Mercurial > hg > CbC > CbC_gcc
annotate gcc/config/rs6000/darwin-ldouble-format @ 55:77e2b8dfacca gcc-4.4.5
update it from 4.4.3 to 4.5.0
| author | ryoma <e075725@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Fri, 12 Feb 2010 23:39:51 +0900 |
| parents | a06113de4d67 |
| children |
| rev | line source |
|---|---|
| 0 | 1 Long double format |
| 2 ================== | |
| 3 | |
| 4 Each long double is made up of two IEEE doubles. The value of the | |
| 5 long double is the sum of the values of the two parts (except for | |
| 6 -0.0). The most significant part is required to be the value of the | |
| 7 long double rounded to the nearest double, as specified by IEEE. For | |
| 8 Inf values, the least significant part is required to be one of +0.0 | |
| 9 or -0.0. No other requirements are made; so, for example, 1.0 may be | |
| 10 represented as (1.0, +0.0) or (1.0, -0.0), and the low part of a NaN | |
| 11 is don't-care. | |
| 12 | |
| 13 Classification | |
| 14 -------------- | |
| 15 | |
| 16 A long double can represent any value of the form | |
| 17 s * 2^e * sum(k=0...105: f_k * 2^(-k)) | |
| 18 where 's' is +1 or -1, 'e' is between 1022 and -968 inclusive, f_0 is | |
| 19 1, and f_k for k>0 is 0 or 1. These are the 'normal' long doubles. | |
| 20 | |
| 21 A long double can also represent any value of the form | |
| 22 s * 2^-968 * sum(k=0...105: f_k * 2^(-k)) | |
| 23 where 's' is +1 or -1, f_0 is 0, and f_k for k>0 is 0 or 1. These are | |
| 24 the 'subnormal' long doubles. | |
| 25 | |
| 26 There are four long doubles that represent zero, two that represent | |
| 27 +0.0 and two that represent -0.0. The sign of the high part is the | |
| 28 sign of the long double, and the sign of the low part is ignored. | |
| 29 | |
| 30 Likewise, there are four long doubles that represent infinities, two | |
| 31 for +Inf and two for -Inf. | |
| 32 | |
| 33 Each NaN, quiet or signalling, that can be represented as a 'double' | |
| 34 can be represented as a 'long double'. In fact, there are 2^64 | |
| 35 equivalent representations for each one. | |
| 36 | |
| 37 There are certain other valid long doubles where both parts are | |
| 38 nonzero but the low part represents a value which has a bit set below | |
| 39 2^(e-105). These, together with the subnormal long doubles, make up | |
| 40 the denormal long doubles. | |
| 41 | |
| 42 Many possible long double bit patterns are not valid long doubles. | |
| 43 These do not represent any value. | |
| 44 | |
| 45 Limits | |
| 46 ------ | |
| 47 | |
| 48 The maximum representable long double is 2^1024-2^918. The smallest | |
| 49 *normal* positive long double is 2^-968. The smallest denormalised | |
| 50 positive long double is 2^-1074 (this is the same as for 'double'). | |
| 51 | |
| 52 Conversions | |
| 53 ----------- | |
| 54 | |
| 55 A double can be converted to a long double by adding a zero low part. | |
| 56 | |
| 57 A long double can be converted to a double by removing the low part. | |
| 58 | |
| 59 Comparisons | |
| 60 ----------- | |
| 61 | |
| 62 Two long doubles can be compared by comparing the high parts, and if | |
| 63 those compare equal, comparing the low parts. | |
| 64 | |
| 65 Arithmetic | |
| 66 ---------- | |
| 67 | |
| 68 The unary negate operation operates by negating the low and high parts. | |
| 69 | |
| 70 An absolute or absolute-negate operation must be done by comparing | |
| 71 against zero and negating if necessary. | |
| 72 | |
| 73 Addition and subtraction are performed using library routines. They | |
| 74 are not at present performed perfectly accurately, the result produced | |
| 75 will be within 1ulp of the range generated by adding or subtracting | |
| 76 1ulp from the input values, where a 'ulp' is 2^(e-106) given the | |
| 77 exponent 'e'. In the presence of cancellation, this may be | |
| 78 arbitrarily inaccurate. Subtraction is done by negation and addition. | |
| 79 | |
| 80 Multiplication is also performed using a library routine. Its result | |
| 81 will be within 2ulp of the correct result. | |
| 82 | |
| 83 Division is also performed using a library routine. Its result will | |
| 84 be within 3ulp of the correct result. | |
|
55
77e2b8dfacca
update it from 4.4.3 to 4.5.0
ryoma <e075725@ie.u-ryukyu.ac.jp>
parents:
0
diff
changeset
|
85 |
|
77e2b8dfacca
update it from 4.4.3 to 4.5.0
ryoma <e075725@ie.u-ryukyu.ac.jp>
parents:
0
diff
changeset
|
86 |
|
77e2b8dfacca
update it from 4.4.3 to 4.5.0
ryoma <e075725@ie.u-ryukyu.ac.jp>
parents:
0
diff
changeset
|
87 Copyright (C) 2004 Free Software Foundation, Inc. |
|
77e2b8dfacca
update it from 4.4.3 to 4.5.0
ryoma <e075725@ie.u-ryukyu.ac.jp>
parents:
0
diff
changeset
|
88 |
|
77e2b8dfacca
update it from 4.4.3 to 4.5.0
ryoma <e075725@ie.u-ryukyu.ac.jp>
parents:
0
diff
changeset
|
89 Copying and distribution of this file, with or without modification, |
|
77e2b8dfacca
update it from 4.4.3 to 4.5.0
ryoma <e075725@ie.u-ryukyu.ac.jp>
parents:
0
diff
changeset
|
90 are permitted in any medium without royalty provided the copyright |
|
77e2b8dfacca
update it from 4.4.3 to 4.5.0
ryoma <e075725@ie.u-ryukyu.ac.jp>
parents:
0
diff
changeset
|
91 notice and this notice are preserved. |