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Diffstat (limited to 'manual/arith.texi')
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1 files changed, 287 insertions, 147 deletions
diff --git a/manual/arith.texi b/manual/arith.texi index d96caa07d7..d33f04fae0 100644 --- a/manual/arith.texi +++ b/manual/arith.texi @@ -9,6 +9,8 @@ These functions are declared in the header files @file{math.h} and @file{complex.h}. @menu +* Integers:: Basic integer types and concepts +* Integer Division:: Integer division with guaranteed rounding. * Floating Point Numbers:: Basic concepts. IEEE 754. * Floating Point Classes:: The five kinds of floating-point number. * Floating Point Errors:: When something goes wrong in a calculation. @@ -17,11 +19,253 @@ These functions are declared in the header files @file{math.h} and * Arithmetic Functions:: Fundamental operations provided by the library. * Complex Numbers:: The types. Writing complex constants. * Operations on Complex:: Projection, conjugation, decomposition. -* Integer Division:: Integer division with guaranteed rounding. * Parsing of Numbers:: Converting strings to numbers. * System V Number Conversion:: An archaic way to convert numbers to strings. @end menu +@node Integers +@section Integers +@cindex integer + +The C language defines several integer data types: integer, short integer, +long integer, and character, all in both signed and unsigned varieties. +The GNU C compiler extends the language to contain long long integers +as well. +@cindex signedness + +The C integer types were intended to allow code to be portable among +machines with different inherent data sizes (word sizes), so each type +may have different ranges on different machines. The problem with +this is that a program often needs to be written for a particular range +of integers, and sometimes must be written for a particular size of +storage, regardless of what machine the program runs on. + +To address this problem, the GNU C library contains C type definitions +you can use to declare integers that meet your exact needs. Because the +GNU C library header files are customized to a specific machine, your +program source code doesn't have to be. + +These @code{typedef}s are in @file{stdint.h}. +@pindex stdint.h + +If you require that an integer be represented in exactly N bits, use one +of the following types, with the obvious mapping to bit size and signedness: + +@itemize @w +@item int8_t +@item int16_t +@item int32_t +@item int64_t +@item uint8_t +@item uint16_t +@item uint32_t +@item uint64_t +@end itemize + +If your C compiler and target machine do not allow integers of a certain +size, the corresponding above type does not exist. + +If you don't need a specific storage size, but want the smallest data +structure with @emph{at least} N bits, use one of these: + +@itemize @w +@item int8_least_t +@item int16_least_t +@item int32_least_t +@item int64_least_t +@item uint8_least_t +@item uint16_least_t +@item uint32_least_t +@item uint64_least_t +@end itemize + +If you don't need a specific storage size, but want the data structure +that allows the fastest access while having at least N bits (and +among data structures with the same access speed, the smallest one), use +one of these: + +@itemize @w +@item int8_fast_t +@item int16_fast_t +@item int32_fast_t +@item int64_fast_t +@item uint8_fast_t +@item uint16_fast_t +@item uint32_fast_t +@item uint64_fast_t +@end itemize + +If you want an integer with the widest range possible on the platform on +which it is being used, use one of the following. If you use these, +you should write code that takes into account the variable size and range +of the integer. + +@itemize @w +@item intmax_t +@item uintmax_t +@end itemize + +The GNU C library also provides macros that tell you the maximum and +minimum possible values for each integer data type. The macro names +follow these examples: @code{INT32_MAX}, @code{UINT8_MAX}, +@code{INT_FAST32_MIN}, @code{INT_LEAST64_MIN}, @code{UINTMAX_MAX}, +@code{INTMAX_MAX}, @code{INTMAX_MIN}. Note that there are no macros for +unsigned integer minima. These are always zero. +@cindex maximum possible integer +@cindex mininum possible integer + +There are similar macros for use with C's built in integer types which +should come with your C compiler. These are described in @ref{Data Type +Measurements}. + +Don't forget you can use the C @code{sizeof} function with any of these +data types to get the number of bytes of storage each uses. + + +@node Integer Division +@section Integer Division +@cindex integer division functions + +This section describes functions for performing integer division. These +functions are redundant when GNU CC is used, because in GNU C the +@samp{/} operator always rounds towards zero. But in other C +implementations, @samp{/} may round differently with negative arguments. +@code{div} and @code{ldiv} are useful because they specify how to round +the quotient: towards zero. The remainder has the same sign as the +numerator. + +These functions are specified to return a result @var{r} such that the value +@code{@var{r}.quot*@var{denominator} + @var{r}.rem} equals +@var{numerator}. + +@pindex stdlib.h +To use these facilities, you should include the header file +@file{stdlib.h} in your program. + +@comment stdlib.h +@comment ISO +@deftp {Data Type} div_t +This is a structure type used to hold the result returned by the @code{div} +function. It has the following members: + +@table @code +@item int quot +The quotient from the division. + +@item int rem +The remainder from the division. +@end table +@end deftp + +@comment stdlib.h +@comment ISO +@deftypefun div_t div (int @var{numerator}, int @var{denominator}) +This function @code{div} computes the quotient and remainder from +the division of @var{numerator} by @var{denominator}, returning the +result in a structure of type @code{div_t}. + +If the result cannot be represented (as in a division by zero), the +behavior is undefined. + +Here is an example, albeit not a very useful one. + +@smallexample +div_t result; +result = div (20, -6); +@end smallexample + +@noindent +Now @code{result.quot} is @code{-3} and @code{result.rem} is @code{2}. +@end deftypefun + +@comment stdlib.h +@comment ISO +@deftp {Data Type} ldiv_t +This is a structure type used to hold the result returned by the @code{ldiv} +function. It has the following members: + +@table @code +@item long int quot +The quotient from the division. + +@item long int rem +The remainder from the division. +@end table + +(This is identical to @code{div_t} except that the components are of +type @code{long int} rather than @code{int}.) +@end deftp + +@comment stdlib.h +@comment ISO +@deftypefun ldiv_t ldiv (long int @var{numerator}, long int @var{denominator}) +The @code{ldiv} function is similar to @code{div}, except that the +arguments are of type @code{long int} and the result is returned as a +structure of type @code{ldiv_t}. +@end deftypefun + +@comment stdlib.h +@comment ISO +@deftp {Data Type} lldiv_t +This is a structure type used to hold the result returned by the @code{lldiv} +function. It has the following members: + +@table @code +@item long long int quot +The quotient from the division. + +@item long long int rem +The remainder from the division. +@end table + +(This is identical to @code{div_t} except that the components are of +type @code{long long int} rather than @code{int}.) +@end deftp + +@comment stdlib.h +@comment ISO +@deftypefun lldiv_t lldiv (long long int @var{numerator}, long long int @var{denominator}) +The @code{lldiv} function is like the @code{div} function, but the +arguments are of type @code{long long int} and the result is returned as +a structure of type @code{lldiv_t}. + +The @code{lldiv} function was added in @w{ISO C99}. +@end deftypefun + +@comment inttypes.h +@comment ISO +@deftp {Data Type} imaxdiv_t +This is a structure type used to hold the result returned by the @code{imaxdiv} +function. It has the following members: + +@table @code +@item intmax_t quot +The quotient from the division. + +@item intmax_t rem +The remainder from the division. +@end table + +(This is identical to @code{div_t} except that the components are of +type @code{intmax_t} rather than @code{int}.) + +See @ref{Integers} for a description of the @code{intmax_t} type. + +@end deftp + +@comment inttypes.h +@comment ISO +@deftypefun imaxdiv_t imaxdiv (intmax_t @var{numerator}, intmax_t @var{denominator}) +The @code{imaxdiv} function is like the @code{div} function, but the +arguments are of type @code{intmax_t} and the result is returned as +a structure of type @code{imaxdiv_t}. + +See @ref{Integers} for a description of the @code{intmax_t} type. + +The @code{imaxdiv} function was added in @w{ISO C99}. +@end deftypefun + + @node Floating Point Numbers @section Floating Point Numbers @cindex floating point @@ -919,6 +1163,9 @@ the absolute value of @code{INT_MIN} (the smallest possible @code{int}) cannot be represented; thus, @w{@code{abs (INT_MIN)}} is not defined. @code{llabs} and @code{imaxdiv} are new to @w{ISO C99}. + +See @ref{Integers} for a description of the @code{intmax_t} type. + @end deftypefun @comment math.h @@ -1784,145 +2031,6 @@ INFINITY + I * copysign (0.0, cimag (z)) @end smallexample @end deftypefun -@node Integer Division -@section Integer Division -@cindex integer division functions - -This section describes functions for performing integer division. These -functions are redundant when GNU CC is used, because in GNU C the -@samp{/} operator always rounds towards zero. But in other C -implementations, @samp{/} may round differently with negative arguments. -@code{div} and @code{ldiv} are useful because they specify how to round -the quotient: towards zero. The remainder has the same sign as the -numerator. - -These functions are specified to return a result @var{r} such that the value -@code{@var{r}.quot*@var{denominator} + @var{r}.rem} equals -@var{numerator}. - -@pindex stdlib.h -To use these facilities, you should include the header file -@file{stdlib.h} in your program. - -@comment stdlib.h -@comment ISO -@deftp {Data Type} div_t -This is a structure type used to hold the result returned by the @code{div} -function. It has the following members: - -@table @code -@item int quot -The quotient from the division. - -@item int rem -The remainder from the division. -@end table -@end deftp - -@comment stdlib.h -@comment ISO -@deftypefun div_t div (int @var{numerator}, int @var{denominator}) -This function @code{div} computes the quotient and remainder from -the division of @var{numerator} by @var{denominator}, returning the -result in a structure of type @code{div_t}. - -If the result cannot be represented (as in a division by zero), the -behavior is undefined. - -Here is an example, albeit not a very useful one. - -@smallexample -div_t result; -result = div (20, -6); -@end smallexample - -@noindent -Now @code{result.quot} is @code{-3} and @code{result.rem} is @code{2}. -@end deftypefun - -@comment stdlib.h -@comment ISO -@deftp {Data Type} ldiv_t -This is a structure type used to hold the result returned by the @code{ldiv} -function. It has the following members: - -@table @code -@item long int quot -The quotient from the division. - -@item long int rem -The remainder from the division. -@end table - -(This is identical to @code{div_t} except that the components are of -type @code{long int} rather than @code{int}.) -@end deftp - -@comment stdlib.h -@comment ISO -@deftypefun ldiv_t ldiv (long int @var{numerator}, long int @var{denominator}) -The @code{ldiv} function is similar to @code{div}, except that the -arguments are of type @code{long int} and the result is returned as a -structure of type @code{ldiv_t}. -@end deftypefun - -@comment stdlib.h -@comment ISO -@deftp {Data Type} lldiv_t -This is a structure type used to hold the result returned by the @code{lldiv} -function. It has the following members: - -@table @code -@item long long int quot -The quotient from the division. - -@item long long int rem -The remainder from the division. -@end table - -(This is identical to @code{div_t} except that the components are of -type @code{long long int} rather than @code{int}.) -@end deftp - -@comment stdlib.h -@comment ISO -@deftypefun lldiv_t lldiv (long long int @var{numerator}, long long int @var{denominator}) -The @code{lldiv} function is like the @code{div} function, but the -arguments are of type @code{long long int} and the result is returned as -a structure of type @code{lldiv_t}. - -The @code{lldiv} function was added in @w{ISO C99}. -@end deftypefun - -@comment inttypes.h -@comment ISO -@deftp {Data Type} imaxdiv_t -This is a structure type used to hold the result returned by the @code{imaxdiv} -function. It has the following members: - -@table @code -@item intmax_t quot -The quotient from the division. - -@item intmax_t rem -The remainder from the division. -@end table - -(This is identical to @code{div_t} except that the components are of -type @code{intmax_t} rather than @code{int}.) -@end deftp - -@comment inttypes.h -@comment ISO -@deftypefun imaxdiv_t imaxdiv (intmax_t @var{numerator}, intmax_t @var{denominator}) -The @code{imaxdiv} function is like the @code{div} function, but the -arguments are of type @code{intmax_t} and the result is returned as -a structure of type @code{imaxdiv_t}. - -The @code{imaxdiv} function was added in @w{ISO C99}. -@end deftypefun - - @node Parsing of Numbers @section Parsing of Numbers @cindex parsing numbers (in formatted input) @@ -2016,11 +2124,15 @@ There is an example at the end of this section. @comment ISO @deftypefun {unsigned long int} strtoul (const char *@var{string}, char **@var{tailptr}, int @var{base}) The @code{strtoul} (``string-to-unsigned-long'') function is like -@code{strtol} except it returns an @code{unsigned long int} value. If -the number has a leading @samp{-} sign, the return value is negated. +@code{strtol} except it converts to an @code{unsigned long int} value. The syntax is the same as described above for @code{strtol}. The value -returned on overflow is @code{ULONG_MAX} (@pxref{Range of -Type}). +returned on overflow is @code{ULONG_MAX} (@pxref{Range of Type}). + +If @var{string} depicts a negative number, @code{strtoul} acts the same +as @var{strtol} but casts the result to an unsigned integer. That means +for example that @code{strtoul} on @code{"-1"} returns @code{ULONG_MAX} +and an input more negative than @code{LONG_MIN} returns +(@code{ULONG_MAX} + 1) / 2. @code{strtoul} sets @var{errno} to @code{EINVAL} if @var{base} is out of range, or @code{ERANGE} on overflow. @@ -2051,9 +2163,8 @@ The @code{strtoll} function was introduced in @w{ISO C99}. @comment stdlib.h @comment ISO @deftypefun {unsigned long long int} strtoull (const char *@var{string}, char **@var{tailptr}, int @var{base}) -The @code{strtoull} function is like @code{strtoul} except that it -returns an @code{unsigned long long int}. The value returned on overflow -is @code{ULONG_LONG_MAX} (@pxref{Range of Type}). +The @code{strtoull} function is related to @code{strtoll} the same way +@code{strtoul} is related to @code{strtol}. The @code{strtoull} function was introduced in @w{ISO C99}. @end deftypefun @@ -2064,6 +2175,35 @@ The @code{strtoull} function was introduced in @w{ISO C99}. @code{strtouq} is the BSD name for @code{strtoull}. @end deftypefun +@comment inttypes.h +@comment ??? +@deftypefun {long long int} strtoimax (const char *@var{string}, char **@var{tailptr}, int @var{base}) +The @code{strtoimax} function is like @code{strtol} except that it returns +a @code{intmax_t} value, and accepts numbers of a corresponding range. + +If the string has valid syntax for an integer but the value is not +representable because of overflow, @code{strtoimax} returns either +@code{INTMAX_MAX} or @code{INTMAX_MIN} (@pxref{Integers}), as +appropriate for the sign of the value. It also sets @code{errno} to +@code{ERANGE} to indicate there was overflow. + +The symbols for @code{strtoimax} are declared in @file{inttypes.h}. + +See @ref{Integers} for a description of the @code{intmax_t} type. + +@end deftypefun + +@comment inttypes.h +@comment ??? +@deftypefun uintmax_t strtoumax (const char *@var{string}, char **@var{tailptr}, int @var{base}) +The @code{strtoumax} function is related to @code{strtoimax} +the same way that @code{strtoul} is related to @code{strtol}. + +The symbols for @code{strtoimax} are declared in @file{inttypes.h}. + +See @ref{Integers} for a description of the @code{intmax_t} type. +@end deftypefun + @comment stdlib.h @comment ISO @deftypefun {long int} atol (const char *@var{string}) |