", 10));

        #[cfg(feature = "std")]
        assert!(atof64_bytes(b"NaN", 10).is_nan());
        assert!(atof64_bytes(b"inf", 10).is_infinite());
        assert!(atof64_bytes(b"+inf", 10).is_infinite());
        assert!(atof64_bytes(b"-inf", 10).is_infinite());
    }

    #[test]
    #[should_panic]
    fn limit_test() {
        assert_relative_eq!(1.2345e-320, 0.0, epsilon=5e-324);
    }

    #[test]
    fn atof64_basen_test() {
        assert_relative_eq!(1234.0, atof64_bytes(b"YA", 36));
    }

    #[test]
    fn try_atof32_base10_test() {
        assert_eq!(Err(0), try_atof32_bytes(b"", 10));
        assert_eq!(Ok(0.0), try_atof32_bytes(b"0.0", 10));
        assert_eq!(Err(1), try_atof32_bytes(b"1a", 10));
    }

    #[test]
    fn try_atof64_base10_test() {
        assert_eq!(Err(0), try_atof64_bytes(b"", 10));
        assert_eq!(Ok(0.0), try_atof64_bytes(b"0.0", 10));
        assert_eq!(Err(1), try_atof64_bytes(b"1a", 10));
    }
}