This chapter contains information about functions for doing basic arithmetic operations, such as splitting a float into its integer and fractional parts or retrieving the imaginary part of a complex value. These functions are declared in the header files `math.h' and `complex.h'.
The C language defines several integer data types: integer, short integer, long integer, and character, all in both signed and unsigned varieties. The GNU C compiler extends the language to contain long long integers as well.
The C integer types were intended to allow code to be portable among machines with different inherent data sizes (word sizes), so each type may have different ranges on different machines. The problem with this is that a program often needs to be written for a particular range of integers, and sometimes must be written for a particular size of storage, regardless of what machine the program runs on.
To address this problem, the GNU C library contains C type definitions you can use to declare integers that meet your exact needs. Because the GNU C library header files are customized to a specific machine, your program source code doesn't have to be.
These typedefs are in `stdint.h'.
If you require that an integer be represented in exactly N bits, use one of the following types, with the obvious mapping to bit size and signedness:
If your C compiler and target machine do not allow integers of a certain size, the corresponding above type does not exist.
If you don't need a specific storage size, but want the smallest data structure with at least N bits, use one of these:
If you don't need a specific storage size, but want the data structure that allows the fastest access while having at least N bits (and among data structures with the same access speed, the smallest one), use one of these:
If you want an integer with the widest range possible on the platform on which it is being used, use one of the following. If you use these, you should write code that takes into account the variable size and range of the integer.
The GNU C library also provides macros that tell you the maximum and
minimum possible values for each integer data type. The macro names
follow these examples: INT32_MAX, UINT8_MAX,
INT_FAST32_MIN, INT_LEAST64_MIN, UINTMAX_MAX,
INTMAX_MAX, INTMAX_MIN. Note that there are no macros for
unsigned integer minima. These are always zero.
There are similar macros for use with C's built in integer types which should come with your C compiler. These are described in section Data Type Measurements.
Don't forget you can use the C sizeof function with any of these
data types to get the number of bytes of storage each uses.
This section describes functions for performing integer division. These
functions are redundant when GNU CC is used, because in GNU C the
`/' operator always rounds towards zero. But in other C
implementations, `/' may round differently with negative arguments.
div and ldiv are useful because they specify how to round
the quotient: towards zero. The remainder has the same sign as the
numerator.
These functions are specified to return a result r such that the value
r.quot*denominator + r.rem equals
numerator.
To use these facilities, you should include the header file `stdlib.h' in your program.
div
function. It has the following members:
int quot
int rem
div computes the quotient and remainder from
the division of numerator by denominator, returning the
result in a structure of type div_t.
If the result cannot be represented (as in a division by zero), the behavior is undefined.
Here is an example, albeit not a very useful one.
div_t result; result = div (20, -6);
Now result.quot is -3 and result.rem is 2.
ldiv
function. It has the following members:
long int quot
long int rem
(This is identical to div_t except that the components are of
type long int rather than int.)
ldiv function is similar to div, except that the
arguments are of type long int and the result is returned as a
structure of type ldiv_t.
lldiv
function. It has the following members:
long long int quot
long long int rem
(This is identical to div_t except that the components are of
type long long int rather than int.)
lldiv function is like the div function, but the
arguments are of type long long int and the result is returned as
a structure of type lldiv_t.
The lldiv function was added in ISO C99.
imaxdiv
function. It has the following members:
intmax_t quot
intmax_t rem
(This is identical to div_t except that the components are of
type intmax_t rather than int.)
See section Integers for a description of the intmax_t type.
imaxdiv function is like the div function, but the
arguments are of type intmax_t and the result is returned as
a structure of type imaxdiv_t.
See section Integers for a description of the intmax_t type.
The imaxdiv function was added in ISO C99.
Most computer hardware has support for two different kinds of numbers: integers (@math{...-3, -2, -1, 0, 1, 2, 3...}) and floating-point numbers. Floating-point numbers have three parts: the mantissa, the exponent, and the sign bit. The real number represented by a floating-point value is given by @ifnottex @math{(s ? -1 : 1) @mul{} 2^e @mul{} M} where @math{s} is the sign bit, @math{e} the exponent, and @math{M} the mantissa. See section Floating Point Representation Concepts, for details. (It is possible to have a different base for the exponent, but all modern hardware uses @math{2}.)
Floating-point numbers can represent a finite subset of the real numbers. While this subset is large enough for most purposes, it is important to remember that the only reals that can be represented exactly are rational numbers that have a terminating binary expansion shorter than the width of the mantissa. Even simple fractions such as @math{1/5} can only be approximated by floating point.
Mathematical operations and functions frequently need to produce values that are not representable. Often these values can be approximated closely enough for practical purposes, but sometimes they can't. Historically there was no way to tell when the results of a calculation were inaccurate. Modern computers implement the IEEE 754 standard for numerical computations, which defines a framework for indicating to the program when the results of calculation are not trustworthy. This framework consists of a set of exceptions that indicate why a result could not be represented, and the special values infinity and not a number (NaN).
ISO C99 defines macros that let you determine what sort of floating-point number a variable holds.
int. The possible values are:
FP_NAN
FP_INFINITE
FP_ZERO
FP_SUBNORMAL
fpclassify returns this value
for values of x in this alternate format.
FP_NORMAL
fpclassify is most useful if more than one property of a number
must be tested. There are more specific macros which only test one
property at a time. Generally these macros execute faster than
fpclassify, since there is special hardware support for them.
You should therefore use the specific macros whenever possible.
(fpclassify (x) != FP_NAN && fpclassify (x) != FP_INFINITE)
isfinite is implemented as a macro which accepts any
floating-point type.
(fpclassify (x) == FP_NORMAL)
(fpclassify (x) == FP_NAN)
Another set of floating-point classification functions was provided by BSD. The GNU C library also supports these functions; however, we recommend that you use the ISO C99 macros in new code. Those are standard and will be available more widely. Also, since they are macros, you do not have to worry about the type of their argument.
-1 if x represents negative infinity,
1 if x represents positive infinity, and 0 otherwise.
Note: The isnan macro defined by ISO C99 overrides
the BSD function. This is normally not a problem, because the two
routines behave identically. However, if you really need to get the BSD
function for some reason, you can write
(isnan) (x)
EDOM or ERANGE; infnan returns the
value that a math function would return if it set errno to that
value. See section Error Reporting by Mathematical Functions. -ERANGE is also acceptable
as an argument, and corresponds to -HUGE_VAL as a value.
In the BSD library, on certain machines, infnan raises a fatal
signal in all cases. The GNU library does not do likewise, because that
does not fit the ISO C specification.
Portability Note: The functions listed in this section are BSD extensions.
The IEEE 754 standard defines five exceptions that can occur during a calculation. Each corresponds to a particular sort of error, such as overflow.
When exceptions occur (when exceptions are raised, in the language of the standard), one of two things can happen. By default the exception is simply noted in the floating-point status word, and the program continues as if nothing had happened. The operation produces a default value, which depends on the exception (see the table below). Your program can check the status word to find out which exceptions happened.
Alternatively, you can enable traps for exceptions. In that case,
when an exception is raised, your program will receive the SIGFPE
signal. The default action for this signal is to terminate the
program. See section Signal Handling, for how you can change the effect of
the signal.
In the System V math library, the user-defined function matherr
is called when certain exceptions occur inside math library functions.
However, the Unix98 standard deprecates this interface. We support it
for historical compatibility, but recommend that you do not use it in
new programs.
The exceptions defined in IEEE 754 are:
IEEE 754 floating point numbers can represent positive or negative infinity, and NaN (not a number). These three values arise from calculations whose result is undefined or cannot be represented accurately. You can also deliberately set a floating-point variable to any of them, which is sometimes useful. Some examples of calculations that produce infinity or NaN:
@ifnottex
@math{1/0 = @infinity{}}
@math{log (0) = -@infinity{}}
@math{sqrt (-1) = NaN}
When a calculation produces any of these values, an exception also occurs; see section FP Exceptions.
The basic operations and math functions all accept infinity and NaN and produce sensible output. Infinities propagate through calculations as one would expect: for example, @math{2 + @infinity{} = @infinity{}}, @math{4/@infinity{} = 0}, atan @math{(@infinity{}) = @pi{}/2}. NaN, on the other hand, infects any calculation that involves it. Unless the calculation would produce the same result no matter what real value replaced NaN, the result is NaN.
In comparison operations, positive infinity is larger than all values
except itself and NaN, and negative infinity is smaller than all values
except itself and NaN. NaN is unordered: it is not equal to,
greater than, or less than anything, including itself. x ==
x is false if the value of x is NaN. You can use this to test
whether a value is NaN or not, but the recommended way to test for NaN
is with the isnan function (see section Floating-Point Number Classification Functions). In
addition, <, >, <=, and >= will raise an
exception when applied to NaNs.
`math.h' defines macros that allow you to explicitly set a variable to infinity or NaN.
1.0 / 0.0.
-INFINITY represents negative infinity.
You can test whether a floating-point value is infinite by comparing it
to this macro. However, this is not recommended; you should use the
isfinite macro instead. See section Floating-Point Number Classification Functions.
This macro was introduced in the ISO C99 standard.
You can use `#ifdef NAN' to test whether the machine supports
NaN. (Of course, you must arrange for GNU extensions to be visible,
such as by defining _GNU_SOURCE, and then you must include
`math.h'.)
IEEE 754 also allows for another unusual value: negative zero. This
value is produced when you divide a positive number by negative
infinity, or when a negative result is smaller than the limits of
representation. Negative zero behaves identically to zero in all
calculations, unless you explicitly test the sign bit with
signbit or copysign.
ISO C99 defines functions to query and manipulate the floating-point status word. You can use these functions to check for untrapped exceptions when it's convenient, rather than worrying about them in the middle of a calculation.
These constants represent the various IEEE 754 exceptions. Not all FPUs report all the different exceptions. Each constant is defined if and only if the FPU you are compiling for supports that exception, so you can test for FPU support with `#ifdef'. They are defined in `fenv.h'.
FE_INEXACT
FE_DIVBYZERO
FE_UNDERFLOW
FE_OVERFLOW
FE_INVALID
The macro FE_ALL_EXCEPT is the bitwise OR of all exception macros
which are supported by the FP implementation.
These functions allow you to clear exception flags, test for exceptions, and save and restore the set of exceptions flagged.
The function returns zero in case the operation was successful, a non-zero value otherwise.
FE_OVERFLOW) or underflow (FE_UNDERFLOW) are
raised before inexact (FE_INEXACT). Whether for overflow or
underflow the inexact exception is also raised is also implementation
dependent.
The function returns zero in case the operation was successful, a non-zero value otherwise.
To understand these functions, imagine that the status word is an
integer variable named status. feclearexcept is then
equivalent to `status &= ~excepts' and fetestexcept is
equivalent to `(status & excepts)'. The actual implementation may
be very different, of course.
Exception flags are only cleared when the program explicitly requests it,
by calling feclearexcept. If you want to check for exceptions
from a set of calculations, you should clear all the flags first. Here
is a simple example of the way to use fetestexcept:
{
double f;
int raised;
feclearexcept (FE_ALL_EXCEPT);
f = compute ();
raised = fetestexcept (FE_OVERFLOW | FE_INVALID);
if (raised & FE_OVERFLOW) { /* ... */ }
if (raised & FE_INVALID) { /* ... */ }
/* ... */
}
You cannot explicitly set bits in the status word. You can, however, save the entire status word and restore it later. This is done with the following functions:
The function returns zero in case the operation was successful, a non-zero value otherwise.
The function returns zero in case the operation was successful, a non-zero value otherwise.
Note that the value stored in fexcept_t bears no resemblance to
the bit mask returned by fetestexcept. The type may not even be
an integer. Do not attempt to modify an fexcept_t variable.
Many of the math functions are defined only over a subset of the real or complex numbers. Even if they are mathematically defined, their result may be larger or smaller than the range representable by their return type. These are known as domain errors, overflows, and underflows, respectively. Math functions do several things when one of these errors occurs. In this manual we will refer to the complete response as signalling a domain error, overflow, or underflow.
When a math function suffers a domain error, it raises the invalid
exception and returns NaN. It also sets errno to EDOM;
this is for compatibility with old systems that do not support IEEE
754 exception handling. Likewise, when overflow occurs, math
functions raise the overflow exception and return @math{@infinity{}} or
@math{-@infinity{}} as appropriate. They also set errno to
ERANGE. When underflow occurs, the underflow exception is
raised, and zero (appropriately signed) is returned. errno may be
set to ERANGE, but this is not guaranteed.
Some of the math functions are defined mathematically to result in a
complex value over parts of their domains. The most familiar example of
this is taking the square root of a negative number. The complex math
functions, such as csqrt, will return the appropriate complex value
in this case. The real-valued functions, such as sqrt, will
signal a domain error.
Some older hardware does not support infinities. On that hardware, overflows instead return a particular very large number (usually the largest representable number). `math.h' defines macros you can use to test for overflow on both old and new hardware.
HUGE_VAL is infinity.
On other machines, it's typically the largest positive number that can
be represented.
Mathematical functions return the appropriately typed version of
HUGE_VAL or -HUGE_VAL when the result is too large
to be represented.
Floating-point calculations are carried out internally with extra precision, and then rounded to fit into the destination type. This ensures that results are as precise as the input data. IEEE 754 defines four possible rounding modes:
FLT_EPSILON.
`fenv.h' defines constants which you can use to refer to the various rounding modes. Each one will be defined if and only if the FPU supports the corresponding rounding mode.
FE_TONEAREST
FE_UPWARD
FE_DOWNWARD
FE_TOWARDZERO
Underflow is an unusual case. Normally, IEEE 754 floating point
numbers are always normalized (see section Floating Point Representation Concepts).
Numbers smaller than @math{2^r} (where @math{r} is the minimum exponent,
FLT_MIN_RADIX-1 for float) cannot be represented as
normalized numbers. Rounding all such numbers to zero or @math{2^r}
would cause some algorithms to fail at 0. Therefore, they are left in
denormalized form. That produces loss of precision, since some bits of
the mantissa are stolen to indicate the decimal point.
If a result is too small to be represented as a denormalized number, it
is rounded to zero. However, the sign of the result is preserved; if
the calculation was negative, the result is negative zero.
Negative zero can also result from some operations on infinity, such as
@math{4/-@infinity{}}. Negative zero behaves identically to zero except
when the copysign or signbit functions are used to check
the sign bit directly.
At any time one of the above four rounding modes is selected. You can find out which one with this function:
To change the rounding mode, use this function:
fesetround returns zero if it changed the
rounding mode, a nonzero value if the mode is not supported.
You should avoid changing the rounding mode if possible. It can be an expensive operation; also, some hardware requires you to compile your program differently for it to work. The resulting code may run slower. See your compiler documentation for details.
IEEE 754 floating-point implementations allow the programmer to
decide whether traps will occur for each of the exceptions, by setting
bits in the control word. In C, traps result in the program
receiving the SIGFPE signal; see section Signal Handling.
Note: IEEE 754 says that trap handlers are given details of the exceptional situation, and can set the result value. C signals do not provide any mechanism to pass this information back and forth. Trapping exceptions in C is therefore not very useful.
It is sometimes necessary to save the state of the floating-point unit while you perform some calculation. The library provides functions which save and restore the exception flags, the set of exceptions that generate traps, and the rounding mode. This information is known as the floating-point environment.
The functions to save and restore the floating-point environment all use
a variable of type fenv_t to store information. This type is
defined in `fenv.h'. Its size and contents are
implementation-defined. You should not attempt to manipulate a variable
of this type directly.
To save the state of the FPU, use one of these functions:
The function returns zero in case the operation was successful, a non-zero value otherwise.
feholdexcept cannot set this mode, it returns nonzero value. If it
succeeds, it returns zero.
The functions which restore the floating-point environment can take these kinds of arguments:
fenv_t objects, which were initialized previously by a
call to fegetenv or feholdexcept.
FE_DFL_ENV which represents the floating-point
environment as it was available at program start.
FE_ and
having type fenv_t *.
If possible, the GNU C Library defines a macro FE_NOMASK_ENV
which represents an environment where every exception raised causes a
trap to occur. You can test for this macro using #ifdef. It is
only defined if _GNU_SOURCE is defined.
Some platforms might define other predefined environments.
To set the floating-point environment, you can use either of these functions:
The function returns zero in case the operation was successful, a non-zero value otherwise.
fesetenv, this function sets the floating-point environment
to that described by envp. However, if any exceptions were
flagged in the status word before feupdateenv was called, they
remain flagged after the call. In other words, after feupdateenv
is called, the status word is the bitwise OR of the previous status word
and the one saved in envp.
The function returns zero in case the operation was successful, a non-zero value otherwise.
To control for individual exceptions if raising them causes a trap to occur, you can use the following two functions.
Portability Note: These functions are all GNU extensions.
The function returns the previous enabled exceptions in case the
operation was successful, -1 otherwise.
The function returns the previous enabled exceptions in case the
operation was successful, -1 otherwise.
-1 in case of failure.
The C library provides functions to do basic operations on floating-point numbers. These include absolute value, maximum and minimum, normalization, bit twiddling, rounding, and a few others.
These functions are provided for obtaining the absolute value (or
magnitude) of a number. The absolute value of a real number
x is x if x is positive, -x if x is
negative. For a complex number z, whose real part is x and
whose imaginary part is y, the absolute value is sqrt
(x*x + y*y).
Prototypes for abs, labs and llabs are in `stdlib.h';
imaxabs is declared in `inttypes.h';
fabs, fabsf and fabsl are declared in `math.h'.
cabs, cabsf and cabsl are declared in `complex.h'.
Most computers use a two's complement integer representation, in which
the absolute value of INT_MIN (the smallest possible int)
cannot be represented; thus, abs (INT_MIN) is not defined.
llabs and imaxdiv are new to ISO C99.
See section Integers for a description of the intmax_t type.
sqrt (creal (z) * creal (z) + cimag (z) * cimag (z))
This function should always be used instead of the direct formula
because it takes special care to avoid losing precision. It may also
take advantage of hardware support for this operation. See hypot
in section Exponentiation and Logarithms.
The functions described in this section are primarily provided as a way to efficiently perform certain low-level manipulations on floating point numbers that are represented internally using a binary radix; see section Floating Point Representation Concepts. These functions are required to have equivalent behavior even if the representation does not use a radix of 2, but of course they are unlikely to be particularly efficient in those cases.
All these functions are declared in `math.h'.
If the argument value is not zero, the return value is value
times a power of two, and is always in the range 1/2 (inclusive) to 1
(exclusive). The corresponding exponent is stored in
*exponent; the return value multiplied by 2 raised to this
exponent equals the original number value.
For example, frexp (12.8, &exponent) returns 0.8 and
stores 4 in exponent.
If value is zero, then the return value is zero and
zero is stored in *exponent.
frexp.)
For example, ldexp (0.8, 4) returns 12.8.
The following functions, which come from BSD, provide facilities
equivalent to those of ldexp and frexp.
double. This is
the highest integer power of 2 contained in x. The sign of
x is ignored. For example, logb (3.5) is 1.0 and
logb (4.0) is 2.0.
When 2 raised to this power is divided into x, it gives a
quotient between 1 (inclusive) and 2 (exclusive).
If x is zero, the return value is minus infinity if the machine supports infinities, and a very small number if it does not. If x is infinity, the return value is infinity.
For finite x, the value returned by logb is one less than
the value that frexp would store into *exponent.
scalb function is the BSD name for ldexp.
scalbn is identical to scalb, except that the exponent
n is an int instead of a floating-point number.
scalbln is identical to scalb, except that the exponent
n is a long int instead of a floating-point number.
significand returns the mantissa of x scaled to the range
@math{[1, 2)}.
It is equivalent to scalb (x, (double) -ilogb (x)).
This function exists mainly for use in certain standardized tests of IEEE 754 conformance.
The functions listed here perform operations such as rounding and truncation of floating-point values. Some of these functions convert floating point numbers to integer values. They are all declared in `math.h'.
You can also convert floating-point numbers to integers simply by
casting them to int. This discards the fractional part,
effectively rounding towards zero. However, this only works if the
result can actually be represented as an int---for very large
numbers, this is impossible. The functions listed here return the
result as a double instead to get around this problem.
double. Thus, ceil (1.5)
is 2.0.
double. Thus, floor
(1.5) is 1.0 and floor (-1.5) is -2.0.
trunc functions round x towards zero to the nearest
integer (returned in floating-point format). Thus, trunc (1.5)
is 1.0 and trunc (-1.5) is -1.0.
If x was not initially an integer, these functions raise the inexact exception.
rint functions, but
do not raise the inexact exception if x is not an integer.
rint, but they round halfway
cases away from zero instead of to the nearest even integer.
rint, but they return a
long int instead of a floating-point number.
rint, but they return a
long long int instead of a floating-point number.
round, but they return a
long int instead of a floating-point number.
round, but they return a
long long int instead of a floating-point number.
-1 and 1, exclusive). Their sum
equals value. Each of the parts has the same sign as value,
and the integer part is always rounded toward zero.
modf stores the integer part in *integer-part, and
returns the fractional part. For example, modf (2.5, &intpart)
returns 0.5 and stores 2.0 into intpart.
The functions in this section compute the remainder on division of two floating-point numbers. Each is a little different; pick the one that suits your problem.
numerator - n * denominator, where n
is the quotient of numerator divided by denominator, rounded
towards zero to an integer. Thus, fmod (6.5, 2.3) returns
1.9, which is 6.5 minus 4.6.
The result has the same sign as the numerator and has magnitude less than the magnitude of the denominator.
If denominator is zero, fmod signals a domain error.
fmod except that they rounds the
internal quotient n to the nearest integer instead of towards zero
to an integer. For example, drem (6.5, 2.3) returns -0.4,
which is 6.5 minus 6.9.
The absolute value of the result is less than or equal to half the
absolute value of the denominator. The difference between
fmod (numerator, denominator) and drem
(numerator, denominator) is always either
denominator, minus denominator, or zero.
If denominator is zero, drem signals a domain error.
drem.
There are some operations that are too complicated or expensive to perform by hand on floating-point numbers. ISO C99 defines functions to do these operations, which mostly involve changing single bits.
copysign never raises an exception.
This function is defined in IEC 559 (and the appendix with recommended functions in IEEE 754/IEEE 854).
signbit is a generic macro which can work on all floating-point
types. It returns a nonzero value if the value of x has its sign
bit set.
This is not the same as x < 0.0, because IEEE 754 floating
point allows zero to be signed. The comparison -0.0 < 0.0 is
false, but signbit (-0.0) will return a nonzero value.
nextafter function returns the next representable neighbor of
x in the direction towards y. The size of the step between
x and the result depends on the type of the result. If
@math{x = y} the function simply returns y. If either
value is NaN, NaN is returned. Otherwise
a value corresponding to the value of the least significant bit in the
mantissa is added or subtracted, depending on the direction.
nextafter will signal overflow or underflow if the result goes
outside of the range of normalized numbers.
This function is defined in IEC 559 (and the appendix with recommended functions in IEEE 754/IEEE 854).
nextafter except that their second argument is a long
double.
nan function returns a representation of NaN, provided that
NaN is supported by the target platform.
nan ("n-char-sequence") is equivalent to
strtod ("NAN(n-char-sequence)").
The argument tagp is used in an unspecified manner. On IEEE 754 systems, there are many representations of NaN, and tagp selects one. On other systems it may do nothing.
The standard C comparison operators provoke exceptions when one or other of the operands is NaN. For example,
int v = a < 1.0;
will raise an exception if a is NaN. (This does not
happen with == and !=; those merely return false and true,
respectively, when NaN is examined.) Frequently this exception is
undesirable. ISO C99 therefore defines comparison functions that
do not raise exceptions when NaN is examined. All of the functions are
implemented as macros which allow their arguments to be of any
floating-point type. The macros are guaranteed to evaluate their
arguments only once.
(x) > (y), but no
exception is raised if x or y are NaN.
(x) >= (y), but no
exception is raised if x or y are NaN.
(x) < (y), but no exception is
raised if x or y are NaN.
(x) <= (y), but no
exception is raised if x or y are NaN.
(x) < (y) ||
(x) > (y) (although it only evaluates x and y
once), but no exception is raised if x or y are NaN.
This macro is not equivalent to x != y, because that
expression is true if x or y are NaN.
Not all machines provide hardware support for these operations. On machines that don't, the macros can be very slow. Therefore, you should not use these functions when NaN is not a concern.
Note: There are no macros isequal or isunequal.
They are unnecessary, because the == and != operators do
not throw an exception if one or both of the operands are NaN.
The functions in this section perform miscellaneous but common operations that are awkward to express with C operators. On some processors these functions can use special machine instructions to perform these operations faster than the equivalent C code.
fmin function returns the lesser of the two values x
and y. It is similar to the expression
((x) < (y) ? (x) : (y))
except that x and y are only evaluated once.
If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.
fmax function returns the greater of the two values x
and y.
If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.
fdim function returns the positive difference between
x and y. The positive difference is @math{x -
y} if x is greater than y, and @math{0} otherwise.
If x, y, or both are NaN, NaN is returned.
fma function performs floating-point multiply-add. This is
the operation @math{(x @mul{} y) + z}, but the
intermediate result is not rounded to the destination type. This can
sometimes improve the precision of a calculation.
This function was introduced because some processors have a special
instruction to perform multiply-add. The C compiler cannot use it
directly, because the expression `x*y + z' is defined to round the
intermediate result. fma lets you choose when you want to round
only once.
On processors which do not implement multiply-add in hardware,
fma can be very slow since it must avoid intermediate rounding.
`math.h' defines the symbols FP_FAST_FMA,
FP_FAST_FMAF, and FP_FAST_FMAL when the corresponding
version of fma is no slower than the expression `x*y + z'.
In the GNU C library, this always means the operation is implemented in
hardware.
ISO C99 introduces support for complex numbers in C. This is done
with a new type qualifier, complex. It is a keyword if and only
if `complex.h' has been included. There are three complex types,
corresponding to the three real types: float complex,
double complex, and long double complex.
To construct complex numbers you need a way to indicate the imaginary part of a number. There is no standard notation for an imaginary floating point constant. Instead, `complex.h' defines two macros that can be used to create complex numbers.
_Complex_I gives a
complex number whose value is purely imaginary. You can use this to
construct complex constants:
@math{3.0 + 4.0i} = 3.0 + 4.0 * _Complex_I
Note that _Complex_I * _Complex_I has the value -1, but
the type of that value is complex.
_Complex_I is a bit of a mouthful. `complex.h' also defines
a shorter name for the same constant.
_Complex_I. Most of the
time it is preferable. However, it causes problems if you want to use
the identifier I for something else. You can safely write
#include <complex.h> #undef I
if you need I for your own purposes. (In that case we recommend
you also define some other short name for _Complex_I, such as
J.)
ISO C99 also defines functions that perform basic operations on complex numbers, such as decomposition and conjugation. The prototypes for all these functions are in `complex.h'. All functions are available in three variants, one for each of the three complex types.
carg has a branch cut along the positive real axis.
INFINITY + I * copysign (0.0, cimag (z))
This section describes functions for "reading" integer and
floating-point numbers from a string. It may be more convenient in some
cases to use sscanf or one of the related functions; see
section Formatted Input. But often you can make a program more robust by
finding the tokens in the string by hand, then converting the numbers
one by one.
The `str' functions are declared in `stdlib.h' and those
beginning with `wcs' are declared in `wchar.h'. One might
wonder about the use of restrict in the prototypes of the
functions in this section. It is seemingly useless but the ISO C
standard uses it (for the functions defined there) so we have to do it
as well.
strtol ("string-to-long") function converts the initial
part of string to a signed integer, which is returned as a value
of type long int.
This function attempts to decompose string as follows:
isspace function
(see section Classification of Characters). These are discarded.
2 and 36.
If base is 16, the digits may optionally be preceded by
`0x' or `0X'. If base has no legal value the value returned
is 0l and the global variable errno is set to EINVAL.
strtol stores a pointer to this tail in
*tailptr.
If the string is empty, contains only whitespace, or does not contain an
initial substring that has the expected syntax for an integer in the
specified base, no conversion is performed. In this case,
strtol returns a value of zero and the value stored in
*tailptr is the value of string.
In a locale other than the standard "C" locale, this function
may recognize additional implementation-dependent syntax.
If the string has valid syntax for an integer but the value is not
representable because of overflow, strtol returns either
LONG_MAX or LONG_MIN (see section Range of an Integer Type), as
appropriate for the sign of the value. It also sets errno
to ERANGE to indicate there was overflow.
You should not check for errors by examining the return value of
strtol, because the string might be a valid representation of
0l, LONG_MAX, or LONG_MIN. Instead, check whether
tailptr points to what you expect after the number
(e.g. '\0' if the string should end after the number). You also
need to clear errno before the call and check it afterward, in
case there was overflow.
There is an example at the end of this section.
wcstol function is equivalent to the strtol function
in nearly all aspects but handles wide character strings.
The wcstol function was introduced in Amendment 1 of ISO C90.
strtoul ("string-to-unsigned-long") function is like
strtol except it converts to an unsigned long int value.
The syntax is the same as described above for strtol. The value
returned on overflow is ULONG_MAX (see section Range of an Integer Type).
If string depicts a negative number, strtoul acts the same
as strtol but casts the result to an unsigned integer. That means
for example that strtoul on "-1" returns ULONG_MAX
and an input more negative than LONG_MIN returns
(ULONG_MAX + 1) / 2.
strtoul sets errno to EINVAL if base is out of
range, or ERANGE on overflow.
wcstoul function is equivalent to the strtoul function
in nearly all aspects but handles wide character strings.
The wcstoul function was introduced in Amendment 1 of ISO C90.
strtoll function is like strtol except that it returns
a long long int value, and accepts numbers with a correspondingly
larger range.
If the string has valid syntax for an integer but the value is not
representable because of overflow, strtoll returns either
LONG_LONG_MAX or LONG_LONG_MIN (see section Range of an Integer Type), as
appropriate for the sign of the value. It also sets errno to
ERANGE to indicate there was overflow.
The strtoll function was introduced in ISO C99.
wcstoll function is equivalent to the strtoll function
in nearly all aspects but handles wide character strings.
The wcstoll function was introduced in Amendment 1 of ISO C90.
strtoq ("string-to-quad-word") is the BSD name for strtoll.
wcstoq function is equivalent to the strtoq function
in nearly all aspects but handles wide character strings.
The wcstoq function is a GNU extension.
strtoull function is related to strtoll the same way
strtoul is related to strtol.
The strtoull function was introduced in ISO C99.
wcstoull function is equivalent to the strtoull function
in nearly all aspects but handles wide character strings.
The wcstoull function was introduced in Amendment 1 of ISO C90.
strtouq is the BSD name for strtoull.
wcstouq function is equivalent to the strtouq function
in nearly all aspects but handles wide character strings.
The wcstoq function is a GNU extension.
strtoimax function is like strtol except that it returns
a intmax_t value, and accepts numbers of a corresponding range.
If the string has valid syntax for an integer but the value is not
representable because of overflow, strtoimax returns either
INTMAX_MAX or INTMAX_MIN (see section Integers), as
appropriate for the sign of the value. It also sets errno to
ERANGE to indicate there was overflow.
See section Integers for a description of the intmax_t type. The
strtoimax function was introduced in ISO C99.
wcstoimax function is equivalent to the strtoimax function
in nearly all aspects but handles wide character strings.
The wcstoimax function was introduced in ISO C99.
strtoumax function is related to strtoimax
the same way that strtoul is related to strtol.
See section Integers for a description of the intmax_t type. The
strtoumax function was introduced in ISO C99.
wcstoumax function is equivalent to the strtoumax function
in nearly all aspects but handles wide character strings.
The wcstoumax function was introduced in ISO C99.
strtol function with a base
argument of 10, except that it need not detect overflow errors.
The atol function is provided mostly for compatibility with
existing code; using strtol is more robust.
atol, except that it returns an int.
The atoi function is also considered obsolete; use strtol
instead.
atol, except it returns a long
long int.
The atoll function was introduced in ISO C99. It too is
obsolete (despite having just been added); use strtoll instead.
All the functions mentioned in this section so far do not handle
alternative representations of characters as described in the locale
data. Some locales specify thousands separator and the way they have to
be used which can help to make large numbers more readable. To read
such numbers one has to use the scanf functions with the `''
flag.
Here is a function which parses a string as a sequence of integers and returns the sum of them:
int
sum_ints_from_string (char *string)
{
int sum = 0;
while (1) {
char *tail;
int next;
/* Skip whitespace by hand, to detect the end. */
while (isspace (*string)) string++;
if (*string == 0)
break;
/* There is more nonwhitespace, */
/* so it ought to be another number. */
errno = 0;
/* Parse it. */
next = strtol (string, &tail, 0);
/* Add it in, if not overflow. */
if (errno)
printf ("Overflow\n");
else
sum += next;
/* Advance past it. */
string = tail;
}
return sum;
}
The `str' functions are declared in `stdlib.h' and those
beginning with `wcs' are declared in `wchar.h'. One might
wonder about the use of restrict in the prototypes of the
functions in this section. It is seemingly useless but the ISO C
standard uses it (for the functions defined there) so we have to do it
as well.
strtod ("string-to-double") function converts the initial
part of string to a floating-point number, which is returned as a
value of type double.
This function attempts to decompose string as follows:
isspace function
(see section Classification of Characters). These are discarded.
*tailptr.
If the string is empty, contains only whitespace, or does not contain an
initial substring that has the expected syntax for a floating-point
number, no conversion is performed. In this case, strtod returns
a value of zero and the value returned in *tailptr is the
value of string.
In a locale other than the standard "C" or "POSIX" locales,
this function may recognize additional locale-dependent syntax.
If the string has valid syntax for a floating-point number but the value
is outside the range of a double, strtod will signal
overflow or underflow as described in section Error Reporting by Mathematical Functions.
strtod recognizes four special input strings. The strings
"inf" and "infinity" are converted to @math{@infinity{}},
or to the largest representable value if the floating-point format
doesn't support infinities. You can prepend a "+" or "-"
to specify the sign. Case is ignored when scanning these strings.
The strings "nan" and "nan(chars...)" are converted
to NaN. Again, case is ignored. If chars... are provided, they
are used in some unspecified fashion to select a particular
representation of NaN (there can be several).
Since zero is a valid result as well as the value returned on error, you
should check for errors in the same way as for strtol, by
examining errno and tailptr.
strtod, but return float
and long double values respectively. They report errors in the
same way as strtod. strtof can be substantially faster
than strtod, but has less precision; conversely, strtold
can be much slower but has more precision (on systems where long
double is a separate type).
These functions have been GNU extensions and are new to ISO C99.
wcstod, wcstof, and wcstol functions are
equivalent in nearly all aspect to the strtod, strtof, and
strtold functions but it handles wide character string.
The wcstod function was introduced in Amendment 1 of ISO
C90. The wcstof and wcstold functions were introduced in
ISO C99.
strtod function, except that it
need not detect overflow and underflow errors. The atof function
is provided mostly for compatibility with existing code; using
strtod is more robust.
The GNU C library also provides `_l' versions of these functions, which take an additional argument, the locale to use in conversion. See section Parsing of Integers.
The old System V C library provided three functions to convert numbers to strings, with unusual and hard-to-use semantics. The GNU C library also provides these functions and some natural extensions.
These functions are only available in glibc and on systems descended
from AT&T Unix. Therefore, unless these functions do precisely what you
need, it is better to use sprintf, which is standard.
All these functions are defined in `stdlib.h'.
ecvt converts the floating-point number value
to a string with at most ndigit decimal digits. The
returned string contains no decimal point or sign. The first digit of
the string is non-zero (unless value is actually zero) and the
last digit is rounded to nearest. *decpt is set to the
index in the string of the first digit after the decimal point.
*neg is set to a nonzero value if value is negative,
zero otherwise.
If ndigit decimal digits would exceed the precision of a
double it is reduced to a system-specific value.
The returned string is statically allocated and overwritten by each call
to ecvt.
If value is zero, it is implementation defined whether
*decpt is 0 or 1.
For example: ecvt (12.3, 5, &d, &n) returns "12300"
and sets d to 2 and n to 0.
fcvt is like ecvt, but ndigit specifies
the number of digits after the decimal point. If ndigit is less
than zero, value is rounded to the @math{ndigit+1}'th place to the
left of the decimal point. For example, if ndigit is -1,
value will be rounded to the nearest 10. If ndigit is
negative and larger than the number of digits to the left of the decimal
point in value, value will be rounded to one significant digit.
If ndigit decimal digits would exceed the precision of a
double it is reduced to a system-specific value.
The returned string is statically allocated and overwritten by each call
to fcvt.
gcvt is functionally equivalent to `sprintf(buf, "%*g",
ndigit, value'. It is provided only for compatibility's sake. It
returns buf.
If ndigit decimal digits would exceed the precision of a
double it is reduced to a system-specific value.
As extensions, the GNU C library provides versions of these three
functions that take long double arguments.
ecvt except that it takes a
long double for the first parameter and that ndigit is
restricted by the precision of a long double.
fcvt except that it
takes a long double for the first parameter and that ndigit is
restricted by the precision of a long double.
gcvt except that it takes a
long double for the first parameter and that ndigit is
restricted by the precision of a long double.
The ecvt and fcvt functions, and their long double
equivalents, all return a string located in a static buffer which is
overwritten by the next call to the function. The GNU C library
provides another set of extended functions which write the converted
string into a user-supplied buffer. These have the conventional
_r suffix.
gcvt_r is not necessary, because gcvt already uses a
user-supplied buffer.
ecvt_r function is the same as ecvt, except
that it places its result into the user-specified buffer pointed to by
buf, with length len.
This function is a GNU extension.
fcvt_r function is the same as fcvt, except
that it places its result into the user-specified buffer pointed to by
buf, with length len.
This function is a GNU extension.
qecvt_r function is the same as qecvt, except
that it places its result into the user-specified buffer pointed to by
buf, with length len.
This function is a GNU extension.
qfcvt_r function is the same as qfcvt, except
that it places its result into the user-specified buffer pointed to by
buf, with length len.
This function is a GNU extension.
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