/usr/share/gnu-smalltalk/kernel/Number.st is in gnu-smalltalk-common 3.2.5-1.
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"
]
]
|