This table is reproduced unchanged from ISO/IEC TR 10176:1998, produced by ISO/IEC
JTC 1/SC 22/WG 20, except for the omission of ranges that are part of the basic character
sets.
- Latin: 00AA, 00BA, 00C0-00D6, 00D8-00F6, 00F8-01F5, 01FA-0217,
-<pre>
+<table border=1>
+<tr><td> Latin: <td> 00AA, 00BA, 00C0-00D6, 00D8-00F6, 00F8-01F5, 01FA-0217,
0250-02A8, 1E00-1E9B, 1EA0-1EF9, 207F
-</pre>
- Greek: 0386, 0388-038A, 038C, 038E-03A1, 03A3-03CE, 03D0-03D6,
-<pre>
+<tr><td> Greek: <td> 0386, 0388-038A, 038C, 038E-03A1, 03A3-03CE, 03D0-03D6,
03DA, 03DC, 03DE, 03E0, 03E2-03F3, 1F00-1F15, 1F18-1F1D,
1F20-1F45, 1F48-1F4D, 1F50-1F57, 1F59, 1F5B, 1F5D,
1F5F-1F7D, 1F80-1FB4, 1FB6-1FBC, 1FC2-1FC4, 1FC6-1FCC,
1FD0-1FD3, 1FD6-1FDB, 1FE0-1FEC, 1FF2-1FF4, 1FF6-1FFC
-</pre>
- Cyrillic: 0401-040C, 040E-044F, 0451-045C, 045E-0481, 0490-04C4,
-<pre>
+<tr><td> Cyrillic: <td> 0401-040C, 040E-044F, 0451-045C, 045E-0481, 0490-04C4,
04C7-04C8, 04CB-04CC, 04D0-04EB, 04EE-04F5, 04F8-04F9
-</pre>
- Armenian: 0531-0556, 0561-0587
- Hebrew: 05B0-05B9, 05BB-05BD, 05BF, 05C1-05C2, 05D0-05EA,
-<pre>
+<tr><td> Armenian: <td> 0531-0556, 0561-0587
+<tr><td> Hebrew: <td> 05B0-05B9, 05BB-05BD, 05BF, 05C1-05C2, 05D0-05EA,
05F0-05F2
-</pre>
- Arabic: 0621-063A, 0640-0652, 0670-06B7, 06BA-06BE, 06C0-06CE,
-<pre>
+<tr><td> Arabic: <td> 0621-063A, 0640-0652, 0670-06B7, 06BA-06BE, 06C0-06CE,
06D0-06DC, 06E5-06E8, 06EA-06ED
-</pre>
- Devanagari: 0901-0903, 0905-0939, 093E-094D, 0950-0952, 0958-0963
- Bengali: 0981-0983, 0985-098C, 098F-0990, 0993-09A8, 09AA-09B0,
-<pre>
+<tr><td> Devanagari:<td> 0901-0903, 0905-0939, 093E-094D, 0950-0952, 0958-0963
+<tr><td> Bengali: <td> 0981-0983, 0985-098C, 098F-0990, 0993-09A8, 09AA-09B0,
09B2, 09B6-09B9, 09BE-09C4, 09C7-09C8, 09CB-09CD,
09DC-09DD, 09DF-09E3, 09F0-09F1
-</pre>
- Gurmukhi: 0A02, 0A05-0A0A, 0A0F-0A10, 0A13-0A28, 0A2A-0A30,
-<pre>
+<tr><td> Gurmukhi: <td> 0A02, 0A05-0A0A, 0A0F-0A10, 0A13-0A28, 0A2A-0A30,
0A32-0A33, 0A35-0A36, 0A38-0A39, 0A3E-0A42, 0A47-0A48,
0A4B-0A4D, 0A59-0A5C, 0A5E, 0A74
-</pre>
- Gujarati: 0A81-0A83, 0A85-0A8B, 0A8D, 0A8F-0A91, 0A93-0AA8,
-<pre>
+<tr><td> Gujarati: <td> 0A81-0A83, 0A85-0A8B, 0A8D, 0A8F-0A91, 0A93-0AA8,
0AAA-0AB0, 0AB2-0AB3, 0AB5-0AB9, 0ABD-0AC5,
0AC7-0AC9, 0ACB-0ACD, 0AD0, 0AE0
-</pre>
- Oriya: 0B01-0B03, 0B05-0B0C, 0B0F-0B10, 0B13-0B28, 0B2A-0B30,
+<tr><td> Oriya: <td> 0B01-0B03, 0B05-0B0C, 0B0F-0B10, 0B13-0B28, 0B2A-0B30,
<!--page 453 -->
-<pre>
0B32-0B33, 0B36-0B39, 0B3E-0B43, 0B47-0B48, 0B4B-0B4D,
0B5C-0B5D, 0B5F-0B61
-</pre>
- Tamil: 0B82-0B83, 0B85-0B8A, 0B8E-0B90, 0B92-0B95, 0B99-0B9A,
-<pre>
+<tr><td> Tamil: <td> 0B82-0B83, 0B85-0B8A, 0B8E-0B90, 0B92-0B95, 0B99-0B9A,
0B9C, 0B9E-0B9F, 0BA3-0BA4, 0BA8-0BAA, 0BAE-0BB5,
0BB7-0BB9, 0BBE-0BC2, 0BC6-0BC8, 0BCA-0BCD
-</pre>
- Telugu: 0C01-0C03, 0C05-0C0C, 0C0E-0C10, 0C12-0C28, 0C2A-0C33,
-<pre>
+<tr><td> Telugu: <td> 0C01-0C03, 0C05-0C0C, 0C0E-0C10, 0C12-0C28, 0C2A-0C33,
0C35-0C39, 0C3E-0C44, 0C46-0C48, 0C4A-0C4D, 0C60-0C61
-</pre>
- Kannada: 0C82-0C83, 0C85-0C8C, 0C8E-0C90, 0C92-0CA8, 0CAA-0CB3,
-<pre>
+<tr><td> Kannada: <td> 0C82-0C83, 0C85-0C8C, 0C8E-0C90, 0C92-0CA8, 0CAA-0CB3,
0CB5-0CB9, 0CBE-0CC4, 0CC6-0CC8, 0CCA-0CCD, 0CDE,
0CE0-0CE1
-</pre>
- Malayalam: 0D02-0D03, 0D05-0D0C, 0D0E-0D10, 0D12-0D28, 0D2A-0D39,
-<pre>
+<tr><td> Malayalam: <td> 0D02-0D03, 0D05-0D0C, 0D0E-0D10, 0D12-0D28, 0D2A-0D39,
0D3E-0D43, 0D46-0D48, 0D4A-0D4D, 0D60-0D61
-</pre>
- Thai: 0E01-0E3A, 0E40-0E5B
- Lao: 0E81-0E82, 0E84, 0E87-0E88, 0E8A, 0E8D, 0E94-0E97,
-<pre>
+<tr><td> Thai: <td> 0E01-0E3A, 0E40-0E5B
+<tr><td> Lao: <td> 0E81-0E82, 0E84, 0E87-0E88, 0E8A, 0E8D, 0E94-0E97,
0E99-0E9F, 0EA1-0EA3, 0EA5, 0EA7, 0EAA-0EAB,
0EAD-0EAE, 0EB0-0EB9, 0EBB-0EBD, 0EC0-0EC4, 0EC6,
0EC8-0ECD, 0EDC-0EDD
-</pre>
- Tibetan: 0F00, 0F18-0F19, 0F35, 0F37, 0F39, 0F3E-0F47, 0F49-0F69,
-<pre>
+<tr><td> Tibetan: <td> 0F00, 0F18-0F19, 0F35, 0F37, 0F39, 0F3E-0F47, 0F49-0F69,
0F71-0F84, 0F86-0F8B, 0F90-0F95, 0F97, 0F99-0FAD,
0FB1-0FB7, 0FB9
-</pre>
- Georgian: 10A0-10C5, 10D0-10F6
- Hiragana: 3041-3093, 309B-309C
- Katakana: 30A1-30F6, 30FB-30FC
- Bopomofo: 3105-312C
- CJK Unified Ideographs: 4E00-9FA5
- Hangul: AC00-D7A3
- Digits: 0660-0669, 06F0-06F9, 0966-096F, 09E6-09EF, 0A66-0A6F,
-<pre>
+<tr><td> Georgian: <td> 10A0-10C5, 10D0-10F6
+<tr><td> Hiragana: <td> 3041-3093, 309B-309C
+<tr><td> Katakana: <td> 30A1-30F6, 30FB-30FC
+<tr><td> Bopomofo: <td> 3105-312C
+<tr><td> CJK Unified Ideographs:<td> 4E00-9FA5
+<tr><td> Hangul: <td> AC00-D7A3
+<tr><td> Digits: <td> 0660-0669, 06F0-06F9, 0966-096F, 09E6-09EF, 0A66-0A6F,
0AE6-0AEF, 0B66-0B6F, 0BE7-0BEF, 0C66-0C6F, 0CE6-0CEF,
0D66-0D6F, 0E50-0E59, 0ED0-0ED9, 0F20-0F33
-</pre>
- Special characters: 00B5, 00B7, 02B0-02B8, 02BB, 02BD-02C1, 02D0-02D1,
+<tr><td> Special characters:<td> 00B5, 00B7, 02B0-02B8, 02BB, 02BD-02C1, 02D0-02D1,
<!--page 454 -->
-<pre>
02E0-02E4, 037A, 0559, 093D, 0B3D, 1FBE, 203F-2040, 2102,
2107, 210A-2113, 2115, 2118-211D, 2124, 2126, 2128, 212A-2131,
2133-2138, 2160-2182, 3005-3007, 3021-3029
-</pre>
+</table>
<h2><a name="E" href="#E">Annex E</a></h2>
<pre>
<h4><a name="F.8.2" href="#F.8.2">F.8.2 Expression transformations</a></h4>
<p><!--para 1 -->
- x / 2 <-> x * 0.5 Although similar transformations involving inexact
-<pre>
+<table border=1>
+<tr><td><pre> x / 2 <-> x * 0.5 </pre><td> Although similar transformations involving inexact
constants generally do not yield numerically equivalent
expressions, if the constants are exact then such
transformations can be made on IEC 60559 machines
and others that round perfectly.
-</pre>
- 1 * x and x / 1 -> x The expressions 1 * x, x / 1, and x are equivalent
-<pre>
+<tr><td><pre> 1 * x and x / 1 -> x </pre><td> The expressions 1 * x, x / 1, and x are equivalent
(on IEC 60559 machines, among others).<sup><a href="#note317"><b>317)</b></a></sup>
-</pre>
- x / x -> 1.0 The expressions x / x and 1.0 are not equivalent if x
-<pre>
+<tr><td><pre> x / x -> 1.0 </pre><td> The expressions x / x and 1.0 are not equivalent if x
can be zero, infinite, or NaN.
-</pre>
- x - y <-> x + (-y) The expressions x - y, x + (-y), and (-y) + x
-<pre>
+<tr><td><pre> x - y <-> x + (-y) </pre><td> The expressions x - y, x + (-y), and (-y) + x
are equivalent (on IEC 60559 machines, among others).
-</pre>
- x - y <-> -(y - x) The expressions x - y and -(y - x) are not
-<pre>
+<tr><td><pre> x - y <-> -(y - x) </pre><td> The expressions x - y and -(y - x) are not
equivalent because 1 - 1 is +0 but -(1 - 1) is -0 (in the
default rounding direction).<sup><a href="#note318"><b>318)</b></a></sup>
-</pre>
- x - x -> 0.0 The expressions x - x and 0.0 are not equivalent if
-<pre>
+<tr><td><pre> x - x -> 0.0 </pre><td> The expressions x - x and 0.0 are not equivalent if
x is a NaN or infinite.
-</pre>
- 0 * x -> 0.0 The expressions 0 * x and 0.0 are not equivalent if
-<pre>
+<tr><td><pre> 0 * x -> 0.0 </pre><td> The expressions 0 * x and 0.0 are not equivalent if
x is a NaN, infinite, or -0.
-</pre>
- x + 0->x The expressions x + 0 and x are not equivalent if x is
-<pre>
+<tr><td><pre> x + 0 -> x </pre><td> The expressions x + 0 and x are not equivalent if x is
-0, because (-0) + (+0) yields +0 (in the default
rounding direction), not -0.
-</pre>
- x - 0->x (+0) - (+0) yields -0 when rounding is downward
-<pre>
+<tr><td><pre> x - 0 -> x </pre><td> (+0) - (+0) yields -0 when rounding is downward
(toward -(inf)), but +0 otherwise, and (-0) - (+0) always
yields -0; so, if the state of the FENV_ACCESS pragma
is ''off'', promising default rounding, then the
implementation can replace x - 0 by x, even if x
-</pre>
-
-
<!--page 465 -->
-<pre>
might be zero.
-</pre>
- -x <-> 0 - x The expressions -x and 0 - x are not equivalent if x
-<pre>
+<tr><td><pre> -x <-> 0 - x </pre><td> The expressions -x and 0 - x are not equivalent if x
is +0, because -(+0) yields -0, but 0 - (+0) yields +0
(unless rounding is downward).
-</pre>
+</table>
<p><b>Footnotes</b>
<p><small><a name="note317" href="#note317">317)</a> Strict support for signaling NaNs -- not required by this specification -- would invalidate these and
<h4><a name="F.8.3" href="#F.8.3">F.8.3 Relational operators</a></h4>
<p><!--para 1 -->
- x != x -> false The statement x != x is true if x is a NaN.
- x == x -> true The statement x == x is false if x is a NaN.
- x < y -> isless(x,y) (and similarly for <=, >, >=) Though numerically
-<pre>
+<table border=1>
+<tr><td><pre> x != x -> false </pre><td> The statement x != x is true if x is a NaN.
+<tr><td><pre> x == x -> true </pre><td> The statement x == x is false if x is a NaN.
+<tr><td><pre> x < y -> isless(x,y) </pre><td> (and similarly for <=, >, >=) Though numerically
equal, these expressions are not equivalent because of
side effects when x or y is a NaN and the state of the
FENV_ACCESS pragma is ''on''. This transformation,
cause the ''invalid'' floating-point exception for
unordered cases, could be performed provided the state
of the FENV_ACCESS pragma is ''off''.
-</pre>
+</table>
The sense of relational operators shall be maintained. This includes handling unordered
cases as expressed by the source code.
<p><!--para 2 -->
and the result, the result has the same sign as the argument.
<p><!--para 3 -->
The functions are continuous onto both sides of their branch cuts, taking into account the
- sign of zero. For example, csqrt(-2 (+-) i0) = (+-)i(sqrt)2. ???
+ sign of zero. For example, csqrt(-2 (+-) i0) = (+-)i(sqrt)(2).
<p><!--para 4 -->
Since complex and imaginary values are composed of real values, each function may be
regarded as computing real values from real values. Except as noted, the functions treat
only integer divide-by-zero need be detected.
<p><!--para 2 -->
The parameters for the integer data types can be accessed by the following:
- maxint INT_MAX, LONG_MAX, LLONG_MAX, UINT_MAX, ULONG_MAX,
<pre>
+ maxint INT_MAX, LONG_MAX, LLONG_MAX, UINT_MAX, ULONG_MAX,
ULLONG_MAX
-</pre>
minint INT_MIN, LONG_MIN, LLONG_MIN
+</pre>
<p><!--para 3 -->
The parameter ''bounded'' is always true, and is not provided. The parameter ''minint''
is always 0 for the unsigned types, and is not provided for those types.
<h5><a name="H.2.2.1" href="#H.2.2.1">H.2.2.1 Integer operations</a></h5>
<p><!--para 1 -->
The integer operations on integer types are the following:
+<pre>
addI x + y
subI x - y
mulI x * y
leqI x <= y
gtrI x > y
geqI x >= y
+</pre>
where x and y are expressions of the same integer type.
<h4><a name="H.2.3" href="#H.2.3">H.2.3 Floating-point types</a></h4>
<h5><a name="H.2.3.1" href="#H.2.3.1">H.2.3.1 Floating-point parameters</a></h5>
<p><!--para 1 -->
The parameters for a floating point data type can be accessed by the following:
+<pre>
r FLT_RADIX
p FLT_MANT_DIG, DBL_MANT_DIG, LDBL_MANT_DIG
emax FLT_MAX_EXP, DBL_MAX_EXP, LDBL_MAX_EXP
emin FLT_MIN_EXP, DBL_MIN_EXP, LDBL_MIN_EXP
+</pre>
<p><!--para 2 -->
The derived constants for the floating point types are accessed by the following:
<!--page 495 -->
+<pre>
fmax FLT_MAX, DBL_MAX, LDBL_MAX
fminN FLT_MIN, DBL_MIN, LDBL_MIN
epsilon FLT_EPSILON, DBL_EPSILON, LDBL_EPSILON
rnd_style FLT_ROUNDS
+</pre>
<h5><a name="H.2.3.2" href="#H.2.3.2">H.2.3.2 Floating-point operations</a></h5>
<p><!--para 1 -->
The floating-point operations on floating-point types are the following:
+<pre>
addF x + y
subF x - y
mulF x * y
absF fabsf(x), fabs(x), fabsl(x)
exponentF 1.f+logbf(x), 1.0+logb(x), 1.L+logbl(x)
scaleF scalbnf(x, n), scalbn(x, n), scalbnl(x, n),
-<pre>
scalblnf(x, li), scalbln(x, li), scalblnl(x, li)
-</pre>
intpartF modff(x, &y), modf(x, &y), modfl(x, &y)
fractpartF modff(x, &y), modf(x, &y), modfl(x, &y)
eqF x == y
leqF x <= y
gtrF x > y
geqF x >= y
+</pre>
where x and y are expressions of the same floating point type, n is of type int, and li
is of type long int.
that only one identifier for each is provided to map to LIA-1.
<p><!--para 2 -->
The FLT_ROUNDS parameter can be used to indicate the LIA-1 rounding styles:
+<pre>
truncate FLT_ROUNDS == 0
<!--page 496 -->
nearest FLT_ROUNDS == 1
other FLT_ROUNDS != 0 && FLT_ROUNDS != 1
+</pre>
provided that an implementation extends FLT_ROUNDS to cover the rounding style used
in all relevant LIA-1 operations, not just addition as in C.
<h4><a name="H.2.4" href="#H.2.4">H.2.4 Type conversions</a></h4>
<p><!--para 1 -->
The LIA-1 type conversions are the following type casts:
- cvtI' -> I (int)i, (long int)i, (long long int)i,
<pre>
+ cvtI' -> I (int)i, (long int)i, (long long int)i,
(unsigned int)i, (unsigned long int)i,
(unsigned long long int)i
-</pre>
cvtF -> I (int)x, (long int)x, (long long int)x,
-<pre>
(unsigned int)x, (unsigned long int)x,
(unsigned long long int)x
-</pre>
cvtI -> F (float)i, (double)i, (long double)i
cvtF' -> F (float)x, (double)x, (long double)x
+</pre>
<p><!--para 2 -->
In the above conversions from floating to integer, the use of (cast)x can be replaced with
(cast)round(x), (cast)rint(x), (cast)nearbyint(x), (cast)trunc(x),
C's <a href="#7.6"><fenv.h></a> status flags are compatible with the LIA-1 indicators.
<p><!--para 2 -->
The following mapping is for floating-point types:
+<pre>
undefined FE_INVALID, FE_DIVBYZERO
floating_overflow FE_OVERFLOW
underflow FE_UNDERFLOW
+</pre>
<p><!--para 3 -->
The floating-point indicator interrogation and manipulation operations are:
+<pre>
set_indicators feraiseexcept(i)
clear_indicators feclearexcept(i)
test_indicators fetestexcept(i)
current_indicators fetestexcept(FE_ALL_EXCEPT)
+</pre>
where i is an expression of type int representing a subset of the LIA-1 indicators.
<p><!--para 4 -->
C allows an implementation to provide the following LIA-1 required behavior: at
<h2><a name="Index" href="#Index">Index</a></h2>
<pre>
-
??? x ???, <a href="#3.18">3.18</a> , (comma punctuator), <a href="#6.5.2">6.5.2</a>, <a href="#6.7">6.7</a>, <a href="#6.7.2.1">6.7.2.1</a>, <a href="#6.7.2.2">6.7.2.2</a>,
+
[^ x ^], <a href="#3.18">3.18</a> , (comma punctuator), <a href="#6.5.2">6.5.2</a>, <a href="#6.7">6.7</a>, <a href="#6.7.2.1">6.7.2.1</a>, <a href="#6.7.2.2">6.7.2.2</a>,
<a href="#6.7.2.3">6.7.2.3</a>, <a href="#6.7.8">6.7.8</a>
-
??? x ???, <a href="#3.19">3.19</a> - (subtraction operator), <a href="#6.5.6">6.5.6</a>, <a href="#F.3">F.3</a>, <a href="#G.5.2">G.5.2</a>
+
[_ x _], <a href="#3.19">3.19</a> - (subtraction operator), <a href="#6.5.6">6.5.6</a>, <a href="#F.3">F.3</a>, <a href="#G.5.2">G.5.2</a>
! (logical negation operator), <a href="#6.5.3.3">6.5.3.3</a> - (unary minus operator), <a href="#6.5.3.3">6.5.3.3</a>, <a href="#F.3">F.3</a>
!= (inequality operator), <a href="#6.5.9">6.5.9</a> -- (postfix decrement operator), <a href="#6.3.2.1">6.3.2.1</a>, <a href="#6.5.2.4">6.5.2.4</a>
# operator, <a href="#6.10.3.2">6.10.3.2</a> -- (prefix decrement operator), <a href="#6.3.2.1">6.3.2.1</a>, <a href="#6.5.3.1">6.5.3.1</a>
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