1 @node Arithmetic, Date and Time, Mathematics, Top
2 @c %MENU% Low level arithmetic functions
3 @chapter Arithmetic Functions
5 This chapter contains information about functions for doing basic
6 arithmetic operations, such as splitting a float into its integer and
7 fractional parts or retrieving the imaginary part of a complex value.
8 These functions are declared in the header files @file{math.h} and
12 * Integers:: Basic integer types and concepts
13 * Integer Division:: Integer division with guaranteed rounding.
14 * Floating Point Numbers:: Basic concepts. IEEE 754.
15 * Floating Point Classes:: The five kinds of floating-point number.
16 * Floating Point Errors:: When something goes wrong in a calculation.
17 * Rounding:: Controlling how results are rounded.
18 * Control Functions:: Saving and restoring the FPU's state.
19 * Arithmetic Functions:: Fundamental operations provided by the library.
20 * Complex Numbers:: The types. Writing complex constants.
21 * Operations on Complex:: Projection, conjugation, decomposition.
22 * Parsing of Numbers:: Converting strings to numbers.
23 * System V Number Conversion:: An archaic way to convert numbers to strings.
30 The C language defines several integer data types: integer, short integer,
31 long integer, and character, all in both signed and unsigned varieties.
32 The GNU C compiler extends the language to contain long long integers
36 The C integer types were intended to allow code to be portable among
37 machines with different inherent data sizes (word sizes), so each type
38 may have different ranges on different machines. The problem with
39 this is that a program often needs to be written for a particular range
40 of integers, and sometimes must be written for a particular size of
41 storage, regardless of what machine the program runs on.
43 To address this problem, @theglibc{} contains C type definitions
44 you can use to declare integers that meet your exact needs. Because the
45 @glibcadj{} header files are customized to a specific machine, your
46 program source code doesn't have to be.
48 These @code{typedef}s are in @file{stdint.h}.
51 If you require that an integer be represented in exactly N bits, use one
52 of the following types, with the obvious mapping to bit size and signedness:
65 If your C compiler and target machine do not allow integers of a certain
66 size, the corresponding above type does not exist.
68 If you don't need a specific storage size, but want the smallest data
69 structure with @emph{at least} N bits, use one of these:
82 If you don't need a specific storage size, but want the data structure
83 that allows the fastest access while having at least N bits (and
84 among data structures with the same access speed, the smallest one), use
98 If you want an integer with the widest range possible on the platform on
99 which it is being used, use one of the following. If you use these,
100 you should write code that takes into account the variable size and range
108 @Theglibc{} also provides macros that tell you the maximum and
109 minimum possible values for each integer data type. The macro names
110 follow these examples: @code{INT32_MAX}, @code{UINT8_MAX},
111 @code{INT_FAST32_MIN}, @code{INT_LEAST64_MIN}, @code{UINTMAX_MAX},
112 @code{INTMAX_MAX}, @code{INTMAX_MIN}. Note that there are no macros for
113 unsigned integer minima. These are always zero.
114 @cindex maximum possible integer
115 @cindex minimum possible integer
117 There are similar macros for use with C's built in integer types which
118 should come with your C compiler. These are described in @ref{Data Type
121 Don't forget you can use the C @code{sizeof} function with any of these
122 data types to get the number of bytes of storage each uses.
125 @node Integer Division
126 @section Integer Division
127 @cindex integer division functions
129 This section describes functions for performing integer division. These
130 functions are redundant when GNU CC is used, because in GNU C the
131 @samp{/} operator always rounds towards zero. But in other C
132 implementations, @samp{/} may round differently with negative arguments.
133 @code{div} and @code{ldiv} are useful because they specify how to round
134 the quotient: towards zero. The remainder has the same sign as the
137 These functions are specified to return a result @var{r} such that the value
138 @code{@var{r}.quot*@var{denominator} + @var{r}.rem} equals
142 To use these facilities, you should include the header file
143 @file{stdlib.h} in your program.
147 @deftp {Data Type} div_t
148 This is a structure type used to hold the result returned by the @code{div}
149 function. It has the following members:
153 The quotient from the division.
156 The remainder from the division.
162 @deftypefun div_t div (int @var{numerator}, int @var{denominator})
163 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
164 @c Functions in this section are pure, and thus safe.
165 This function @code{div} computes the quotient and remainder from
166 the division of @var{numerator} by @var{denominator}, returning the
167 result in a structure of type @code{div_t}.
169 If the result cannot be represented (as in a division by zero), the
170 behavior is undefined.
172 Here is an example, albeit not a very useful one.
176 result = div (20, -6);
180 Now @code{result.quot} is @code{-3} and @code{result.rem} is @code{2}.
185 @deftp {Data Type} ldiv_t
186 This is a structure type used to hold the result returned by the @code{ldiv}
187 function. It has the following members:
191 The quotient from the division.
194 The remainder from the division.
197 (This is identical to @code{div_t} except that the components are of
198 type @code{long int} rather than @code{int}.)
203 @deftypefun ldiv_t ldiv (long int @var{numerator}, long int @var{denominator})
204 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
205 The @code{ldiv} function is similar to @code{div}, except that the
206 arguments are of type @code{long int} and the result is returned as a
207 structure of type @code{ldiv_t}.
212 @deftp {Data Type} lldiv_t
213 This is a structure type used to hold the result returned by the @code{lldiv}
214 function. It has the following members:
217 @item long long int quot
218 The quotient from the division.
220 @item long long int rem
221 The remainder from the division.
224 (This is identical to @code{div_t} except that the components are of
225 type @code{long long int} rather than @code{int}.)
230 @deftypefun lldiv_t lldiv (long long int @var{numerator}, long long int @var{denominator})
231 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
232 The @code{lldiv} function is like the @code{div} function, but the
233 arguments are of type @code{long long int} and the result is returned as
234 a structure of type @code{lldiv_t}.
236 The @code{lldiv} function was added in @w{ISO C99}.
241 @deftp {Data Type} imaxdiv_t
242 This is a structure type used to hold the result returned by the @code{imaxdiv}
243 function. It has the following members:
247 The quotient from the division.
250 The remainder from the division.
253 (This is identical to @code{div_t} except that the components are of
254 type @code{intmax_t} rather than @code{int}.)
256 See @ref{Integers} for a description of the @code{intmax_t} type.
262 @deftypefun imaxdiv_t imaxdiv (intmax_t @var{numerator}, intmax_t @var{denominator})
263 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
264 The @code{imaxdiv} function is like the @code{div} function, but the
265 arguments are of type @code{intmax_t} and the result is returned as
266 a structure of type @code{imaxdiv_t}.
268 See @ref{Integers} for a description of the @code{intmax_t} type.
270 The @code{imaxdiv} function was added in @w{ISO C99}.
274 @node Floating Point Numbers
275 @section Floating Point Numbers
276 @cindex floating point
278 @cindex IEEE floating point
280 Most computer hardware has support for two different kinds of numbers:
281 integers (@math{@dots{}-3, -2, -1, 0, 1, 2, 3@dots{}}) and
282 floating-point numbers. Floating-point numbers have three parts: the
283 @dfn{mantissa}, the @dfn{exponent}, and the @dfn{sign bit}. The real
284 number represented by a floating-point value is given by
286 $(s \mathrel? -1 \mathrel: 1) \cdot 2^e \cdot M$
289 @math{(s ? -1 : 1) @mul{} 2^e @mul{} M}
291 where @math{s} is the sign bit, @math{e} the exponent, and @math{M}
292 the mantissa. @xref{Floating Point Concepts}, for details. (It is
293 possible to have a different @dfn{base} for the exponent, but all modern
294 hardware uses @math{2}.)
296 Floating-point numbers can represent a finite subset of the real
297 numbers. While this subset is large enough for most purposes, it is
298 important to remember that the only reals that can be represented
299 exactly are rational numbers that have a terminating binary expansion
300 shorter than the width of the mantissa. Even simple fractions such as
301 @math{1/5} can only be approximated by floating point.
303 Mathematical operations and functions frequently need to produce values
304 that are not representable. Often these values can be approximated
305 closely enough for practical purposes, but sometimes they can't.
306 Historically there was no way to tell when the results of a calculation
307 were inaccurate. Modern computers implement the @w{IEEE 754} standard
308 for numerical computations, which defines a framework for indicating to
309 the program when the results of calculation are not trustworthy. This
310 framework consists of a set of @dfn{exceptions} that indicate why a
311 result could not be represented, and the special values @dfn{infinity}
312 and @dfn{not a number} (NaN).
314 @node Floating Point Classes
315 @section Floating-Point Number Classification Functions
316 @cindex floating-point classes
317 @cindex classes, floating-point
320 @w{ISO C99} defines macros that let you determine what sort of
321 floating-point number a variable holds.
325 @deftypefn {Macro} int fpclassify (@emph{float-type} @var{x})
326 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
327 This is a generic macro which works on all floating-point types and
328 which returns a value of type @code{int}. The possible values are:
332 The floating-point number @var{x} is ``Not a Number'' (@pxref{Infinity
335 The value of @var{x} is either plus or minus infinity (@pxref{Infinity
338 The value of @var{x} is zero. In floating-point formats like @w{IEEE
339 754}, where zero can be signed, this value is also returned if
340 @var{x} is negative zero.
342 Numbers whose absolute value is too small to be represented in the
343 normal format are represented in an alternate, @dfn{denormalized} format
344 (@pxref{Floating Point Concepts}). This format is less precise but can
345 represent values closer to zero. @code{fpclassify} returns this value
346 for values of @var{x} in this alternate format.
348 This value is returned for all other values of @var{x}. It indicates
349 that there is nothing special about the number.
354 @code{fpclassify} is most useful if more than one property of a number
355 must be tested. There are more specific macros which only test one
356 property at a time. Generally these macros execute faster than
357 @code{fpclassify}, since there is special hardware support for them.
358 You should therefore use the specific macros whenever possible.
362 @deftypefn {Macro} int isfinite (@emph{float-type} @var{x})
363 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
364 This macro returns a nonzero value if @var{x} is finite: not plus or
365 minus infinity, and not NaN. It is equivalent to
368 (fpclassify (x) != FP_NAN && fpclassify (x) != FP_INFINITE)
371 @code{isfinite} is implemented as a macro which accepts any
377 @deftypefn {Macro} int isnormal (@emph{float-type} @var{x})
378 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
379 This macro returns a nonzero value if @var{x} is finite and normalized.
383 (fpclassify (x) == FP_NORMAL)
389 @deftypefn {Macro} int isnan (@emph{float-type} @var{x})
390 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
391 This macro returns a nonzero value if @var{x} is NaN. It is equivalent
395 (fpclassify (x) == FP_NAN)
401 @deftypefn {Macro} int issignaling (@emph{float-type} @var{x})
402 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
403 This macro returns a nonzero value if @var{x} is a signaling NaN
404 (sNaN). It is from TS 18661-1:2014.
407 Another set of floating-point classification functions was provided by
408 BSD. @Theglibc{} also supports these functions; however, we
409 recommend that you use the ISO C99 macros in new code. Those are standard
410 and will be available more widely. Also, since they are macros, you do
411 not have to worry about the type of their argument.
415 @deftypefun int isinf (double @var{x})
418 @deftypefunx int isinff (float @var{x})
421 @deftypefunx int isinfl (long double @var{x})
422 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
423 This function returns @code{-1} if @var{x} represents negative infinity,
424 @code{1} if @var{x} represents positive infinity, and @code{0} otherwise.
429 @deftypefun int isnan (double @var{x})
432 @deftypefunx int isnanf (float @var{x})
435 @deftypefunx int isnanl (long double @var{x})
436 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
437 This function returns a nonzero value if @var{x} is a ``not a number''
438 value, and zero otherwise.
440 @strong{NB:} The @code{isnan} macro defined by @w{ISO C99} overrides
441 the BSD function. This is normally not a problem, because the two
442 routines behave identically. However, if you really need to get the BSD
443 function for some reason, you can write
452 @deftypefun int finite (double @var{x})
455 @deftypefunx int finitef (float @var{x})
458 @deftypefunx int finitel (long double @var{x})
459 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
460 This function returns a nonzero value if @var{x} is finite or a ``not a
461 number'' value, and zero otherwise.
464 @strong{Portability Note:} The functions listed in this section are BSD
468 @node Floating Point Errors
469 @section Errors in Floating-Point Calculations
472 * FP Exceptions:: IEEE 754 math exceptions and how to detect them.
473 * Infinity and NaN:: Special values returned by calculations.
474 * Status bit operations:: Checking for exceptions after the fact.
475 * Math Error Reporting:: How the math functions report errors.
479 @subsection FP Exceptions
483 @cindex division by zero
484 @cindex inexact exception
485 @cindex invalid exception
486 @cindex overflow exception
487 @cindex underflow exception
489 The @w{IEEE 754} standard defines five @dfn{exceptions} that can occur
490 during a calculation. Each corresponds to a particular sort of error,
493 When exceptions occur (when exceptions are @dfn{raised}, in the language
494 of the standard), one of two things can happen. By default the
495 exception is simply noted in the floating-point @dfn{status word}, and
496 the program continues as if nothing had happened. The operation
497 produces a default value, which depends on the exception (see the table
498 below). Your program can check the status word to find out which
501 Alternatively, you can enable @dfn{traps} for exceptions. In that case,
502 when an exception is raised, your program will receive the @code{SIGFPE}
503 signal. The default action for this signal is to terminate the
504 program. @xref{Signal Handling}, for how you can change the effect of
508 In the System V math library, the user-defined function @code{matherr}
509 is called when certain exceptions occur inside math library functions.
510 However, the Unix98 standard deprecates this interface. We support it
511 for historical compatibility, but recommend that you do not use it in
512 new programs. When this interface is used, exceptions may not be
516 The exceptions defined in @w{IEEE 754} are:
519 @item Invalid Operation
520 This exception is raised if the given operands are invalid for the
521 operation to be performed. Examples are
522 (see @w{IEEE 754}, @w{section 7}):
525 Addition or subtraction: @math{@infinity{} - @infinity{}}. (But
526 @math{@infinity{} + @infinity{} = @infinity{}}).
528 Multiplication: @math{0 @mul{} @infinity{}}.
530 Division: @math{0/0} or @math{@infinity{}/@infinity{}}.
532 Remainder: @math{x} REM @math{y}, where @math{y} is zero or @math{x} is
535 Square root if the operand is less then zero. More generally, any
536 mathematical function evaluated outside its domain produces this
539 Conversion of a floating-point number to an integer or decimal
540 string, when the number cannot be represented in the target format (due
541 to overflow, infinity, or NaN).
543 Conversion of an unrecognizable input string.
545 Comparison via predicates involving @math{<} or @math{>}, when one or
546 other of the operands is NaN. You can prevent this exception by using
547 the unordered comparison functions instead; see @ref{FP Comparison Functions}.
550 If the exception does not trap, the result of the operation is NaN.
552 @item Division by Zero
553 This exception is raised when a finite nonzero number is divided
554 by zero. If no trap occurs the result is either @math{+@infinity{}} or
555 @math{-@infinity{}}, depending on the signs of the operands.
558 This exception is raised whenever the result cannot be represented
559 as a finite value in the precision format of the destination. If no trap
560 occurs the result depends on the sign of the intermediate result and the
561 current rounding mode (@w{IEEE 754}, @w{section 7.3}):
564 Round to nearest carries all overflows to @math{@infinity{}}
565 with the sign of the intermediate result.
567 Round toward @math{0} carries all overflows to the largest representable
568 finite number with the sign of the intermediate result.
570 Round toward @math{-@infinity{}} carries positive overflows to the
571 largest representable finite number and negative overflows to
575 Round toward @math{@infinity{}} carries negative overflows to the
576 most negative representable finite number and positive overflows
577 to @math{@infinity{}}.
580 Whenever the overflow exception is raised, the inexact exception is also
584 The underflow exception is raised when an intermediate result is too
585 small to be calculated accurately, or if the operation's result rounded
586 to the destination precision is too small to be normalized.
588 When no trap is installed for the underflow exception, underflow is
589 signaled (via the underflow flag) only when both tininess and loss of
590 accuracy have been detected. If no trap handler is installed the
591 operation continues with an imprecise small value, or zero if the
592 destination precision cannot hold the small exact result.
595 This exception is signalled if a rounded result is not exact (such as
596 when calculating the square root of two) or a result overflows without
600 @node Infinity and NaN
601 @subsection Infinity and NaN
606 @w{IEEE 754} floating point numbers can represent positive or negative
607 infinity, and @dfn{NaN} (not a number). These three values arise from
608 calculations whose result is undefined or cannot be represented
609 accurately. You can also deliberately set a floating-point variable to
610 any of them, which is sometimes useful. Some examples of calculations
611 that produce infinity or NaN:
615 @math{1/0 = @infinity{}}
616 @math{log (0) = -@infinity{}}
617 @math{sqrt (-1) = NaN}
621 $${1\over0} = \infty$$
623 $$\sqrt{-1} = \hbox{NaN}$$
626 When a calculation produces any of these values, an exception also
627 occurs; see @ref{FP Exceptions}.
629 The basic operations and math functions all accept infinity and NaN and
630 produce sensible output. Infinities propagate through calculations as
631 one would expect: for example, @math{2 + @infinity{} = @infinity{}},
632 @math{4/@infinity{} = 0}, atan @math{(@infinity{}) = @pi{}/2}. NaN, on
633 the other hand, infects any calculation that involves it. Unless the
634 calculation would produce the same result no matter what real value
635 replaced NaN, the result is NaN.
637 In comparison operations, positive infinity is larger than all values
638 except itself and NaN, and negative infinity is smaller than all values
639 except itself and NaN. NaN is @dfn{unordered}: it is not equal to,
640 greater than, or less than anything, @emph{including itself}. @code{x ==
641 x} is false if the value of @code{x} is NaN. You can use this to test
642 whether a value is NaN or not, but the recommended way to test for NaN
643 is with the @code{isnan} function (@pxref{Floating Point Classes}). In
644 addition, @code{<}, @code{>}, @code{<=}, and @code{>=} will raise an
645 exception when applied to NaNs.
647 @file{math.h} defines macros that allow you to explicitly set a variable
652 @deftypevr Macro float INFINITY
653 An expression representing positive infinity. It is equal to the value
654 produced by mathematical operations like @code{1.0 / 0.0}.
655 @code{-INFINITY} represents negative infinity.
657 You can test whether a floating-point value is infinite by comparing it
658 to this macro. However, this is not recommended; you should use the
659 @code{isfinite} macro instead. @xref{Floating Point Classes}.
661 This macro was introduced in the @w{ISO C99} standard.
666 @deftypevr Macro float NAN
667 An expression representing a value which is ``not a number''. This
668 macro is a GNU extension, available only on machines that support the
669 ``not a number'' value---that is to say, on all machines that support
672 You can use @samp{#ifdef NAN} to test whether the machine supports
673 NaN. (Of course, you must arrange for GNU extensions to be visible,
674 such as by defining @code{_GNU_SOURCE}, and then you must include
678 @w{IEEE 754} also allows for another unusual value: negative zero. This
679 value is produced when you divide a positive number by negative
680 infinity, or when a negative result is smaller than the limits of
683 @node Status bit operations
684 @subsection Examining the FPU status word
686 @w{ISO C99} defines functions to query and manipulate the
687 floating-point status word. You can use these functions to check for
688 untrapped exceptions when it's convenient, rather than worrying about
689 them in the middle of a calculation.
691 These constants represent the various @w{IEEE 754} exceptions. Not all
692 FPUs report all the different exceptions. Each constant is defined if
693 and only if the FPU you are compiling for supports that exception, so
694 you can test for FPU support with @samp{#ifdef}. They are defined in
701 The inexact exception.
705 The divide by zero exception.
709 The underflow exception.
713 The overflow exception.
717 The invalid exception.
720 The macro @code{FE_ALL_EXCEPT} is the bitwise OR of all exception macros
721 which are supported by the FP implementation.
723 These functions allow you to clear exception flags, test for exceptions,
724 and save and restore the set of exceptions flagged.
728 @deftypefun int feclearexcept (int @var{excepts})
729 @safety{@prelim{}@mtsafe{}@assafe{@assposix{}}@acsafe{@acsposix{}}}
730 @c The other functions in this section that modify FP status register
731 @c mostly do so with non-atomic load-modify-store sequences, but since
732 @c the register is thread-specific, this should be fine, and safe for
733 @c cancellation. As long as the FP environment is restored before the
734 @c signal handler returns control to the interrupted thread (like any
735 @c kernel should do), the functions are also safe for use in signal
737 This function clears all of the supported exception flags indicated by
740 The function returns zero in case the operation was successful, a
741 non-zero value otherwise.
746 @deftypefun int feraiseexcept (int @var{excepts})
747 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
748 This function raises the supported exceptions indicated by
749 @var{excepts}. If more than one exception bit in @var{excepts} is set
750 the order in which the exceptions are raised is undefined except that
751 overflow (@code{FE_OVERFLOW}) or underflow (@code{FE_UNDERFLOW}) are
752 raised before inexact (@code{FE_INEXACT}). Whether for overflow or
753 underflow the inexact exception is also raised is also implementation
756 The function returns zero in case the operation was successful, a
757 non-zero value otherwise.
762 @deftypefun int fetestexcept (int @var{excepts})
763 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
764 Test whether the exception flags indicated by the parameter @var{except}
765 are currently set. If any of them are, a nonzero value is returned
766 which specifies which exceptions are set. Otherwise the result is zero.
769 To understand these functions, imagine that the status word is an
770 integer variable named @var{status}. @code{feclearexcept} is then
771 equivalent to @samp{status &= ~excepts} and @code{fetestexcept} is
772 equivalent to @samp{(status & excepts)}. The actual implementation may
773 be very different, of course.
775 Exception flags are only cleared when the program explicitly requests it,
776 by calling @code{feclearexcept}. If you want to check for exceptions
777 from a set of calculations, you should clear all the flags first. Here
778 is a simple example of the way to use @code{fetestexcept}:
784 feclearexcept (FE_ALL_EXCEPT);
786 raised = fetestexcept (FE_OVERFLOW | FE_INVALID);
787 if (raised & FE_OVERFLOW) @{ /* @dots{} */ @}
788 if (raised & FE_INVALID) @{ /* @dots{} */ @}
793 You cannot explicitly set bits in the status word. You can, however,
794 save the entire status word and restore it later. This is done with the
799 @deftypefun int fegetexceptflag (fexcept_t *@var{flagp}, int @var{excepts})
800 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
801 This function stores in the variable pointed to by @var{flagp} an
802 implementation-defined value representing the current setting of the
803 exception flags indicated by @var{excepts}.
805 The function returns zero in case the operation was successful, a
806 non-zero value otherwise.
811 @deftypefun int fesetexceptflag (const fexcept_t *@var{flagp}, int @var{excepts})
812 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
813 This function restores the flags for the exceptions indicated by
814 @var{excepts} to the values stored in the variable pointed to by
817 The function returns zero in case the operation was successful, a
818 non-zero value otherwise.
821 Note that the value stored in @code{fexcept_t} bears no resemblance to
822 the bit mask returned by @code{fetestexcept}. The type may not even be
823 an integer. Do not attempt to modify an @code{fexcept_t} variable.
825 @node Math Error Reporting
826 @subsection Error Reporting by Mathematical Functions
827 @cindex errors, mathematical
831 Many of the math functions are defined only over a subset of the real or
832 complex numbers. Even if they are mathematically defined, their result
833 may be larger or smaller than the range representable by their return
834 type without loss of accuracy. These are known as @dfn{domain errors},
836 @dfn{underflows}, respectively. Math functions do several things when
837 one of these errors occurs. In this manual we will refer to the
838 complete response as @dfn{signalling} a domain error, overflow, or
841 When a math function suffers a domain error, it raises the invalid
842 exception and returns NaN. It also sets @var{errno} to @code{EDOM};
843 this is for compatibility with old systems that do not support @w{IEEE
844 754} exception handling. Likewise, when overflow occurs, math
845 functions raise the overflow exception and, in the default rounding
846 mode, return @math{@infinity{}} or @math{-@infinity{}} as appropriate
847 (in other rounding modes, the largest finite value of the appropriate
848 sign is returned when appropriate for that rounding mode). They also
849 set @var{errno} to @code{ERANGE} if returning @math{@infinity{}} or
850 @math{-@infinity{}}; @var{errno} may or may not be set to
851 @code{ERANGE} when a finite value is returned on overflow. When
852 underflow occurs, the underflow exception is raised, and zero
853 (appropriately signed) or a subnormal value, as appropriate for the
854 mathematical result of the function and the rounding mode, is
855 returned. @var{errno} may be set to @code{ERANGE}, but this is not
856 guaranteed; it is intended that @theglibc{} should set it when the
857 underflow is to an appropriately signed zero, but not necessarily for
860 Some of the math functions are defined mathematically to result in a
861 complex value over parts of their domains. The most familiar example of
862 this is taking the square root of a negative number. The complex math
863 functions, such as @code{csqrt}, will return the appropriate complex value
864 in this case. The real-valued functions, such as @code{sqrt}, will
865 signal a domain error.
867 Some older hardware does not support infinities. On that hardware,
868 overflows instead return a particular very large number (usually the
869 largest representable number). @file{math.h} defines macros you can use
870 to test for overflow on both old and new hardware.
874 @deftypevr Macro double HUGE_VAL
877 @deftypevrx Macro float HUGE_VALF
880 @deftypevrx Macro {long double} HUGE_VALL
881 An expression representing a particular very large number. On machines
882 that use @w{IEEE 754} floating point format, @code{HUGE_VAL} is infinity.
883 On other machines, it's typically the largest positive number that can
886 Mathematical functions return the appropriately typed version of
887 @code{HUGE_VAL} or @code{@minus{}HUGE_VAL} when the result is too large
892 @section Rounding Modes
894 Floating-point calculations are carried out internally with extra
895 precision, and then rounded to fit into the destination type. This
896 ensures that results are as precise as the input data. @w{IEEE 754}
897 defines four possible rounding modes:
900 @item Round to nearest.
901 This is the default mode. It should be used unless there is a specific
902 need for one of the others. In this mode results are rounded to the
903 nearest representable value. If the result is midway between two
904 representable values, the even representable is chosen. @dfn{Even} here
905 means the lowest-order bit is zero. This rounding mode prevents
906 statistical bias and guarantees numeric stability: round-off errors in a
907 lengthy calculation will remain smaller than half of @code{FLT_EPSILON}.
909 @c @item Round toward @math{+@infinity{}}
910 @item Round toward plus Infinity.
911 All results are rounded to the smallest representable value
912 which is greater than the result.
914 @c @item Round toward @math{-@infinity{}}
915 @item Round toward minus Infinity.
916 All results are rounded to the largest representable value which is less
919 @item Round toward zero.
920 All results are rounded to the largest representable value whose
921 magnitude is less than that of the result. In other words, if the
922 result is negative it is rounded up; if it is positive, it is rounded
927 @file{fenv.h} defines constants which you can use to refer to the
928 various rounding modes. Each one will be defined if and only if the FPU
929 supports the corresponding rounding mode.
942 Round toward @math{+@infinity{}}.
948 Round toward @math{-@infinity{}}.
952 @vindex FE_TOWARDZERO
957 Underflow is an unusual case. Normally, @w{IEEE 754} floating point
958 numbers are always normalized (@pxref{Floating Point Concepts}).
959 Numbers smaller than @math{2^r} (where @math{r} is the minimum exponent,
960 @code{FLT_MIN_RADIX-1} for @var{float}) cannot be represented as
961 normalized numbers. Rounding all such numbers to zero or @math{2^r}
962 would cause some algorithms to fail at 0. Therefore, they are left in
963 denormalized form. That produces loss of precision, since some bits of
964 the mantissa are stolen to indicate the decimal point.
966 If a result is too small to be represented as a denormalized number, it
967 is rounded to zero. However, the sign of the result is preserved; if
968 the calculation was negative, the result is @dfn{negative zero}.
969 Negative zero can also result from some operations on infinity, such as
970 @math{4/-@infinity{}}.
972 At any time one of the above four rounding modes is selected. You can
973 find out which one with this function:
977 @deftypefun int fegetround (void)
978 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
979 Returns the currently selected rounding mode, represented by one of the
980 values of the defined rounding mode macros.
984 To change the rounding mode, use this function:
988 @deftypefun int fesetround (int @var{round})
989 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
990 Changes the currently selected rounding mode to @var{round}. If
991 @var{round} does not correspond to one of the supported rounding modes
992 nothing is changed. @code{fesetround} returns zero if it changed the
993 rounding mode, a nonzero value if the mode is not supported.
996 You should avoid changing the rounding mode if possible. It can be an
997 expensive operation; also, some hardware requires you to compile your
998 program differently for it to work. The resulting code may run slower.
999 See your compiler documentation for details.
1000 @c This section used to claim that functions existed to round one number
1001 @c in a specific fashion. I can't find any functions in the library
1002 @c that do that. -zw
1004 @node Control Functions
1005 @section Floating-Point Control Functions
1007 @w{IEEE 754} floating-point implementations allow the programmer to
1008 decide whether traps will occur for each of the exceptions, by setting
1009 bits in the @dfn{control word}. In C, traps result in the program
1010 receiving the @code{SIGFPE} signal; see @ref{Signal Handling}.
1012 @strong{NB:} @w{IEEE 754} says that trap handlers are given details of
1013 the exceptional situation, and can set the result value. C signals do
1014 not provide any mechanism to pass this information back and forth.
1015 Trapping exceptions in C is therefore not very useful.
1017 It is sometimes necessary to save the state of the floating-point unit
1018 while you perform some calculation. The library provides functions
1019 which save and restore the exception flags, the set of exceptions that
1020 generate traps, and the rounding mode. This information is known as the
1021 @dfn{floating-point environment}.
1023 The functions to save and restore the floating-point environment all use
1024 a variable of type @code{fenv_t} to store information. This type is
1025 defined in @file{fenv.h}. Its size and contents are
1026 implementation-defined. You should not attempt to manipulate a variable
1027 of this type directly.
1029 To save the state of the FPU, use one of these functions:
1033 @deftypefun int fegetenv (fenv_t *@var{envp})
1034 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1035 Store the floating-point environment in the variable pointed to by
1038 The function returns zero in case the operation was successful, a
1039 non-zero value otherwise.
1044 @deftypefun int feholdexcept (fenv_t *@var{envp})
1045 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1046 Store the current floating-point environment in the object pointed to by
1047 @var{envp}. Then clear all exception flags, and set the FPU to trap no
1048 exceptions. Not all FPUs support trapping no exceptions; if
1049 @code{feholdexcept} cannot set this mode, it returns nonzero value. If it
1050 succeeds, it returns zero.
1053 The functions which restore the floating-point environment can take these
1058 Pointers to @code{fenv_t} objects, which were initialized previously by a
1059 call to @code{fegetenv} or @code{feholdexcept}.
1062 The special macro @code{FE_DFL_ENV} which represents the floating-point
1063 environment as it was available at program start.
1065 Implementation defined macros with names starting with @code{FE_} and
1066 having type @code{fenv_t *}.
1068 @vindex FE_NOMASK_ENV
1069 If possible, @theglibc{} defines a macro @code{FE_NOMASK_ENV}
1070 which represents an environment where every exception raised causes a
1071 trap to occur. You can test for this macro using @code{#ifdef}. It is
1072 only defined if @code{_GNU_SOURCE} is defined.
1074 Some platforms might define other predefined environments.
1078 To set the floating-point environment, you can use either of these
1083 @deftypefun int fesetenv (const fenv_t *@var{envp})
1084 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1085 Set the floating-point environment to that described by @var{envp}.
1087 The function returns zero in case the operation was successful, a
1088 non-zero value otherwise.
1093 @deftypefun int feupdateenv (const fenv_t *@var{envp})
1094 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1095 Like @code{fesetenv}, this function sets the floating-point environment
1096 to that described by @var{envp}. However, if any exceptions were
1097 flagged in the status word before @code{feupdateenv} was called, they
1098 remain flagged after the call. In other words, after @code{feupdateenv}
1099 is called, the status word is the bitwise OR of the previous status word
1100 and the one saved in @var{envp}.
1102 The function returns zero in case the operation was successful, a
1103 non-zero value otherwise.
1107 To control for individual exceptions if raising them causes a trap to
1108 occur, you can use the following two functions.
1110 @strong{Portability Note:} These functions are all GNU extensions.
1114 @deftypefun int feenableexcept (int @var{excepts})
1115 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1116 This functions enables traps for each of the exceptions as indicated by
1117 the parameter @var{except}. The individual exceptions are described in
1118 @ref{Status bit operations}. Only the specified exceptions are
1119 enabled, the status of the other exceptions is not changed.
1121 The function returns the previous enabled exceptions in case the
1122 operation was successful, @code{-1} otherwise.
1127 @deftypefun int fedisableexcept (int @var{excepts})
1128 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1129 This functions disables traps for each of the exceptions as indicated by
1130 the parameter @var{except}. The individual exceptions are described in
1131 @ref{Status bit operations}. Only the specified exceptions are
1132 disabled, the status of the other exceptions is not changed.
1134 The function returns the previous enabled exceptions in case the
1135 operation was successful, @code{-1} otherwise.
1140 @deftypefun int fegetexcept (void)
1141 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1142 The function returns a bitmask of all currently enabled exceptions. It
1143 returns @code{-1} in case of failure.
1146 @node Arithmetic Functions
1147 @section Arithmetic Functions
1149 The C library provides functions to do basic operations on
1150 floating-point numbers. These include absolute value, maximum and minimum,
1151 normalization, bit twiddling, rounding, and a few others.
1154 * Absolute Value:: Absolute values of integers and floats.
1155 * Normalization Functions:: Extracting exponents and putting them back.
1156 * Rounding Functions:: Rounding floats to integers.
1157 * Remainder Functions:: Remainders on division, precisely defined.
1158 * FP Bit Twiddling:: Sign bit adjustment. Adding epsilon.
1159 * FP Comparison Functions:: Comparisons without risk of exceptions.
1160 * Misc FP Arithmetic:: Max, min, positive difference, multiply-add.
1163 @node Absolute Value
1164 @subsection Absolute Value
1165 @cindex absolute value functions
1167 These functions are provided for obtaining the @dfn{absolute value} (or
1168 @dfn{magnitude}) of a number. The absolute value of a real number
1169 @var{x} is @var{x} if @var{x} is positive, @minus{}@var{x} if @var{x} is
1170 negative. For a complex number @var{z}, whose real part is @var{x} and
1171 whose imaginary part is @var{y}, the absolute value is @w{@code{sqrt
1172 (@var{x}*@var{x} + @var{y}*@var{y})}}.
1176 Prototypes for @code{abs}, @code{labs} and @code{llabs} are in @file{stdlib.h};
1177 @code{imaxabs} is declared in @file{inttypes.h};
1178 @code{fabs}, @code{fabsf} and @code{fabsl} are declared in @file{math.h}.
1179 @code{cabs}, @code{cabsf} and @code{cabsl} are declared in @file{complex.h}.
1183 @deftypefun int abs (int @var{number})
1186 @deftypefunx {long int} labs (long int @var{number})
1189 @deftypefunx {long long int} llabs (long long int @var{number})
1192 @deftypefunx intmax_t imaxabs (intmax_t @var{number})
1193 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1194 These functions return the absolute value of @var{number}.
1196 Most computers use a two's complement integer representation, in which
1197 the absolute value of @code{INT_MIN} (the smallest possible @code{int})
1198 cannot be represented; thus, @w{@code{abs (INT_MIN)}} is not defined.
1200 @code{llabs} and @code{imaxdiv} are new to @w{ISO C99}.
1202 See @ref{Integers} for a description of the @code{intmax_t} type.
1208 @deftypefun double fabs (double @var{number})
1211 @deftypefunx float fabsf (float @var{number})
1214 @deftypefunx {long double} fabsl (long double @var{number})
1215 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1216 This function returns the absolute value of the floating-point number
1222 @deftypefun double cabs (complex double @var{z})
1225 @deftypefunx float cabsf (complex float @var{z})
1228 @deftypefunx {long double} cabsl (complex long double @var{z})
1229 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1230 These functions return the absolute value of the complex number @var{z}
1231 (@pxref{Complex Numbers}). The absolute value of a complex number is:
1234 sqrt (creal (@var{z}) * creal (@var{z}) + cimag (@var{z}) * cimag (@var{z}))
1237 This function should always be used instead of the direct formula
1238 because it takes special care to avoid losing precision. It may also
1239 take advantage of hardware support for this operation. See @code{hypot}
1240 in @ref{Exponents and Logarithms}.
1243 @node Normalization Functions
1244 @subsection Normalization Functions
1245 @cindex normalization functions (floating-point)
1247 The functions described in this section are primarily provided as a way
1248 to efficiently perform certain low-level manipulations on floating point
1249 numbers that are represented internally using a binary radix;
1250 see @ref{Floating Point Concepts}. These functions are required to
1251 have equivalent behavior even if the representation does not use a radix
1252 of 2, but of course they are unlikely to be particularly efficient in
1256 All these functions are declared in @file{math.h}.
1260 @deftypefun double frexp (double @var{value}, int *@var{exponent})
1263 @deftypefunx float frexpf (float @var{value}, int *@var{exponent})
1266 @deftypefunx {long double} frexpl (long double @var{value}, int *@var{exponent})
1267 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1268 These functions are used to split the number @var{value}
1269 into a normalized fraction and an exponent.
1271 If the argument @var{value} is not zero, the return value is @var{value}
1272 times a power of two, and its magnitude is always in the range 1/2
1273 (inclusive) to 1 (exclusive). The corresponding exponent is stored in
1274 @code{*@var{exponent}}; the return value multiplied by 2 raised to this
1275 exponent equals the original number @var{value}.
1277 For example, @code{frexp (12.8, &exponent)} returns @code{0.8} and
1278 stores @code{4} in @code{exponent}.
1280 If @var{value} is zero, then the return value is zero and
1281 zero is stored in @code{*@var{exponent}}.
1286 @deftypefun double ldexp (double @var{value}, int @var{exponent})
1289 @deftypefunx float ldexpf (float @var{value}, int @var{exponent})
1292 @deftypefunx {long double} ldexpl (long double @var{value}, int @var{exponent})
1293 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1294 These functions return the result of multiplying the floating-point
1295 number @var{value} by 2 raised to the power @var{exponent}. (It can
1296 be used to reassemble floating-point numbers that were taken apart
1299 For example, @code{ldexp (0.8, 4)} returns @code{12.8}.
1302 The following functions, which come from BSD, provide facilities
1303 equivalent to those of @code{ldexp} and @code{frexp}. See also the
1304 @w{ISO C} function @code{logb} which originally also appeared in BSD.
1308 @deftypefun double scalb (double @var{value}, double @var{exponent})
1311 @deftypefunx float scalbf (float @var{value}, float @var{exponent})
1314 @deftypefunx {long double} scalbl (long double @var{value}, long double @var{exponent})
1315 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1316 The @code{scalb} function is the BSD name for @code{ldexp}.
1321 @deftypefun double scalbn (double @var{x}, int @var{n})
1324 @deftypefunx float scalbnf (float @var{x}, int @var{n})
1327 @deftypefunx {long double} scalbnl (long double @var{x}, int @var{n})
1328 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1329 @code{scalbn} is identical to @code{scalb}, except that the exponent
1330 @var{n} is an @code{int} instead of a floating-point number.
1335 @deftypefun double scalbln (double @var{x}, long int @var{n})
1338 @deftypefunx float scalblnf (float @var{x}, long int @var{n})
1341 @deftypefunx {long double} scalblnl (long double @var{x}, long int @var{n})
1342 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1343 @code{scalbln} is identical to @code{scalb}, except that the exponent
1344 @var{n} is a @code{long int} instead of a floating-point number.
1349 @deftypefun double significand (double @var{x})
1352 @deftypefunx float significandf (float @var{x})
1355 @deftypefunx {long double} significandl (long double @var{x})
1356 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1357 @code{significand} returns the mantissa of @var{x} scaled to the range
1359 It is equivalent to @w{@code{scalb (@var{x}, (double) -ilogb (@var{x}))}}.
1361 This function exists mainly for use in certain standardized tests
1362 of @w{IEEE 754} conformance.
1365 @node Rounding Functions
1366 @subsection Rounding Functions
1367 @cindex converting floats to integers
1370 The functions listed here perform operations such as rounding and
1371 truncation of floating-point values. Some of these functions convert
1372 floating point numbers to integer values. They are all declared in
1375 You can also convert floating-point numbers to integers simply by
1376 casting them to @code{int}. This discards the fractional part,
1377 effectively rounding towards zero. However, this only works if the
1378 result can actually be represented as an @code{int}---for very large
1379 numbers, this is impossible. The functions listed here return the
1380 result as a @code{double} instead to get around this problem.
1384 @deftypefun double ceil (double @var{x})
1387 @deftypefunx float ceilf (float @var{x})
1390 @deftypefunx {long double} ceill (long double @var{x})
1391 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1392 These functions round @var{x} upwards to the nearest integer,
1393 returning that value as a @code{double}. Thus, @code{ceil (1.5)}
1399 @deftypefun double floor (double @var{x})
1402 @deftypefunx float floorf (float @var{x})
1405 @deftypefunx {long double} floorl (long double @var{x})
1406 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1407 These functions round @var{x} downwards to the nearest
1408 integer, returning that value as a @code{double}. Thus, @code{floor
1409 (1.5)} is @code{1.0} and @code{floor (-1.5)} is @code{-2.0}.
1414 @deftypefun double trunc (double @var{x})
1417 @deftypefunx float truncf (float @var{x})
1420 @deftypefunx {long double} truncl (long double @var{x})
1421 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1422 The @code{trunc} functions round @var{x} towards zero to the nearest
1423 integer (returned in floating-point format). Thus, @code{trunc (1.5)}
1424 is @code{1.0} and @code{trunc (-1.5)} is @code{-1.0}.
1429 @deftypefun double rint (double @var{x})
1432 @deftypefunx float rintf (float @var{x})
1435 @deftypefunx {long double} rintl (long double @var{x})
1436 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1437 These functions round @var{x} to an integer value according to the
1438 current rounding mode. @xref{Floating Point Parameters}, for
1439 information about the various rounding modes. The default
1440 rounding mode is to round to the nearest integer; some machines
1441 support other modes, but round-to-nearest is always used unless
1442 you explicitly select another.
1444 If @var{x} was not initially an integer, these functions raise the
1450 @deftypefun double nearbyint (double @var{x})
1453 @deftypefunx float nearbyintf (float @var{x})
1456 @deftypefunx {long double} nearbyintl (long double @var{x})
1457 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1458 These functions return the same value as the @code{rint} functions, but
1459 do not raise the inexact exception if @var{x} is not an integer.
1464 @deftypefun double round (double @var{x})
1467 @deftypefunx float roundf (float @var{x})
1470 @deftypefunx {long double} roundl (long double @var{x})
1471 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1472 These functions are similar to @code{rint}, but they round halfway
1473 cases away from zero instead of to the nearest integer (or other
1474 current rounding mode).
1479 @deftypefun {long int} lrint (double @var{x})
1482 @deftypefunx {long int} lrintf (float @var{x})
1485 @deftypefunx {long int} lrintl (long double @var{x})
1486 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1487 These functions are just like @code{rint}, but they return a
1488 @code{long int} instead of a floating-point number.
1493 @deftypefun {long long int} llrint (double @var{x})
1496 @deftypefunx {long long int} llrintf (float @var{x})
1499 @deftypefunx {long long int} llrintl (long double @var{x})
1500 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1501 These functions are just like @code{rint}, but they return a
1502 @code{long long int} instead of a floating-point number.
1507 @deftypefun {long int} lround (double @var{x})
1510 @deftypefunx {long int} lroundf (float @var{x})
1513 @deftypefunx {long int} lroundl (long double @var{x})
1514 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1515 These functions are just like @code{round}, but they return a
1516 @code{long int} instead of a floating-point number.
1521 @deftypefun {long long int} llround (double @var{x})
1524 @deftypefunx {long long int} llroundf (float @var{x})
1527 @deftypefunx {long long int} llroundl (long double @var{x})
1528 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1529 These functions are just like @code{round}, but they return a
1530 @code{long long int} instead of a floating-point number.
1536 @deftypefun double modf (double @var{value}, double *@var{integer-part})
1539 @deftypefunx float modff (float @var{value}, float *@var{integer-part})
1542 @deftypefunx {long double} modfl (long double @var{value}, long double *@var{integer-part})
1543 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1544 These functions break the argument @var{value} into an integer part and a
1545 fractional part (between @code{-1} and @code{1}, exclusive). Their sum
1546 equals @var{value}. Each of the parts has the same sign as @var{value},
1547 and the integer part is always rounded toward zero.
1549 @code{modf} stores the integer part in @code{*@var{integer-part}}, and
1550 returns the fractional part. For example, @code{modf (2.5, &intpart)}
1551 returns @code{0.5} and stores @code{2.0} into @code{intpart}.
1554 @node Remainder Functions
1555 @subsection Remainder Functions
1557 The functions in this section compute the remainder on division of two
1558 floating-point numbers. Each is a little different; pick the one that
1563 @deftypefun double fmod (double @var{numerator}, double @var{denominator})
1566 @deftypefunx float fmodf (float @var{numerator}, float @var{denominator})
1569 @deftypefunx {long double} fmodl (long double @var{numerator}, long double @var{denominator})
1570 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1571 These functions compute the remainder from the division of
1572 @var{numerator} by @var{denominator}. Specifically, the return value is
1573 @code{@var{numerator} - @w{@var{n} * @var{denominator}}}, where @var{n}
1574 is the quotient of @var{numerator} divided by @var{denominator}, rounded
1575 towards zero to an integer. Thus, @w{@code{fmod (6.5, 2.3)}} returns
1576 @code{1.9}, which is @code{6.5} minus @code{4.6}.
1578 The result has the same sign as the @var{numerator} and has magnitude
1579 less than the magnitude of the @var{denominator}.
1581 If @var{denominator} is zero, @code{fmod} signals a domain error.
1586 @deftypefun double drem (double @var{numerator}, double @var{denominator})
1589 @deftypefunx float dremf (float @var{numerator}, float @var{denominator})
1592 @deftypefunx {long double} dreml (long double @var{numerator}, long double @var{denominator})
1593 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1594 These functions are like @code{fmod} except that they round the
1595 internal quotient @var{n} to the nearest integer instead of towards zero
1596 to an integer. For example, @code{drem (6.5, 2.3)} returns @code{-0.4},
1597 which is @code{6.5} minus @code{6.9}.
1599 The absolute value of the result is less than or equal to half the
1600 absolute value of the @var{denominator}. The difference between
1601 @code{fmod (@var{numerator}, @var{denominator})} and @code{drem
1602 (@var{numerator}, @var{denominator})} is always either
1603 @var{denominator}, minus @var{denominator}, or zero.
1605 If @var{denominator} is zero, @code{drem} signals a domain error.
1610 @deftypefun double remainder (double @var{numerator}, double @var{denominator})
1613 @deftypefunx float remainderf (float @var{numerator}, float @var{denominator})
1616 @deftypefunx {long double} remainderl (long double @var{numerator}, long double @var{denominator})
1617 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1618 This function is another name for @code{drem}.
1621 @node FP Bit Twiddling
1622 @subsection Setting and modifying single bits of FP values
1623 @cindex FP arithmetic
1625 There are some operations that are too complicated or expensive to
1626 perform by hand on floating-point numbers. @w{ISO C99} defines
1627 functions to do these operations, which mostly involve changing single
1632 @deftypefun double copysign (double @var{x}, double @var{y})
1635 @deftypefunx float copysignf (float @var{x}, float @var{y})
1638 @deftypefunx {long double} copysignl (long double @var{x}, long double @var{y})
1639 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1640 These functions return @var{x} but with the sign of @var{y}. They work
1641 even if @var{x} or @var{y} are NaN or zero. Both of these can carry a
1642 sign (although not all implementations support it) and this is one of
1643 the few operations that can tell the difference.
1645 @code{copysign} never raises an exception.
1646 @c except signalling NaNs
1648 This function is defined in @w{IEC 559} (and the appendix with
1649 recommended functions in @w{IEEE 754}/@w{IEEE 854}).
1654 @deftypefun int signbit (@emph{float-type} @var{x})
1655 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1656 @code{signbit} is a generic macro which can work on all floating-point
1657 types. It returns a nonzero value if the value of @var{x} has its sign
1660 This is not the same as @code{x < 0.0}, because @w{IEEE 754} floating
1661 point allows zero to be signed. The comparison @code{-0.0 < 0.0} is
1662 false, but @code{signbit (-0.0)} will return a nonzero value.
1667 @deftypefun double nextafter (double @var{x}, double @var{y})
1670 @deftypefunx float nextafterf (float @var{x}, float @var{y})
1673 @deftypefunx {long double} nextafterl (long double @var{x}, long double @var{y})
1674 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1675 The @code{nextafter} function returns the next representable neighbor of
1676 @var{x} in the direction towards @var{y}. The size of the step between
1677 @var{x} and the result depends on the type of the result. If
1678 @math{@var{x} = @var{y}} the function simply returns @var{y}. If either
1679 value is @code{NaN}, @code{NaN} is returned. Otherwise
1680 a value corresponding to the value of the least significant bit in the
1681 mantissa is added or subtracted, depending on the direction.
1682 @code{nextafter} will signal overflow or underflow if the result goes
1683 outside of the range of normalized numbers.
1685 This function is defined in @w{IEC 559} (and the appendix with
1686 recommended functions in @w{IEEE 754}/@w{IEEE 854}).
1691 @deftypefun double nexttoward (double @var{x}, long double @var{y})
1694 @deftypefunx float nexttowardf (float @var{x}, long double @var{y})
1697 @deftypefunx {long double} nexttowardl (long double @var{x}, long double @var{y})
1698 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1699 These functions are identical to the corresponding versions of
1700 @code{nextafter} except that their second argument is a @code{long
1706 @deftypefun double nextup (double @var{x})
1709 @deftypefunx float nextupf (float @var{x})
1712 @deftypefunx {long double} nextupl (long double @var{x})
1713 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1714 The @code{nextup} function returns the next representable neighbor of @var{x}
1715 in the direction of positive infinity. If @var{x} is the smallest negative
1716 subnormal number in the type of @var{x} the function returns @code{-0}. If
1717 @math{@var{x} = @code{0}} the function returns the smallest positive subnormal
1718 number in the type of @var{x}. If @var{x} is NaN, NaN is returned.
1719 If @var{x} is @math{+@infinity{}}, @math{+@infinity{}} is returned.
1720 @code{nextup} is from TS 18661-1:2014.
1721 @code{nextup} never raises an exception except for signaling NaNs.
1726 @deftypefun double nextdown (double @var{x})
1729 @deftypefunx float nextdownf (float @var{x})
1732 @deftypefunx {long double} nextdownl (long double @var{x})
1733 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1734 The @code{nextdown} function returns the next representable neighbor of @var{x}
1735 in the direction of negative infinity. If @var{x} is the smallest positive
1736 subnormal number in the type of @var{x} the function returns @code{+0}. If
1737 @math{@var{x} = @code{0}} the function returns the smallest negative subnormal
1738 number in the type of @var{x}. If @var{x} is NaN, NaN is returned.
1739 If @var{x} is @math{-@infinity{}}, @math{-@infinity{}} is returned.
1740 @code{nextdown} is from TS 18661-1:2014.
1741 @code{nextdown} never raises an exception except for signaling NaNs.
1747 @deftypefun double nan (const char *@var{tagp})
1750 @deftypefunx float nanf (const char *@var{tagp})
1753 @deftypefunx {long double} nanl (const char *@var{tagp})
1754 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
1755 @c The unsafe-but-ruled-safe locale use comes from strtod.
1756 The @code{nan} function returns a representation of NaN, provided that
1757 NaN is supported by the target platform.
1758 @code{nan ("@var{n-char-sequence}")} is equivalent to
1759 @code{strtod ("NAN(@var{n-char-sequence})")}.
1761 The argument @var{tagp} is used in an unspecified manner. On @w{IEEE
1762 754} systems, there are many representations of NaN, and @var{tagp}
1763 selects one. On other systems it may do nothing.
1766 @node FP Comparison Functions
1767 @subsection Floating-Point Comparison Functions
1768 @cindex unordered comparison
1770 The standard C comparison operators provoke exceptions when one or other
1771 of the operands is NaN. For example,
1778 will raise an exception if @var{a} is NaN. (This does @emph{not}
1779 happen with @code{==} and @code{!=}; those merely return false and true,
1780 respectively, when NaN is examined.) Frequently this exception is
1781 undesirable. @w{ISO C99} therefore defines comparison functions that
1782 do not raise exceptions when NaN is examined. All of the functions are
1783 implemented as macros which allow their arguments to be of any
1784 floating-point type. The macros are guaranteed to evaluate their
1785 arguments only once.
1789 @deftypefn Macro int isgreater (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
1790 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1791 This macro determines whether the argument @var{x} is greater than
1792 @var{y}. It is equivalent to @code{(@var{x}) > (@var{y})}, but no
1793 exception is raised if @var{x} or @var{y} are NaN.
1798 @deftypefn Macro int isgreaterequal (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
1799 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1800 This macro determines whether the argument @var{x} is greater than or
1801 equal to @var{y}. It is equivalent to @code{(@var{x}) >= (@var{y})}, but no
1802 exception is raised if @var{x} or @var{y} are NaN.
1807 @deftypefn Macro int isless (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
1808 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1809 This macro determines whether the argument @var{x} is less than @var{y}.
1810 It is equivalent to @code{(@var{x}) < (@var{y})}, but no exception is
1811 raised if @var{x} or @var{y} are NaN.
1816 @deftypefn Macro int islessequal (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
1817 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1818 This macro determines whether the argument @var{x} is less than or equal
1819 to @var{y}. It is equivalent to @code{(@var{x}) <= (@var{y})}, but no
1820 exception is raised if @var{x} or @var{y} are NaN.
1825 @deftypefn Macro int islessgreater (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
1826 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1827 This macro determines whether the argument @var{x} is less or greater
1828 than @var{y}. It is equivalent to @code{(@var{x}) < (@var{y}) ||
1829 (@var{x}) > (@var{y})} (although it only evaluates @var{x} and @var{y}
1830 once), but no exception is raised if @var{x} or @var{y} are NaN.
1832 This macro is not equivalent to @code{@var{x} != @var{y}}, because that
1833 expression is true if @var{x} or @var{y} are NaN.
1838 @deftypefn Macro int isunordered (@emph{real-floating} @var{x}, @emph{real-floating} @var{y})
1839 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1840 This macro determines whether its arguments are unordered. In other
1841 words, it is true if @var{x} or @var{y} are NaN, and false otherwise.
1844 Not all machines provide hardware support for these operations. On
1845 machines that don't, the macros can be very slow. Therefore, you should
1846 not use these functions when NaN is not a concern.
1848 @strong{NB:} There are no macros @code{isequal} or @code{isunequal}.
1849 They are unnecessary, because the @code{==} and @code{!=} operators do
1850 @emph{not} throw an exception if one or both of the operands are NaN.
1852 @node Misc FP Arithmetic
1853 @subsection Miscellaneous FP arithmetic functions
1856 @cindex positive difference
1857 @cindex multiply-add
1859 The functions in this section perform miscellaneous but common
1860 operations that are awkward to express with C operators. On some
1861 processors these functions can use special machine instructions to
1862 perform these operations faster than the equivalent C code.
1866 @deftypefun double fmin (double @var{x}, double @var{y})
1869 @deftypefunx float fminf (float @var{x}, float @var{y})
1872 @deftypefunx {long double} fminl (long double @var{x}, long double @var{y})
1873 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1874 The @code{fmin} function returns the lesser of the two values @var{x}
1875 and @var{y}. It is similar to the expression
1877 ((x) < (y) ? (x) : (y))
1879 except that @var{x} and @var{y} are only evaluated once.
1881 If an argument is NaN, the other argument is returned. If both arguments
1882 are NaN, NaN is returned.
1887 @deftypefun double fmax (double @var{x}, double @var{y})
1890 @deftypefunx float fmaxf (float @var{x}, float @var{y})
1893 @deftypefunx {long double} fmaxl (long double @var{x}, long double @var{y})
1894 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1895 The @code{fmax} function returns the greater of the two values @var{x}
1898 If an argument is NaN, the other argument is returned. If both arguments
1899 are NaN, NaN is returned.
1904 @deftypefun double fdim (double @var{x}, double @var{y})
1907 @deftypefunx float fdimf (float @var{x}, float @var{y})
1910 @deftypefunx {long double} fdiml (long double @var{x}, long double @var{y})
1911 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1912 The @code{fdim} function returns the positive difference between
1913 @var{x} and @var{y}. The positive difference is @math{@var{x} -
1914 @var{y}} if @var{x} is greater than @var{y}, and @math{0} otherwise.
1916 If @var{x}, @var{y}, or both are NaN, NaN is returned.
1921 @deftypefun double fma (double @var{x}, double @var{y}, double @var{z})
1924 @deftypefunx float fmaf (float @var{x}, float @var{y}, float @var{z})
1927 @deftypefunx {long double} fmal (long double @var{x}, long double @var{y}, long double @var{z})
1929 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
1930 The @code{fma} function performs floating-point multiply-add. This is
1931 the operation @math{(@var{x} @mul{} @var{y}) + @var{z}}, but the
1932 intermediate result is not rounded to the destination type. This can
1933 sometimes improve the precision of a calculation.
1935 This function was introduced because some processors have a special
1936 instruction to perform multiply-add. The C compiler cannot use it
1937 directly, because the expression @samp{x*y + z} is defined to round the
1938 intermediate result. @code{fma} lets you choose when you want to round
1942 On processors which do not implement multiply-add in hardware,
1943 @code{fma} can be very slow since it must avoid intermediate rounding.
1944 @file{math.h} defines the symbols @code{FP_FAST_FMA},
1945 @code{FP_FAST_FMAF}, and @code{FP_FAST_FMAL} when the corresponding
1946 version of @code{fma} is no slower than the expression @samp{x*y + z}.
1947 In @theglibc{}, this always means the operation is implemented in
1951 @node Complex Numbers
1952 @section Complex Numbers
1954 @cindex complex numbers
1956 @w{ISO C99} introduces support for complex numbers in C. This is done
1957 with a new type qualifier, @code{complex}. It is a keyword if and only
1958 if @file{complex.h} has been included. There are three complex types,
1959 corresponding to the three real types: @code{float complex},
1960 @code{double complex}, and @code{long double complex}.
1962 To construct complex numbers you need a way to indicate the imaginary
1963 part of a number. There is no standard notation for an imaginary
1964 floating point constant. Instead, @file{complex.h} defines two macros
1965 that can be used to create complex numbers.
1967 @deftypevr Macro {const float complex} _Complex_I
1968 This macro is a representation of the complex number ``@math{0+1i}''.
1969 Multiplying a real floating-point value by @code{_Complex_I} gives a
1970 complex number whose value is purely imaginary. You can use this to
1971 construct complex constants:
1974 @math{3.0 + 4.0i} = @code{3.0 + 4.0 * _Complex_I}
1977 Note that @code{_Complex_I * _Complex_I} has the value @code{-1}, but
1978 the type of that value is @code{complex}.
1981 @c Put this back in when gcc supports _Imaginary_I. It's too confusing.
1984 Without an optimizing compiler this is more expensive than the use of
1985 @code{_Imaginary_I} but with is better than nothing. You can avoid all
1986 the hassles if you use the @code{I} macro below if the name is not
1989 @deftypevr Macro {const float imaginary} _Imaginary_I
1990 This macro is a representation of the value ``@math{1i}''. I.e., it is
1994 _Imaginary_I * _Imaginary_I = -1
1998 The result is not of type @code{float imaginary} but instead @code{float}.
1999 One can use it to easily construct complex number like in
2002 3.0 - _Imaginary_I * 4.0
2006 which results in the complex number with a real part of 3.0 and a
2007 imaginary part -4.0.
2012 @code{_Complex_I} is a bit of a mouthful. @file{complex.h} also defines
2013 a shorter name for the same constant.
2015 @deftypevr Macro {const float complex} I
2016 This macro has exactly the same value as @code{_Complex_I}. Most of the
2017 time it is preferable. However, it causes problems if you want to use
2018 the identifier @code{I} for something else. You can safely write
2021 #include <complex.h>
2026 if you need @code{I} for your own purposes. (In that case we recommend
2027 you also define some other short name for @code{_Complex_I}, such as
2031 If the implementation does not support the @code{imaginary} types
2032 @code{I} is defined as @code{_Complex_I} which is the second best
2033 solution. It still can be used in the same way but requires a most
2034 clever compiler to get the same results.
2038 @node Operations on Complex
2039 @section Projections, Conjugates, and Decomposing of Complex Numbers
2040 @cindex project complex numbers
2041 @cindex conjugate complex numbers
2042 @cindex decompose complex numbers
2045 @w{ISO C99} also defines functions that perform basic operations on
2046 complex numbers, such as decomposition and conjugation. The prototypes
2047 for all these functions are in @file{complex.h}. All functions are
2048 available in three variants, one for each of the three complex types.
2052 @deftypefun double creal (complex double @var{z})
2055 @deftypefunx float crealf (complex float @var{z})
2058 @deftypefunx {long double} creall (complex long double @var{z})
2059 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2060 These functions return the real part of the complex number @var{z}.
2065 @deftypefun double cimag (complex double @var{z})
2068 @deftypefunx float cimagf (complex float @var{z})
2071 @deftypefunx {long double} cimagl (complex long double @var{z})
2072 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2073 These functions return the imaginary part of the complex number @var{z}.
2078 @deftypefun {complex double} conj (complex double @var{z})
2081 @deftypefunx {complex float} conjf (complex float @var{z})
2084 @deftypefunx {complex long double} conjl (complex long double @var{z})
2085 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2086 These functions return the conjugate value of the complex number
2087 @var{z}. The conjugate of a complex number has the same real part and a
2088 negated imaginary part. In other words, @samp{conj(a + bi) = a + -bi}.
2093 @deftypefun double carg (complex double @var{z})
2096 @deftypefunx float cargf (complex float @var{z})
2099 @deftypefunx {long double} cargl (complex long double @var{z})
2100 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2101 These functions return the argument of the complex number @var{z}.
2102 The argument of a complex number is the angle in the complex plane
2103 between the positive real axis and a line passing through zero and the
2104 number. This angle is measured in the usual fashion and ranges from
2105 @math{-@pi{}} to @math{@pi{}}.
2107 @code{carg} has a branch cut along the negative real axis.
2112 @deftypefun {complex double} cproj (complex double @var{z})
2115 @deftypefunx {complex float} cprojf (complex float @var{z})
2118 @deftypefunx {complex long double} cprojl (complex long double @var{z})
2119 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2120 These functions return the projection of the complex value @var{z} onto
2121 the Riemann sphere. Values with an infinite imaginary part are projected
2122 to positive infinity on the real axis, even if the real part is NaN. If
2123 the real part is infinite, the result is equivalent to
2126 INFINITY + I * copysign (0.0, cimag (z))
2130 @node Parsing of Numbers
2131 @section Parsing of Numbers
2132 @cindex parsing numbers (in formatted input)
2133 @cindex converting strings to numbers
2134 @cindex number syntax, parsing
2135 @cindex syntax, for reading numbers
2137 This section describes functions for ``reading'' integer and
2138 floating-point numbers from a string. It may be more convenient in some
2139 cases to use @code{sscanf} or one of the related functions; see
2140 @ref{Formatted Input}. But often you can make a program more robust by
2141 finding the tokens in the string by hand, then converting the numbers
2145 * Parsing of Integers:: Functions for conversion of integer values.
2146 * Parsing of Floats:: Functions for conversion of floating-point
2150 @node Parsing of Integers
2151 @subsection Parsing of Integers
2155 The @samp{str} functions are declared in @file{stdlib.h} and those
2156 beginning with @samp{wcs} are declared in @file{wchar.h}. One might
2157 wonder about the use of @code{restrict} in the prototypes of the
2158 functions in this section. It is seemingly useless but the @w{ISO C}
2159 standard uses it (for the functions defined there) so we have to do it
2164 @deftypefun {long int} strtol (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
2165 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2166 @c strtol uses the thread-local pointer to the locale in effect, and
2167 @c strtol_l loads the LC_NUMERIC locale data from it early on and once,
2168 @c but if the locale is the global locale, and another thread calls
2169 @c setlocale in a way that modifies the pointer to the LC_CTYPE locale
2170 @c category, the behavior of e.g. IS*, TOUPPER will vary throughout the
2171 @c execution of the function, because they re-read the locale data from
2172 @c the given locale pointer. We solved this by documenting setlocale as
2174 The @code{strtol} (``string-to-long'') function converts the initial
2175 part of @var{string} to a signed integer, which is returned as a value
2176 of type @code{long int}.
2178 This function attempts to decompose @var{string} as follows:
2182 A (possibly empty) sequence of whitespace characters. Which characters
2183 are whitespace is determined by the @code{isspace} function
2184 (@pxref{Classification of Characters}). These are discarded.
2187 An optional plus or minus sign (@samp{+} or @samp{-}).
2190 A nonempty sequence of digits in the radix specified by @var{base}.
2192 If @var{base} is zero, decimal radix is assumed unless the series of
2193 digits begins with @samp{0} (specifying octal radix), or @samp{0x} or
2194 @samp{0X} (specifying hexadecimal radix); in other words, the same
2195 syntax used for integer constants in C.
2197 Otherwise @var{base} must have a value between @code{2} and @code{36}.
2198 If @var{base} is @code{16}, the digits may optionally be preceded by
2199 @samp{0x} or @samp{0X}. If base has no legal value the value returned
2200 is @code{0l} and the global variable @code{errno} is set to @code{EINVAL}.
2203 Any remaining characters in the string. If @var{tailptr} is not a null
2204 pointer, @code{strtol} stores a pointer to this tail in
2205 @code{*@var{tailptr}}.
2208 If the string is empty, contains only whitespace, or does not contain an
2209 initial substring that has the expected syntax for an integer in the
2210 specified @var{base}, no conversion is performed. In this case,
2211 @code{strtol} returns a value of zero and the value stored in
2212 @code{*@var{tailptr}} is the value of @var{string}.
2214 In a locale other than the standard @code{"C"} locale, this function
2215 may recognize additional implementation-dependent syntax.
2217 If the string has valid syntax for an integer but the value is not
2218 representable because of overflow, @code{strtol} returns either
2219 @code{LONG_MAX} or @code{LONG_MIN} (@pxref{Range of Type}), as
2220 appropriate for the sign of the value. It also sets @code{errno}
2221 to @code{ERANGE} to indicate there was overflow.
2223 You should not check for errors by examining the return value of
2224 @code{strtol}, because the string might be a valid representation of
2225 @code{0l}, @code{LONG_MAX}, or @code{LONG_MIN}. Instead, check whether
2226 @var{tailptr} points to what you expect after the number
2227 (e.g. @code{'\0'} if the string should end after the number). You also
2228 need to clear @var{errno} before the call and check it afterward, in
2229 case there was overflow.
2231 There is an example at the end of this section.
2236 @deftypefun {long int} wcstol (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
2237 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2238 The @code{wcstol} function is equivalent to the @code{strtol} function
2239 in nearly all aspects but handles wide character strings.
2241 The @code{wcstol} function was introduced in @w{Amendment 1} of @w{ISO C90}.
2246 @deftypefun {unsigned long int} strtoul (const char *retrict @var{string}, char **restrict @var{tailptr}, int @var{base})
2247 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2248 The @code{strtoul} (``string-to-unsigned-long'') function is like
2249 @code{strtol} except it converts to an @code{unsigned long int} value.
2250 The syntax is the same as described above for @code{strtol}. The value
2251 returned on overflow is @code{ULONG_MAX} (@pxref{Range of Type}).
2253 If @var{string} depicts a negative number, @code{strtoul} acts the same
2254 as @var{strtol} but casts the result to an unsigned integer. That means
2255 for example that @code{strtoul} on @code{"-1"} returns @code{ULONG_MAX}
2256 and an input more negative than @code{LONG_MIN} returns
2257 (@code{ULONG_MAX} + 1) / 2.
2259 @code{strtoul} sets @var{errno} to @code{EINVAL} if @var{base} is out of
2260 range, or @code{ERANGE} on overflow.
2265 @deftypefun {unsigned long int} wcstoul (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
2266 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2267 The @code{wcstoul} function is equivalent to the @code{strtoul} function
2268 in nearly all aspects but handles wide character strings.
2270 The @code{wcstoul} function was introduced in @w{Amendment 1} of @w{ISO C90}.
2275 @deftypefun {long long int} strtoll (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
2276 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2277 The @code{strtoll} function is like @code{strtol} except that it returns
2278 a @code{long long int} value, and accepts numbers with a correspondingly
2281 If the string has valid syntax for an integer but the value is not
2282 representable because of overflow, @code{strtoll} returns either
2283 @code{LLONG_MAX} or @code{LLONG_MIN} (@pxref{Range of Type}), as
2284 appropriate for the sign of the value. It also sets @code{errno} to
2285 @code{ERANGE} to indicate there was overflow.
2287 The @code{strtoll} function was introduced in @w{ISO C99}.
2292 @deftypefun {long long int} wcstoll (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
2293 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2294 The @code{wcstoll} function is equivalent to the @code{strtoll} function
2295 in nearly all aspects but handles wide character strings.
2297 The @code{wcstoll} function was introduced in @w{Amendment 1} of @w{ISO C90}.
2302 @deftypefun {long long int} strtoq (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
2303 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2304 @code{strtoq} (``string-to-quad-word'') is the BSD name for @code{strtoll}.
2309 @deftypefun {long long int} wcstoq (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
2310 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2311 The @code{wcstoq} function is equivalent to the @code{strtoq} function
2312 in nearly all aspects but handles wide character strings.
2314 The @code{wcstoq} function is a GNU extension.
2319 @deftypefun {unsigned long long int} strtoull (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
2320 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2321 The @code{strtoull} function is related to @code{strtoll} the same way
2322 @code{strtoul} is related to @code{strtol}.
2324 The @code{strtoull} function was introduced in @w{ISO C99}.
2329 @deftypefun {unsigned long long int} wcstoull (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
2330 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2331 The @code{wcstoull} function is equivalent to the @code{strtoull} function
2332 in nearly all aspects but handles wide character strings.
2334 The @code{wcstoull} function was introduced in @w{Amendment 1} of @w{ISO C90}.
2339 @deftypefun {unsigned long long int} strtouq (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
2340 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2341 @code{strtouq} is the BSD name for @code{strtoull}.
2346 @deftypefun {unsigned long long int} wcstouq (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
2347 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2348 The @code{wcstouq} function is equivalent to the @code{strtouq} function
2349 in nearly all aspects but handles wide character strings.
2351 The @code{wcstouq} function is a GNU extension.
2356 @deftypefun intmax_t strtoimax (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
2357 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2358 The @code{strtoimax} function is like @code{strtol} except that it returns
2359 a @code{intmax_t} value, and accepts numbers of a corresponding range.
2361 If the string has valid syntax for an integer but the value is not
2362 representable because of overflow, @code{strtoimax} returns either
2363 @code{INTMAX_MAX} or @code{INTMAX_MIN} (@pxref{Integers}), as
2364 appropriate for the sign of the value. It also sets @code{errno} to
2365 @code{ERANGE} to indicate there was overflow.
2367 See @ref{Integers} for a description of the @code{intmax_t} type. The
2368 @code{strtoimax} function was introduced in @w{ISO C99}.
2373 @deftypefun intmax_t wcstoimax (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
2374 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2375 The @code{wcstoimax} function is equivalent to the @code{strtoimax} function
2376 in nearly all aspects but handles wide character strings.
2378 The @code{wcstoimax} function was introduced in @w{ISO C99}.
2383 @deftypefun uintmax_t strtoumax (const char *restrict @var{string}, char **restrict @var{tailptr}, int @var{base})
2384 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2385 The @code{strtoumax} function is related to @code{strtoimax}
2386 the same way that @code{strtoul} is related to @code{strtol}.
2388 See @ref{Integers} for a description of the @code{intmax_t} type. The
2389 @code{strtoumax} function was introduced in @w{ISO C99}.
2394 @deftypefun uintmax_t wcstoumax (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr}, int @var{base})
2395 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2396 The @code{wcstoumax} function is equivalent to the @code{strtoumax} function
2397 in nearly all aspects but handles wide character strings.
2399 The @code{wcstoumax} function was introduced in @w{ISO C99}.
2404 @deftypefun {long int} atol (const char *@var{string})
2405 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2406 This function is similar to the @code{strtol} function with a @var{base}
2407 argument of @code{10}, except that it need not detect overflow errors.
2408 The @code{atol} function is provided mostly for compatibility with
2409 existing code; using @code{strtol} is more robust.
2414 @deftypefun int atoi (const char *@var{string})
2415 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2416 This function is like @code{atol}, except that it returns an @code{int}.
2417 The @code{atoi} function is also considered obsolete; use @code{strtol}
2423 @deftypefun {long long int} atoll (const char *@var{string})
2424 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2425 This function is similar to @code{atol}, except it returns a @code{long
2428 The @code{atoll} function was introduced in @w{ISO C99}. It too is
2429 obsolete (despite having just been added); use @code{strtoll} instead.
2432 All the functions mentioned in this section so far do not handle
2433 alternative representations of characters as described in the locale
2434 data. Some locales specify thousands separator and the way they have to
2435 be used which can help to make large numbers more readable. To read
2436 such numbers one has to use the @code{scanf} functions with the @samp{'}
2439 Here is a function which parses a string as a sequence of integers and
2440 returns the sum of them:
2444 sum_ints_from_string (char *string)
2452 /* @r{Skip whitespace by hand, to detect the end.} */
2453 while (isspace (*string)) string++;
2457 /* @r{There is more nonwhitespace,} */
2458 /* @r{so it ought to be another number.} */
2461 next = strtol (string, &tail, 0);
2462 /* @r{Add it in, if not overflow.} */
2464 printf ("Overflow\n");
2467 /* @r{Advance past it.} */
2475 @node Parsing of Floats
2476 @subsection Parsing of Floats
2479 The @samp{str} functions are declared in @file{stdlib.h} and those
2480 beginning with @samp{wcs} are declared in @file{wchar.h}. One might
2481 wonder about the use of @code{restrict} in the prototypes of the
2482 functions in this section. It is seemingly useless but the @w{ISO C}
2483 standard uses it (for the functions defined there) so we have to do it
2488 @deftypefun double strtod (const char *restrict @var{string}, char **restrict @var{tailptr})
2489 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2490 @c Besides the unsafe-but-ruled-safe locale uses, this uses a lot of
2491 @c mpn, but it's all safe.
2494 @c get_rounding_mode ok
2498 @c MPN2FLOAT -> mpn_construct_(float|double|long_double) ok
2500 @c mpn_mul_1 -> umul_ppmm ok
2502 @c mpn_lshift_1 -> mpn_lshift ok
2506 @c STRNCASECMP ok, wide and narrow
2507 @c round_and_return ok
2513 @c count_leading_zeros ok
2518 The @code{strtod} (``string-to-double'') function converts the initial
2519 part of @var{string} to a floating-point number, which is returned as a
2520 value of type @code{double}.
2522 This function attempts to decompose @var{string} as follows:
2526 A (possibly empty) sequence of whitespace characters. Which characters
2527 are whitespace is determined by the @code{isspace} function
2528 (@pxref{Classification of Characters}). These are discarded.
2531 An optional plus or minus sign (@samp{+} or @samp{-}).
2533 @item A floating point number in decimal or hexadecimal format. The
2538 A nonempty sequence of digits optionally containing a decimal-point
2539 character---normally @samp{.}, but it depends on the locale
2540 (@pxref{General Numeric}).
2543 An optional exponent part, consisting of a character @samp{e} or
2544 @samp{E}, an optional sign, and a sequence of digits.
2548 The hexadecimal format is as follows:
2552 A 0x or 0X followed by a nonempty sequence of hexadecimal digits
2553 optionally containing a decimal-point character---normally @samp{.}, but
2554 it depends on the locale (@pxref{General Numeric}).
2557 An optional binary-exponent part, consisting of a character @samp{p} or
2558 @samp{P}, an optional sign, and a sequence of digits.
2563 Any remaining characters in the string. If @var{tailptr} is not a null
2564 pointer, a pointer to this tail of the string is stored in
2565 @code{*@var{tailptr}}.
2568 If the string is empty, contains only whitespace, or does not contain an
2569 initial substring that has the expected syntax for a floating-point
2570 number, no conversion is performed. In this case, @code{strtod} returns
2571 a value of zero and the value returned in @code{*@var{tailptr}} is the
2572 value of @var{string}.
2574 In a locale other than the standard @code{"C"} or @code{"POSIX"} locales,
2575 this function may recognize additional locale-dependent syntax.
2577 If the string has valid syntax for a floating-point number but the value
2578 is outside the range of a @code{double}, @code{strtod} will signal
2579 overflow or underflow as described in @ref{Math Error Reporting}.
2581 @code{strtod} recognizes four special input strings. The strings
2582 @code{"inf"} and @code{"infinity"} are converted to @math{@infinity{}},
2583 or to the largest representable value if the floating-point format
2584 doesn't support infinities. You can prepend a @code{"+"} or @code{"-"}
2585 to specify the sign. Case is ignored when scanning these strings.
2587 The strings @code{"nan"} and @code{"nan(@var{chars@dots{}})"} are converted
2588 to NaN. Again, case is ignored. If @var{chars@dots{}} are provided, they
2589 are used in some unspecified fashion to select a particular
2590 representation of NaN (there can be several).
2592 Since zero is a valid result as well as the value returned on error, you
2593 should check for errors in the same way as for @code{strtol}, by
2594 examining @var{errno} and @var{tailptr}.
2599 @deftypefun float strtof (const char *@var{string}, char **@var{tailptr})
2602 @deftypefunx {long double} strtold (const char *@var{string}, char **@var{tailptr})
2603 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2604 These functions are analogous to @code{strtod}, but return @code{float}
2605 and @code{long double} values respectively. They report errors in the
2606 same way as @code{strtod}. @code{strtof} can be substantially faster
2607 than @code{strtod}, but has less precision; conversely, @code{strtold}
2608 can be much slower but has more precision (on systems where @code{long
2609 double} is a separate type).
2611 These functions have been GNU extensions and are new to @w{ISO C99}.
2616 @deftypefun double wcstod (const wchar_t *restrict @var{string}, wchar_t **restrict @var{tailptr})
2619 @deftypefunx float wcstof (const wchar_t *@var{string}, wchar_t **@var{tailptr})
2622 @deftypefunx {long double} wcstold (const wchar_t *@var{string}, wchar_t **@var{tailptr})
2623 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2624 The @code{wcstod}, @code{wcstof}, and @code{wcstol} functions are
2625 equivalent in nearly all aspect to the @code{strtod}, @code{strtof}, and
2626 @code{strtold} functions but it handles wide character string.
2628 The @code{wcstod} function was introduced in @w{Amendment 1} of @w{ISO
2629 C90}. The @code{wcstof} and @code{wcstold} functions were introduced in
2635 @deftypefun double atof (const char *@var{string})
2636 @safety{@prelim{}@mtsafe{@mtslocale{}}@assafe{}@acsafe{}}
2637 This function is similar to the @code{strtod} function, except that it
2638 need not detect overflow and underflow errors. The @code{atof} function
2639 is provided mostly for compatibility with existing code; using
2640 @code{strtod} is more robust.
2643 @Theglibc{} also provides @samp{_l} versions of these functions,
2644 which take an additional argument, the locale to use in conversion.
2646 See also @ref{Parsing of Integers}.
2648 @node System V Number Conversion
2649 @section Old-fashioned System V number-to-string functions
2651 The old @w{System V} C library provided three functions to convert
2652 numbers to strings, with unusual and hard-to-use semantics. @Theglibc{}
2653 also provides these functions and some natural extensions.
2655 These functions are only available in @theglibc{} and on systems descended
2656 from AT&T Unix. Therefore, unless these functions do precisely what you
2657 need, it is better to use @code{sprintf}, which is standard.
2659 All these functions are defined in @file{stdlib.h}.
2662 @comment SVID, Unix98
2663 @deftypefun {char *} ecvt (double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg})
2664 @safety{@prelim{}@mtunsafe{@mtasurace{:ecvt}}@asunsafe{}@acsafe{}}
2665 The function @code{ecvt} converts the floating-point number @var{value}
2666 to a string with at most @var{ndigit} decimal digits. The
2667 returned string contains no decimal point or sign. The first digit of
2668 the string is non-zero (unless @var{value} is actually zero) and the
2669 last digit is rounded to nearest. @code{*@var{decpt}} is set to the
2670 index in the string of the first digit after the decimal point.
2671 @code{*@var{neg}} is set to a nonzero value if @var{value} is negative,
2674 If @var{ndigit} decimal digits would exceed the precision of a
2675 @code{double} it is reduced to a system-specific value.
2677 The returned string is statically allocated and overwritten by each call
2680 If @var{value} is zero, it is implementation defined whether
2681 @code{*@var{decpt}} is @code{0} or @code{1}.
2683 For example: @code{ecvt (12.3, 5, &d, &n)} returns @code{"12300"}
2684 and sets @var{d} to @code{2} and @var{n} to @code{0}.
2688 @comment SVID, Unix98
2689 @deftypefun {char *} fcvt (double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg})
2690 @safety{@prelim{}@mtunsafe{@mtasurace{:fcvt}}@asunsafe{@ascuheap{}}@acunsafe{@acsmem{}}}
2691 The function @code{fcvt} is like @code{ecvt}, but @var{ndigit} specifies
2692 the number of digits after the decimal point. If @var{ndigit} is less
2693 than zero, @var{value} is rounded to the @math{@var{ndigit}+1}'th place to the
2694 left of the decimal point. For example, if @var{ndigit} is @code{-1},
2695 @var{value} will be rounded to the nearest 10. If @var{ndigit} is
2696 negative and larger than the number of digits to the left of the decimal
2697 point in @var{value}, @var{value} will be rounded to one significant digit.
2699 If @var{ndigit} decimal digits would exceed the precision of a
2700 @code{double} it is reduced to a system-specific value.
2702 The returned string is statically allocated and overwritten by each call
2707 @comment SVID, Unix98
2708 @deftypefun {char *} gcvt (double @var{value}, int @var{ndigit}, char *@var{buf})
2709 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2710 @c gcvt calls sprintf, that ultimately calls vfprintf, which malloc()s
2711 @c args_value if it's too large, but gcvt never exercises this path.
2712 @code{gcvt} is functionally equivalent to @samp{sprintf(buf, "%*g",
2713 ndigit, value}. It is provided only for compatibility's sake. It
2716 If @var{ndigit} decimal digits would exceed the precision of a
2717 @code{double} it is reduced to a system-specific value.
2720 As extensions, @theglibc{} provides versions of these three
2721 functions that take @code{long double} arguments.
2725 @deftypefun {char *} qecvt (long double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg})
2726 @safety{@prelim{}@mtunsafe{@mtasurace{:qecvt}}@asunsafe{}@acsafe{}}
2727 This function is equivalent to @code{ecvt} except that it takes a
2728 @code{long double} for the first parameter and that @var{ndigit} is
2729 restricted by the precision of a @code{long double}.
2734 @deftypefun {char *} qfcvt (long double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg})
2735 @safety{@prelim{}@mtunsafe{@mtasurace{:qfcvt}}@asunsafe{@ascuheap{}}@acunsafe{@acsmem{}}}
2736 This function is equivalent to @code{fcvt} except that it
2737 takes a @code{long double} for the first parameter and that @var{ndigit} is
2738 restricted by the precision of a @code{long double}.
2743 @deftypefun {char *} qgcvt (long double @var{value}, int @var{ndigit}, char *@var{buf})
2744 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2745 This function is equivalent to @code{gcvt} except that it takes a
2746 @code{long double} for the first parameter and that @var{ndigit} is
2747 restricted by the precision of a @code{long double}.
2752 The @code{ecvt} and @code{fcvt} functions, and their @code{long double}
2753 equivalents, all return a string located in a static buffer which is
2754 overwritten by the next call to the function. @Theglibc{}
2755 provides another set of extended functions which write the converted
2756 string into a user-supplied buffer. These have the conventional
2759 @code{gcvt_r} is not necessary, because @code{gcvt} already uses a
2760 user-supplied buffer.
2764 @deftypefun int ecvt_r (double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
2765 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2766 The @code{ecvt_r} function is the same as @code{ecvt}, except
2767 that it places its result into the user-specified buffer pointed to by
2768 @var{buf}, with length @var{len}. The return value is @code{-1} in
2769 case of an error and zero otherwise.
2771 This function is a GNU extension.
2775 @comment SVID, Unix98
2776 @deftypefun int fcvt_r (double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
2777 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2778 The @code{fcvt_r} function is the same as @code{fcvt}, except that it
2779 places its result into the user-specified buffer pointed to by
2780 @var{buf}, with length @var{len}. The return value is @code{-1} in
2781 case of an error and zero otherwise.
2783 This function is a GNU extension.
2788 @deftypefun int qecvt_r (long double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
2789 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2790 The @code{qecvt_r} function is the same as @code{qecvt}, except
2791 that it places its result into the user-specified buffer pointed to by
2792 @var{buf}, with length @var{len}. The return value is @code{-1} in
2793 case of an error and zero otherwise.
2795 This function is a GNU extension.
2800 @deftypefun int qfcvt_r (long double @var{value}, int @var{ndigit}, int *@var{decpt}, int *@var{neg}, char *@var{buf}, size_t @var{len})
2801 @safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
2802 The @code{qfcvt_r} function is the same as @code{qfcvt}, except
2803 that it places its result into the user-specified buffer pointed to by
2804 @var{buf}, with length @var{len}. The return value is @code{-1} in
2805 case of an error and zero otherwise.
2807 This function is a GNU extension.