This file is indexed.

/usr/share/gnu-smalltalk/kernel/Number.st is in gnu-smalltalk-common 3.2.4-2.1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

   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
"======================================================================
|
|   Number Method Definitions
|
|
 ======================================================================"

"======================================================================
|
| Copyright 1988,92,94,95,99,2000,2001,2002,2007,2008,2009
| Free Software Foundation, Inc.
| Written by Steve Byrne.
|
| This file is part of the GNU Smalltalk class library.
|
| The GNU Smalltalk class library is free software; you can redistribute it
| and/or modify it under the terms of the GNU Lesser General Public License
| as published by the Free Software Foundation; either version 2.1, or (at
| your option) any later version.
| 
| The GNU Smalltalk class library is distributed in the hope that it will be
| useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser
| General Public License for more details.
| 
| You should have received a copy of the GNU Lesser General Public License
| along with the GNU Smalltalk class library; see the file COPYING.LIB.
| If not, write to the Free Software Foundation, 59 Temple Place - Suite
| 330, Boston, MA 02110-1301, USA.  
|
 ======================================================================"



Magnitude subclass: Number [
    
    <category: 'Language-Data types'>
    <comment: 'I am an abstract class that provides operations on numbers, both floating
point and integer.  I provide some generic predicates, and supply the 
implicit type coercing code for binary operations.'>

    Number class >> coerce: aNumber [
	"Answer aNumber - whatever class it belongs to, it is good"

	<category: 'converting'>
	aNumber class == Fraction ifTrue: [ ^aNumber asFloatD ].
	^aNumber
    ]

    Number class >> readFrom: aStream radix: anInteger [
	"Answer the number read from the rest of aStream, converted to an
	 instance of the receiver. If the receiver is number, the class of the
	 result is undefined -- but the result is good.

         The exponent (for example 1.2e-1) is only parsed if anInteger is 10."

	<category: 'converting'>
        | c sgn int intexp frac exp isfloat |
        isfloat := false.
        sgn     := 1.
        int     := 0.
        intexp  := 1.
     
        c := aStream peek.
        c isNil ifTrue: [ ^0 ].
        c = $- ifTrue: [ sgn := -1. aStream next. ].
     
        c := aStream peek.
        c isNil ifTrue: [ ^0 ].
        c := c asUppercase.
        ((c isDigit: anInteger) or: [ c = $. ]) ifFalse: [ ^0 ].
     
        [ c notNil and: [
               c := c asUppercase.
               c isDigit: anInteger ] ] whileTrue: [
           aStream next.
           int := sgn * c digitValue + (int * anInteger).
           c := aStream peek
        ].
        c isNil ifTrue: [ ^int ].
     
        c = $. ifTrue: [
           aStream next.
           isfloat := true.
           [ c := aStream peek. c notNil and: [
                  c := c asUppercase.
                  c isDigit: anInteger ] ] whileTrue: [
              sgn := sgn / anInteger.
              int := sgn * c digitValue + int.
              aStream next
           ]
        ].
     
        exp := 0.
        (anInteger = 10 and: [c = $E]) ifFalse: [
             ^isfloat ifTrue: [ int asFloat ] ifFalse: [ int ] ].
     
        aStream next.
        c := aStream peek.
        c isNil ifTrue: [ ^int ].
        sgn := 1.
        c = $+ ifTrue: [ sgn :=  1. aStream next ].
        c = $- ifTrue: [ sgn := -1. aStream next ].
     
        [ c := aStream peek. c notNil and: [ c isDigit ] ] whileTrue: [
           exp := c digitValue + (exp * 10).
           aStream next
        ].
     
        int := int * (10 raisedToInteger: exp * sgn).
        ^int asFloat
    ]

    Number class >> readFrom: aStream [
	"Answer the number read from the rest of aStream, converted to an
	 instance of the receiver. If the receiver is number, the class of the
	 result is undefined -- but the result is good."

	<category: 'converting'>
	^self readFrom: aStream radix: 10
    ]

    Number class >> isImmediate [
	"Answer whether, if x is an instance of the receiver, x copy == x"

	<category: 'testing'>
	^true
    ]

    shallowCopy [
	"Return the receiver - it's an immediate (immutable) object"

	<category: 'copying'>
	^self
    ]

    deepCopy [
	"Return the receiver - it's an immediate (immutable) object"

	<category: 'copying'>
	^self
    ]

    asNumber [
	"Answer the receiver, since it is already a number"

	<category: 'converting'>
	^self
    ]

    asString [
	"Answer the receiver's #displayString, which should be a good enough
	 conversion to String for a number."

	<category: 'converting'>
	^self displayString
    ]

    degreesToRadians [
	"Convert the receiver to radians"

	<category: 'converting'>
	^self asFloatD / 57.29577951308232
    ]

    radiansToDegrees [
	"Convert the receiver from radians to degrees"

	<category: 'converting'>
	^self asFloatD * 57.29577951308232
    ]

    coerce: aNumber [
	"Answer aNumber, converted to an integer or floating-point number."

	<category: 'converting'>
	aNumber class == Fraction ifTrue: [ ^aNumber asFloatD ].
	^aNumber
    ]

    zero [
	"Coerce 0 to the receiver's class. The default implementation works,
	 but is inefficient"

	<category: 'converting'>
	^self coerce: 0
    ]

    unity [
	"Coerce 1 to the receiver's class. The default implementation works,
	 but is inefficient"

	<category: 'converting'>
	^self coerce: 1
    ]

    generality [
	"Answer the receiver's generality"

	<category: 'converting'>
	self subclassResponsibility
    ]

    asScaledDecimal: n [
	"Answer the receiver, converted to a ScaledDecimal object."

	<category: 'converting'>
	^ScaledDecimal newFromNumber: self asFraction scale: n
    ]

    asScaledDecimal: denDigits radix: base scale: n [
	"Answer the receiver, divided by base^denDigits and converted to
	 a ScaledDecimal object."

	<category: 'converting'>
	^ScaledDecimal 
	    newFromNumber: self asFraction * (base raisedToInteger: denDigits)
	    scale: n
    ]

    asCNumber [
	"Convert the receiver to a kind of number that is understood by
	 the C call-out mechanism."
	<category: 'coercion'>
	self subclassResponsibility
    ]

    asFloat [
	"Convert the receiver to an arbitrary subclass of Float"

	<category: 'converting'>
	^self asFloatD
    ]

    asFloatD [
	<category: 'converting'>
	self subclassResponsibility
    ]

    asFloatE [
	<category: 'converting'>
	self subclassResponsibility
    ]

    asFloatQ [
	<category: 'converting'>
	self subclassResponsibility
    ]

    asFraction [
	<category: 'converting'>
	self subclassResponsibility
    ]

    asExactFraction [
	"Return the receiver, converted to a Fraction retaining the exact
	 value of the receiver."

	<category: 'converting'>
	^self asFraction
    ]

    retryError [
	"Raise an error---a retrying method was called with two arguments
	 having the same generality."

	<category: 'retrying'>
	^self 
	    error: 'retry:coercing: called with arguments of the same generality'
    ]

    retry: aSymbol coercing: aNumber [
	"Coerce to the other number's class the one number between the receiver and
	 aNumber which has the lowest, and retry calling aSymbol.  aSymbol is
	 supposed not to be #= or #~= (since those don't fail if aNumber is not
	 a Number)."

	<category: 'retrying'>
	| selfGen aNumGen |
	selfGen := self generality.
	aNumGen := aNumber generality.
	selfGen > aNumGen 
	    ifTrue: [^self perform: aSymbol with: (self coerce: aNumber)].
	selfGen < aNumGen 
	    ifTrue: [^(aNumber coerce: self) perform: aSymbol with: aNumber].
	self retryError
    ]

    retryRelationalOp: aSymbol coercing: aNumber [
	"Coerce to the other number's class the one number between the receiver and
	 aNumber which has the lowest, and retry calling aSymbol (<, <=, >, >=)."

	<category: 'retrying'>
	| delta |
	delta := self retryDifferenceCoercing: aNumber.

	"Avoids a #perform: which is usually more expensive -- all the comparisons
	 below are inlined by both the compiler and the interpreter"
	aSymbol == #< ifTrue: [^delta < delta zero].
	aSymbol == #<= ifTrue: [^delta <= delta zero].
	aSymbol == #>= ifTrue: [^delta >= delta zero].
	aSymbol == #> ifTrue: [^delta > delta zero].
	self error: 'bad relational operator'
    ]

    retryEqualityCoercing: aNumber [
	"Coerce to the other number's class the one number between the receiver and
	 aNumber which has the lowest, and retry calling #=."

	<category: 'retrying'>
	| selfGen aNumGen |
	(aNumber isKindOf: Number) ifFalse: [^false].
	selfGen := self generality.
	aNumGen := aNumber generality.
	aNumGen isNil ifTrue: [^false].
	selfGen > aNumGen ifTrue: [^self = (self coerce: aNumber)].
	selfGen < aNumGen ifTrue: [^(aNumber coerce: self) = aNumber].
	self retryError
    ]

    retryInequalityCoercing: aNumber [
	"Coerce to the other number's class the one number between the receiver and
	 aNumber which has the lowest, and retry calling #~=."

	<category: 'retrying'>
	| selfGen aNumGen |
	(aNumber isKindOf: Number) ifFalse: [^true].
	selfGen := self generality.
	aNumGen := aNumber generality.
	aNumGen isNil ifTrue: [^true].
	selfGen > aNumGen ifTrue: [^false == (self = (self coerce: aNumber))].
	selfGen < aNumGen ifTrue: [^false == ((aNumber coerce: self) = aNumber)].
	self retryError
    ]

    retrySumCoercing: aNumber [
	"Coerce to the other number's class the one number between the receiver and
	 aNumber which has the lowest, and retry calling #+."

	<category: 'retrying'>
	| selfGen aNumGen |
	selfGen := self generality.
	aNumGen := aNumber generality.
	aNumGen isNil ifTrue: [^aNumber sumFromNumber: self].
	selfGen > aNumGen ifTrue: [^self + (self coerce: aNumber)].
	selfGen < aNumGen ifTrue: [^(aNumber coerce: self) + aNumber].
	self retryError
    ]

    retryDifferenceCoercing: aNumber [
	"Coerce to the other number's class the one number between the receiver and
	 aNumber which has the lowest, and retry calling #-."

	<category: 'retrying'>
	| selfGen aNumGen |
	selfGen := self generality.
	aNumGen := aNumber generality.
	aNumGen isNil ifTrue: [^aNumber differenceFromNumber: self].
	selfGen > aNumGen ifTrue: [^self - (self coerce: aNumber)].
	selfGen < aNumGen ifTrue: [^(aNumber coerce: self) - aNumber].
	self retryError
    ]

    retryMultiplicationCoercing: aNumber [
	"Coerce to the other number's class the one number between the receiver and
	 aNumber which has the lowest, and retry calling #*."

	<category: 'retrying'>
	| selfGen aNumGen |
	selfGen := self generality.
	aNumGen := aNumber generality.
	aNumGen isNil ifTrue: [^aNumber productFromNumber: self].
	selfGen > aNumGen ifTrue: [^self * (self coerce: aNumber)].
	selfGen < aNumGen ifTrue: [^(aNumber coerce: self) * aNumber].
	self retryError
    ]

    retryDivisionCoercing: aNumber [
	"Coerce to the other number's class the one number between the receiver and
	 aNumber which has the lowest, and retry calling #/."

	<category: 'retrying'>
	| selfGen aNumGen |
	selfGen := self generality.
	aNumGen := aNumber generality.
	selfGen > aNumGen ifTrue: [^self / (self coerce: aNumber)].
	selfGen < aNumGen ifTrue: [^(aNumber coerce: self) / aNumber].
	self retryError
    ]

    + aNumber [
	"Sum the receiver and aNumber, answer the result"

	<category: 'arithmetic'>
	self subclassResponsibility
    ]

    - aNumber [
	"Subtract aNumber from the receiver, answer the result"

	<category: 'arithmetic'>
	self subclassResponsibility
    ]

    * aNumber [
	"Subtract the receiver and aNumber, answer the result"

	<category: 'arithmetic'>
	self subclassResponsibility
    ]

    / aNumber [
	"Divide the receiver by aNumber, answer the result (no loss of
	 precision).  Raise a ZeroDivide exception or return a valid
	 (possibly infinite) continuation value if aNumber is zero."

	<category: 'arithmetic'>
	self subclassResponsibility
    ]

    // aNumber [
	"Return the integer quotient of dividing the receiver by aNumber with
	 truncation towards negative infinity.  Raise a ZeroDivide
	 exception if aNumber is zero"

	<category: 'arithmetic'>
	aNumber = 0 ifTrue: [self zeroDivide].
	^(self / aNumber) floor
    ]

    \\ aNumber [
	"Return the remainder of dividing the receiver by aNumber with
	 truncation towards negative infinity.  Raise a ZeroDivide
	 exception if aNumber is zero"

	<category: 'arithmetic'>
	aNumber = 0 ifTrue: [self zeroDivide].
	^self - (self // aNumber * aNumber)
    ]

    quo: aNumber [
	"Return the integer quotient of dividing the receiver by aNumber with
	 truncation towards zero.  Raise a ZeroDivide exception if aNumber is
	 zero"

	<category: 'arithmetic'>
	aNumber = 0 ifTrue: [self zeroDivide].
	^(self / aNumber) truncated
    ]

    rem: aNumber [
	"Return the remainder of dividing the receiver by aNumber with
	 truncation towards zero.  Raise a ZeroDivide exception if aNumber is
	 zero"

	<category: 'arithmetic'>
	^self - ((self quo: aNumber) * aNumber)
    ]

    integerPart [
	"Answer the receiver, truncated towards zero"

	<category: 'truncation and round off'>
	^self truncated
    ]

    fractionPart [
	"Answer a number which, summed to the #integerPart of the
	 receiver, gives the receiver itself."

	<category: 'truncation and round off'>
	^self - self integerPart
    ]

    asInteger [
	"Answer the receiver, rounded to the nearest integer"

	<category: 'truncation and round off'>
	^self rounded
    ]

    truncated [
	"Answer the receiver, truncated towards zero"

	<category: 'truncation and round off'>
	^self subclassResponsibility
    ]

    truncateTo: aNumber [
	"Answer the receiver, truncated towards zero to a multiple
	 of aNumber"

	<category: 'truncation and round off'>
	^(self coerce: (self quo: aNumber)) * aNumber
    ]

    rounded [
	"Returns the integer nearest the receiver"

	<category: 'truncation and round off'>
	^self negative 
	    ifTrue: [(self - (self unity / 2)) ceiling]
	    ifFalse: [(self + (self unity / 2)) floor]
    ]

    roundTo: aNumber [
	"Answer the receiver, truncated to the nearest multiple
	 of aNumber"

	<category: 'truncation and round off'>
	^(self coerce: (self / aNumber) rounded) * aNumber
    ]

    closeTo: num [
	"Answer whether the receiver can be considered sufficiently
	 close to num (this is done by checking equality if num is
	 not a number, and by checking with 0.01% tolerance if num
	 is a number)."

	<category: 'testing'>
	"Shortcut common cases.  But the first one is also needed
	 so that FloatD infinity closeTo: FloatD infinity!"
	self = num ifTrue: [^true].
	num isNumber ifFalse: [^false].
	self = self zero ifTrue: [^num abs < 0.0001].
	num = num zero ifTrue: [^self abs < 0.0001].

	^(self - num) abs / (self abs max: num abs) <= 0.0001
    ]

    isExact [
	"Answer whether the receiver performs exact arithmetic.  Most
	 numeric classes do (in fact the only exceptions is Float and
	 its descendants), so the default is to answer true rather than
	 calling #subclassResponsibility."

	<category: 'testing'>
	^true
    ]

    isNaN [
	"Answer whether the receiver is a Not-A-Number.  Most numeric
	 classes don't handle nans, so the default is to answer false
	 rather than calling #subclassResponsibility."

	<category: 'testing'>
	^false
    ]

    isFinite [
	"Answer whether the receiver represents a finite quantity.  Most
	 numeric classes are for finite quantities, so the default is to
	 answer true rather than calling #subclassResponsibility."

	<category: 'testing'>
	^true
    ]

    isInfinite [
	"Answer whether the receiver represents an infinite quantity.  Most
	 numeric classes are for finite quantities, so the default is to
	 answer false rather than calling #subclassResponsibility."

	<category: 'testing'>
	^false
    ]

    isRational [
	"Answer whether the receiver is rational - false by default"

	<category: 'testing'>
	^false
    ]

    isNumber [
	<category: 'testing'>
	^true
    ]

    negative [
	"Answer whether the receiver is < 0"

	<category: 'testing'>
	^self < self zero
    ]

    positive [
	"Answer whether the receiver is >= 0"

	<category: 'testing'>
	^self >= self zero
    ]

    strictlyPositive [
	"Answer whether the receiver is > 0"

	<category: 'testing'>
	^self > self zero
    ]

    sign [
	"Returns the sign of the receiver."

	<category: 'testing'>
	self < self zero ifTrue: [^-1].
	self > self zero ifTrue: [^1].
	^0
    ]

    even [
	"Returns true if self is divisible by 2"

	<category: 'testing'>
	^self truncated even
    ]

    odd [
	"Returns true if self is not divisible by 2"

	<category: 'testing'>
	^self truncated odd
    ]

    min: aNumber [
	"Answer the minimum between the receiver and aNumber.  Redefine
	 in subclasses if necessary to ensure that if either self or
	 aNumber is a NaN, it is always answered."

	"If both self and aNumber are zero, return aNumber in case it
	 has a negative sign, because we assume our zero is positive.
	 If the test is false, always answer aNumber in case it is a
	 NaN, because we assume that self is not a NaN."

	<category: 'comparing'>
	^aNumber > self ifTrue: [self] ifFalse: [aNumber]
    ]

    max: aNumber [
	"Answer the maximum between the receiver and aNumber.  Redefine
	 in subclasses if necessary to ensure that if either self or
	 aNumber is a NaN, it is always answered."

	"If both self and aNumber are zero, return self in case aNumber
	 has a negative sign, because we assume our zero is positive.
	 If the test is false, always answer aNumber in case it is a
	 NaN, because we assume that self is not a NaN."

	<category: 'comparing'>
	^aNumber <= self ifTrue: [self] ifFalse: [aNumber]
    ]

    positiveDifference: aNumber [
	"Answer the positive difference of the receiver and
	 aNumber, that is self - aNumber if it is positive,
	 0 otherwise."

	<category: 'misc math'>
	| diff |
	diff := self - aNumber.
	diff isNaN ifTrue: [^diff].
	^diff negative ifTrue: [diff zero] ifFalse: [diff]
    ]

    squared [
	"Answer the square of the receiver"

	<category: 'misc math'>
	^self * self
    ]

    abs [
	"Answer the absolute value of the receiver"

	<category: 'misc math'>
	^self > self zero ifTrue: [self] ifFalse: [self negated]
    ]

    negated [
	"Answer the negated of the receiver"

	<category: 'misc math'>
	^self zero - self
    ]

    sin [
	"Answer the sine of the receiver"

	<category: 'misc math'>
	^self asFloatD sin
    ]

    cos [
	"Answer the cosine of the receiver"

	<category: 'misc math'>
	^self asFloatD cos
    ]

    tan [
	"Answer the tangent of the receiver"

	<category: 'misc math'>
	^self asFloatD tan
    ]

    arcSin [
	"Answer the arc sine of the receiver"

	<category: 'misc math'>
	^self asFloatD arcSin
    ]

    arcCos [
	"Answer the arc cosine of the receiver"

	<category: 'misc math'>
	^self asFloatD arcCos
    ]

    arcTan [
	"Answer the arc tangent of the receiver"

	<category: 'misc math'>
	^self asFloatD arcTan
    ]

    arcTan: x [
	"Answer the angle (measured counterclockwise) between (x, self) and
	 a ray starting in (0, 0) and moving towards (1, 0) - i.e. 3 o'clock"

	<category: 'misc math'>
	| result |
	x = 0 
	    ifTrue: 
		["Always adopt the most general number representation of pi.
		 If none of the number is a floating point number, go with
		 a FloatD."

		^self generality < x generality 
		    ifTrue: 
			[x generality < 0.0e generality 
			    ifTrue: [FloatD pi * self sign / 2]
			    ifFalse: [x class pi * self sign / 2]]
		    ifFalse: 
			[self generality < 0.0e generality 
			    ifTrue: [FloatD pi * self sign / 2]
			    ifFalse: [self class pi * self sign / 2]]].
	result := (self / x) arcTan.
	^x < 0 
	    ifFalse: [result]
	    ifTrue: 
		[result > result zero 
		    ifFalse: [result + result class pi]
		    ifTrue: [result - result class pi]]
    ]

    cosh [
	"Answer the hyperbolic cosine of the receiver."

	<category: 'misc math'>
	^(self exp + self negated exp) / 2
    ]

    sinh [
	"Answer the hyperbolic sine of the receiver."

	<category: 'misc math'>
	^(self exp - self negated exp) / 2
    ]

    tanh [
	"Answer the hyperbolic tangent of the receiver."

	<category: 'misc math'>
	| ep en |
	ep := self exp.
	en := self negated exp.
	^(ep - en) / (ep + en)
    ]

    arcCosh [
	"Answer the hyperbolic arc-cosine of the receiver."

	<category: 'misc math'>
	^(self + (self squared - 1) sqrt) ln
    ]

    arcSinh [
	"Answer the hyperbolic arc-sine of the receiver."

	<category: 'misc math'>
	^(self + (self squared + 1) sqrt) ln
    ]

    arcTanh [
	"Answer the hyperbolic arc-tangent of the receiver."

	<category: 'misc math'>
	^((1 + self) / (1 - self)) ln / 2
    ]

    sqrt [
	"Answer the square root of the receiver"

	<category: 'misc math'>
	^self asFloatD sqrt
    ]

    exp [
	"Answer e raised to the receiver"

	<category: 'misc math'>
	^self asFloatD exp
    ]

    ln [
	"Answer log base e of the receiver"

	<category: 'misc math'>
	^self asFloatD ln
    ]

    estimatedLog [
	"Answer an estimate of (self abs floorLog: 10). This method
	 should be overridden by subclasses, but Number's implementation
	 does not raise errors - simply, it gives a correct result, so
	 it is slow."

	<category: 'misc math'>
	^self abs floorLog: 10
    ]

    log [
	"Answer log base 10 of the receiver"

	<category: 'misc math'>
	^self asFloatD ln / FloatD ln10
    ]

    log: aNumber [
	"Answer log base aNumber of the receiver"

	<category: 'misc math'>
	^self asFloatD ln / aNumber asFloatD ln
    ]

    floorLog: radix [
	"Answer (self log: radix) floor. Optimized to answer an integer."

	<category: 'misc math'>
	| me that answer |
	self < self zero 
	    ifTrue: 
		[^self arithmeticError: 'cannot extract logarithm of a negative number'].
	radix <= radix unity 
	    ifTrue: 
		[radix <= radix zero ifTrue: [^self arithmeticError: 'bad radix'].
		radix = radix unity ifTrue: [^self arithmeticError: 'bad radix'].
		^(self ceilingLog: radix reciprocal) negated].
	answer := -1.
	self < self unity 
	    ifTrue: 
		[me := self.
		
		[me := me * radix.
		me < me unity] whileTrue: [answer := answer - 1]]
	    ifFalse: 
		[that := 1.
		[that <= self] whileTrue: 
			[that := that * radix.
			answer := answer + 1]].
	^answer
    ]

    ceilingLog: radix [
	"Answer (self log: radix) ceiling. Optimized to answer an integer."

	<category: 'misc math'>
	| me that answer |
	self < self zero 
	    ifTrue: 
		[^self arithmeticError: 'cannot extract logarithm of a negative number'].
	radix <= radix unity 
	    ifTrue: 
		[radix <= radix zero ifTrue: [^self arithmeticError: 'bad radix'].
		radix = radix unity ifTrue: [^self arithmeticError: 'bad radix'].
		^(self floorLog: radix reciprocal) negated].
	answer := 0.
	self < self unity 
	    ifTrue: 
		[me := self.
		
		[me := me * radix.
		me <= me unity] whileTrue: [answer := answer - 1]]
	    ifFalse: 
		[that := 1.
		[that < self] whileTrue: 
			[that := that * radix.
			answer := answer + 1]].
	^answer
    ]

    raisedTo: aNumber [
	"Return self raised to aNumber power"

	<category: 'misc math'>
	aNumber isInteger 
	    ifTrue: [^self raisedToInteger: aNumber].
	^aNumber generality > 1.0d generality
	    ifTrue: [(aNumber coerce: self) raisedTo: aNumber]
	    ifFalse: [self asFloatD raisedTo: aNumber asFloatD]
    ]

    raisedToInteger: anInteger [
	"Return self raised to the anInteger-th power"

	"Some special cases first"

	<category: 'misc math'>
	anInteger isInteger 
	    ifFalse: [SystemExceptions.WrongClass signalOn: anInteger mustBe: Integer].
	anInteger < 0 ifTrue: [^self reciprocal raisedToInteger: 0 - anInteger].
	anInteger = 0 ifTrue: [
	    self = self zero ifTrue: [self arithmeticError: 'invalid operands'].
	    ^self unity].
	anInteger = 1 ifTrue: [^self].

	"Fire the big loop."
	^self raisedToInteger: anInteger
	    withCache: ((Array new: (255 min: anInteger))
		    at: 1 put: self;
		    yourself)
    ]

    withSignOf: aNumber [
	"Answer the receiver, with its sign possibly changed to match
	 that of aNumber."

	<category: 'misc math'>
	^aNumber positive == self positive ifTrue: [self] ifFalse: [self negated]
    ]

    floor [
	"Return the integer nearest the receiver toward negative infinity."

	<category: 'truncation and round off'>
	| selfTruncated |
	selfTruncated := self truncated.
	"If positive, truncation to zero is what we want."
	self >= self zero ifTrue: [^selfTruncated].

	"Must be negative."
	self = (self coerce: selfTruncated) 
	    ifTrue: [^selfTruncated]
	    ifFalse: [^selfTruncated - 1]
    ]

    reciprocal [
	"Return the reciprocal of the receiver"

	<category: 'arithmetic'>
	self = self zero ifTrue: [self zeroDivide] ifFalse: [^self unity / self]
    ]

    to: stop [
	"Return an interval going from the receiver to stop by 1"

	<category: 'shortcuts and iterators'>
	^Interval from: self to: stop
    ]

    to: stop by: step [
	"Return an interval going from the receiver to stop with the given step"

	<category: 'shortcuts and iterators'>
	^Interval 
	    from: self
	    to: stop
	    by: step
    ]

    to: stop by: step do: aBlock [
	"Evaluate aBlock for each value in the interval going from the receiver
	 to stop with the given step. Compiled in-line for integer literal steps,
	 and for one-argument aBlocks without temporaries, and therefore
	 not overridable."

	<category: 'shortcuts and iterators'>
	| i |
	i := self.
	step > step zero 
	    ifTrue: [[i <= stop] whileTrue: 
			[aBlock value: i.
			i := i + step]]
	    ifFalse: [[i >= stop] whileTrue: 
			[aBlock value: i.
			i := i + step]].
	^stop
    ]

    to: stop do: aBlock [
	"Evaluate aBlock for each value in the interval going from the receiver
	 to stop by 1. Compiled in-line for one-argument aBlocks without
	 temporaries, and therefore not overridable."

	<category: 'shortcuts and iterators'>
	| i |
	i := self.
	[i <= stop] whileTrue: 
		[aBlock value: i.
		i := i + self unity]
    ]

    to: stop collect: aBlock [
	"Evaluate aBlock for each value in the interval going from the receiver
         to stop by 1.  The results are collected in an Array and returned."

	<category: 'shortcuts and iterators'>
	| size result i j |
        size := (stop - self) truncated + 1 max: 0.
	result := Array new: size.
	i := self.
	j := 1.
	[j <= size] whileTrue: 
		[result at: j put: (aBlock value: i).
		i := i + self unity. j := j + 1].
	^result
    ]

    to: stop by: step collect: aBlock [
	"Evaluate aBlock for each value in the interval going from the receiver
         to stop with the given step.  The results are collected in an Array
	 and returned."

	<category: 'shortcuts and iterators'>
	| size result i j |
        size := step > 0
            ifTrue: [stop >= self ifTrue: [(stop - self) // step + 1] ifFalse: [0]]
            ifFalse: [self >= stop ifTrue: [(stop - self) // step + 1] ifFalse: [0]].

	result := Array new: size.
	i := self.
	j := 1.
	[j <= size] whileTrue: 
		[result at: j put: (aBlock value: i).
		i := i + step. j := j + 1].
	^result
    ]

    arithmeticError: message [
	<category: 'errors'>
	self error: message
    ]

    zeroDivide [
	<category: 'errors'>
	self error: 'cannot divide by zero'
    ]

    raisedToInteger: n withCache: cache [
	"Internal implementation of #raisedToInteger:."

	<category: 'private'>
	"For very big numbers, remove the rightmost bit."

	| result index |
	n > 255 
	    ifTrue: 
		[result := self raisedToInteger: n // 2 withCache: cache.
		^(n bitAnd: 1) = 0 
		    ifTrue: [result squared]
		    ifFalse: [result * (result * self)]].

	"Else, use a table with the optimal choice of k so that
	 self^k * self^(n - k) does as few multiplications as possible."
	result := cache at: n.
	result isNil 
	    ifTrue: 
		[index := self powerTable at: n.
		result := (self raisedToInteger: n - index withCache: cache) 
			    * (self raisedToInteger: index withCache: cache).
		cache at: n put: result].
	^result
    ]

    powerTable [
	"Internal table for #raisedToInteger:withCache:.  Example:
	 (powerTable at: 9) == 6 means that n^9 is best computed
	 as n^3 * n^6.  From Knuth's Seminumerical Algorithms."

	<category: 'private'>
	^#[0 1 2 2 3 3 4 4 6 5 6 6 10 7 9 8 16 9 16 10 12 11 13 12 17 13 18 14 24 15 26 16 17 17 19 18 33 19 26 20 25 21 40 22 27 23 44 24 32 25 34 26 29 27 44 28 31 29 34 30 60 31 36 32 64 33 34 34 46 35 37 36 65 37 50 38 48 39 69 40 49 41 43 42 51 43 58 44 64 45 47 46 59 47 76 48 65 49 66 50 67 51 66 52 70 53 74 54 104 55 74 56 64 57 69 58 78 59 68 60 61 61 80 62 75 63 68 64 65 65 128 66 129 67 90 68 73 69 131 70 94 71 88 72 128 73 98 74 132 75 121 76 102 77 124 78 132 79 106 80 97 81 160 82 99 83 134 84 86 85 95 86 160 87 100 88 113 89 98 90 107 91 122 92 111 93 102 94 126 95 150 96 128 97 130 98 133 99 195 100 128 101 123 102 164 103 138 104 145 105 146 106 109 107 149 108 200 109 146 110 170 111 157 112 128 113 130 114 182 115 132 116 200 117 132 118 158 119 206 120 240 121 162 122 147 123 152 124 166 125 214 126 138 127 153]	"1 -   7"	"8 -  15"	"16 -  23"	"24 -  31"	"32 -  39"	"40 -  47"	"48 -  55"	"56 -  63"	"64 -  71"	"72 -  79"	"80 -  87"	"88 -  95"	"96 - 103"	"104 - 111"	"112 - 119"	"120 - 127"	"128 - 135"	"136 - 143"	"144 - 151"	"152 - 159"	"160 - 167"	"168 - 175"	"176 - 183"	"184 - 191"	"192 - 199"	"200 - 207"	"208 - 215"	"216 - 223"	"224 - 231"	"232 - 239"	"240 - 247"	"248 - 255"
    ]
]