core/num/
f128.rs

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
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
//! Constants for the `f128` quadruple-precision floating point type.
//!
//! *[See also the `f128` primitive type][f128].*
//!
//! Mathematically significant numbers are provided in the `consts` sub-module.
//!
//! For the constants defined directly in this module
//! (as distinct from those defined in the `consts` sub-module),
//! new code should instead use the associated constants
//! defined directly on the `f128` type.

#![unstable(feature = "f128", issue = "116909")]

use crate::convert::FloatToInt;
#[cfg(not(test))]
use crate::intrinsics;
use crate::mem;
use crate::num::FpCategory;

/// Basic mathematical constants.
#[unstable(feature = "f128", issue = "116909")]
pub mod consts {
    // FIXME: replace with mathematical constants from cmath.

    /// Archimedes' constant (π)
    #[unstable(feature = "f128", issue = "116909")]
    pub const PI: f128 = 3.14159265358979323846264338327950288419716939937510582097494_f128;

    /// The full circle constant (τ)
    ///
    /// Equal to 2π.
    #[unstable(feature = "f128", issue = "116909")]
    pub const TAU: f128 = 6.28318530717958647692528676655900576839433879875021164194989_f128;

    /// The golden ratio (φ)
    #[unstable(feature = "f128", issue = "116909")]
    // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
    pub const PHI: f128 = 1.61803398874989484820458683436563811772030917980576286213545_f128;

    /// The Euler-Mascheroni constant (γ)
    #[unstable(feature = "f128", issue = "116909")]
    // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
    pub const EGAMMA: f128 = 0.577215664901532860606512090082402431042159335939923598805767_f128;

    /// π/2
    #[unstable(feature = "f128", issue = "116909")]
    pub const FRAC_PI_2: f128 = 1.57079632679489661923132169163975144209858469968755291048747_f128;

    /// π/3
    #[unstable(feature = "f128", issue = "116909")]
    pub const FRAC_PI_3: f128 = 1.04719755119659774615421446109316762806572313312503527365831_f128;

    /// π/4
    #[unstable(feature = "f128", issue = "116909")]
    pub const FRAC_PI_4: f128 = 0.785398163397448309615660845819875721049292349843776455243736_f128;

    /// π/6
    #[unstable(feature = "f128", issue = "116909")]
    pub const FRAC_PI_6: f128 = 0.523598775598298873077107230546583814032861566562517636829157_f128;

    /// π/8
    #[unstable(feature = "f128", issue = "116909")]
    pub const FRAC_PI_8: f128 = 0.392699081698724154807830422909937860524646174921888227621868_f128;

    /// 1/π
    #[unstable(feature = "f128", issue = "116909")]
    pub const FRAC_1_PI: f128 = 0.318309886183790671537767526745028724068919291480912897495335_f128;

    /// 1/sqrt(π)
    #[unstable(feature = "f128", issue = "116909")]
    // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
    pub const FRAC_1_SQRT_PI: f128 =
        0.564189583547756286948079451560772585844050629328998856844086_f128;

    /// 1/sqrt(2π)
    #[doc(alias = "FRAC_1_SQRT_TAU")]
    #[unstable(feature = "f128", issue = "116909")]
    // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
    pub const FRAC_1_SQRT_2PI: f128 =
        0.398942280401432677939946059934381868475858631164934657665926_f128;

    /// 2/π
    #[unstable(feature = "f128", issue = "116909")]
    pub const FRAC_2_PI: f128 = 0.636619772367581343075535053490057448137838582961825794990669_f128;

    /// 2/sqrt(π)
    #[unstable(feature = "f128", issue = "116909")]
    pub const FRAC_2_SQRT_PI: f128 =
        1.12837916709551257389615890312154517168810125865799771368817_f128;

    /// sqrt(2)
    #[unstable(feature = "f128", issue = "116909")]
    pub const SQRT_2: f128 = 1.41421356237309504880168872420969807856967187537694807317668_f128;

    /// 1/sqrt(2)
    #[unstable(feature = "f128", issue = "116909")]
    pub const FRAC_1_SQRT_2: f128 =
        0.707106781186547524400844362104849039284835937688474036588340_f128;

    /// sqrt(3)
    #[unstable(feature = "f128", issue = "116909")]
    // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
    pub const SQRT_3: f128 = 1.73205080756887729352744634150587236694280525381038062805581_f128;

    /// 1/sqrt(3)
    #[unstable(feature = "f128", issue = "116909")]
    // Also, #[unstable(feature = "more_float_constants", issue = "103883")]
    pub const FRAC_1_SQRT_3: f128 =
        0.577350269189625764509148780501957455647601751270126876018602_f128;

    /// Euler's number (e)
    #[unstable(feature = "f128", issue = "116909")]
    pub const E: f128 = 2.71828182845904523536028747135266249775724709369995957496697_f128;

    /// log<sub>2</sub>(10)
    #[unstable(feature = "f128", issue = "116909")]
    pub const LOG2_10: f128 = 3.32192809488736234787031942948939017586483139302458061205476_f128;

    /// log<sub>2</sub>(e)
    #[unstable(feature = "f128", issue = "116909")]
    pub const LOG2_E: f128 = 1.44269504088896340735992468100189213742664595415298593413545_f128;

    /// log<sub>10</sub>(2)
    #[unstable(feature = "f128", issue = "116909")]
    pub const LOG10_2: f128 = 0.301029995663981195213738894724493026768189881462108541310427_f128;

    /// log<sub>10</sub>(e)
    #[unstable(feature = "f128", issue = "116909")]
    pub const LOG10_E: f128 = 0.434294481903251827651128918916605082294397005803666566114454_f128;

    /// ln(2)
    #[unstable(feature = "f128", issue = "116909")]
    pub const LN_2: f128 = 0.693147180559945309417232121458176568075500134360255254120680_f128;

    /// ln(10)
    #[unstable(feature = "f128", issue = "116909")]
    pub const LN_10: f128 = 2.30258509299404568401799145468436420760110148862877297603333_f128;
}

#[cfg(not(test))]
impl f128 {
    // FIXME(f16_f128): almost all methods in this `impl` are missing examples and a const
    // implementation. Add these once we can run code on all platforms and have f16/f128 in CTFE.

    /// The radix or base of the internal representation of `f128`.
    #[unstable(feature = "f128", issue = "116909")]
    pub const RADIX: u32 = 2;

    /// Number of significant digits in base 2.
    #[unstable(feature = "f128", issue = "116909")]
    pub const MANTISSA_DIGITS: u32 = 113;

    /// Approximate number of significant digits in base 10.
    ///
    /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
    /// significant digits can be converted to `f128` and back without loss.
    ///
    /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
    ///
    /// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS
    #[unstable(feature = "f128", issue = "116909")]
    pub const DIGITS: u32 = 33;

    /// [Machine epsilon] value for `f128`.
    ///
    /// This is the difference between `1.0` and the next larger representable number.
    ///
    /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
    ///
    /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
    /// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS
    #[unstable(feature = "f128", issue = "116909")]
    pub const EPSILON: f128 = 1.92592994438723585305597794258492732e-34_f128;

    /// Smallest finite `f128` value.
    ///
    /// Equal to &minus;[`MAX`].
    ///
    /// [`MAX`]: f128::MAX
    #[unstable(feature = "f128", issue = "116909")]
    pub const MIN: f128 = -1.18973149535723176508575932662800702e+4932_f128;
    /// Smallest positive normal `f128` value.
    ///
    /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
    ///
    /// [`MIN_EXP`]: f128::MIN_EXP
    #[unstable(feature = "f128", issue = "116909")]
    pub const MIN_POSITIVE: f128 = 3.36210314311209350626267781732175260e-4932_f128;
    /// Largest finite `f128` value.
    ///
    /// Equal to
    /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
    ///
    /// [`MANTISSA_DIGITS`]: f128::MANTISSA_DIGITS
    /// [`MAX_EXP`]: f128::MAX_EXP
    #[unstable(feature = "f128", issue = "116909")]
    pub const MAX: f128 = 1.18973149535723176508575932662800702e+4932_f128;

    /// One greater than the minimum possible normal power of 2 exponent.
    ///
    /// If <i>x</i>&nbsp;=&nbsp;`MIN_EXP`, then normal numbers
    /// ≥&nbsp;0.5&nbsp;×&nbsp;2<sup><i>x</i></sup>.
    #[unstable(feature = "f128", issue = "116909")]
    pub const MIN_EXP: i32 = -16_381;
    /// Maximum possible power of 2 exponent.
    ///
    /// If <i>x</i>&nbsp;=&nbsp;`MAX_EXP`, then normal numbers
    /// &lt;&nbsp;1&nbsp;×&nbsp;2<sup><i>x</i></sup>.
    #[unstable(feature = "f128", issue = "116909")]
    pub const MAX_EXP: i32 = 16_384;

    /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
    ///
    /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
    ///
    /// [`MIN_POSITIVE`]: f128::MIN_POSITIVE
    #[unstable(feature = "f128", issue = "116909")]
    pub const MIN_10_EXP: i32 = -4_931;
    /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
    ///
    /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
    ///
    /// [`MAX`]: f128::MAX
    #[unstable(feature = "f128", issue = "116909")]
    pub const MAX_10_EXP: i32 = 4_932;

    /// Not a Number (NaN).
    ///
    /// Note that IEEE 754 doesn't define just a single NaN value;
    /// a plethora of bit patterns are considered to be NaN.
    /// Furthermore, the standard makes a difference
    /// between a "signaling" and a "quiet" NaN,
    /// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
    /// This constant isn't guaranteed to equal to any specific NaN bitpattern,
    /// and the stability of its representation over Rust versions
    /// and target platforms isn't guaranteed.
    #[allow(clippy::eq_op)]
    #[rustc_diagnostic_item = "f128_nan"]
    #[unstable(feature = "f128", issue = "116909")]
    pub const NAN: f128 = 0.0_f128 / 0.0_f128;

    /// Infinity (∞).
    #[unstable(feature = "f128", issue = "116909")]
    pub const INFINITY: f128 = 1.0_f128 / 0.0_f128;

    /// Negative infinity (−∞).
    #[unstable(feature = "f128", issue = "116909")]
    pub const NEG_INFINITY: f128 = -1.0_f128 / 0.0_f128;

    /// Sign bit
    pub(crate) const SIGN_MASK: u128 = 0x8000_0000_0000_0000_0000_0000_0000_0000;

    /// Exponent mask
    pub(crate) const EXP_MASK: u128 = 0x7fff_0000_0000_0000_0000_0000_0000_0000;

    /// Mantissa mask
    pub(crate) const MAN_MASK: u128 = 0x0000_ffff_ffff_ffff_ffff_ffff_ffff_ffff;

    /// Minimum representable positive value (min subnormal)
    const TINY_BITS: u128 = 0x1;

    /// Minimum representable negative value (min negative subnormal)
    const NEG_TINY_BITS: u128 = Self::TINY_BITS | Self::SIGN_MASK;

    /// Returns `true` if this value is NaN.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `unordtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let nan = f128::NAN;
    /// let f = 7.0_f128;
    ///
    /// assert!(nan.is_nan());
    /// assert!(!f.is_nan());
    /// # }
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
    pub const fn is_nan(self) -> bool {
        self != self
    }

    // FIXME(#50145): `abs` is publicly unavailable in core due to
    // concerns about portability, so this implementation is for
    // private use internally.
    #[inline]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub(crate) const fn abs_private(self) -> f128 {
        // SAFETY: This transmutation is fine just like in `to_bits`/`from_bits`.
        unsafe {
            mem::transmute::<u128, f128>(mem::transmute::<f128, u128>(self) & !Self::SIGN_MASK)
        }
    }

    /// Returns `true` if this value is positive infinity or negative infinity, and
    /// `false` otherwise.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let f = 7.0f128;
    /// let inf = f128::INFINITY;
    /// let neg_inf = f128::NEG_INFINITY;
    /// let nan = f128::NAN;
    ///
    /// assert!(!f.is_infinite());
    /// assert!(!nan.is_infinite());
    ///
    /// assert!(inf.is_infinite());
    /// assert!(neg_inf.is_infinite());
    /// # }
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub const fn is_infinite(self) -> bool {
        (self == f128::INFINITY) | (self == f128::NEG_INFINITY)
    }

    /// Returns `true` if this number is neither infinite nor NaN.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `lttf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let f = 7.0f128;
    /// let inf: f128 = f128::INFINITY;
    /// let neg_inf: f128 = f128::NEG_INFINITY;
    /// let nan: f128 = f128::NAN;
    ///
    /// assert!(f.is_finite());
    ///
    /// assert!(!nan.is_finite());
    /// assert!(!inf.is_finite());
    /// assert!(!neg_inf.is_finite());
    /// # }
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub const fn is_finite(self) -> bool {
        // There's no need to handle NaN separately: if self is NaN,
        // the comparison is not true, exactly as desired.
        self.abs_private() < Self::INFINITY
    }

    /// Returns `true` if the number is [subnormal].
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128
    /// let max = f128::MAX;
    /// let lower_than_min = 1.0e-4960_f128;
    /// let zero = 0.0_f128;
    ///
    /// assert!(!min.is_subnormal());
    /// assert!(!max.is_subnormal());
    ///
    /// assert!(!zero.is_subnormal());
    /// assert!(!f128::NAN.is_subnormal());
    /// assert!(!f128::INFINITY.is_subnormal());
    /// // Values between `0` and `min` are Subnormal.
    /// assert!(lower_than_min.is_subnormal());
    /// # }
    /// ```
    ///
    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub const fn is_subnormal(self) -> bool {
        matches!(self.classify(), FpCategory::Subnormal)
    }

    /// Returns `true` if the number is neither zero, infinite, [subnormal], or NaN.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128
    /// let max = f128::MAX;
    /// let lower_than_min = 1.0e-4960_f128;
    /// let zero = 0.0_f128;
    ///
    /// assert!(min.is_normal());
    /// assert!(max.is_normal());
    ///
    /// assert!(!zero.is_normal());
    /// assert!(!f128::NAN.is_normal());
    /// assert!(!f128::INFINITY.is_normal());
    /// // Values between `0` and `min` are Subnormal.
    /// assert!(!lower_than_min.is_normal());
    /// # }
    /// ```
    ///
    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub const fn is_normal(self) -> bool {
        matches!(self.classify(), FpCategory::Normal)
    }

    /// Returns the floating point category of the number. If only one property
    /// is going to be tested, it is generally faster to use the specific
    /// predicate instead.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// use std::num::FpCategory;
    ///
    /// let num = 12.4_f128;
    /// let inf = f128::INFINITY;
    ///
    /// assert_eq!(num.classify(), FpCategory::Normal);
    /// assert_eq!(inf.classify(), FpCategory::Infinite);
    /// # }
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub const fn classify(self) -> FpCategory {
        let bits = self.to_bits();
        match (bits & Self::MAN_MASK, bits & Self::EXP_MASK) {
            (0, Self::EXP_MASK) => FpCategory::Infinite,
            (_, Self::EXP_MASK) => FpCategory::Nan,
            (0, 0) => FpCategory::Zero,
            (_, 0) => FpCategory::Subnormal,
            _ => FpCategory::Normal,
        }
    }

    /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
    /// positive sign bit and positive infinity.
    ///
    /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
    /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
    /// conserved over arithmetic operations, the result of `is_sign_positive` on
    /// a NaN might produce an unexpected or non-portable result. See the [specification
    /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
    /// if you need fully portable behavior (will return `false` for all NaNs).
    ///
    /// ```
    /// #![feature(f128)]
    ///
    /// let f = 7.0_f128;
    /// let g = -7.0_f128;
    ///
    /// assert!(f.is_sign_positive());
    /// assert!(!g.is_sign_positive());
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    pub fn is_sign_positive(self) -> bool {
        !self.is_sign_negative()
    }

    /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
    /// negative sign bit and negative infinity.
    ///
    /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
    /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
    /// conserved over arithmetic operations, the result of `is_sign_negative` on
    /// a NaN might produce an unexpected or non-portable result. See the [specification
    /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
    /// if you need fully portable behavior (will return `false` for all NaNs).
    ///
    /// ```
    /// #![feature(f128)]
    ///
    /// let f = 7.0_f128;
    /// let g = -7.0_f128;
    ///
    /// assert!(!f.is_sign_negative());
    /// assert!(g.is_sign_negative());
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    pub fn is_sign_negative(self) -> bool {
        // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
        // applies to zeros and NaNs as well.
        // SAFETY: This is just transmuting to get the sign bit, it's fine.
        (self.to_bits() & (1 << 127)) != 0
    }

    /// Returns the least number greater than `self`.
    ///
    /// Let `TINY` be the smallest representable positive `f128`. Then,
    ///  - if `self.is_nan()`, this returns `self`;
    ///  - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
    ///  - if `self` is `-TINY`, this returns -0.0;
    ///  - if `self` is -0.0 or +0.0, this returns `TINY`;
    ///  - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
    ///  - otherwise the unique least value greater than `self` is returned.
    ///
    /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
    /// is finite `x == x.next_up().next_down()` also holds.
    ///
    /// ```rust
    /// #![feature(f128)]
    /// #![feature(float_next_up_down)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// // f128::EPSILON is the difference between 1.0 and the next number up.
    /// assert_eq!(1.0f128.next_up(), 1.0 + f128::EPSILON);
    /// // But not for most numbers.
    /// assert!(0.1f128.next_up() < 0.1 + f128::EPSILON);
    /// assert_eq!(4611686018427387904f128.next_up(), 4611686018427387904.000000000000001);
    /// # }
    /// ```
    ///
    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
    /// [`INFINITY`]: Self::INFINITY
    /// [`MIN`]: Self::MIN
    /// [`MAX`]: Self::MAX
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    // #[unstable(feature = "float_next_up_down", issue = "91399")]
    pub fn next_up(self) -> Self {
        // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
        // denormals to zero. This is in general unsound and unsupported, but here
        // we do our best to still produce the correct result on such targets.
        let bits = self.to_bits();
        if self.is_nan() || bits == Self::INFINITY.to_bits() {
            return self;
        }

        let abs = bits & !Self::SIGN_MASK;
        let next_bits = if abs == 0 {
            Self::TINY_BITS
        } else if bits == abs {
            bits + 1
        } else {
            bits - 1
        };
        Self::from_bits(next_bits)
    }

    /// Returns the greatest number less than `self`.
    ///
    /// Let `TINY` be the smallest representable positive `f128`. Then,
    ///  - if `self.is_nan()`, this returns `self`;
    ///  - if `self` is [`INFINITY`], this returns [`MAX`];
    ///  - if `self` is `TINY`, this returns 0.0;
    ///  - if `self` is -0.0 or +0.0, this returns `-TINY`;
    ///  - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
    ///  - otherwise the unique greatest value less than `self` is returned.
    ///
    /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
    /// is finite `x == x.next_down().next_up()` also holds.
    ///
    /// ```rust
    /// #![feature(f128)]
    /// #![feature(float_next_up_down)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let x = 1.0f128;
    /// // Clamp value into range [0, 1).
    /// let clamped = x.clamp(0.0, 1.0f128.next_down());
    /// assert!(clamped < 1.0);
    /// assert_eq!(clamped.next_up(), 1.0);
    /// # }
    /// ```
    ///
    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
    /// [`INFINITY`]: Self::INFINITY
    /// [`MIN`]: Self::MIN
    /// [`MAX`]: Self::MAX
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    // #[unstable(feature = "float_next_up_down", issue = "91399")]
    pub fn next_down(self) -> Self {
        // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
        // denormals to zero. This is in general unsound and unsupported, but here
        // we do our best to still produce the correct result on such targets.
        let bits = self.to_bits();
        if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
            return self;
        }

        let abs = bits & !Self::SIGN_MASK;
        let next_bits = if abs == 0 {
            Self::NEG_TINY_BITS
        } else if bits == abs {
            bits - 1
        } else {
            bits + 1
        };
        Self::from_bits(next_bits)
    }

    /// Takes the reciprocal (inverse) of a number, `1/x`.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let x = 2.0_f128;
    /// let abs_difference = (x.recip() - (1.0 / x)).abs();
    ///
    /// assert!(abs_difference <= f128::EPSILON);
    /// # }
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the operation, without modifying the original"]
    pub fn recip(self) -> Self {
        1.0 / self
    }

    /// Converts radians to degrees.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let angle = std::f128::consts::PI;
    ///
    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
    /// assert!(abs_difference <= f128::EPSILON);
    /// # }
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the operation, without modifying the original"]
    pub fn to_degrees(self) -> Self {
        // Use a literal for better precision.
        const PIS_IN_180: f128 = 57.2957795130823208767981548141051703324054724665643215491602_f128;
        self * PIS_IN_180
    }

    /// Converts degrees to radians.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let angle = 180.0f128;
    ///
    /// let abs_difference = (angle.to_radians() - std::f128::consts::PI).abs();
    ///
    /// assert!(abs_difference <= 1e-30);
    /// # }
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the operation, without modifying the original"]
    pub fn to_radians(self) -> f128 {
        // Use a literal for better precision.
        const RADS_PER_DEG: f128 =
            0.0174532925199432957692369076848861271344287188854172545609719_f128;
        self * RADS_PER_DEG
    }

    /// Returns the maximum of the two numbers, ignoring NaN.
    ///
    /// If one of the arguments is NaN, then the other argument is returned.
    /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
    /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
    /// This also matches the behavior of libm’s fmax.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // Using aarch64 because `reliable_f128_math` is needed
    /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
    ///
    /// let x = 1.0f128;
    /// let y = 2.0f128;
    ///
    /// assert_eq!(x.max(y), y);
    /// # }
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the comparison, without modifying either input"]
    pub fn max(self, other: f128) -> f128 {
        intrinsics::maxnumf128(self, other)
    }

    /// Returns the minimum of the two numbers, ignoring NaN.
    ///
    /// If one of the arguments is NaN, then the other argument is returned.
    /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
    /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
    /// This also matches the behavior of libm’s fmin.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // Using aarch64 because `reliable_f128_math` is needed
    /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
    ///
    /// let x = 1.0f128;
    /// let y = 2.0f128;
    ///
    /// assert_eq!(x.min(y), x);
    /// # }
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the comparison, without modifying either input"]
    pub fn min(self, other: f128) -> f128 {
        intrinsics::minnumf128(self, other)
    }

    /// Returns the maximum of the two numbers, propagating NaN.
    ///
    /// This returns NaN when *either* argument is NaN, as opposed to
    /// [`f128::max`] which only returns NaN when *both* arguments are NaN.
    ///
    /// ```
    /// #![feature(f128)]
    /// #![feature(float_minimum_maximum)]
    /// # // Using aarch64 because `reliable_f128_math` is needed
    /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
    ///
    /// let x = 1.0f128;
    /// let y = 2.0f128;
    ///
    /// assert_eq!(x.maximum(y), y);
    /// assert!(x.maximum(f128::NAN).is_nan());
    /// # }
    /// ```
    ///
    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
    /// Note that this follows the semantics specified in IEEE 754-2019.
    ///
    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
    #[must_use = "this returns the result of the comparison, without modifying either input"]
    pub fn maximum(self, other: f128) -> f128 {
        if self > other {
            self
        } else if other > self {
            other
        } else if self == other {
            if self.is_sign_positive() && other.is_sign_negative() { self } else { other }
        } else {
            self + other
        }
    }

    /// Returns the minimum of the two numbers, propagating NaN.
    ///
    /// This returns NaN when *either* argument is NaN, as opposed to
    /// [`f128::min`] which only returns NaN when *both* arguments are NaN.
    ///
    /// ```
    /// #![feature(f128)]
    /// #![feature(float_minimum_maximum)]
    /// # // Using aarch64 because `reliable_f128_math` is needed
    /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
    ///
    /// let x = 1.0f128;
    /// let y = 2.0f128;
    ///
    /// assert_eq!(x.minimum(y), x);
    /// assert!(x.minimum(f128::NAN).is_nan());
    /// # }
    /// ```
    ///
    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
    /// Note that this follows the semantics specified in IEEE 754-2019.
    ///
    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    // #[unstable(feature = "float_minimum_maximum", issue = "91079")]
    #[must_use = "this returns the result of the comparison, without modifying either input"]
    pub fn minimum(self, other: f128) -> f128 {
        if self < other {
            self
        } else if other < self {
            other
        } else if self == other {
            if self.is_sign_negative() && other.is_sign_positive() { self } else { other }
        } else {
            // At least one input is NaN. Use `+` to perform NaN propagation and quieting.
            self + other
        }
    }

    /// Calculates the middle point of `self` and `rhs`.
    ///
    /// This returns NaN when *either* argument is NaN or if a combination of
    /// +inf and -inf is provided as arguments.
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(f128)]
    /// #![feature(num_midpoint)]
    /// # // Using aarch64 because `reliable_f128_math` is needed
    /// # #[cfg(all(target_arch = "aarch64", target_os = "linux"))] {
    ///
    /// assert_eq!(1f128.midpoint(4.0), 2.5);
    /// assert_eq!((-5.5f128).midpoint(8.0), 1.25);
    /// # }
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    // #[unstable(feature = "num_midpoint", issue = "110840")]
    pub fn midpoint(self, other: f128) -> f128 {
        const LO: f128 = f128::MIN_POSITIVE * 2.;
        const HI: f128 = f128::MAX / 2.;

        let (a, b) = (self, other);
        let abs_a = a.abs_private();
        let abs_b = b.abs_private();

        if abs_a <= HI && abs_b <= HI {
            // Overflow is impossible
            (a + b) / 2.
        } else if abs_a < LO {
            // Not safe to halve `a` (would underflow)
            a + (b / 2.)
        } else if abs_b < LO {
            // Not safe to halve `b` (would underflow)
            (a / 2.) + b
        } else {
            // Safe to halve `a` and `b`
            (a / 2.) + (b / 2.)
        }
    }

    /// Rounds toward zero and converts to any primitive integer type,
    /// assuming that the value is finite and fits in that type.
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `float*itf` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let value = 4.6_f128;
    /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
    /// assert_eq!(rounded, 4);
    ///
    /// let value = -128.9_f128;
    /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
    /// assert_eq!(rounded, i8::MIN);
    /// # }
    /// ```
    ///
    /// # Safety
    ///
    /// The value must:
    ///
    /// * Not be `NaN`
    /// * Not be infinite
    /// * Be representable in the return type `Int`, after truncating off its fractional part
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the operation, without modifying the original"]
    pub unsafe fn to_int_unchecked<Int>(self) -> Int
    where
        Self: FloatToInt<Int>,
    {
        // SAFETY: the caller must uphold the safety contract for
        // `FloatToInt::to_int_unchecked`.
        unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
    }

    /// Raw transmutation to `u128`.
    ///
    /// This is currently identical to `transmute::<f128, u128>(self)` on all platforms.
    ///
    /// See [`from_bits`](#method.from_bits) for some discussion of the
    /// portability of this operation (there are almost no issues).
    ///
    /// Note that this function is distinct from `as` casting, which attempts to
    /// preserve the *numeric* value, and not the bitwise value.
    ///
    /// ```
    /// #![feature(f128)]
    ///
    /// # // FIXME(f16_f128): enable this once const casting works
    /// # // assert_ne!((1f128).to_bits(), 1f128 as u128); // to_bits() is not casting!
    /// assert_eq!((12.5f128).to_bits(), 0x40029000000000000000000000000000);
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the operation, without modifying the original"]
    pub const fn to_bits(self) -> u128 {
        // SAFETY: `u128` is a plain old datatype so we can always transmute to it.
        unsafe { mem::transmute(self) }
    }

    /// Raw transmutation from `u128`.
    ///
    /// This is currently identical to `transmute::<u128, f128>(v)` on all platforms.
    /// It turns out this is incredibly portable, for two reasons:
    ///
    /// * Floats and Ints have the same endianness on all supported platforms.
    /// * IEEE 754 very precisely specifies the bit layout of floats.
    ///
    /// However there is one caveat: prior to the 2008 version of IEEE 754, how
    /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
    /// (notably x86 and ARM) picked the interpretation that was ultimately
    /// standardized in 2008, but some didn't (notably MIPS). As a result, all
    /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
    ///
    /// Rather than trying to preserve signaling-ness cross-platform, this
    /// implementation favors preserving the exact bits. This means that
    /// any payloads encoded in NaNs will be preserved even if the result of
    /// this method is sent over the network from an x86 machine to a MIPS one.
    ///
    /// If the results of this method are only manipulated by the same
    /// architecture that produced them, then there is no portability concern.
    ///
    /// If the input isn't NaN, then there is no portability concern.
    ///
    /// If you don't care about signalingness (very likely), then there is no
    /// portability concern.
    ///
    /// Note that this function is distinct from `as` casting, which attempts to
    /// preserve the *numeric* value, and not the bitwise value.
    ///
    /// ```
    /// #![feature(f128)]
    /// #  // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let v = f128::from_bits(0x40029000000000000000000000000000);
    /// assert_eq!(v, 12.5);
    /// # }
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub const fn from_bits(v: u128) -> Self {
        // It turns out the safety issues with sNaN were overblown! Hooray!
        // SAFETY: `u128` is a plain old datatype so we can always transmute from it.
        unsafe { mem::transmute(v) }
    }

    /// Returns the memory representation of this floating point number as a byte array in
    /// big-endian (network) byte order.
    ///
    /// See [`from_bits`](Self::from_bits) for some discussion of the
    /// portability of this operation (there are almost no issues).
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(f128)]
    ///
    /// let bytes = 12.5f128.to_be_bytes();
    /// assert_eq!(
    ///     bytes,
    ///     [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00,
    ///      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
    /// );
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the operation, without modifying the original"]
    pub const fn to_be_bytes(self) -> [u8; 16] {
        self.to_bits().to_be_bytes()
    }

    /// Returns the memory representation of this floating point number as a byte array in
    /// little-endian byte order.
    ///
    /// See [`from_bits`](Self::from_bits) for some discussion of the
    /// portability of this operation (there are almost no issues).
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(f128)]
    ///
    /// let bytes = 12.5f128.to_le_bytes();
    /// assert_eq!(
    ///     bytes,
    ///     [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
    ///      0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40]
    /// );
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the operation, without modifying the original"]
    pub const fn to_le_bytes(self) -> [u8; 16] {
        self.to_bits().to_le_bytes()
    }

    /// Returns the memory representation of this floating point number as a byte array in
    /// native byte order.
    ///
    /// As the target platform's native endianness is used, portable code
    /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
    ///
    /// [`to_be_bytes`]: f128::to_be_bytes
    /// [`to_le_bytes`]: f128::to_le_bytes
    ///
    /// See [`from_bits`](Self::from_bits) for some discussion of the
    /// portability of this operation (there are almost no issues).
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(f128)]
    ///
    /// let bytes = 12.5f128.to_ne_bytes();
    /// assert_eq!(
    ///     bytes,
    ///     if cfg!(target_endian = "big") {
    ///         [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00,
    ///          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
    ///     } else {
    ///         [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
    ///          0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40]
    ///     }
    /// );
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    #[must_use = "this returns the result of the operation, without modifying the original"]
    pub const fn to_ne_bytes(self) -> [u8; 16] {
        self.to_bits().to_ne_bytes()
    }

    /// Creates a floating point value from its representation as a byte array in big endian.
    ///
    /// See [`from_bits`](Self::from_bits) for some discussion of the
    /// portability of this operation (there are almost no issues).
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let value = f128::from_be_bytes(
    ///     [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00,
    ///      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
    /// );
    /// assert_eq!(value, 12.5);
    /// # }
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub const fn from_be_bytes(bytes: [u8; 16]) -> Self {
        Self::from_bits(u128::from_be_bytes(bytes))
    }

    /// Creates a floating point value from its representation as a byte array in little endian.
    ///
    /// See [`from_bits`](Self::from_bits) for some discussion of the
    /// portability of this operation (there are almost no issues).
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let value = f128::from_le_bytes(
    ///     [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
    ///      0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40]
    /// );
    /// assert_eq!(value, 12.5);
    /// # }
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub const fn from_le_bytes(bytes: [u8; 16]) -> Self {
        Self::from_bits(u128::from_le_bytes(bytes))
    }

    /// Creates a floating point value from its representation as a byte array in native endian.
    ///
    /// As the target platform's native endianness is used, portable code
    /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
    /// appropriate instead.
    ///
    /// [`from_be_bytes`]: f128::from_be_bytes
    /// [`from_le_bytes`]: f128::from_le_bytes
    ///
    /// See [`from_bits`](Self::from_bits) for some discussion of the
    /// portability of this operation (there are almost no issues).
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `eqtf2` is available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// let value = f128::from_ne_bytes(if cfg!(target_endian = "big") {
    ///     [0x40, 0x02, 0x90, 0x00, 0x00, 0x00, 0x00, 0x00,
    ///      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
    /// } else {
    ///     [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
    ///      0x00, 0x00, 0x00, 0x00, 0x00, 0x90, 0x02, 0x40]
    /// });
    /// assert_eq!(value, 12.5);
    /// # }
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    #[rustc_const_unstable(feature = "f128", issue = "116909")]
    pub const fn from_ne_bytes(bytes: [u8; 16]) -> Self {
        Self::from_bits(u128::from_ne_bytes(bytes))
    }

    /// Returns the ordering between `self` and `other`.
    ///
    /// Unlike the standard partial comparison between floating point numbers,
    /// this comparison always produces an ordering in accordance to
    /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
    /// floating point standard. The values are ordered in the following sequence:
    ///
    /// - negative quiet NaN
    /// - negative signaling NaN
    /// - negative infinity
    /// - negative numbers
    /// - negative subnormal numbers
    /// - negative zero
    /// - positive zero
    /// - positive subnormal numbers
    /// - positive numbers
    /// - positive infinity
    /// - positive signaling NaN
    /// - positive quiet NaN.
    ///
    /// The ordering established by this function does not always agree with the
    /// [`PartialOrd`] and [`PartialEq`] implementations of `f128`. For example,
    /// they consider negative and positive zero equal, while `total_cmp`
    /// doesn't.
    ///
    /// The interpretation of the signaling NaN bit follows the definition in
    /// the IEEE 754 standard, which may not match the interpretation by some of
    /// the older, non-conformant (e.g. MIPS) hardware implementations.
    ///
    /// # Example
    ///
    /// ```
    /// #![feature(f128)]
    ///
    /// struct GoodBoy {
    ///     name: &'static str,
    ///     weight: f128,
    /// }
    ///
    /// let mut bois = vec![
    ///     GoodBoy { name: "Pucci", weight: 0.1 },
    ///     GoodBoy { name: "Woofer", weight: 99.0 },
    ///     GoodBoy { name: "Yapper", weight: 10.0 },
    ///     GoodBoy { name: "Chonk", weight: f128::INFINITY },
    ///     GoodBoy { name: "Abs. Unit", weight: f128::NAN },
    ///     GoodBoy { name: "Floaty", weight: -5.0 },
    /// ];
    ///
    /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
    ///
    /// // `f128::NAN` could be positive or negative, which will affect the sort order.
    /// if f128::NAN.is_sign_negative() {
    ///     bois.into_iter().map(|b| b.weight)
    ///         .zip([f128::NAN, -5.0, 0.1, 10.0, 99.0, f128::INFINITY].iter())
    ///         .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
    /// } else {
    ///     bois.into_iter().map(|b| b.weight)
    ///         .zip([-5.0, 0.1, 10.0, 99.0, f128::INFINITY, f128::NAN].iter())
    ///         .for_each(|(a, b)| assert_eq!(a.to_bits(), b.to_bits()))
    /// }
    /// ```
    #[inline]
    #[must_use]
    #[unstable(feature = "f128", issue = "116909")]
    pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
        let mut left = self.to_bits() as i128;
        let mut right = other.to_bits() as i128;

        // In case of negatives, flip all the bits except the sign
        // to achieve a similar layout as two's complement integers
        //
        // Why does this work? IEEE 754 floats consist of three fields:
        // Sign bit, exponent and mantissa. The set of exponent and mantissa
        // fields as a whole have the property that their bitwise order is
        // equal to the numeric magnitude where the magnitude is defined.
        // The magnitude is not normally defined on NaN values, but
        // IEEE 754 totalOrder defines the NaN values also to follow the
        // bitwise order. This leads to order explained in the doc comment.
        // However, the representation of magnitude is the same for negative
        // and positive numbers – only the sign bit is different.
        // To easily compare the floats as signed integers, we need to
        // flip the exponent and mantissa bits in case of negative numbers.
        // We effectively convert the numbers to "two's complement" form.
        //
        // To do the flipping, we construct a mask and XOR against it.
        // We branchlessly calculate an "all-ones except for the sign bit"
        // mask from negative-signed values: right shifting sign-extends
        // the integer, so we "fill" the mask with sign bits, and then
        // convert to unsigned to push one more zero bit.
        // On positive values, the mask is all zeros, so it's a no-op.
        left ^= (((left >> 127) as u128) >> 1) as i128;
        right ^= (((right >> 127) as u128) >> 1) as i128;

        left.cmp(&right)
    }

    /// Restrict a value to a certain interval unless it is NaN.
    ///
    /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
    /// less than `min`. Otherwise this returns `self`.
    ///
    /// Note that this function returns NaN if the initial value was NaN as
    /// well.
    ///
    /// # Panics
    ///
    /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(f128)]
    /// # // FIXME(f16_f128): remove when `{eq,gt,unord}tf` are available
    /// # #[cfg(all(target_arch = "x86_64", target_os = "linux"))] {
    ///
    /// assert!((-3.0f128).clamp(-2.0, 1.0) == -2.0);
    /// assert!((0.0f128).clamp(-2.0, 1.0) == 0.0);
    /// assert!((2.0f128).clamp(-2.0, 1.0) == 1.0);
    /// assert!((f128::NAN).clamp(-2.0, 1.0).is_nan());
    /// # }
    /// ```
    #[inline]
    #[unstable(feature = "f128", issue = "116909")]
    #[must_use = "method returns a new number and does not mutate the original value"]
    pub fn clamp(mut self, min: f128, max: f128) -> f128 {
        assert!(min <= max, "min > max, or either was NaN. min = {min:?}, max = {max:?}");
        if self < min {
            self = min;
        }
        if self > max {
            self = max;
        }
        self
    }
}