author | ca |
Fri, 04 Jun 2004 15:22:43 +0200 | |
changeset 8371 | 4493f5ac7405 |
parent 8303 | 837daadaab78 |
child 8634 | 2c838074e754 |
permissions | -rw-r--r-- |
1 | 1 |
" |
5 | 2 |
COPYRIGHT (c) 1988 by Claus Gittinger |
5322 | 3 |
All Rights Reserved |
1 | 4 |
|
5 |
This software is furnished under a license and may be used |
|
6 |
only in accordance with the terms of that license and with the |
|
7 |
inclusion of the above copyright notice. This software may not |
|
8 |
be provided or otherwise made available to, or used by, any |
|
9 |
other person. No title to or ownership of the software is |
|
10 |
hereby transferred. |
|
11 |
" |
|
12 |
||
5360 | 13 |
"{ Package: 'stx:libbasic' }" |
14 |
||
1 | 15 |
ArithmeticValue subclass:#Number |
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16 |
instanceVariableNames:'' |
8301 | 17 |
classVariableNames:'DecimalPointCharacter DecimalPointCharacters' |
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|
18 |
poolDictionaries:'' |
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|
19 |
category:'Magnitude-Numbers' |
1 | 20 |
! |
21 |
||
1892 | 22 |
!Number class methodsFor:'documentation'! |
88 | 23 |
|
24 |
copyright |
|
25 |
" |
|
26 |
COPYRIGHT (c) 1988 by Claus Gittinger |
|
5322 | 27 |
All Rights Reserved |
1 | 28 |
|
88 | 29 |
This software is furnished under a license and may be used |
30 |
only in accordance with the terms of that license and with the |
|
31 |
inclusion of the above copyright notice. This software may not |
|
32 |
be provided or otherwise made available to, or used by, any |
|
33 |
other person. No title to or ownership of the software is |
|
34 |
hereby transferred. |
|
35 |
" |
|
36 |
! |
|
1 | 37 |
|
88 | 38 |
documentation |
39 |
" |
|
40 |
abstract superclass for all kinds of numbers |
|
1295 | 41 |
|
42 |
[author:] |
|
5322 | 43 |
Claus Gittinger |
1628 | 44 |
|
45 |
[see also:] |
|
5322 | 46 |
Integer LargeInteger SmallInteger |
47 |
LimitedPrecisionReal Float ShortFloat |
|
48 |
Fraction FixedPoint |
|
88 | 49 |
" |
50 |
! ! |
|
1 | 51 |
|
1892 | 52 |
!Number class methodsFor:'instance creation'! |
1 | 53 |
|
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fromString:aString |
55 |
"for compatibility with other smalltalks - same as #readFrom:" |
|
56 |
||
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57 |
|s num| |
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58 |
|
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59 |
s := aString readStream. |
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60 |
num := self readFrom:s onError:[^ self error:'invalid number']. |
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61 |
s atEnd ifFalse:[^ self error:'garbage at end of number']. |
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62 |
^ num. |
3060 | 63 |
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3716 | 64 |
" |
65 |
Number fromString:'12345' |
|
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Number fromString:'abc' |
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|
67 |
Number fromString:'1abc' |
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'12345' asNumber |
69 |
" |
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||
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"Modified: / 3.8.1998 / 20:05:11 / cg" |
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! |
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74 |
fromString:aString onError:exceptionBlock |
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"for compatibility with other smalltalks - same as #readFrom:" |
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76 |
||
77 |
^ self readFrom:aString onError:exceptionBlock |
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||
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" |
80 |
Number fromString:'12345' onError:0 |
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Number fromString:'fooBarBaz' onError:0 |
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" |
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||
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"Modified: / 3.8.1998 / 20:05:34 / cg" |
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! |
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|
87 |
readFrom:aStringOrStream onError:exceptionBlock |
1 | 88 |
"return the next Number from the (character-)stream aStream; |
202 | 89 |
skipping all whitespace first; return the value of exceptionBlock, |
7356 | 90 |
if no number can be read. |
91 |
This method is less strict than the smalltalk number reader; it |
|
92 |
allows for prefixed + and also allows missing fractional part after eE" |
|
1 | 93 |
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94 |
^ [ |
8301 | 95 |
|value intValue mantissaAndScale scale decimalPointCharacters decimalMantissa str |
7356 | 96 |
nextChar radix negative signExp exp denom| |
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8301 | 98 |
decimalPointCharacters := self decimalPointCharacters. |
99 |
||
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str := aStringOrStream readStream. |
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101 |
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102 |
nextChar := str skipSeparators. |
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103 |
nextChar isNil ifTrue:[^ exceptionBlock value]. |
3 | 104 |
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(nextChar == $-) ifTrue:[ |
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106 |
negative := true. |
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107 |
str next. |
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|
108 |
nextChar := str peekOrNil |
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109 |
] ifFalse:[ |
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110 |
negative := false. |
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|
111 |
(nextChar == $+) ifTrue:[ |
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112 |
str next. |
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113 |
nextChar := str peekOrNil |
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114 |
] |
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115 |
]. |
8301 | 116 |
(nextChar isDigit or:[(decimalPointCharacters includes:nextChar)]) ifFalse:[ |
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117 |
^ exceptionBlock value. |
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118 |
"/ value := super readFrom:str. |
339 | 119 |
"/ negative ifTrue:[value := value negated]. |
120 |
"/ ^ value |
|
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121 |
]. |
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(decimalPointCharacters includes:nextChar) ifTrue:[ |
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123 |
radix := 10. |
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|
124 |
value := 0.0. |
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125 |
intValue := 0. |
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126 |
] ifFalse:[ |
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127 |
value := Integer readFrom:str radix:10. |
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|
128 |
nextChar := str peekOrNil. |
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129 |
((nextChar == $r) or:[ nextChar == $R]) ifTrue:[ |
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130 |
str next. |
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131 |
radix := value. |
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|
132 |
value := Integer readFrom:str radix:radix. |
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133 |
] ifFalse:[ |
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134 |
radix := 10 |
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135 |
]. |
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136 |
intValue := value. |
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137 |
]. |
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allow for degenerate float to be read
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|
138 |
|
8301 | 139 |
(decimalPointCharacters includes:nextChar) ifTrue:[ |
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140 |
str next. |
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|
141 |
nextChar := str peekOrNil. |
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|
142 |
scale := 0. |
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|
143 |
decimalMantissa := 0. |
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144 |
(nextChar notNil and:[nextChar isDigitRadix:radix]) ifTrue:[ |
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145 |
mantissaAndScale := Number readMantissaAndScaleFrom:str radix:radix. |
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|
146 |
value := value asFloat + (mantissaAndScale first). |
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|
147 |
nextChar := str peekOrNil |
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148 |
] |
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149 |
]. |
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|
150 |
('eEdDqQ' includes:nextChar) ifTrue:[ |
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|
151 |
str next. |
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|
152 |
nextChar := str peekOrNil. |
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|
153 |
signExp := 1. |
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|
154 |
(nextChar == $+) ifTrue:[ |
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|
155 |
str next. |
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|
156 |
nextChar := str peekOrNil. |
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|
157 |
] ifFalse:[ |
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|
158 |
(nextChar == $-) ifTrue:[ |
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|
159 |
str next. |
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|
160 |
nextChar := str peekOrNil. |
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|
161 |
signExp := -1 |
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|
162 |
] |
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|
163 |
]. |
7356 | 164 |
('qQ' includes:nextChar) ifTrue:[ |
165 |
value := value asLongFloat. |
|
166 |
] ifFalse:[ |
|
167 |
value := value asFloat. |
|
168 |
"/ future: (for now, always create Doubles for Dolphin,Squeak etc. compatibility |
|
169 |
"/ ('eE' includes:nextChar) ifTrue:[ |
|
170 |
"/ value := value asShortFloat |
|
171 |
"/ ] |
|
172 |
]. |
|
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|
173 |
(nextChar notNil and:[(nextChar isDigitRadix:radix)]) ifTrue:[ |
7356 | 174 |
exp := (Integer readFrom:str radix:radix) * signExp. |
175 |
value := value * ((value class unity * 10.0) raisedToInteger:exp) |
|
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176 |
] |
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|
177 |
] ifFalse:[ |
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|
178 |
('s' includes:nextChar) ifTrue:[ |
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|
179 |
mantissaAndScale isNil ifTrue:[ |
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|
180 |
value := intValue asFixedPoint:0. |
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|
181 |
] ifFalse:[ |
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|
182 |
denom := 10 raisedTo:mantissaAndScale last. |
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|
183 |
value := FixedPoint |
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|
184 |
numerator:(intValue * denom) + (mantissaAndScale second) |
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|
185 |
denominator:denom |
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|
186 |
scale:mantissaAndScale last. |
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|
187 |
]. |
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|
188 |
] ifFalse:[ |
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|
189 |
value isLimitedPrecisionReal ifTrue:[ |
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|
190 |
value := value asFloat. |
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|
191 |
] |
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care to not always return longFloats
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|
192 |
]. |
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|
193 |
]. |
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|
194 |
negative ifTrue:[ |
65014fd967d9
Avoid creation of block in #readFrom:onError:
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|
195 |
value := value negated |
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|
196 |
]. |
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|
197 |
value. |
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|
198 |
] on:Error do:exceptionBlock |
1 | 199 |
|
329 | 200 |
" |
201 |
Number readFrom:(ReadStream on:'54.32e-01') |
|
202 |
Number readFrom:(ReadStream on:'12345678901234567890') |
|
7356 | 203 |
Number readFrom:(ReadStream on:'12345678901234567890.0') |
204 |
Number readFrom:(ReadStream on:'12345678901234567890.012345678901234567890') |
|
329 | 205 |
Number readFrom:(ReadStream on:'16rAAAAFFFFAAAAFFFF') |
569
7134eb78cf48
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diff
changeset
|
206 |
Number readFrom:'16rAAAAFFFFAAAAFFFF' |
7134eb78cf48
readFrom:onError: can now also read from a string
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parents:
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diff
changeset
|
207 |
Number readFrom:'0.000001' |
329 | 208 |
'+00000123.45' asNumber |
6899
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|
209 |
Number readFrom:'99s' |
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changeset
|
210 |
Number readFrom:'99.00s' |
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parents:
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diff
changeset
|
211 |
Number readFrom:'99.0000000s' |
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parents:
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diff
changeset
|
212 |
Number readFrom:'.0000000s' |
7356 | 213 |
Number readFrom:'.0000000q' |
214 |
Number readFrom:'.0000000f' |
|
215 |
Number readFrom:'.0000000e' |
|
216 |
Number readFrom:'.0000000s1' |
|
217 |
Number readFrom:'.0000000q1' |
|
218 |
Number readFrom:'.0000000f1' |
|
219 |
Number readFrom:'.0000000e1' |
|
8301 | 220 |
|
221 |
DecimalPointCharacters := #( $. $, ). |
|
222 |
Number readFrom:'99,00' |
|
223 |
||
224 |
DecimalPointCharacters := #( $. ). |
|
225 |
Number readFrom:'99,00' |
|
329 | 226 |
" |
569
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parents:
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diff
changeset
|
227 |
|
3375
7c64da3964e4
faster conversion from string (due to slow #pastEnd)
Claus Gittinger <cg@exept.de>
parents:
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diff
changeset
|
228 |
"Modified: / 14.4.1998 / 19:22:50 / cg" |
296 | 229 |
! |
230 |
||
231 |
readSmalltalkSyntaxFrom:aStream |
|
232 |
"ST-80 compatibility (thanks to a note from alpha testers) |
|
233 |
read and return the next Number in smalltalk syntax from the |
|
7356 | 234 |
(character-) aStream. |
235 |
Returns nil if aStream contains no valid number." |
|
329 | 236 |
|
3613
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|
237 |
^ Scanner scanNumberFrom:aStream |
75629df7f224
fixed readSmalltalkSyntax (dont read behind number)
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changeset
|
238 |
"/ ^ Compiler evaluate:aStream compile:false "/ self readFrom:aStream. |
296 | 239 |
|
329 | 240 |
" |
6899
9ed8494c9f10
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diff
changeset
|
241 |
Number readSmalltalkSyntaxFrom:'99d' |
9ed8494c9f10
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parents:
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diff
changeset
|
242 |
Number readSmalltalkSyntaxFrom:'99.00d' |
329 | 243 |
Number readSmalltalkSyntaxFrom:(ReadStream on:'54.32e-01') |
244 |
Number readSmalltalkSyntaxFrom:(ReadStream on:'12345678901234567890') |
|
245 |
Number readSmalltalkSyntaxFrom:(ReadStream on:'16rAAAAFFFFAAAAFFFF') |
|
246 |
Number readSmalltalkSyntaxFrom:(ReadStream on:'(1/10)') |
|
247 |
Number readFrom:(ReadStream on:'(1/10)') |
|
248 |
Number readSmalltalkSyntaxFrom:(ReadStream on:'+00000123.45') |
|
249 |
Number readFrom:(ReadStream on:'+00000123.45') |
|
5013 | 250 |
|
251 |
|s| |
|
252 |
s := ReadStream on:'2.'. |
|
253 |
Number readSmalltalkSyntaxFrom:s. |
|
254 |
s next |
|
255 |
||
256 |
|s| |
|
257 |
s := ReadStream on:'2.0.'. |
|
258 |
Number readSmalltalkSyntaxFrom:s. |
|
259 |
s next |
|
329 | 260 |
" |
3613
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fixed readSmalltalkSyntax (dont read behind number)
Claus Gittinger <cg@exept.de>
parents:
3394
diff
changeset
|
261 |
|
5013 | 262 |
"Modified: / 19.11.1999 / 18:26:47 / cg" |
1 | 263 |
! ! |
701 | 264 |
|
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
265 |
!Number class methodsFor:'constants'! |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
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diff
changeset
|
266 |
|
8301 | 267 |
decimalPointCharacter |
268 |
"printed" |
|
269 |
||
270 |
DecimalPointCharacter isNil ifTrue:[ |
|
271 |
DecimalPointCharacter := $. |
|
272 |
]. |
|
273 |
! |
|
274 |
||
8303 | 275 |
decimalPointCharacter:aCharacter |
276 |
"printed" |
|
277 |
||
278 |
DecimalPointCharacter := aCharacter |
|
279 |
||
280 |
" |
|
281 |
1.5 printString |
|
282 |
||
283 |
Number decimalPointCharacter:$,. |
|
284 |
1.5 printString |
|
285 |
Number decimalPointCharacter:$.. |
|
286 |
" |
|
287 |
! |
|
288 |
||
8301 | 289 |
decimalPointCharacters |
290 |
"accepted when converting from a string" |
|
291 |
||
292 |
DecimalPointCharacters isNil ifTrue:[ |
|
293 |
DecimalPointCharacters := #( $. ) |
|
294 |
]. |
|
295 |
^ DecimalPointCharacters |
|
8303 | 296 |
|
297 |
" |
|
298 |
1.5 printString |
|
299 |
||
300 |
Number decimalPointCharacters:#( $. $,) . |
|
301 |
Number fromString:'1.5'. |
|
302 |
Number fromString:'1,5'. |
|
303 |
Number decimalPointCharacters:#( $. ). |
|
304 |
" |
|
305 |
! |
|
306 |
||
307 |
decimalPointCharacters:aCollectionOfCharacters |
|
308 |
"accepted when converting from a string" |
|
309 |
||
310 |
DecimalPointCharacters := aCollectionOfCharacters |
|
311 |
||
312 |
" |
|
313 |
Number decimalPointCharacters:#( $. $,) . |
|
314 |
Number fromString:'1.5'. |
|
315 |
Number fromString:'1,5'. |
|
316 |
Number decimalPointCharacters:#( $. ). |
|
317 |
" |
|
8301 | 318 |
! |
319 |
||
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
320 |
epsilon |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
321 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
322 |
^ self subclassResponsibility |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
323 |
! ! |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
324 |
|
1892 | 325 |
!Number class methodsFor:'error reporting'! |
701 | 326 |
|
6195 | 327 |
raise:aSignalSymbolOrErrorClass receiver:someNumber selector:sel arg:arg errorString:text |
3394 | 328 |
"ST-80 compatible signal raising. Provided for PD numeric classes" |
329 |
||
4558 | 330 |
<context: #return> |
331 |
||
6195 | 332 |
^ self |
333 |
raise:aSignalSymbolOrErrorClass |
|
334 |
receiver:someNumber |
|
335 |
selector:sel |
|
336 |
arguments:(Array with:arg) |
|
337 |
errorString:text |
|
3394 | 338 |
|
339 |
" |
|
340 |
Number |
|
6195 | 341 |
raise:#domainErrorSignal |
342 |
receiver:1.0 |
|
343 |
selector:#sin |
|
344 |
arg:nil |
|
345 |
errorString:'foo bar test' |
|
3394 | 346 |
" |
6195 | 347 |
|
348 |
"Modified: / 16.11.2001 / 14:12:50 / cg" |
|
3394 | 349 |
! |
350 |
||
6195 | 351 |
raise:aSignalSymbolOrErrorClass receiver:someNumber selector:sel arguments:argArray errorString:text |
6194
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
352 |
"ST-80 compatible signal raising. Provided for PD numeric classes. |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
353 |
aSignalSymbolOrErrorClass is either an Error-subclass, or |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
354 |
the selector which is sent to myself, to retrieve the Exception class / Signal." |
701 | 355 |
|
4558 | 356 |
<context: #return> |
357 |
||
6194
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
358 |
|msg signalOrException| |
701 | 359 |
|
360 |
msg := MessageSend |
|
6194
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
361 |
receiver:someNumber |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
362 |
selector:sel |
6195 | 363 |
arguments:argArray. |
3394 | 364 |
|
6194
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
365 |
aSignalSymbolOrErrorClass isSymbol ifTrue:[ |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
366 |
signalOrException := self perform:aSignalSymbolOrErrorClass. |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
367 |
] ifFalse:[ |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
368 |
signalOrException := aSignalSymbolOrErrorClass. "/ assume its an Error-Subclass |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
369 |
]. |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
370 |
|
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
371 |
^ signalOrException |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
372 |
raiseRequestWith:msg |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
373 |
errorString:text |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
374 |
in:thisContext sender |
701 | 375 |
|
376 |
" |
|
3394 | 377 |
Number |
6194
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
378 |
raise:#domainErrorSignal |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
379 |
receiver:1.0 |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
380 |
selector:#foo |
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
381 |
errorString:'foo bar test' |
701 | 382 |
" |
6194
e060dbb4f75c
allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents:
6155
diff
changeset
|
383 |
|
6195 | 384 |
"Modified: / 16.11.2001 / 14:12:09 / cg" |
385 |
! |
|
386 |
||
387 |
raise:aSignalSymbolOrErrorClass receiver:someNumber selector:sel errorString:text |
|
388 |
"ST-80 compatible signal raising. Provided for PD numeric classes. |
|
389 |
aSignalSymbolOrErrorClass is either an Error-subclass, or |
|
390 |
the selector which is sent to myself, to retrieve the Exception class / Signal." |
|
391 |
||
392 |
<context: #return> |
|
393 |
||
394 |
^ self |
|
395 |
raise:aSignalSymbolOrErrorClass |
|
396 |
receiver:someNumber |
|
397 |
selector:sel |
|
398 |
arguments:#() |
|
399 |
errorString:text |
|
400 |
||
401 |
" |
|
402 |
Number |
|
403 |
raise:#domainErrorSignal |
|
404 |
receiver:1.0 |
|
405 |
selector:#foo |
|
406 |
errorString:'foo bar test' |
|
407 |
" |
|
408 |
||
409 |
"Modified: / 16.11.2001 / 14:13:16 / cg" |
|
701 | 410 |
! ! |
411 |
||
1892 | 412 |
!Number class methodsFor:'private'! |
701 | 413 |
|
6899
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
414 |
readMantissaAndScaleFrom:aStream radix:radix |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
415 |
"helper for readFrom: - |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
416 |
return the mantissa (post-decimal-point digits) from the (character-)stream aStream; |
7356 | 417 |
In addition, the scale (number of postDecimalPoint digits) is returned |
418 |
(to support reading fixedPoint numbers). |
|
6899
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
419 |
No whitespace is skipped. |
7356 | 420 |
Errs if no number is available on aStream." |
6899
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
421 |
|
7388
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
422 |
|nextChar value factor intMantissa scale highPrecision| |
6899
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
423 |
|
7388
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
424 |
highPrecision := false. |
6899
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
425 |
value := 0.0. |
7388
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
426 |
factor := 1.0 asLongFloat / radix. |
6899
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
427 |
scale := 0. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
428 |
intMantissa := 0. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
429 |
nextChar := aStream peekOrNil. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
430 |
[nextChar notNil and:[nextChar isDigitRadix:radix]] whileTrue:[ |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
431 |
value := value + (nextChar digitValue * factor). |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
432 |
intMantissa := (intMantissa * radix) + nextChar digitValue. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
433 |
factor := factor / radix. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
434 |
scale := scale + 1. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
435 |
aStream next. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
436 |
nextChar := aStream peekOrNil |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
437 |
]. |
7388
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
438 |
|
6899
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
439 |
^ (Array with:value with:intMantissa with:scale). |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
440 |
|
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
441 |
" |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
442 |
Number readMantissaAndScaleFrom:'234' readStream radix:10. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
443 |
Number readMantissaAndScaleFrom:'2' readStream radix:10. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
444 |
Number readMantissaAndScaleFrom:'234567' readStream radix:10. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
445 |
Number readMantissaAndScaleFrom:'234000' readStream radix:10. |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
446 |
Number readMantissaAndScaleFrom:'234' readStream radix:10. |
7356 | 447 |
|
448 |
Number readMantissaAndScaleFrom:'12345678901234567890' readStream radix:10. |
|
6899
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
449 |
" |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
450 |
|
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
451 |
"Modified: / 14.4.1998 / 18:47:47 / cg" |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
452 |
! |
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
453 |
|
701 | 454 |
readMantissaFrom:aStream radix:radix |
455 |
"helper for readFrom: - |
|
6692 | 456 |
return the mantissa (post-decimal-point digits) |
457 |
from the (character-)stream aStream; |
|
458 |
No whitespace is skipped. |
|
459 |
Errs if no number available." |
|
701 | 460 |
|
6899
9ed8494c9f10
support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents:
6702
diff
changeset
|
461 |
^ (self readMantissaAndScaleFrom:aStream radix:radix) first |
3375
7c64da3964e4
faster conversion from string (due to slow #pastEnd)
Claus Gittinger <cg@exept.de>
parents:
3060
diff
changeset
|
462 |
|
6692 | 463 |
" |
464 |
Number readMantissaFrom:'234' readStream radix:10. |
|
465 |
Number readMantissaFrom:'2' readStream radix:10. |
|
466 |
Number readMantissaFrom:'234567' readStream radix:10. |
|
467 |
" |
|
468 |
||
3375
7c64da3964e4
faster conversion from string (due to slow #pastEnd)
Claus Gittinger <cg@exept.de>
parents:
3060
diff
changeset
|
469 |
"Modified: / 14.4.1998 / 18:47:47 / cg" |
701 | 470 |
! ! |
471 |
||
7261 | 472 |
!Number methodsFor:'Compatibility-Squeak'! |
4988 | 473 |
|
474 |
asSmallAngleDegrees |
|
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
475 |
"Return the receiver normalized to lie within the range (-180, 180)" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
476 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
477 |
| pos | |
4988 | 478 |
|
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
479 |
pos := self \\ 360. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
480 |
pos > 180 ifTrue: [pos := pos - 360]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
481 |
^ pos |
4988 | 482 |
|
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
483 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
484 |
#(-500 -300 -150 -5 0 5 150 300 500 1200) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
485 |
collect: [:n | n asSmallAngleDegrees] |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
486 |
" |
6072 | 487 |
! |
4988 | 488 |
|
6335
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
489 |
closeFrom:aNumber |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
490 |
"are these two numbers close?" |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
491 |
|
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
492 |
| fuzz | |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
493 |
|
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
494 |
self isNaN == aNumber isNaN ifFalse: [^ false]. |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
495 |
self isInfinite == aNumber isInfinite ifFalse: [^ false]. |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
496 |
|
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
497 |
fuzz := (self abs max:aNumber abs) * 0.0001. |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
498 |
^ (self - aNumber) abs <= fuzz |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
499 |
|
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
500 |
" |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
501 |
9.0 closeTo: 8.9999 |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
502 |
9.9 closeTo: 9 |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
503 |
(9/3) closeTo: 2.9999 |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
504 |
1 closeTo: 0.9999 |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
505 |
1 closeTo: 1.0001 |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
506 |
1 closeTo: 1.001 |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
507 |
1 closeTo: 0.999 |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
508 |
|
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
509 |
0.9999 closeTo: 1 |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
510 |
1.0001 closeTo: 1 |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
511 |
1.001 closeTo: 1 |
6345 | 512 |
0.999 closeTo: 1 |
513 |
Float NaN closeTo:Float NaN |
|
514 |
Float infinity closeTo:Float infinity |
|
6335
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
515 |
" |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
516 |
! |
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
517 |
|
6143 | 518 |
closeTo:num |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
519 |
"are these two numbers close to each other?" |
6143 | 520 |
|
6374 | 521 |
num isNumber ifFalse:[^false]. |
6335
8286bc57d05e
closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents:
6258
diff
changeset
|
522 |
^ num closeFrom:self |
6143 | 523 |
|
524 |
" |
|
525 |
1 closeTo:1.0000000001 |
|
526 |
1 closeTo:1.001 |
|
527 |
" |
|
6155 | 528 |
|
529 |
"Created: / 5.11.2001 / 18:07:26 / cg" |
|
6143 | 530 |
! |
531 |
||
4988 | 532 |
newTileMorphRepresentative |
533 |
^ TileMorph new addArrows; setLiteral: self; addSuffixIfCan |
|
534 |
! |
|
535 |
||
536 |
stringForReadout |
|
537 |
^ self rounded printString |
|
538 |
! ! |
|
539 |
||
6692 | 540 |
!Number methodsFor:'coercing'! |
541 |
||
542 |
retry: aSymbol coercing: aNumber |
|
543 |
"Arithmetic represented by the symbol, aSymbol, |
|
544 |
could not be performed with the receiver and the argument, |
|
545 |
aNumber, because of the differences in representation. Coerce either |
|
546 |
the receiver or the argument, depending on which has higher generality, and |
|
547 |
try again. If the symbol is the equals sign, answer false if the argument |
|
548 |
is not a Number. If the generalities are the same, create an error message." |
|
549 |
||
550 |
|myGenerality otherGenerality| |
|
551 |
||
552 |
(aSymbol == #=) ifTrue:[ |
|
6702
545b50725894
infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents:
6692
diff
changeset
|
553 |
(aNumber respondsTo:#generality) ifFalse:[^ false] |
6692 | 554 |
] ifFalse:[ |
6702
545b50725894
infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents:
6692
diff
changeset
|
555 |
(aNumber respondsTo:#generality) ifFalse:[ |
545b50725894
infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents:
6692
diff
changeset
|
556 |
self error:'retry:coercing: argument is not a number'. |
545b50725894
infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents:
6692
diff
changeset
|
557 |
^ self |
545b50725894
infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents:
6692
diff
changeset
|
558 |
] |
6692 | 559 |
]. |
560 |
myGenerality := self generality. |
|
561 |
otherGenerality := aNumber generality. |
|
562 |
(myGenerality > otherGenerality) ifTrue:[ |
|
6702
545b50725894
infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents:
6692
diff
changeset
|
563 |
^ self perform:aSymbol with:(self coerce:aNumber) |
6692 | 564 |
]. |
565 |
(myGenerality < otherGenerality) ifTrue:[ |
|
6702
545b50725894
infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents:
6692
diff
changeset
|
566 |
^ (aNumber coerce:self) perform:aSymbol with:aNumber |
6692 | 567 |
]. |
568 |
self error:'retry:coercing: oops - same generality' |
|
569 |
! ! |
|
570 |
||
701 | 571 |
!Number methodsFor:'converting'! |
572 |
||
3634 | 573 |
% aNumber |
574 |
"Return a complex number with the receiver as the real part and |
|
575 |
aNumber as the imaginary part" |
|
576 |
||
577 |
^ Complex real:self imaginary:aNumber |
|
578 |
||
579 |
"Modified: / 9.7.1998 / 10:18:12 / cg" |
|
580 |
! |
|
581 |
||
701 | 582 |
@ aNumber |
583 |
"return a Point with the receiver as x-coordinate and the argument |
|
584 |
as y-coordinate" |
|
585 |
||
586 |
%{ /* NOCONTEXT */ |
|
587 |
||
588 |
/* |
|
589 |
* I cannot tell if this special code is worth anything |
|
590 |
*/ |
|
5322 | 591 |
if (__CanDoQuickNew(sizeof(struct __Point))) { /* OBJECT ALLOCATION */ |
7857
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
592 |
OBJ newPoint; |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
593 |
int spc; |
701 | 594 |
|
7857
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
595 |
__qCheckedAlignedNew(newPoint, sizeof(struct __Point)); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
596 |
__InstPtr(newPoint)->o_class = @global(Point); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
597 |
__qSTORE(newPoint, @global(Point)); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
598 |
__PointInstPtr(newPoint)->p_x = self; |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
599 |
__PointInstPtr(newPoint)->p_y = aNumber; |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
600 |
if (! __bothSmallInteger(self, aNumber)) { |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
601 |
spc = __qSpace(newPoint); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
602 |
__STORE_SPC(newPoint, aNumber, spc); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
603 |
__STORE_SPC(newPoint, self, spc); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
604 |
} |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
605 |
RETURN ( newPoint ); |
701 | 606 |
} |
607 |
%} |
|
608 |
. |
|
609 |
^ Point x:self y:aNumber |
|
610 |
! |
|
611 |
||
3634 | 612 |
asComplex |
613 |
"Return a complex number with the receiver as the real part and |
|
614 |
zero as the imaginary part" |
|
615 |
||
7356 | 616 |
^ Complex real:self |
3634 | 617 |
|
618 |
"Modified: / 9.7.1998 / 10:18:16 / cg" |
|
619 |
! |
|
620 |
||
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
621 |
asMetaNumber |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
622 |
^ SomeNumber new realNumber:self |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
623 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
624 |
|
7214 | 625 |
asNumber |
626 |
||
627 |
^ self. |
|
628 |
! |
|
629 |
||
701 | 630 |
asPoint |
631 |
"return a new Point with the receiver as all coordinates; |
|
632 |
often used to supply the same value in two dimensions, as with |
|
633 |
symmetrical gridding or scaling." |
|
634 |
||
635 |
%{ /* NOCONTEXT */ |
|
636 |
||
5322 | 637 |
if (__CanDoQuickNew(sizeof(struct __Point))) { /* OBJECT ALLOCATION */ |
7857
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
638 |
OBJ newPoint; |
701 | 639 |
|
7857
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
640 |
__qCheckedAlignedNew(newPoint, sizeof(struct __Point)); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
641 |
__InstPtr(newPoint)->o_class = @global(Point); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
642 |
__qSTORE(newPoint, @global(Point)); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
643 |
__PointInstPtr(newPoint)->p_x = self; |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
644 |
__PointInstPtr(newPoint)->p_y = self; |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
645 |
__STORE(newPoint, self); |
51971c337c26
Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents:
7729
diff
changeset
|
646 |
RETURN ( newPoint ); |
701 | 647 |
} |
648 |
%}. |
|
649 |
^ Point x:self y:self |
|
650 |
! |
|
651 |
||
2416 | 652 |
decodeAsLiteralArray |
653 |
"given a literalEncoding in the receiver, |
|
654 |
create & return the corresponding object. |
|
655 |
The inverse operation to #literalArrayEncoding." |
|
656 |
||
657 |
^ self |
|
658 |
||
659 |
"Created: 25.2.1997 / 19:17:06 / cg" |
|
660 |
"Modified: 25.2.1997 / 19:17:42 / cg" |
|
661 |
! |
|
662 |
||
701 | 663 |
degreesToRadians |
664 |
"interpreting the receiver as radians, return the degrees" |
|
665 |
||
8203 | 666 |
^ self * (Float pi / 180.0) |
7388
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
667 |
|
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
668 |
" |
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
669 |
180 degreesToRadians |
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
670 |
Float pi radiansToDegrees |
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
671 |
" |
701 | 672 |
! |
673 |
||
674 |
literalArrayEncoding |
|
1245 | 675 |
"encode myself as an array literal, from which a copy of the receiver |
676 |
can be reconstructed with #decodeAsLiteralArray." |
|
701 | 677 |
|
678 |
^ self |
|
679 |
||
680 |
"Modified: 1.9.1995 / 02:25:26 / claus" |
|
1245 | 681 |
"Modified: 22.4.1996 / 13:00:27 / cg" |
701 | 682 |
! |
683 |
||
684 |
radiansToDegrees |
|
685 |
"interpreting the receiver as degrees, return the radians" |
|
686 |
||
8203 | 687 |
^ self * (180.0 / Float pi) |
7388
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
688 |
|
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
689 |
" |
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
690 |
180 degreesToRadians |
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
691 |
Float pi radiansToDegrees |
bb89a53e2682
fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents:
7356
diff
changeset
|
692 |
" |
6637 | 693 |
! |
694 |
||
695 |
withScale:newScale |
|
8203 | 696 |
"return a fixedPoint number representing the same value as the receiver, |
6637 | 697 |
with newScale number of post-decimal digits" |
698 |
||
699 |
^ self asFixedPoint:newScale |
|
700 |
||
701 |
" |
|
702 |
1234 withScale:2 |
|
703 |
1234.1 withScale:2 |
|
704 |
1234.12 withScale:2 |
|
705 |
1234.123 withScale:2 |
|
706 |
(1/7) withScale:2 |
|
707 |
" |
|
701 | 708 |
! ! |
709 |
||
710 |
!Number methodsFor:'intervals'! |
|
711 |
||
6072 | 712 |
downTo:stop |
713 |
"return an interval from receiver down to the argument, incrementing by -1" |
|
714 |
||
715 |
^ self to:stop by:-1 |
|
716 |
||
717 |
" |
|
718 |
(10 downTo:1) do:[:i | Transcript showCR:i]. |
|
719 |
" |
|
720 |
! |
|
721 |
||
701 | 722 |
to:stop |
723 |
"return an interval from receiver up to the argument, incrementing by 1" |
|
724 |
||
725 |
^ Interval from:self to:stop |
|
726 |
! |
|
727 |
||
728 |
to:stop by:step |
|
729 |
"return an interval from receiver up to the argument, incrementing by step" |
|
730 |
||
731 |
^ Interval from:self to:stop by:step |
|
6154 | 732 |
! |
733 |
||
734 |
to:stop byFactor:factor |
|
735 |
"return a geometric series from receiver up to the argument; |
|
736 |
elements have a constant factor in between" |
|
737 |
||
738 |
^ GeometricSeries from:self to:stop byFactor:factor |
|
739 |
||
740 |
" |
|
741 |
(1 to:256 byFactor:2) |
|
742 |
(256 to:1 byFactor:1/2) |
|
743 |
" |
|
701 | 744 |
! ! |
745 |
||
746 |
!Number methodsFor:'iteration'! |
|
747 |
||
748 |
timesRepeat:aBlock |
|
749 |
"evaluate the argument, aBlock self times" |
|
750 |
||
751 |
|count| |
|
752 |
||
753 |
count := self. |
|
754 |
[count > 0] whileTrue:[ |
|
5322 | 755 |
aBlock value. |
756 |
count := count - 1 |
|
701 | 757 |
] |
758 |
! ! |
|
759 |
||
3634 | 760 |
!Number methodsFor:'mathematical functions'! |
761 |
||
762 |
conjugated |
|
763 |
"Return the complex conjugate of this Number." |
|
764 |
||
765 |
^ self |
|
766 |
||
767 |
"Modified: / 9.7.1998 / 10:17:31 / cg" |
|
768 |
! |
|
769 |
||
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
770 |
exp |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
771 |
"compute e**x of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
772 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
773 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
774 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
775 |
^ self asFloat exp. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
776 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
777 |
^ self exp_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
778 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
779 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
780 |
floorLog:radix |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
781 |
"return the logarithm truncated as an integer" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
782 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
783 |
^ (self log:radix) floor |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
784 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
785 |
|
3634 | 786 |
imaginary |
787 |
"Return the imaginary part of this Number." |
|
788 |
||
789 |
^ 0 |
|
790 |
||
791 |
"Modified: / 9.7.1998 / 10:17:24 / cg" |
|
792 |
! |
|
793 |
||
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
794 |
ln |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
795 |
"compute ln of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
796 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
797 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
798 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
799 |
^ self asFloat ln. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
800 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
801 |
^ self ln_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
802 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
803 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
804 |
log |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
805 |
"return log base 10 of the receiver. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
806 |
Alias for log10." |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
807 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
808 |
^ self log10 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
809 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
810 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
811 |
log10 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
812 |
"return log base 10 of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
813 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
814 |
^ self log:10 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
815 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
816 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
817 |
log:aNumber |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
818 |
"return log base aNumber of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
819 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
820 |
^ self ln / aNumber ln |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
821 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
822 |
|
7468
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
823 |
raisedTo:aNumber |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
824 |
"return the receiver raised to aNumber" |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
825 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
826 |
aNumber = 0 ifTrue:[^ 1]. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
827 |
aNumber = 1 ifTrue:[^ self]. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
828 |
aNumber isInteger ifTrue:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
829 |
^ self raisedToInteger:aNumber |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
830 |
]. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
831 |
^ self asFloat raisedTo:aNumber |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
832 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
833 |
" |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
834 |
2 raisedTo: 4 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
835 |
10 raisedTo: 4 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
836 |
" |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
837 |
! |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
838 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
839 |
raisedToInteger:exp |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
840 |
"return the receiver raised to exp" |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
841 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
842 |
|result e t| |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
843 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
844 |
"use the addition chaining algorithm, |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
845 |
which is much faster for big exp-arguments" |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
846 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
847 |
result := 1. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
848 |
t := self. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
849 |
exp < 0 ifTrue:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
850 |
e := exp negated. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
851 |
] ifFalse:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
852 |
e := exp. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
853 |
]. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
854 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
855 |
[e ~~ 0] whileTrue:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
856 |
[(e bitAnd:1) == 0] whileTrue:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
857 |
e := e bitShift:-1. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
858 |
t := t * t. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
859 |
]. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
860 |
e := e - 1. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
861 |
result := result * t. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
862 |
]. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
863 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
864 |
(exp < 0) ifTrue:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
865 |
^ 1 / result |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
866 |
]. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
867 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
868 |
^ result |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
869 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
870 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
871 |
" |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
872 |
(2 raisedToInteger:216) |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
873 |
(2 raisedTo:216) |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
874 |
-> 105312291668557186697918027683670432318895095400549111254310977536 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
875 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
876 |
(2 raisedToInteger:216) asFloat |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
877 |
(2 raisedTo:216) asFloat |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
878 |
-> 1.05312E+65 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
879 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
880 |
(2 raisedToInteger:500) |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
881 |
(2 raisedTo:500) |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
882 |
-> 3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
883 |
2 raisedToInteger:10 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
884 |
-> 1024 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
885 |
-2 raisedToInteger:10 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
886 |
-> 1024 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
887 |
-2 raisedToInteger:9 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
888 |
-> -512 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
889 |
10 raisedToInteger:-10 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
890 |
-> (1/10000000000) |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
891 |
2 raisedToInteger:0 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
892 |
-> 1 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
893 |
2 raisedToInteger:-1 |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
894 |
-> (1/2) |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
895 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
896 |
Time millisecondsToRun:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
897 |
10000 timesRepeat:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
898 |
(2 raisedToInteger:500) |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
899 |
] |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
900 |
] |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
901 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
902 |
Time millisecondsToRun:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
903 |
|bigNum| |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
904 |
bigNum := 2 raisedToInteger:500. |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
905 |
10 timesRepeat:[ |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
906 |
(bigNum raisedToInteger:500) |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
907 |
] |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
908 |
] |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
909 |
" |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
910 |
|
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
911 |
"Created: / 27.4.1999 / 15:19:22 / stefan" |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
912 |
"Modified: / 27.4.1999 / 16:16:11 / stefan" |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
913 |
! |
61c8a3053bf4
moved math functions to number
Claus Gittinger <cg@exept.de>
parents:
7456
diff
changeset
|
914 |
|
3634 | 915 |
real |
916 |
"Return the real part of this Number." |
|
917 |
||
918 |
^ self |
|
919 |
||
920 |
"Modified: / 9.7.1998 / 10:17:17 / cg" |
|
6258 | 921 |
! |
922 |
||
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
923 |
sqrt |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
924 |
"return the square root of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
925 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
926 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
927 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
928 |
^ self asFloat sqrt. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
929 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
930 |
^ self sqrt_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
931 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
932 |
|
6258 | 933 |
timesTwoPower:anInteger |
934 |
"Return the receiver multiplied by 2.0 raised to the power of the argument. |
|
935 |
For protocol completeness wrt. Squeak and ST80." |
|
936 |
||
937 |
^ self * (2.0 raisedToInteger:anInteger) |
|
938 |
||
939 |
" |
|
940 |
123 timesTwoPower:0 |
|
941 |
123 timesTwoPower:1 |
|
942 |
123 timesTwoPower:2 |
|
943 |
123 timesTwoPower:3 |
|
944 |
" |
|
3634 | 945 |
! ! |
946 |
||
701 | 947 |
!Number methodsFor:'printing & storing'! |
948 |
||
5299
92b363dbd833
added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents:
5238
diff
changeset
|
949 |
printOn:aStream paddedWith:padCharacter to:size base:radix |
92b363dbd833
added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents:
5238
diff
changeset
|
950 |
|s| |
92b363dbd833
added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents:
5238
diff
changeset
|
951 |
|
8301 | 952 |
radix == 10 ifTrue:[ |
953 |
s := self printString. |
|
954 |
] ifFalse:[ |
|
955 |
s := self printStringRadix:radix. |
|
956 |
]. |
|
5299
92b363dbd833
added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents:
5238
diff
changeset
|
957 |
s printOn: aStream leftPaddedTo:size with: padCharacter |
8301 | 958 |
! |
5299
92b363dbd833
added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents:
5238
diff
changeset
|
959 |
|
8301 | 960 |
printStringRadix:radix |
961 |
self subclassResponsibility |
|
5299
92b363dbd833
added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents:
5238
diff
changeset
|
962 |
! |
92b363dbd833
added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents:
5238
diff
changeset
|
963 |
|
701 | 964 |
storeOn:aStream |
965 |
"append a string for storing the receiver onto the argument, |
|
966 |
aStream - since numbers are literals,they store as they print." |
|
967 |
||
968 |
^ self printOn:aStream |
|
969 |
! |
|
970 |
||
971 |
storeString |
|
972 |
"return a string for storing |
|
973 |
- since numbers are literals, they store as they print." |
|
974 |
||
975 |
^ self printString |
|
976 |
! ! |
|
977 |
||
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
978 |
!Number methodsFor:'taylor series'! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
979 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
980 |
arcSin_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
981 |
"compute the arcSine of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
982 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
983 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
984 |
"/ 1*x^3 1*3 * x^5 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
985 |
"/ arcSin = x + ----- + ---------- + ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
986 |
"/ 2* 3 2*4 * 5 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
987 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
988 |
|x2 num numf den denf approx lastApprox d| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
989 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
990 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
991 |
num := (x2 * self). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
992 |
approx := self + (num / 6). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
993 |
lastApprox := self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
994 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
995 |
numf := 3. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
996 |
denf := 4. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
997 |
den := 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
998 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
999 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1000 |
num := (num * x2) * numf. numf := numf + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1001 |
den := den * denf. denf := denf + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1002 |
d := den * numf. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1003 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1004 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1005 |
approx := approx + (num / d). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1006 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1007 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1008 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1009 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1010 |
0.5 arcSin 0.523599 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1011 |
0.5 asLongFloat arcSin 0.523598776 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1012 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1013 |
0.5 asLongFloat arcSin_withAccuracy:1 0.520833333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1014 |
0.5 asLongFloat arcSin_withAccuracy:0.1 0.520833333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1015 |
0.5 asLongFloat arcSin_withAccuracy:0.01 0.523177083 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1016 |
0.5 asLongFloat arcSin_withAccuracy:0.001 0.523525856 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1017 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1018 |
0.5 asLongFloat arcSin_withAccuracy:1e-20 0.523598776 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1019 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1020 |
0.5 asLargeFloat arcSin_withAccuracy:1e-30 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1021 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1022 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1023 |
0.1 arcSin 0.100167 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1024 |
0.1 asLongFloat arcSin 0.100167421 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1025 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1026 |
0.1 asLongFloat arcSin_withAccuracy:1 0.100166667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1027 |
0.1 asLongFloat arcSin_withAccuracy:0.1 0.100166667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1028 |
0.1 asLongFloat arcSin_withAccuracy:0.01 0.100166667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1029 |
0.1 asLongFloat arcSin_withAccuracy:0.001 0.100166667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1030 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1031 |
0.1 asLongFloat arcSin_withAccuracy:1e-20 0.100167421 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1032 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1033 |
0.1 asLargeFloat arcSin_withAccuracy:1e-30 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1034 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1035 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1036 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1037 |
arcSinh_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1038 |
"compute the hyperbolic arcSine of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1039 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1040 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1041 |
"/ 1*x^3 1*3 * x^5 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1042 |
"/ arcSinh = x - ----- + --------- - ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1043 |
"/ 2* 3 2*4 * 5 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1044 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1045 |
|x2 num numf den denf approx lastApprox d| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1046 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1047 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1048 |
num := (x2 * self) negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1049 |
approx := self + (num / 6). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1050 |
lastApprox := self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1051 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1052 |
numf := 3. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1053 |
denf := 4. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1054 |
den := 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1055 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1056 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1057 |
num := (num * x2) * numf. numf := numf + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1058 |
num := num negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1059 |
den := den * denf. denf := denf + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1060 |
d := den * numf. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1061 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1062 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1063 |
approx := approx + (num / d). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1064 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1065 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1066 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1067 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1068 |
0.5 arcSinh 0.481212 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1069 |
0.5 asLongFloat arcSinh 0.481211825 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1070 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1071 |
0.5 asLongFloat arcSinh_withAccuracy:1 0.479166667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1072 |
0.5 asLongFloat arcSinh_withAccuracy:0.1 0.479166667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1073 |
0.5 asLongFloat arcSinh_withAccuracy:0.01 0.481510417 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1074 |
0.5 asLongFloat arcSinh_withAccuracy:0.001 0.481161644 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1075 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1076 |
0.5 asLongFloat arcSinh_withAccuracy:1e-20 0.481211825 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1077 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1078 |
0.5 asLargeFloat arcSinh_withAccuracy:1e-30 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1079 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1080 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1081 |
0.1 arcSinh 0.0998341 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1082 |
0.1 asLongFloat arcSinh 0.0998340789 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1083 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1084 |
0.1 asLongFloat arcSinh_withAccuracy:1 0.0998333333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1085 |
0.1 asLongFloat arcSinh_withAccuracy:0.1 0.0998333333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1086 |
0.1 asLongFloat arcSinh_withAccuracy:0.01 0.0998333333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1087 |
0.1 asLongFloat arcSinh_withAccuracy:0.001 0.0998333333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1088 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1089 |
0.1 asLongFloat arcSinh_withAccuracy:1e-20 0.0998340789 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1090 |
0.1 asLongFloat arcSinh_withAccuracy:1e-30 0.0998340789 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1091 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1092 |
0.1 asLargeFloat arcSinh_withAccuracy:1e-30 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1093 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1094 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1095 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1096 |
arcTan_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1097 |
"compute the arcTangent of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1098 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1099 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1100 |
"/ x^3 x^5 x^7 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1101 |
"/ arcTan = x - --- + --- - --- ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1102 |
"/ 3 5 7 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1103 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1104 |
|x2 num den approx lastApprox| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1105 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1106 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1107 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1108 |
num := (x2 * self) negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1109 |
den := 3. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1110 |
approx := self + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1111 |
lastApprox := self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1112 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1113 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1114 |
den := den + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1115 |
num := (num * x2) negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1116 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1117 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1118 |
approx := approx + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1119 |
"/Transcript show:num; show:' '. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1120 |
"/Transcript show:den; show:' '. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1121 |
"/Transcript showCR:(num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1122 |
"/Transcript showCR:approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1123 |
"/Transcript cr. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1124 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1125 |
Transcript showCR:(lastApprox - approx) abs. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1126 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1127 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1128 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1129 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1130 |
1.0 arcTan 0.785398 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1131 |
1.0 asLongFloat arcTan 0.785398163 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1132 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1133 |
1.0 asLongFloat arcTan_withAccuracy:1 0.666666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1134 |
1.0 asLongFloat arcTan_withAccuracy:0.1 0.744011544 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1135 |
1.0 asLongFloat arcTan_withAccuracy:0.01 0.790299653 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1136 |
1.0 asLongFloat arcTan_withAccuracy:0.001 0.785897165 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1137 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1138 |
1.0 asLongFloat arcTan_withAccuracy:1e-20 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1139 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1140 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1141 |
0.5 arcTan 0.463648 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1142 |
0.5 asLongFloat arcTan 0.463647609 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1143 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1144 |
0.5 asLongFloat arcTan_withAccuracy:1 0.458333333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1145 |
0.5 asLongFloat arcTan_withAccuracy:0.1 0.458333333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1146 |
0.5 asLongFloat arcTan_withAccuracy:0.01 0.464583333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1147 |
0.5 asLongFloat arcTan_withAccuracy:0.001 0.463684276 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1148 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1149 |
0.5 asLongFloat arcTan_withAccuracy:1e-20 0.463647609 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1150 |
0.5 asLargeFloat arcTan_withAccuracy:1e-30 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1151 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1152 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1153 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1154 |
arcTanh_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1155 |
"compute the hyperbolic arcTangent of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1156 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1157 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1158 |
"/ x^3 x^5 x^7 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1159 |
"/ arcTanh = x + --- + --- + --- ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1160 |
"/ 3 5 7 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1161 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1162 |
|x2 num den approx lastApprox| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1163 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1164 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1165 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1166 |
num := (x2 * self). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1167 |
den := 3. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1168 |
approx := self + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1169 |
lastApprox := self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1170 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1171 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1172 |
den := den + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1173 |
num := (num * x2). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1174 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1175 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1176 |
approx := approx + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1177 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1178 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1179 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1180 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1181 |
0.5 arcTanh 0.549306 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1182 |
0.5 asLongFloat arcTanh 0.549306144 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1183 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1184 |
0.5 asLongFloat arcTanh_withAccuracy:1 0.541666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1185 |
0.5 asLongFloat arcTanh_withAccuracy:0.1 0.541666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1186 |
0.5 asLongFloat arcTanh_withAccuracy:0.01 0.547916667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1187 |
0.5 asLongFloat arcTanh_withAccuracy:0.001 0.549249752 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1188 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1189 |
0.5 asLongFloat arcTanh_withAccuracy:1e-20 0.549306144 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1190 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1191 |
0.5 asLargeFloat arcTanh_withAccuracy:1e-30 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1192 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1193 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1194 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1195 |
cos_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1196 |
"compute the cosine of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1197 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1198 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1199 |
"/ x^2 x^4 x^6 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1200 |
"/ cos = 1 - --- + --- - --- ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1201 |
"/ 2!! 4!! 6!! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1202 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1203 |
|x2 facN num den approx lastApprox| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1204 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1205 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1206 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1207 |
num := x2 negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1208 |
den := 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1209 |
facN := 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1210 |
approx := 1 + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1211 |
lastApprox := 1. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1212 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1213 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1214 |
facN := facN + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1215 |
den := den * (facN - 1) * facN. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1216 |
num := (num * x2) negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1217 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1218 |
approx := approx + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1219 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1220 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1221 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1222 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1223 |
1.0 cos 0.540302 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1224 |
1.0 asLongFloat cos_withAccuracy:1 0.5 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1225 |
1.0 asLongFloat cos_withAccuracy:0.1 0.541666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1226 |
1.0 asLongFloat cos_withAccuracy:0.01 0.540277778 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1227 |
1.0 asLongFloat cos_withAccuracy:0.001 0.540302579 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1228 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1229 |
1.0 asLongFloat cos_withAccuracy:1e-40 0.540302306 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1230 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1231 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1232 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1233 |
cosh_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1234 |
"compute the hyperbolic cosine of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1235 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1236 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1237 |
"/ x^2 x^4 x^6 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1238 |
"/ cosh = x + --- + --- + --- ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1239 |
"/ 2!! 4!! 6!! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1240 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1241 |
|x2 facN num den approx lastApprox| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1242 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1243 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1244 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1245 |
num := x2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1246 |
den := 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1247 |
facN := 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1248 |
approx := self + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1249 |
lastApprox := self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1250 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1251 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1252 |
facN := facN + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1253 |
den := den * (facN - 1) * facN. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1254 |
num := num * x2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1255 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1256 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1257 |
approx := approx + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1258 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1259 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1260 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1261 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1262 |
1.0 cosh 1.54308 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1263 |
1.0 asLongFloat cosh_withAccuracy:1 1.5 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1264 |
1.0 asLongFloat cosh_withAccuracy:0.1 1.54308 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1265 |
1.0 asLongFloat cosh_withAccuracy:0.01 1.54308 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1266 |
1.0 asLongFloat cosh_withAccuracy:0.001 1.54308 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1267 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1268 |
1.0 asLongFloat cosh_withAccuracy:1e-40 -> 1.543080 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1269 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1270 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1271 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1272 |
exp_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1273 |
"compute e**x of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1274 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1275 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1276 |
"/ x x^2 x^3 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1277 |
"/ e = 1 + --- + --- + --- ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1278 |
"/ 1!! 2!! 3!! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1279 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1280 |
|x2 facN num den approx lastApprox| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1281 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1282 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1283 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1284 |
num := x2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1285 |
den := 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1286 |
facN := 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1287 |
approx := self + self + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1288 |
lastApprox := self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1289 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1290 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1291 |
facN := facN + 1. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1292 |
den := den * facN. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1293 |
num := num * self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1294 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1295 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1296 |
approx := approx + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1297 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1298 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1299 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1300 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1301 |
1.0 exp 2.71828 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1302 |
1.0 asLongFloat exp 2.71828183 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1303 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1304 |
1.0 asLongFloat exp_withAccuracy:1 2.66666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1305 |
1.0 asLongFloat exp_withAccuracy:0.1 2.70833333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1306 |
1.0 asLongFloat exp_withAccuracy:0.01 2.71666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1307 |
1.0 asLongFloat exp_withAccuracy:0.001 2.71825397 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1308 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1309 |
1.0 asLongFloat exp_withAccuracy:1e-40 2.71828183 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1310 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1311 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1312 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1313 |
ln_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1314 |
"compute ln of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1315 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1316 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1317 |
"/ x^2 x^3 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1318 |
"/ ln = u - --- + --- ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1319 |
"/ 2 3 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1320 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1321 |
|u u2 num den approx lastApprox| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1322 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1323 |
u := self - 1. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1324 |
u2 := u squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1325 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1326 |
num := u2 negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1327 |
den := 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1328 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1329 |
approx := u + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1330 |
lastApprox := self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1331 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1332 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1333 |
den := den + 1. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1334 |
num := (num * u) negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1335 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1336 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1337 |
approx := approx + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1338 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1339 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1340 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1341 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1342 |
2.0 ln 0.693147 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1343 |
2.0 asLongFloat ln 0.693147181 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1344 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1345 |
2.0 asLongFloat ln_withAccuracy:1 0.833333333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1346 |
2.0 asLongFloat ln_withAccuracy:0.1 0.645634921 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1347 |
2.0 asLongFloat ln_withAccuracy:0.01 0.688172179 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1348 |
2.0 asLongFloat ln_withAccuracy:0.001 0.692647431 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1349 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1350 |
2.0 asLongFloat ln_withAccuracy:1e-10 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1351 |
2.0 asLongFloat ln_withAccuracy:1e-20 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1352 |
2.0 asLongFloat ln_withAccuracy:1e-40 2.71828183 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1353 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1354 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1355 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1356 |
sin_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1357 |
"compute the sine of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1358 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1359 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1360 |
"/ x^3 x^5 x^7 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1361 |
"/ sin = x - --- + --- - --- ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1362 |
"/ 3!! 5!! 7!! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1363 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1364 |
|x2 facN num den approx lastApprox| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1365 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1366 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1367 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1368 |
num := (x2 * self) negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1369 |
den := 2*3. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1370 |
facN := 3. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1371 |
approx := self + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1372 |
lastApprox := self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1373 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1374 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1375 |
facN := facN + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1376 |
den := den * (facN - 1) * facN. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1377 |
num := (num * x2) negated. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1378 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1379 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1380 |
approx := approx + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1381 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1382 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1383 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1384 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1385 |
1.0 sin 0.841471 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1386 |
1.0 asLongFloat sin 0.841470985 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1387 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1388 |
1.0 asLongFloat sin_withAccuracy:1 0.833333333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1389 |
1.0 asLongFloat sin_withAccuracy:0.1 0.841666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1390 |
1.0 asLongFloat sin_withAccuracy:0.01 0.841666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1391 |
1.0 asLongFloat sin_withAccuracy:0.001 0.841468254 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1392 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1393 |
1.0 asLongFloat sin_withAccuracy:1e-40 0.841470985 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1394 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1395 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1396 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1397 |
sinh_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1398 |
"compute the hyperbolic sine of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1399 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1400 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1401 |
"/ x^3 x^5 x^7 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1402 |
"/ sinh = x + --- + --- + --- ... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1403 |
"/ 3!! 5!! 7!! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1404 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1405 |
|x2 facN num den approx lastApprox| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1406 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1407 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1408 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1409 |
num := x2 * self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1410 |
den := 2*3. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1411 |
facN := 3. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1412 |
approx := self + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1413 |
lastApprox := self. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1414 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1415 |
[ (lastApprox - approx) abs > epsilon ] whileTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1416 |
facN := facN + 2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1417 |
den := den * (facN - 1) * facN. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1418 |
num := num * x2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1419 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1420 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1421 |
approx := approx + (num / den). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1422 |
]. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1423 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1424 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1425 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1426 |
1.0 sinh 1.1752 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1427 |
1.0 asLongFloat sinh 1.17520119 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1428 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1429 |
1.0 asLongFloat sinh_withAccuracy:1 1.16666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1430 |
1.0 asLongFloat sinh_withAccuracy:0.1 1.175 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1431 |
1.0 asLongFloat sinh_withAccuracy:0.01 1.175 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1432 |
1.0 asLongFloat sinh_withAccuracy:0.001 1.17519841 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1433 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1434 |
1.0 asLongFloat sinh_withAccuracy:1e-40 1.17520119 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1435 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1436 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1437 |
|
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1438 |
sqrt_withAccuracy:epsilon |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1439 |
"compute square root of the receiver" |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1440 |
" |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1441 |
Use the Heron Algorithm: |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1442 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1443 |
x_n + (a / x_n) |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1444 |
x_n+1 = --------------- |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1445 |
2 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1446 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1447 |
sqrt(a) = x_n |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1448 |
" |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1449 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1450 |
|approx| |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1451 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1452 |
self <= 0 ifTrue:[ |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1453 |
self = 0 ifTrue:[ |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1454 |
^ self |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1455 |
]. |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1456 |
self error:'negative number in sqrt'. |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1457 |
]. |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1458 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1459 |
approx := 1. |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1460 |
[ |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1461 |
|lastApprox| |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1462 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1463 |
lastApprox := approx. |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1464 |
approx := ((self / approx) + approx) / 2. |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1465 |
(approx - lastApprox) abs > epsilon |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1466 |
] whileTrue. |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1467 |
^ approx |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1468 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1469 |
" |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1470 |
2 sqrt 1.41421 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1471 |
2 asLongFloat sqrt_withAccuracy:0.01 1.41666667 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1472 |
2 asLongFloat sqrt_withAccuracy:0.0001 1.41421569 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1473 |
2 asLongFloat sqrt_withAccuracy:0.0000001 1.41421356 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1474 |
2 asLongFloat sqrt_withAccuracy:0.0000000001 1.41421356 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1475 |
2 asLongFloat sqrt_withAccuracy:0.000000000001 1.41421356 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1476 |
2 asLongFloat sqrt_withAccuracy:LongFloat epsilon 1.41421356 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1477 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1478 |
(4 sqrt_withAccuracy:Integer epsilon) asFloat |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1479 |
|
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1480 |
MessageTally spyOn:[ |arg| |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1481 |
arg := 2 asLongFloat. |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1482 |
1000000 timesRepeat:[ |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1483 |
arg sqrt_withAccuracy:0.000000000001 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1484 |
] |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1485 |
] |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1486 |
Time millisecondsToRun:[ |arg| |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1487 |
arg := 2 asLongFloat. |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1488 |
1000000 timesRepeat:[ |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1489 |
arg sqrt_withAccuracy:0.000000000001 |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1490 |
] |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1491 |
] |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1492 |
" |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1493 |
! |
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1494 |
|
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1495 |
tan_withAccuracy:epsilon |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1496 |
"compute the tangens of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1497 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1498 |
"/ uses taylor series: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1499 |
"/ x^3 x^5 x^7 x^9 2^2n * ( 2^2n - 1) * B2n * x^(2n-1) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1500 |
"/ tan = x + 1*--- + 2*--- + 17*--- + 62*----... ----------------------------------... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1501 |
"/ 3 15 315 2835 (2n)!! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1502 |
"/ where Bi is the ith bernoulli number. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1503 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1504 |
|factors idx x2 num t approx lastApprox| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1505 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1506 |
"/ (1 to:20) collect:[:n| |num den| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1507 |
"/ num := (2 raisedTo:(2*n)) * ((2 raisedTo:(2*n))-1) * ((n*2) bernoulli). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1508 |
"/ den := (2*n) factorial. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1509 |
"/ num / den |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1510 |
"/ ] |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1511 |
factors := #( |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1512 |
(1 3) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1513 |
(2 15) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1514 |
(17 315) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1515 |
(62 2835) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1516 |
(1382 155925) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1517 |
(21844 6081075) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1518 |
(929569 638512875) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1519 |
(6404582 10854718875) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1520 |
(443861162 1856156927625) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1521 |
(18888466084 194896477400625) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1522 |
(113927491862 2900518163668125) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1523 |
(58870668456604 3698160658676859375) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1524 |
(8374643517010684 1298054391195577640625) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1525 |
(689005380505609448 263505041412702261046875) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1526 |
(129848163681107301953 122529844256906551386796875) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1527 |
(1736640792209901647222 4043484860477916195764296875) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1528 |
(418781231495293038913922 2405873491984360136479756640625) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1529 |
(56518638202982204522669764 801155872830791925447758961328125) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1530 |
(32207686319158956594455462 1126482925555250126673224649609375)). |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1531 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1532 |
x2 := self squared. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1533 |
|
8203 | 1534 |
num := x2 * self. "/ = x^3 |
1535 |
approx := self + (num / 3). "/ do the first iteration |
|
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1536 |
lastApprox := self. |
8203 | 1537 |
idx := 2. |
1538 |
[ |
|
1539 |
t := factors at:idx. |
|
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1540 |
idx := idx + 1. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1541 |
num := num * x2. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1542 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1543 |
lastApprox := approx. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1544 |
approx := approx + (num * t first / t second). |
8203 | 1545 |
epsilon < (lastApprox - approx) abs |
1546 |
] whileTrue. |
|
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1547 |
^ approx |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1548 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1549 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1550 |
0.5 tan 0.546302 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1551 |
0.5 asLongFloat tan 0.54630249 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1552 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1553 |
0.5 asLongFloat tan_withAccuracy:1 0.541666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1554 |
0.5 asLongFloat tan_withAccuracy:0.1 0.541666667 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1555 |
0.5 asLongFloat tan_withAccuracy:0.01 0.545833333 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1556 |
0.5 asLongFloat tan_withAccuracy:0.001 0.54625496 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1557 |
0.5 asLongFloat tan_withAccuracy:1e-15 0.54630249 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1558 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1559 |
0.5 asLongFloat tan_withAccuracy:1e-40 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1560 |
" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1561 |
! ! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1562 |
|
701 | 1563 |
!Number methodsFor:'testing'! |
1564 |
||
5360 | 1565 |
isDivisibleBy:aNumber |
1566 |
"return true, if the receiver can be divided by the argument, aNumber without a remainder. |
|
1567 |
Notice, that the result is only worth trusting, if the receiver is an integer." |
|
1568 |
||
1569 |
aNumber = 0 ifTrue: [^ false]. |
|
1570 |
aNumber isInteger ifFalse: [^ false]. |
|
1571 |
^ (self \\ aNumber) = 0 |
|
1572 |
||
1573 |
" |
|
1574 |
3 isDivisibleBy:2 |
|
1575 |
4 isDivisibleBy:2 |
|
1576 |
4.0 isDivisibleBy:2 |
|
1577 |
4.5 isDivisibleBy:4.5 |
|
1578 |
4.5 isDivisibleBy:1.0 |
|
1579 |
" |
|
1580 |
! |
|
1581 |
||
6692 | 1582 |
isFinite |
1583 |
^true |
|
1584 |
! |
|
6143 | 1585 |
|
6692 | 1586 |
isInfinite |
1587 |
^false |
|
6143 | 1588 |
! |
1589 |
||
1590 |
isNaN |
|
1591 |
"return true, if the receiver is an invalid float (NaN - not a number)." |
|
1592 |
||
1593 |
^ false |
|
6155 | 1594 |
|
1595 |
"Created: / 5.11.2001 / 18:07:26 / cg" |
|
6143 | 1596 |
! |
1597 |
||
701 | 1598 |
isNumber |
1599 |
"return true, if the receiver is a kind of number" |
|
1600 |
||
1601 |
^ true |
|
1602 |
! |
|
1603 |
||
6087 | 1604 |
isReal |
1605 |
"return true, if the receiver is some kind of real number (as opposed to a complex); |
|
1606 |
true is returned here - the method is redefined from Object." |
|
1607 |
||
1608 |
^ true |
|
1609 |
! |
|
1610 |
||
701 | 1611 |
isZero |
1557 | 1612 |
"return true, if the receiver is zero" |
1613 |
||
701 | 1614 |
^ self = 0 |
1557 | 1615 |
|
1616 |
"Modified: 18.7.1996 / 12:40:49 / cg" |
|
701 | 1617 |
! ! |
1618 |
||
4659
cdf37afc0e26
moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents:
4637
diff
changeset
|
1619 |
!Number methodsFor:'tracing'! |
cdf37afc0e26
moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents:
4637
diff
changeset
|
1620 |
|
4682 | 1621 |
traceInto:aRequestor level:level from:referrer |
4659
cdf37afc0e26
moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents:
4637
diff
changeset
|
1622 |
"double dispatch into tracer, passing my type implicitely in the selector" |
cdf37afc0e26
moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents:
4637
diff
changeset
|
1623 |
|
4682 | 1624 |
^ aRequestor traceNumber:self level:level from:referrer |
4659
cdf37afc0e26
moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents:
4637
diff
changeset
|
1625 |
|
cdf37afc0e26
moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents:
4637
diff
changeset
|
1626 |
|
cdf37afc0e26
moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents:
4637
diff
changeset
|
1627 |
! ! |
cdf37afc0e26
moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents:
4637
diff
changeset
|
1628 |
|
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1629 |
!Number methodsFor:'trigonometric'! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1630 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1631 |
arcCos |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1632 |
"return the arccosine of the receiver (in radians)" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1633 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1634 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1635 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1636 |
^ self asFloat arcCos. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1637 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1638 |
^ self arcCos_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1639 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1640 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1641 |
arcCosh |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1642 |
"return the hyperbolic arccosine of the receiver." |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1643 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1644 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1645 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1646 |
^ self asFloat arcCosh. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1647 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1648 |
^ self arcCosh_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1649 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1650 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1651 |
arcSin |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1652 |
"return the arcsine of the receiver (in radians)" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1653 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1654 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1655 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1656 |
^ self asFloat arcSin. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1657 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1658 |
^ self arcSin_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1659 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1660 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1661 |
arcSinh |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1662 |
"return the hyperbolic arcsine of the receiver." |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1663 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1664 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1665 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1666 |
^ self asFloat arcSinh. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1667 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1668 |
^ self arcSinh_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1669 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1670 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1671 |
arcTan |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1672 |
"return the arctangent of the receiver (as radians)" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1673 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1674 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1675 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1676 |
^ self asFloat arcTan. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1677 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1678 |
^ self arcTan_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1679 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1680 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1681 |
arcTanh |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1682 |
"return the hyperbolic arctangent of the receiver." |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1683 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1684 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1685 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1686 |
^ self asFloat arcTanh. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1687 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1688 |
^ self arcTanh_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1689 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1690 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1691 |
cos |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1692 |
"return the cosine of the receiver (interpreted as radians)" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1693 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1694 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1695 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1696 |
^ self asFloat cos. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1697 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1698 |
^ self cos_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1699 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1700 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1701 |
cosh |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1702 |
"return the hyperbolic cosine of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1703 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1704 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1705 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1706 |
^ self asFloat cosh. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1707 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1708 |
^ self cosh_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1709 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1710 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1711 |
sin |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1712 |
"return the sine of the receiver (interpreted as radians)" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1713 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1714 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1715 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1716 |
^ self asFloat sin. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1717 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1718 |
^ self sin_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1719 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1720 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1721 |
sinh |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1722 |
"return the hyperbolic sine of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1723 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1724 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1725 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1726 |
^ self asFloat sinh. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1727 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1728 |
^ self sinh_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1729 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1730 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1731 |
tan |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1732 |
"return the tangens of the receiver (interpreted as radians)" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1733 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1734 |
^ self sin / self cos |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1735 |
! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1736 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1737 |
tanh |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1738 |
"return the hyperbolic tangens of the receiver" |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1739 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1740 |
(self isLimitedPrecisionReal not |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1741 |
or:[self generality < 1.0 generality]) ifTrue:[ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1742 |
^ self asFloat tanh. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1743 |
]. |
7729
bbd20db09d1b
Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents:
7468
diff
changeset
|
1744 |
^ self tanh_withAccuracy:self class epsilon |
7449
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1745 |
|
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1746 |
"/ If a fast exp is available, the following might be better... |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1747 |
"/ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1748 |
"/ |exp nexp| |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1749 |
"/ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1750 |
"/ "/ tanh is: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1751 |
"/ "/ sinh(x) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1752 |
"/ "/ ------- |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1753 |
"/ "/ cosh(x) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1754 |
"/ "/ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1755 |
"/ "/ which is: |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1756 |
"/ "/ (exp(x) - exp(-x)) / 2 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1757 |
"/ "/ ---------------------- |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1758 |
"/ "/ (exp(x) + exp(-x)) / 2 |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1759 |
"/ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1760 |
"/ exp := self exp. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1761 |
"/ nexp := self negated exp. |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1762 |
"/ |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1763 |
"/ ^ (exp - nexp) / (exp + nexp) |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1764 |
! ! |
192789c6e1c2
fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents:
7388
diff
changeset
|
1765 |
|
5552 | 1766 |
!Number methodsFor:'truncation & rounding'! |
3900
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1767 |
|
4895 | 1768 |
detentBy: detent atMultiplesOf: grid snap: snap |
1769 |
"Map all values that are within detent/2 of any multiple of grid |
|
1770 |
to that multiple. |
|
1771 |
Otherwise, if snap is true, return self, meaning that the values |
|
1772 |
in the dead zone will never be returned. |
|
1773 |
If snap is false, then expand the range between dead zones |
|
1774 |
so that it covers the range between multiples of the grid, |
|
1775 |
and scale the value by that factor." |
|
1776 |
||
1777 |
| r1 r2 | |
|
1778 |
||
1779 |
r1 := self roundTo: grid. "Nearest multiple of grid" |
|
1780 |
(self roundTo: detent) = r1 ifTrue: [^ r1]. "Snap to that multiple..." |
|
1781 |
snap ifTrue: [^ self]. "...or return self" |
|
1782 |
||
1783 |
r2 := self < r1 "Nearest end of dead zone" |
|
5322 | 1784 |
ifTrue: [r1 - (detent asFloat/2)] |
1785 |
ifFalse: [r1 + (detent asFloat/2)]. |
|
4895 | 1786 |
|
1787 |
"Scale values between dead zones to fill range between multiples" |
|
1788 |
^ r1 + ((self - r2) * grid asFloat / (grid - detent)) |
|
1789 |
||
1790 |
" |
|
1791 |
(170 to: 190 by: 2) collect: [:a | a detentBy: 10 atMultiplesOf: 90 snap: true] |
|
1792 |
(170 to: 190 by: 2) collect: [:a | a detentBy: 10 atMultiplesOf: 90 snap: false] |
|
1793 |
(3.9 to: 4.1 by: 0.02) collect: [:a | a detentBy: 0.1 atMultiplesOf: 1.0 snap: true] |
|
1794 |
(-3.9 to: -4.1 by: -0.02) collect: [:a | a detentBy: 0.1 atMultiplesOf: 1.0 snap: false] |
|
1795 |
" |
|
1796 |
! |
|
1797 |
||
3900
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1798 |
fractionPart |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1799 |
"return a float with value from digits after the decimal point. |
7356 | 1800 |
i.e. the receiver minus its truncated value, |
1801 |
such that (self truncated + self fractionPart) = self" |
|
3900
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1802 |
|
7356 | 1803 |
^ self - self truncated |
3900
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1804 |
|
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1805 |
" |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1806 |
1234.56789 fractionPart |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1807 |
1.2345e6 fractionPart |
7356 | 1808 |
|
1809 |
1.6 asLongFloat fractionPart + 1.6 asLongFloat truncated |
|
1810 |
-1.6 asLongFloat fractionPart + -1.6 asLongFloat truncated |
|
3900
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1811 |
" |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1812 |
|
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1813 |
"Modified: / 4.11.1996 / 20:26:54 / cg" |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1814 |
"Created: / 28.10.1998 / 17:14:40 / cg" |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1815 |
! |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1816 |
|
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1817 |
integerPart |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1818 |
"return a float with value from digits before the decimal point |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1819 |
(i.e. the truncated value)" |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1820 |
|
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1821 |
^ self truncated asFloat |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1822 |
|
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1823 |
" |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1824 |
1234.56789 integerPart |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1825 |
1.2345e6 integerPart |
6154 | 1826 |
12.5 integerPart |
1827 |
-12.5 integerPart |
|
1828 |
(5/3) integerPart |
|
1829 |
(-5/3) integerPart |
|
1830 |
(5/3) truncated |
|
1831 |
(-5/3) truncated |
|
3900
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1832 |
" |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1833 |
|
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1834 |
"Created: / 28.10.1998 / 17:14:56 / cg" |
6154 | 1835 |
"Modified: / 5.11.2001 / 17:54:22 / cg" |
3900
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1836 |
! ! |
c3bc76767cfc
added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents:
3770
diff
changeset
|
1837 |
|
1892 | 1838 |
!Number class methodsFor:'documentation'! |
701 | 1839 |
|
1840 |
version |
|
8303 | 1841 |
^ '$Header: /cvs/stx/stx/libbasic/Number.st,v 1.92 2004-04-07 10:23:50 werner Exp $' |
701 | 1842 |
! ! |