1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/REC-html40/Transitional.dtd">
<html>
<head>
<title>[rational.h] Type: Rational</title>
<meta name="robots" content="noindex">
</head>
<body bgcolor=white>
<h1><font color="#008B8B">[rational.h] Type: Rational</font></h1>
<h2><font color="#008B8B"><a href="styx.html">contents</a></font></h2><br>
<br><a href="standard.htm">#include "standard.h"</a>
<br><a href="integer.htm">#include "integer.h"</a>
<br>
<br>
<br>
<br><hr width="100%" size=2><h2><b> The Type </b></h2>
<br><pre>
[rational] implements the algebraic operations for rationals.
A rational number is represented by its numerator and denominator.
NF: gcd(Z,N)=1 /\ N>0
</pre>
<br>
<table border=0 cellspacing=10>
<TR valign=top>
<td align=left><b>Rational</b>
<td align=left> Abstract rational type
</table>
<br><hr width="100%" size=2><h2><b> Basics </b></h2>
<br><pre>
In the following functions the integer and rational operands won't be
consumed and the resulting integer or rational have to be released.
</pre>
<table border=0 cellspacing=20>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_cons</b>(Integer Z, Integer N)</pre>
<td bgcolor="#FFF0F5" align=left> constructs a rational<br>
from numerator 'Z' and denominator 'N'<br>
<br>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_copy</b>(Rational a)</pre>
<td bgcolor="#FFF0F5" align=left>copies rational 'a'
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>void <b>Rat_free</b>(Rational a)</pre>
<td bgcolor="#FFF0F5" align=left>frees rational 'a'
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_Int_to</b>(Integer a)</pre>
<td bgcolor="#FFF0F5" align=left> constructs a rational from numerator 'a' ( a/1 ) <br>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_Int_div</b>(Integer a, Integer b)</pre>
<td bgcolor="#FFF0F5" align=left> divides integer 'a' thru integer 'b'<br>
giving a rational<br>
<br>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>void <b>Rat_des</b>(Rational r, Integer* z, Integer* n)</pre>
<td bgcolor="#FFF0F5" align=left> destructs rational 'r'<br>
to numerator 'z' and denominator 'n'<br>
<br>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Integer <b>Rat_nom</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>copies numerator of rational 'r'
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Integer <b>Rat_den</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>copies denominator of rational 'r'
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>void <b>showRat</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>prints rational 'r' to stdout; for debugging
</table>
<br><hr width="100%" size=2><h2><b> Comparison </b></h2>
<table border=0 cellspacing=20>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>c_bool <b>Rat_is0</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>r == 0 ?
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>int <b>Rat_cmp</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>a < b ? -1 : a == b ? 0 : 1
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>c_bool <b>Rat_eq</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>a == b ?
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>c_bool <b>Rat_ne</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>a != b ?
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>c_bool <b>Rat_lt</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>a < b ?
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>c_bool <b>Rat_le</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>a <= b ?
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>c_bool <b>Rat_gt</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>a > b ?
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>c_bool <b>Rat_ge</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>a >= b ?
</table>
<br><hr width="100%" size=2><h2><b> Arithmetic </b></h2>
<table border=0 cellspacing=20>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>int <b>Rat_sgn</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>signum of rational 'r' (0,-1,1)
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_abs</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>absolute value |r|
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_neg</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>negation -r
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_inv</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>inverse 1 / r ( r != 0 )
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_add</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>addition a + b
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_sub</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>substraction a - b
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_mlt</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>multiplication a * b
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_quo</b>(Rational a, Rational b)</pre>
<td bgcolor="#FFF0F5" align=left>division a / b
</table>
<br><hr width="100%" size=2><h2><b> Conversion </b></h2>
<br>
<p><b>Q --> Z</b>
<table border=0 cellspacing=20>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Integer <b>Rat_floor</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>greatest Integer z with z <= r
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Integer <b>Rat_ceiling</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>smallest Integer z with z >= r
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Integer <b>Rat_round</b>(Rational r)</pre>
<td bgcolor="#FFF0F5" align=left>rounding
</table>
<br>
<p><b>Q --> Q</b>
<table border=0 cellspacing=20>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_fix_floor</b>(Rational r, int b, long n)</pre>
<td bgcolor="#FFF0F5" align=left> Rational(floor(r * b ^ n), b ^n) <br>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_fix_ceiling</b>(Rational r, int b, long n)</pre>
<td bgcolor="#FFF0F5" align=left> Rational(ceiling(r * b ^ n), b ^n) <br>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_fix_round</b>(Rational r, int b, long n)</pre>
<td bgcolor="#FFF0F5" align=left> Rational(round(r * b ^ n), b ^n) <br>
</table>
<br>
<p><b>Q <--> String</b>
<table border=0 cellspacing=20>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>c_string <b>Rat_to_Str</b>(Rational r, int Base, int Digits)</pre>
<td bgcolor="#FFF0F5" align=left> converts rational 'r' into a string; allocs memory <br>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>Rational <b>Rat_Str_to</b>(c_string s, int Base)</pre>
<td bgcolor="#FFF0F5" align=left> converts string 's' into a rational; not consuming 's' <br>
assuming 'Rat_Str_ok(s,Base)' <br>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>c_bool <b>Rat_s_ok</b>(c_string s, int Base)</pre>
<td bgcolor="#FFF0F5" align=left> whether string 's' represents a fix point numeral <br>
</table>
<br><hr width="100%" size=2><h2><b> Xaron Support </b></h2>
<table border=0 cellspacing=20>
<tr valign=top>
<td bgcolor="#FFF8DC" align=left><pre>void <b>Rat_references</b>(Rational x, StdCPtr (*act)(StdCPtr r))</pre>
<td bgcolor="#FFF0F5" align=left> performs 'act' on all pointer references in rational 'x'<br>
( garbage collection service for xaron )<br>
<br>
</table>
</body>
</html>
|
