![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to float CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [MW Coherent from dump] / coherent / a / usr / man / ALL|
Return to float CVS log | Up to [MW Coherent from dump] / coherent / a / usr / man / ALL |
1.1 root 1:
2:
3: float C Keyword float
4:
5:
6:
7:
8: Data type
9:
10:
11: Floating point numbers are a subset of the real numbers. Each
12: has a built-in radix point (or ``decimal point'') that shifts, or
13: ``floats'', as the value of the number changes. It consists of
14: the following: one sign bit, which indicates whether the number
15: is positive or negative; bits that encode the number's _e_x_p_o_n_e_n_t;
16: and bits that encode the number's _f_r_a_c_t_i_o_n, or the number upon
17: which the exponent works. In general, the magnitude of the num-
18: ber encoded depends upon the number of bits in the exponent,
19: whereas its precision depends upon the number of bits in the
20: fraction.
21:
22: The exponent often uses a bias. This is a value that is sub-
23: tracted from the exponent to yield the power of two by which the
24: fraction will be increased.
25:
26: Floating point numbers come in two levels of precision: single
27: precision, called floats; and double precision, called doubles.
28: With most microprocessors, sizeof(float) returns four, which in-
29: dicates that it is four chars (bytes) long, and sizeof(double)
30: returns eight.
31:
32: Several formats are used to encode floats, including IEEE,
33: DECVAX, and BCD (binary coded decimal). COHERENT uses DECVAX
34: format throughout.
35:
36: The following describes DECVAX, IEEE, and BCD formats, for your
37: information.
38:
39: ***** DECVAX Format *****
40:
41: The 32 bits in a float consist of one sign bit, an eight-bit ex-
42: ponent, and a 24-bit fraction, as follows. Note that in this
43: diagram, `s' indicates ``sign'', `e' indicates ``exponent'', and
44: `f` indicates ``fraction'':
45:
46:
47: ZDDDDDDDDDDD?
48: | seee eeee | Byte 4
49: CDDDDDDDDDDD4
50: | efff ffff | Byte 3
51: CDDDDDDDDDDD4
52: | ffff ffff | Byte 2
53: CDDDDDDDDDDD4
54: | ffff ffff | Byte 1
55: @DDDDDDDDDDDY
56:
57:
58: The exponent has a bias of 129.
59:
60: If the sign bit is set to one, the number is negative; if it is
61: set to zero, then the number is positive. If the number is all
62:
63:
64: COHERENT Lexicon Page 1
65:
66:
67:
68:
69: float C Keyword float
70:
71:
72:
73: zeroes, then it equals zero; an exponent and fraction of zero
74: plus a sign of one (``negative zero'') is by definition not a
75: number. All other forms are numeric values.
76:
77: The most significant bit in the fraction is always set to one and
78: is not stored. It is usually called the ``hidden bit''.
79:
80: The format for doubles simply adds another 32 fraction bits to
81: the end of the float representation, as follows:
82:
83:
84: ZDDDDDDDDDDD?
85: | seee eeee | Byte 8
86: CDDDDDDDDDDD4
87: | efff ffff | Byte 7
88: CDDDDDDDDDDD4
89: | ffff ffff | Byte 6
90: CDDDDDDDDDDD4
91: | ffff ffff | Byte 5
92: CDDDDDDDDDDD4
93: | ffff ffff | Byte 4
94: CDDDDDDDDDDD4
95: | ffff ffff | Byte 3
96: CDDDDDDDDDDD4
97: | ffff ffff | Byte 2
98: CDDDDDDDDDDD4
99: | ffff ffff | Byte 1
100: @DDDDDDDDDDDY
101:
102:
103: ***** IEEE Format *****
104:
105: The IEEE encoding of a float is the same as that in the DECVAX
106: format. Note, however, that the exponent has a bias of 127,
107: rather than 129.
108:
109: Unlike the DECVAX format, IEEE format assigns special values to
110: several floating point numbers. Note that in the following
111: description, a tiny exponent is one that is all zeroes, and a
112: huge exponent is one that is all ones:
113:
114: * A tiny exponent with a fraction of zero equals zero, regard-
115: less of the setting of the sign bit.
116:
117: * A huge exponent with a fraction of zero equals infinity,
118: regardless of the setting of the sign bit.
119:
120: * A tiny exponent with a fraction greater than zero is a denor-
121: malized number, i.e., a number that is less than the least
122: normalized number.
123:
124: * A huge exponent with a fraction greater than zero is, by
125: definition, not a number. These values can be used to handle
126: special conditions.
127:
128:
129:
130: COHERENT Lexicon Page 2
131:
132:
133:
134:
135: float C Keyword float
136:
137:
138:
139: An IEEE double, unlike DECVAX format, increases the number of ex-
140: ponent bits. It consists of a sign bit, an 11-bit exponent, and
141: a 53-bit fraction, as follows:
142:
143:
144: ZDDDDDDDDDDD?
145: | seee eeee | Byte 8
146: CDDDDDDDDDDD4
147: | eeee ffff | Byte 7
148: CDDDDDDDDDDD4
149: | ffff ffff | Byte 6
150: CDDDDDDDDDDD4
151: | ffff ffff | Byte 5
152: CDDDDDDDDDDD4
153: | ffff ffff | Byte 4
154: CDDDDDDDDDDD4
155: | ffff ffff | Byte 3
156: CDDDDDDDDDDD4
157: | ffff ffff | Byte 2
158: CDDDDDDDDDDD4
159: | ffff ffff | Byte 1
160: @DDDDDDDDDDDY
161:
162:
163: The exponent has a bias of 1,023. The rules of encoding are the
164: same as for floats.
165:
166: ***** BCD Format *****
167:
168: The BCD format (``binary coded decimal'', also called ``packed
169: decimal'') is used to eliminate rounding errors that alter the
170: worth of an account by a fraction of a cent. It consists of a
171: sign, an exponent, and a chain of four-bit numbers, each of which
172: is defined to hold the values zero through nine.
173:
174: A BCD float has a sign bit, seven bits of exponent, and six four-
175: bit digits. In the following diagrams, `d' indicates ``digit'':
176:
177:
178: ZDDDDDDDDDDD?
179: | seee eeee | Byte 4
180: CDDDDDDDDDDD4
181: | dddd dddd | Byte 3
182: CDDDDDDDDDDD4
183: | dddd dddd | Byte 2
184: CDDDDDDDDDDD4
185: | dddd dddd | Byte 1
186: @DDDDDDDDDDDY
187:
188:
189: A BCD double has a sign bit, 11 bits of exponent, and 13 four-bit
190: digits, as follows:
191:
192:
193:
194:
195:
196: COHERENT Lexicon Page 3
197:
198:
199:
200:
201: float C Keyword float
202:
203:
204:
205: ZDDDDDDDDDDD?
206: | seee eeee | Byte 8
207: CDDDDDDDDDDD4
208: | eeee dddd | Byte 7
209: CDDDDDDDDDDD4
210: | dddd dddd | Byte 6
211: CDDDDDDDDDDD4
212: | dddd dddd | Byte 5
213: CDDDDDDDDDDD4
214: | dddd dddd | Byte 4
215: CDDDDDDDDDDD4
216: | dddd dddd | Byte 3
217: CDDDDDDDDDDD4
218: | dddd dddd | Byte 2
219: CDDDDDDDDDDD4
220: | dddd dddd | Byte 1
221: @DDDDDDDDDDDY
222:
223:
224: Passing the hexadecimal numbers A through F in a digit yields un-
225: predictable results.
226:
227: The following rules apply when handling BCD numbers:
228:
229: * A tiny exponent with a fraction of zero equals zero.
230:
231: * A tiny exponent with a fraction of non-zero indicates a denor-
232: malized number.
233:
234: * A huge exponent with a fraction of zero indicates infinity.
235:
236: * A huge exponent with a fraction of non-zero is, by definition,
237: not a number; these non-numbers are used to indicate errors.
238:
239: ***** See Also *****
240:
241: C keywords, data formats, double
242: _T_h_e _A_r_t _o_f _C_o_m_p_u_t_e_r _P_r_o_g_r_a_m_m_i_n_g, vol. 2, page 180_f_f
243:
244:
245:
246:
247:
248:
249:
250:
251:
252:
253:
254:
255:
256:
257:
258:
259:
260:
261:
262: COHERENT Lexicon Page 4
263:
264:
This archive runs on limited infrastructure. Preserving old code on modern bandwidth. Automated agents are requested to crawl responsibly.