• Math: | The mathematical functions (‘math.h’). | |
• Complex: | The mathematical complex functions (‘complex.h’). | |
• Reentrancy: | The functions in libm are not reentrant by default. | |
• Long Double Functions: | The long double function support of libm. | |
• Document Index: |
This chapter groups a wide variety of mathematical functions. The corresponding definitions and declarations are in math.h. Two definitions from math.h are of particular interest.
double
is defined as
HUGE_VAL
; this number is returned on overflow by many functions.
The macro HUGE_VALF
is a corresponding value for float
.
exception
is used when you write customized error
handlers for the mathematical functions. You can customize error
handling for most of these functions by defining your own version of
matherr
; see the section on matherr
for details.
Since the error handling code calls fputs
, the mathematical
subroutines require stubs or minimal implementations for the same list
of OS subroutines as fputs
: close
, fstat
,
isatty
, lseek
, read
, sbrk
, write
.
See System Calls in The Red Hat newlib C Library,
for a discussion and for sample minimal implementations of these support
subroutines.
Alternative declarations of the mathematical functions, which exploit specific machine capabilities to operate faster—but generally have less error checking and may reflect additional limitations on some machines—are available when you include fastmath.h instead of math.h.
• version: | Version of library | |
• acos: | Arccosine | |
• acosh: | Inverse hyperbolic cosine | |
• asin: | Arcsine | |
• asinh: | Inverse hyperbolic sine | |
• atan: | Arctangent | |
• atan2: | Arctangent of y/x | |
• atanh: | Inverse hyperbolic tangent | |
• jN: | Bessel functions (jN, yN) | |
• cbrt: | Cube root | |
• copysign: | Sign of Y, magnitude of X | |
• cosh: | Hyperbolic cosine | |
• erf: | Error function (erf, erfc) | |
• exp: | Exponential, base e | |
• exp2: | Exponential, base 2 | |
• expm1: | Exponential, base e, of x - 1 | |
• fabs: | Absolute value (magnitude) | |
• fdim: | Positive difference | |
• floor: | Floor and ceiling (floor, ceil) | |
• fma: | Floating multiply add | |
• fmax: | Maximum | |
• fmin: | Minimum | |
• fmod: | Floating-point remainder (modulo) | |
• fpclassify: | Floating-point classification macro | |
• frexp: | Split floating-point number | |
• gamma: | Logarithmic gamma function | |
• hypot: | Distance from origin | |
• ilogb: | Get exponent | |
• infinity: | Floating infinity | |
• isgreater: | Comparison macros | |
• ldexp: | Scale by a power of 2 | |
• log: | Natural logarithms | |
• log10: | Base 10 logarithms | |
• log1p: | Log of 1 + X | |
• log2: | Base 2 logarithms | |
• logb: | Get exponent | |
• lrint: | Round to integer | |
• lround: | Round to integer, away from zero (lround, llround) | |
• matherr: | Modifiable math error handler | |
• modf: | Split fractional and integer parts | |
• nan: | Floating Not a Number | |
• nearbyint: | Round to integer | |
• nextafter: | Get next representable number | |
• pow: | X to the power Y | |
• remainder: | remainder of X divided by Y | |
• remquo: | Remainder and part of quotient | |
• rint: | Round to integer | |
• round: | Round to integer, away from zero | |
• scalbn: | Scale by a power of FLT_RADIX (2) | |
• signbit: | Does floating-point number have negative sign? | |
• sin: | Sine or cosine (sin, cos) | |
• sinh: | Hyperbolic sine | |
• sqrt: | Positive square root | |
• tan: | Tangent | |
• tanh: | Hyperbolic tangent | |
• trunc: | Round to integer, towards zero |
There are four different versions of the math library routines: IEEE,
POSIX, X/Open, or SVID. The version may be selected at runtime by
setting the global variable _LIB_VERSION
, defined in
math.h. It may be set to one of the following constants defined
in math.h: _IEEE_
, _POSIX_
, _XOPEN_
, or
_SVID_
. The _LIB_VERSION
variable is not specific to any
thread, and changing it will affect all threads.
The versions of the library differ only in how errors are handled.
In IEEE mode, the matherr
function is never called, no warning
messages are printed, and errno
is never set.
In POSIX mode, errno
is set correctly, but the matherr
function is never called and no warning messages are printed.
In X/Open mode, errno
is set correctly, and matherr
is
called, but warning message are not printed.
In SVID mode, functions which overflow return 3.40282346638528860e+38,
the maximum single-precision floating-point value, rather than infinity.
Also, errno
is set correctly, matherr
is called, and, if
matherr
returns 0, warning messages are printed for some errors.
For example, by default ‘log(-1.0)’ writes this message on standard
error output:
log: DOMAIN error
The library is set to X/Open mode by default.
The aforementioned error reporting is the supported Newlib libm error handling method. However, the majority of the functions are written so as to produce the floating-point exceptions (e.g. "invalid", "divide-by-zero") as required by the C and POSIX standards, for floating-point implementations that support them. Newlib does not provide the floating-point exception access routines defined in the standards for fenv.h, though, which is why they are considered unsupported. It is mentioned in case you have separately-provided access routines so that you are aware that they can be caused.
Most of the individual function descriptions describe the standards to which each function complies. However, these descriptions are mostly out of date, having been written before C99 was released. One of these days we’ll get around to updating the rest of them. (If you’d like to help, please let us know.)
“C99” refers to ISO/IEC 9899:1999, “Programming languages–C”. “POSIX” refers to IEEE Standard 1003.1. POSIX® is a registered trademark of The IEEE.
acos
, acosf
—arc cosineSynopsis
#include <math.h> double acos(double x); float acosf(float x);
Description
acos
computes the inverse cosine (arc cosine) of the input value.
Arguments to acos
must be in the range -1 to 1.
acosf
is identical to acos
, except that it performs
its calculations on floats
.
Returns
acos
and acosf
return values in radians, in the range of 0 to pi.
If x is not between -1 and 1, the returned value is NaN
(not a number) the global variable errno
is set to EDOM
, and a
DOMAIN error
message is sent as standard error output.
You can modify error handling for these functions using matherr
.
acosh
, acoshf
—inverse hyperbolic cosineSynopsis
#include <math.h> double acosh(double x); float acoshf(float x);
Description
acosh
calculates the inverse hyperbolic cosine of x.
acosh
is defined as
log(x + sqrt(x*x-1))
x must be a number greater than or equal to 1.
acoshf
is identical, other than taking and returning floats.
Returns
acosh
and acoshf
return the calculated value. If x
less than 1, the return value is NaN and errno
is set to EDOM
.
You can change the error-handling behavior with the non-ANSI
matherr
function.
Portability
Neither acosh
nor acoshf
are ANSI C. They are not recommended
for portable programs.
asin
, asinf
—arc sineSynopsis
#include <math.h> double asin(double x); float asinf(float x);
Description
asin
computes the inverse sine (arc sine) of the argument x.
Arguments to asin
must be in the range -1 to 1.
asinf
is identical to asin
, other than taking and
returning floats.
You can modify error handling for these routines using matherr
.
Returns
asin
returns values in radians, in the range of -pi/2 to pi/2.
If x is not in the range -1 to 1, asin
and asinf
return NaN (not a number), set the global variable errno
to
EDOM
, and issue a DOMAIN error
message.
You can change this error treatment using matherr
.
asinh
, asinhf
—inverse hyperbolic sineSynopsis
#include <math.h> double asinh(double x); float asinhf(float x);
Description
asinh
calculates the inverse hyperbolic sine of x.
asinh
is defined as
sgn(x) * log(abs(x) + sqrt(1+x*x))
asinhf
is identical, other than taking and returning floats.
Returns
asinh
and asinhf
return the calculated value.
Portability
Neither asinh
nor asinhf
are ANSI C.
atan
, atanf
—arc tangentSynopsis
#include <math.h> double atan(double x); float atanf(float x);
Description
atan
computes the inverse tangent (arc tangent) of the input value.
atanf
is identical to atan
, save that it operates on floats
.
Returns
atan
returns a value in radians, in the range of -pi/2 to pi/2.
Portability
atan
is ANSI C. atanf
is an extension.
atan2
, atan2f
—arc tangent of y/xSynopsis
#include <math.h> double atan2(double y,double x); float atan2f(float y,float x);
Description
atan2
computes the inverse tangent (arc tangent) of y/x.
atan2
produces the correct result even for angles near
pi/2 or -pi/2
(that is, when x is near 0).
atan2f
is identical to atan2
, save that it takes and returns
float
.
Returns
atan2
and atan2f
return a value in radians, in the range of
-pi to pi.
You can modify error handling for these functions using matherr
.
Portability
atan2
is ANSI C. atan2f
is an extension.
atanh
, atanhf
—inverse hyperbolic tangentSynopsis
#include <math.h> double atanh(double x); float atanhf(float x);
Description
atanh
calculates the inverse hyperbolic tangent of x.
atanhf
is identical, other than taking and returning
float
values.
Returns
atanh
and atanhf
return the calculated value.
If
x|
is greater than 1, the global errno
is set to EDOM
and
the result is a NaN. A DOMAIN error
is reported.
If
x|
is 1, the global errno
is set to EDOM
; and the result is
infinity with the same sign as x
. A SING error
is reported.
You can modify the error handling for these routines using
matherr
.
Portability
Neither atanh
nor atanhf
are ANSI C.
jN
, jNf
, yN
, yNf
—Bessel functionsSynopsis
#include <math.h> double j0(double x); float j0f(float x); double j1(double x); float j1f(float x); double jn(int n, double x); float jnf(int n, float x); double y0(double x); float y0f(float x); double y1(double x); float y1f(float x); double yn(int n, double x); float ynf(int n, float x);
Description
The Bessel functions are a family of functions that solve the
differential equation
2 2 2 x y'' + xy' + (x - p )y = 0
These functions have many applications in engineering and physics.
jn
calculates the Bessel function of the first kind of order
n. j0
and j1
are special cases for order 0 and order
1 respectively.
Similarly, yn
calculates the Bessel function of the second kind of
order n, and y0
and y1
are special cases for order 0 and
1.
jnf
, j0f
, j1f
, ynf
, y0f
, and y1f
perform the
same calculations, but on float
rather than double
values.
Returns
The value of each Bessel function at x is returned.
Portability
None of the Bessel functions are in ANSI C.
cbrt
, cbrtf
—cube rootSynopsis
#include <math.h> double cbrt(double x); float cbrtf(float x);
Description
cbrt
computes the cube root of the argument.
Returns
The cube root is returned.
Portability
cbrt
is in System V release 4. cbrtf
is an extension.
copysign
, copysignf
—sign of y, magnitude of xSynopsis
#include <math.h> double copysign (double x, double y); float copysignf (float x, float y);
Description
copysign
constructs a number with the magnitude (absolute value)
of its first argument, x, and the sign of its second argument,
y.
copysignf
does the same thing; the two functions differ only in
the type of their arguments and result.
Returns
copysign
returns a double
with the magnitude of
x and the sign of y.
copysignf
returns a float
with the magnitude of
x and the sign of y.
Portability
copysign
is not required by either ANSI C or the System V Interface
Definition (Issue 2).
cosh
, coshf
—hyperbolic cosineSynopsis
#include <math.h> double cosh(double x); float coshf(float x)
Description
cosh
computes the hyperbolic cosine of the argument x.
cosh(x)
is defined as
(exp(x) + exp(-x))/2
Angles are specified in radians.
coshf
is identical, save that it takes and returns float
.
Returns
The computed value is returned. When the correct value would create
an overflow, cosh
returns the value HUGE_VAL
with the
appropriate sign, and the global value errno
is set to ERANGE
.
You can modify error handling for these functions using the
function matherr
.
Portability
cosh
is ANSI.
coshf
is an extension.
erf
, erff
, erfc
, erfcf
—error functionSynopsis
#include <math.h> double erf(double x); float erff(float x); double erfc(double x); float erfcf(float x);
Description
erf
calculates an approximation to the “error function”,
which estimates the probability that an observation will fall within
x standard deviations of the mean (assuming a normal
distribution).
erfc
calculates the complementary probability; that is,
erfc(x)
is 1 - erf(x)
. erfc
is computed directly,
so that you can use it to avoid the loss of precision that would
result from subtracting large probabilities (on large x) from 1.
erff
and erfcf
differ from erf
and erfc
only in the
argument and result types.
Returns
For positive arguments, erf
and all its variants return a
probability—a number between 0 and 1.
Portability
None of the variants of erf
are ANSI C.
exp
, expf
—exponentialSynopsis
#include <math.h> double exp(double x); float expf(float x);
Description
exp
and expf
calculate the exponential of x, that is,
e raised to the power x (where e
is the base of the natural system of logarithms, approximately 2.71828).
You can use the (non-ANSI) function matherr
to specify
error handling for these functions.
Returns
On success, exp
and expf
return the calculated value.
If the result underflows, the returned value is 0
. If the
result overflows, the returned value is HUGE_VAL
. In
either case, errno
is set to ERANGE
.
Portability
exp
is ANSI C. expf
is an extension.
exp2
, exp2f
–exponential, base 2Synopsis
#include <math.h> double exp2(double x); float exp2f(float x);
Description
exp2
and exp2f
calculate 2 ^ x, that is,
2 raised to the power x.
You can use the (non-ANSI) function matherr
to specify
error handling for these functions.
Returns
On success, exp2
and exp2f
return the calculated value.
If the result underflows, the returned value is 0
. If the
result overflows, the returned value is HUGE_VAL
. In
either case, errno
is set to ERANGE
.
Portability
ANSI C, POSIX.
expm1
, expm1f
—exponential minus 1Synopsis
#include <math.h> double expm1(double x); float expm1f(float x);
Description
expm1
and expm1f
calculate the exponential of x
and subtract 1, that is,
e raised to the power x minus 1 (where e
is the base of the natural system of logarithms, approximately
2.71828). The result is accurate even for small values of
x, where using exp(x)-1
would lose many
significant digits.
Returns
e raised to the power x, minus 1.
Portability
Neither expm1
nor expm1f
is required by ANSI C or by
the System V Interface Definition (Issue 2).
fabs
, fabsf
—absolute value (magnitude)Synopsis
#include <math.h> double fabs(double x); float fabsf(float x);
Description
fabs
and fabsf
calculate
the absolute value (magnitude) of the argument x, by direct
manipulation of the bit representation of x.
Returns
The calculated value is returned. No errors are detected.
Portability
fabs
is ANSI.
fabsf
is an extension.
fdim
, fdimf
–positive differenceSynopsis
#include <math.h> double fdim(double x, double y); float fdimf(float x, float y);
Description
The fdim
functions determine the positive difference between their
arguments, returning:
x - y if x > y, or
+0 if x <= y, or
NAN if either argument is NAN.
A range error may occur.
Returns
The fdim
functions return the positive difference value.
Portability
ANSI C, POSIX.
floor
, floorf
, ceil
, ceilf
—floor and ceilingSynopsis
#include <math.h> double floor(double x); float floorf(float x); double ceil(double x); float ceilf(float x);
Description
floor
and floorf
find
the nearest integer less than or equal to x.
ceil
and ceilf
find
the nearest integer greater than or equal to x.
Returns
floor
and ceil
return the integer result as a double.
floorf
and ceilf
return the integer result as a float.
Portability
floor
and ceil
are ANSI.
floorf
and ceilf
are extensions.
fma
, fmaf
–floating multiply addSynopsis
#include <math.h> double fma(double x, double y, double z); float fmaf(float x, float y, float z);
Description
The fma
functions compute (x * y) + z, rounded as one ternary
operation: they compute the value (as if) to infinite precision and round once
to the result format, according to the rounding mode characterized by the value
of FLT_ROUNDS. That is, they are supposed to do this: see below.
Returns
The fma
functions return (x * y) + z, rounded as one ternary
operation.
Bugs
This implementation does not provide the function that it should, purely
returning "(x * y) + z;" with no attempt at all to provide the
simulated infinite precision intermediates which are required. DO NOT USE THEM.
If double has enough more precision than float, then fmaf
should provide
the expected numeric results, as it does use double for the calculation. But
since this is not the case for all platforms, this manual cannot determine
if it is so for your case.
Portability
ANSI C, POSIX.
fmax
, fmaxf
–maximumSynopsis
#include <math.h> double fmax(double x, double y); float fmaxf(float x, float y);
Description
The fmax
functions determine the maximum numeric value of their arguments.
NaN arguments are treated as missing data: if one argument is a NaN and the
other numeric, then the fmax
functions choose the numeric value.
Returns
The fmax
functions return the maximum numeric value of their arguments.
Portability
ANSI C, POSIX.
fmin
, fminf
–minimumSynopsis
#include <math.h> double fmin(double x, double y); float fminf(float x, float y);
Description
The fmin
functions determine the minimum numeric value of their arguments.
NaN arguments are treated as missing data: if one argument is a NaN and the
other numeric, then the fmin
functions choose the numeric value.
Returns
The fmin
functions return the minimum numeric value of their arguments.
Portability
ANSI C, POSIX.
fmod
, fmodf
—floating-point remainder (modulo)Synopsis
#include <math.h> double fmod(double x, double y) float fmodf(float x, float y)
Description
The fmod
and fmodf
functions compute the floating-point
remainder of x/y (x modulo y).
Returns
The fmod
function returns the value
x-i*y,
for the largest integer i such that, if y is nonzero, the
result has the same sign as x and magnitude less than the
magnitude of y.
fmod(x,0)
returns NaN, and sets errno
to EDOM
.
You can modify error treatment for these functions using matherr
.
Portability
fmod
is ANSI C. fmodf
is an extension.
frexp
, frexpf
—split floating-point numberSynopsis
#include <math.h> double frexp(double val, int *exp); float frexpf(float val, int *exp);
Description
All nonzero, normal numbers can be described as m * 2**p.
frexp
represents the double val as a mantissa m
and a power of two p. The resulting mantissa will always
be greater than or equal to 0.5
, and less than 1.0
(as
long as val is nonzero). The power of two will be stored
in *
exp.
m and p are calculated so that
val is m times 2
to the power p.
frexpf
is identical, other than taking and returning
floats rather than doubles.
Returns
frexp
returns the mantissa m. If val is 0
, infinity,
or Nan, frexp
will set *
exp to 0
and return val.
Portability
frexp
is ANSI.
frexpf
is an extension.
gamma
, gammaf
, lgamma
, lgammaf
, gamma_r
, gammaf_r
, lgamma_r
, lgammaf_r
, tgamma
, and tgammaf
–logarithmic and plain gamma functionsSynopsis
#include <math.h> double gamma(double x); float gammaf(float x); double lgamma(double x); float lgammaf(float x); double gamma_r(double x, int *signgamp); float gammaf_r(float x, int *signgamp); double lgamma_r(double x, int *signgamp); float lgammaf_r(float x, int *signgamp); double tgamma(double x); float tgammaf(float x);
Description
gamma
calculates
the natural logarithm of the gamma function of x. The gamma function
(exp(gamma(x))
) is a generalization of factorial, and retains
the property that
exp(gamma(N))
is equivalent to N*exp(gamma(N-1))
.
Accordingly, the results of the gamma function itself grow very
quickly. gamma
is defined as
the natural log of the gamma function, rather than the gamma function
itself,
to extend the useful range of results representable.
The sign of the result is returned in the global variable signgam
,
which is declared in math.h.
gammaf
performs the same calculation as gamma
, but uses and
returns float
values.
lgamma
and lgammaf
are alternate names for gamma
and
gammaf
. The use of lgamma
instead of gamma
is a reminder
that these functions compute the log of the gamma function, rather
than the gamma function itself.
The functions gamma_r
, gammaf_r
, lgamma_r
, and
lgammaf_r
are just like gamma
, gammaf
, lgamma
, and
lgammaf
, respectively, but take an additional argument. This
additional argument is a pointer to an integer. This additional
argument is used to return the sign of the result, and the global
variable signgam
is not used. These functions may be used for
reentrant calls (but they will still set the global variable errno
if an error occurs).
tgamma
and tgammaf
are the "true gamma" functions, returning
the gamma function of x–without a logarithm.
(They are apparently so named because of the prior existence of the old,
poorly-named gamma
functions which returned the log of gamma up
through BSD 4.2.)
Returns
Normally, the computed result is returned.
When x is a nonpositive integer, gamma
returns HUGE_VAL
and errno
is set to EDOM
. If the result overflows, gamma
returns HUGE_VAL
and errno
is set to ERANGE
.
You can modify this error treatment using matherr
.
Portability
Neither gamma
nor gammaf
is ANSI C. It is better not to use either
of these; use lgamma
or tgamma
instead.
lgamma
, lgammaf
, tgamma
, and tgammaf
are nominally C standard
in terms of the base return values, although the matherr
error-handling
is not standard, nor is the signgam global for lgamma
.
hypot
, hypotf
—distance from originSynopsis
#include <math.h> double hypot(double x, double y); float hypotf(float x, float y);
Description
hypot
calculates the Euclidean distance
sqrt(x*x + y*y)
between the origin (0,0) and a point represented by the
Cartesian coordinates (x,y). hypotf
differs only
in the type of its arguments and result.
Returns
Normally, the distance value is returned. On overflow,
hypot
returns HUGE_VAL
and sets errno
to
ERANGE
.
You can change the error treatment with matherr
.
Portability
hypot
and hypotf
are not ANSI C.
ilogb
, ilogbf
—get exponent of floating-point numberSynopsis
#include <math.h> int ilogb(double val); int ilogbf(float val);
Description
All nonzero, normal numbers can be described as m *
2**p. ilogb
and ilogbf
examine the argument
val, and return p. The functions frexp
and
frexpf
are similar to ilogb
and ilogbf
, but also
return m.
Returns
ilogb
and ilogbf
return the power of two used to form the
floating-point argument.
If val is 0
, they return FP_ILOGB0
.
If val is infinite, they return INT_MAX
.
If val is NaN, they return FP_ILOGBNAN
.
(FP_ILOGB0
and FP_ILOGBNAN
are defined in math.h, but in turn are
defined as INT_MIN or INT_MAX from limits.h. The value of FP_ILOGB0 may be
either INT_MIN or -INT_MAX. The value of FP_ILOGBNAN may be either INT_MAX or
INT_MIN.)
Portability
C99, POSIX
infinity
, infinityf
–representation of infinitySynopsis
#include <math.h> double infinity(void); float infinityf(void);
Description
infinity
and infinityf
return the special number IEEE
infinity in double- and single-precision arithmetic
respectively.
Portability
infinity
and infinityf
are neither standard C nor POSIX. C and
POSIX require macros HUGE_VAL and HUGE_VALF to be defined in math.h, which
Newlib defines to be infinities corresponding to these archaic infinity()
and infinityf() functions in floating-point implementations which do have
infinities.
Next: fpclassify, Previous: infinity, Up: Math [Contents][Index]
isgreater
, isgreaterequal
, isless
, islessequal
, islessgreater
, and isunordered
–comparison macrosSynopsis
#include <math.h> int isgreater(real-floating x, real-floating y); int isgreaterequal(real-floating x, real-floating y); int isless(real-floating x, real-floating y); int islessequal(real-floating x, real-floating y); int islessgreater(real-floating x, real-floating y); int isunordered(real-floating x, real-floating y);
Description
isgreater
, isgreaterequal
, isless
, islessequal
,
islessgreater
, and isunordered
are macros defined for use in
comparing floating-point numbers without raising any floating-point
exceptions.
The relational operators (i.e. <, >, <=, and >=) support the usual mathematical relationships between numeric values. For any ordered pair of numeric values exactly one of the relationships–less, greater, and equal–is true. Relational operators may raise the "invalid" floating-point exception when argument values are NaNs. For a NaN and a numeric value, or for two NaNs, just the unordered relationship is true (i.e., if one or both of the arguments a NaN, the relationship is called unordered). The specified macros are quiet (non floating-point exception raising) versions of the relational operators, and other comparison macros that facilitate writing efficient code that accounts for NaNs without suffering the "invalid" floating-point exception. In the synopses shown, "real-floating" indicates that the argument is an expression of real floating type.
Please note that saying that the macros do not raise floating-point exceptions, it is referring to the function that they are performing. It is certainly possible to give them an expression which causes an exception. For example:
NaN < 1.0
causes an "invalid" exception,
isless(NaN, 1.0)
does not, and
isless(NaN*0., 1.0)
causes an exception due to the "NaN*0.", but not from the resultant reduced comparison of isless(NaN, 1.0).
Returns
No floating-point exceptions are raised for any of the macros.
The isgreater
macro returns the value of (x) > (y).
The isgreaterequal
macro returns the value of (x) >= (y).
The isless
macro returns the value of (x) < (y).
The islessequal
macro returns the value of (x) <= (y).
The islessgreater
macro returns the value of (x) < (y) || (x) > (y).
The isunordered
macro returns 1 if either of its arguments is NaN and 0 otherwise.
Portability
C99, POSIX.
fpclassify
, isfinite
, isinf
, isnan
, and isnormal
–floating-point classification macros; finite
, finitef
, isinf
, isinff
, isnan
, isnanf
–test for exceptional numbersSynopsis
[C99 standard macros:] #include <math.h> int fpclassify(real-floating x); int isfinite(real-floating x); int isinf(real-floating x); int isnan(real-floating x); int isnormal(real-floating x); [Archaic SUSv2 functions:] #include <ieeefp.h> int isnan(double arg); int isinf(double arg); int finite(double arg); int isnanf(float arg); int isinff(float arg); int finitef(float arg);
Description
fpclassify
, isfinite
, isinf
, isnan
, and isnormal
are macros
defined for use in classifying floating-point numbers. This is a help because
of special "values" like NaN and infinities. In the synopses shown,
"real-floating" indicates that the argument is an expression of real floating
type. These function-like macros are C99 and POSIX-compliant, and should be
used instead of the now-archaic SUSv2 functions.
The fpclassify
macro classifies its argument value as NaN, infinite, normal,
subnormal, zero, or into another implementation-defined category. First, an
argument represented in a format wider than its semantic type is converted to
its semantic type. Then classification is based on the type of the argument.
The fpclassify
macro returns the value of the number classification macro
appropriate to the value of its argument:
FP_INFINITE
x is either plus or minus infinity;
FP_NAN
x is "Not A Number" (plus or minus);
FP_NORMAL
x is a "normal" number (i.e. is none of the other special forms);
FP_SUBNORMAL
x is too small be stored as a regular normalized number (i.e. loss of precision is likely); or
FP_ZERO
x is 0 (either plus or minus).
The "is
" set of macros provide a useful set of shorthand ways for
classifying floating-point numbers, providing the following equivalent
relations:
isfinite
(x)
returns non-zero if x is finite. (It is equivalent to
(fpclassify
(x) != FP_INFINITE && fpclassify
(x) != FP_NAN).)
isinf
(x)
returns non-zero if x is infinite. (It is equivalent to
(fpclassify
(x) == FP_INFINITE).)
isnan
(x)
returns non-zero if x is NaN. (It is equivalent to
(fpclassify
(x) == FP_NAN).)
isnormal
(x)
returns non-zero if x is normal. (It is equivalent to
(fpclassify
(x) == FP_NORMAL).)
The archaic SUSv2 functions provide information on the floating-point argument supplied.
There are five major number formats ("exponent" referring to the biased exponent in the binary-encoded number):
zero
A number which contains all zero bits, excluding the sign bit.
subnormal
A number with a zero exponent but a nonzero fraction.
normal
A number with an exponent and a fraction.
infinity
A number with an all 1’s exponent and a zero fraction.
NAN
A number with an all 1’s exponent and a nonzero fraction.
isnan
returns 1 if the argument is a nan. isinf
returns 1 if the argument is infinity. finite
returns 1 if the
argument is zero, subnormal or normal.
The isnanf
, isinff
and finitef
functions perform the same
operations as their isnan
, isinf
and finite
counterparts, but on single-precision floating-point numbers.
It should be noted that the C99 standard dictates that isnan
and isinf
are macros that operate on multiple types of
floating-point. The SUSv2 standard declares isnan
as
a function taking double. Newlib has decided to declare
them both as macros in math.h and as functions in ieeefp.h to
maintain backward compatibility.
Returns
The fpclassify macro returns the value corresponding to the appropriate FP_ macro.
The isfinite macro returns nonzero if x is finite, else 0.
The isinf macro returns nonzero if x is infinite, else 0.
The isnan macro returns nonzero if x is an NaN, else 0.
The isnormal macro returns nonzero if x has a normal value, else 0.
Portability
math.h macros are C99, POSIX.
ieeefp.h funtions are outdated and should be avoided.
Next: log, Previous: fpclassify, Up: Math [Contents][Index]
ldexp
, ldexpf
—load exponentSynopsis
#include <math.h> double ldexp(double val, int exp); float ldexpf(float val, int exp);
Description
ldexp
calculates the value
val times 2 to the power exp.
ldexpf
is identical, save that it takes and returns float
rather than double
values.
Returns
ldexp
returns the calculated value.
Underflow and overflow both set errno
to ERANGE
.
On underflow, ldexp
and ldexpf
return 0.0.
On overflow, ldexp
returns plus or minus HUGE_VAL
.
Portability
ldexp
is ANSI. ldexpf
is an extension.
log
, logf
—natural logarithmsSynopsis
#include <math.h> double log(double x); float logf(float x);
Description
Return the natural logarithm of x, that is, its logarithm base e
(where e is the base of the natural system of logarithms, 2.71828…).
log
and logf
are identical save for the return and argument types.
You can use the (non-ANSI) function matherr
to specify error
handling for these functions.
Returns
Normally, returns the calculated value. When x is zero, the
returned value is -HUGE_VAL
and errno
is set to ERANGE
.
When x is negative, the returned value is NaN (not a number) and
errno
is set to EDOM
. You can control the error behavior via
matherr
.
Portability
log
is ANSI. logf
is an extension.
log10
, log10f
—base 10 logarithmsSynopsis
#include <math.h> double log10(double x); float log10f(float x);
Description
log10
returns the base 10 logarithm of x.
It is implemented as log(x) / log(10)
.
log10f
is identical, save that it takes and returns float
values.
Returns
log10
and log10f
return the calculated value.
See the description of log
for information on errors.
Portability
log10
is ANSI C. log10f
is an extension.
log1p
, log1pf
—log of 1 + x
Synopsis
#include <math.h> double log1p(double x); float log1pf(float x);
Description
log1p
calculates
the natural logarithm of 1+x
. You can use log1p
rather
than ‘log(1+x)
’ for greater precision when x is very
small.
log1pf
calculates the same thing, but accepts and returns
float
values rather than double
.
Returns
log1p
returns a double
, the natural log of 1+x
.
log1pf
returns a float
, the natural log of 1+x
.
Portability
Neither log1p
nor log1pf
is required by ANSI C or by the System V
Interface Definition (Issue 2).
log2
, log2f
–base 2 logarithmSynopsis
#include <math.h> double log2(double x); float log2f(float x);
Description
The log2
functions compute the base-2 logarithm of x. A domain error
occurs if the argument is less than zero. A range error occurs if the
argument is zero.
The Newlib implementations are not full, intrinisic calculations, but
rather are derivatives based on log
. (Accuracy might be slightly off from
a direct calculation.) In addition to functions, they are also implemented as
macros defined in math.h:
#define log2(x) (log (x) / _M_LN2) #define log2f(x) (logf (x) / (float) _M_LN2)
To use the functions instead, just undefine the macros first.
You can use the (non-ANSI) function matherr
to specify error
handling for these functions, indirectly through the respective log
function.
Returns
The log2
functions return
log base-2(x)
on success.
When x is zero, the
returned value is -HUGE_VAL
and errno
is set to ERANGE
.
When x is negative, the returned value is NaN (not a number) and
errno
is set to EDOM
. You can control the error behavior via
matherr
.
Portability
C99, POSIX, System V Interface Definition (Issue 6).
logb
, logbf
–get exponent of floating-point numberSynopsis
#include <math.h> double logb(double x); float logbf(float x);
Description
The logb
functions extract the exponent of x, as a signed integer value
in floating-point format. If x is subnormal it is treated as though it were
normalized; thus, for positive finite x,
1 <= (x * FLT_RADIX to the power (-logb(x))) < FLT_RADIX.
A domain error may occur if the argument is zero.
In this floating-point implementation, FLT_RADIX is 2. Which also means
that for finite x, logb
(x) = floor
(log2
(fabs
(x))).
All nonzero, normal numbers can be described as
m * 2**p, where 1.0 <= m < 2.0.
The logb
functions examine the argument x, and return p.
The frexp
functions are similar to the logb
functions, but
returning m adjusted to the interval [.5, 1) or 0, and p+1.
Returns
When x is:
+inf or -inf, +inf is returned;
NaN, NaN is returned;
0, -inf is returned, and the divide-by-zero exception is raised;
otherwise, the logb
functions return the signed exponent of x.
Portability
ANSI C, POSIX
See Also
frexp, ilogb
lrint
, lrintf
, llrint
, llrintf
–round to integerSynopsis
#include <math.h> long int lrint(double x); long int lrintf(float x); long long int llrint(double x); long long int llrintf(float x);
Description
The lrint
and llrint
functions round their argument to the nearest
integer value, using the current rounding direction. If the rounded value is
outside the range of the return type, the numeric result is unspecified. A
range error may occur if the magnitude of x is too large.
The "inexact" floating-point exception is raised in implementations that
support it when the result differs in value from the argument (i.e., when
a fraction actually has been truncated).
Returns
x rounded to an integral value, using the current rounding direction.
See Also
lround
Portability
ANSI C, POSIX
lround
, lroundf
, llround
, llroundf
–round to integer, to nearestSynopsis
#include <math.h> long int lround(double x); long int lroundf(float x); long long int llround(double x); long long int llroundf(float x);
Description
The lround
and llround
functions round their argument to the
nearest integer value, rounding halfway cases away from zero, regardless
of the current rounding direction. If the rounded value is outside the
range of the return type, the numeric result is unspecified (depending
upon the floating-point implementation, not the library). A range
error may occur if the magnitude of x is too large.
Returns
x rounded to an integral value as an integer.
See Also
See the round
functions for the return being the same floating-point type
as the argument. lrint
, llrint
.
Portability
ANSI C, POSIX
matherr
—modifiable math error handlerSynopsis
#include <math.h> int matherr(struct exception *e);
Description
matherr
is called whenever a math library function generates an error.
You can replace matherr
by your own subroutine to customize
error treatment. The customized matherr
must return 0 if
it fails to resolve the error, and non-zero if the error is resolved.
When matherr
returns a nonzero value, no error message is printed
and the value of errno
is not modified. You can accomplish either
or both of these things in your own matherr
using the information
passed in the structure *e
.
This is the exception
structure (defined in ‘math.h
’):
struct exception { int type; char *name; double arg1, arg2, retval; int err; };
The members of the exception structure have the following meanings:
type
The type of mathematical error that occured; macros encoding error
types are also defined in ‘math.h
’.
name
a pointer to a null-terminated string holding the name of the math library function where the error occurred.
arg1, arg2
The arguments which caused the error.
retval
The error return value (what the calling function will return).
err
If set to be non-zero, this is the new value assigned to errno
.
The error types defined in ‘math.h
’ represent possible mathematical
errors as follows:
DOMAIN
An argument was not in the domain of the function; e.g. log(-1.0)
.
SING
The requested calculation would result in a singularity; e.g. pow(0.0,-2.0)
OVERFLOW
A calculation would produce a result too large to represent; e.g.
exp(1000.0)
.
UNDERFLOW
A calculation would produce a result too small to represent; e.g.
exp(-1000.0)
.
TLOSS
Total loss of precision. The result would have no significant digits;
e.g. sin(10e70)
.
PLOSS
Partial loss of precision.
Returns
The library definition for matherr
returns 0
in all cases.
You can change the calling function’s result from a customized matherr
by modifying e->retval
, which propagates backs to the caller.
If matherr
returns 0
(indicating that it was not able to resolve
the error) the caller sets errno
to an appropriate value, and prints
an error message.
Portability
matherr
is not ANSI C.
modf
, modff
—split fractional and integer partsSynopsis
#include <math.h> double modf(double val, double *ipart); float modff(float val, float *ipart);
Description
modf
splits the double val apart into an integer part
and a fractional part, returning the fractional part and
storing the integer part in *ipart
. No rounding
whatsoever is done; the sum of the integer and fractional
parts is guaranteed to be exactly equal to val. That
is, if realpart = modf(val, &intpart); then
‘realpart+intpart
’ is the same as val.
modff
is identical, save that it takes and returns
float
rather than double
values.
Returns
The fractional part is returned. Each result has the same
sign as the supplied argument val.
Portability
modf
is ANSI C. modff
is an extension.
nan
, nanf
—representation of “Not a Number”Synopsis
#include <math.h> double nan(const char *); float nanf(const char *);
Description
nan
and nanf
return an IEEE NaN (Not a Number) in
double- and single-precision arithmetic respectively. The
argument is currently disregarded.
nearbyint
, nearbyintf
–round to integerSynopsis
#include <math.h> double nearbyint(double x); float nearbyintf(float x);
Description
The nearbyint
functions round their argument to an integer value in
floating-point format, using the current rounding direction and
(supposedly) without raising the "inexact" floating-point exception.
See the rint
functions for the same function with the "inexact"
floating-point exception being raised when appropriate.
Bugs
Newlib does not support the floating-point exception model, so that
the floating-point exception control is not present and thereby what may
be seen will be compiler and hardware dependent in this regard.
The Newlib nearbyint
functions are identical to the rint
functions with respect to the floating-point exception behavior, and
will cause the "inexact" exception to be raised for most targets.
Returns
x rounded to an integral value, using the current rounding direction.
Portability
ANSI C, POSIX
See Also
rint
, round
nextafter
, nextafterf
—get next numberSynopsis
#include <math.h> double nextafter(double val, double dir); float nextafterf(float val, float dir);
Description
nextafter
returns the double-precision floating-point number
closest to val in the direction toward dir. nextafterf
performs the same operation in single precision. For example,
nextafter(0.0,1.0)
returns the smallest positive number which is
representable in double precision.
Returns
Returns the next closest number to val in the direction toward
dir.
Portability
Neither nextafter
nor nextafterf
is required by ANSI C
or by the System V Interface Definition (Issue 2).
pow
, powf
—x to the power ySynopsis
#include <math.h> double pow(double x, double y); float powf(float x, float y);
Description
pow
and powf
calculate x raised to the exponent y.
Returns
On success, pow
and powf
return the value calculated.
When the argument values would produce overflow, pow
returns HUGE_VAL
and set errno
to ERANGE
. If the
argument x passed to pow
or powf
is a negative
noninteger, and y is also not an integer, then errno
is set to EDOM
. If x and y are both 0, then
pow
and powf
return 1
.
You can modify error handling for these functions using matherr
.
Portability
pow
is ANSI C. powf
is an extension.
remainder
, remainderf
—round and remainderSynopsis
#include <math.h> double remainder(double x, double y); float remainderf(float x, float y);
Description
remainder
and remainderf
find the remainder of
x/y; this value is in the range -y/2 .. +y/2.
Returns
remainder
returns the integer result as a double.
Portability
remainder
is a System V release 4.
remainderf
is an extension.
remquo
, remquof
–remainder and part of quotientSynopsis
#include <math.h> double remquo(double x, double y, int *quo); float remquof(float x, float y, int *quo);
Description
The remquo
functions compute the same remainder as the remainder
functions; this value is in the range -y/2 ... +y/2. In the object
pointed to by quo
they store a value whose sign is the sign of x
/y
and whose magnitude is congruent modulo 2**n to the magnitude of the integral
quotient of x
/y
. (That is, quo
is given the n lsbs of the
quotient, not counting the sign.) This implementation uses n=31 if int is 32
bits or more, otherwise, n is 1 less than the width of int.
For example:
remquo(-29.0, 3.0, &quo)
returns -1.0 and sets quo=10, and
remquo(-98307.0, 3.0, &quo)
returns -0.0 and sets quo=-32769, although for 16-bit int, quo=-1. In the latter case, the actual quotient of -(32769=0x8001) is reduced to -1 because of the 15-bit limitation for the quotient.
Returns
When either argument is NaN, NaN is returned. If y is 0 or x is
infinite (and neither is NaN), a domain error occurs (i.e. the "invalid"
floating point exception is raised or errno is set to EDOM), and NaN is
returned.
Otherwise, the remquo
functions return x REM y.
Bugs
IEEE754-2008 calls for remquo
(subnormal, inf) to cause the "underflow"
floating-point exception. This implementation does not.
Portability
C99, POSIX.
rint
, rintf
–round to integerSynopsis
#include <math.h> double rint(double x); float rintf(float x);
Description
The rint
functions round their argument to an integer value in
floating-point format, using the current rounding direction. They
raise the "inexact" floating-point exception if the result differs
in value from the argument. See the nearbyint
functions for the
same function with the "inexact" floating-point exception never being
raised. Newlib does not directly support floating-point exceptions.
The rint
functions are written so that the "inexact" exception is
raised in hardware implementations that support it, even though Newlib
does not provide access.
Returns
x rounded to an integral value, using the current rounding direction.
Portability
ANSI C, POSIX
See Also
nearbyint
, round
round
, roundf
–round to integer, to nearestSynopsis
#include <math.h> double round(double x); float roundf(float x);
Description
The round
functions round their argument to the nearest integer
value in floating-point format, rounding halfway cases away from zero,
regardless of the current rounding direction. (While the "inexact"
floating-point exception behavior is unspecified by the C standard, the
round
functions are written so that "inexact" is not raised if the
result does not equal the argument, which behavior is as recommended by
IEEE 754 for its related functions.)
Returns
x rounded to an integral value.
Portability
ANSI C, POSIX
See Also
nearbyint
, rint
scalbn
, scalbnf
, scalbln
, scalblnf
–scale by power of FLT_RADIX (=2)Synopsis
#include <math.h> double scalbn(double x, int n); float scalbnf(float x, int n); double scalbln(double x, long int n); float scalblnf(float x, long int n);
Description
The scalbn
and scalbln
functions compute
x times FLT_RADIX to the power n.
efficiently. The result is computed by manipulating the exponent, rather than
by actually performing an exponentiation or multiplication. In this
floating-point implementation FLT_RADIX=2, which makes the scalbn
functions equivalent to the ldexp
functions.
Returns
x times 2 to the power n. A range error may occur.
Portability
ANSI C, POSIX
See Also
ldexp
signbit
–Does floating-point number have negative sign?Synopsis
#include <math.h> int signbit(real-floating x);
Description
The signbit
macro determines whether the sign of its argument value is
negative. The macro reports the sign of all values, including infinities,
zeros, and NaNs. If zero is unsigned, it is treated as positive. As shown in
the synopsis, the argument is "real-floating," meaning that any of the real
floating-point types (float, double, etc.) may be given to it.
Note that because of the possibilities of signed 0 and NaNs, the expression
"x < 0.0" does not give the same result as signbit
in all cases.
Returns
The signbit
macro returns a nonzero value if and only if the sign of its
argument value is negative.
Portability
C99, POSIX.
sin
, sinf
, cos
, cosf
—sine or cosineSynopsis
#include <math.h> double sin(double x); float sinf(float x); double cos(double x); float cosf(float x);
Description
sin
and cos
compute (respectively) the sine and cosine
of the argument x. Angles are specified in radians.
sinf
and cosf
are identical, save that they take and
return float
values.
Returns
The sine or cosine of x is returned.
Portability
sin
and cos
are ANSI C.
sinf
and cosf
are extensions.
sinh
, sinhf
—hyperbolic sineSynopsis
#include <math.h> double sinh(double x); float sinhf(float x);
Description
sinh
computes the hyperbolic sine of the argument x.
Angles are specified in radians. sinh
(x) is defined as
(exp(x) - exp(-x))/2
sinhf
is identical, save that it takes and returns float
values.
Returns
The hyperbolic sine of x is returned.
When the correct result is too large to be representable (an
overflow), sinh
returns HUGE_VAL
with the
appropriate sign, and sets the global value errno
to
ERANGE
.
You can modify error handling for these functions with matherr
.
Portability
sinh
is ANSI C.
sinhf
is an extension.
sqrt
, sqrtf
—positive square rootSynopsis
#include <math.h> double sqrt(double x); float sqrtf(float x);
Description
sqrt
computes the positive square root of the argument.
You can modify error handling for this function with
matherr
.
Returns
On success, the square root is returned. If x is real and
positive, then the result is positive. If x is real and
negative, the global value errno
is set to EDOM
(domain error).
Portability
sqrt
is ANSI C. sqrtf
is an extension.
tan
, tanf
—tangentSynopsis
#include <math.h> double tan(double x); float tanf(float x);
Description
tan
computes the tangent of the argument x.
Angles are specified in radians.
tanf
is identical, save that it takes and returns float
values.
Returns
The tangent of x is returned.
Portability
tan
is ANSI. tanf
is an extension.
tanh
, tanhf
—hyperbolic tangentSynopsis
#include <math.h> double tanh(double x); float tanhf(float x);
Description
tanh
computes the hyperbolic tangent of
the argument x. Angles are specified in radians.
tanh(x)
is defined as
sinh(x)/cosh(x)
tanhf
is identical, save that it takes and returns float
values.
Returns
The hyperbolic tangent of x is returned.
Portability
tanh
is ANSI C. tanhf
is an extension.
trunc
, truncf
–round to integer, towards zeroSynopsis
#include <math.h> double trunc(double x); float truncf(float x);
Description
The trunc
functions round their argument to the integer value, in
floating format, nearest to but no larger in magnitude than the
argument, regardless of the current rounding direction. (While the
"inexact" floating-point exception behavior is unspecified by the C
standard, the trunc
functions are written so that "inexact" is not
raised if the result does not equal the argument, which behavior is as
recommended by IEEE 754 for its related functions.)
Returns
x truncated to an integral value.
Portability
ANSI C, POSIX
Next: Reentrancy, Previous: Math, Up: Top [Contents][Index]
This chapter groups the complex mathematical functions. The corresponding definitions and declarations are in complex.h. Functions and documentations are taken from NetBSD.
• cabs: | Complex absolute value | |
• cacos: | Complex arc cosine | |
• cacosh: | Complex arc hyperbolic cosine | |
• carg: | Argument (also called phase angle) | |
• casin: | Complex arc sine | |
• casinh: | Complex arc hyperbolic sine | |
• catan: | Complex arc tangent | |
• catanh: | Complex arc hyperbolic tangent | |
• ccos: | Complex cosine | |
• ccosh: | Complex hyperbolic cosine | |
• cexp: | Complex exponent | |
• cimag: | Imaginary part | |
• clog: | Complex natural (base e) logarithm | |
• conj: | Complex conjugate | |
• cpow: | Complex power function | |
• cproj: | Compute a projection on the Riemann sphere | |
• creal: | Real part | |
• csin: | Complex sine | |
• csinh: | Complex hyperbolic sine | |
• csqrt: | Complex square root | |
• ctan: | Complex tangent | |
• ctanh: | Complex hyperbolic tangent |
cabs
, cabsf
—complex absolute-valueSynopsis
#include <complex.h> double cabs(double complex z); float cabsf(float complex z);
Description
These functions compute compute the complex absolute value
(also called norm, modulus, or magnitude) of z.
cabsf
is identical to cabs
, except that it performs
its calculations on floats complex
.
Returns
The cabs functions return the complex absolute value.
Portability
cabs
and cabsf
are ISO C99
cacos
, cacosf
—complex arc cosineSynopsis
#include <complex.h> double complex cacos(double complex z); float complex cacosf(float complex z);
Description
These functions compute the complex arc cosine of z,
with branch cuts outside the interval [-1, +1] along the real axis.
cacosf
is identical to cacos
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex arc cosine value, in the range
of a strip mathematically unbounded along the imaginary axis
and in the interval [0, pi] along the real axis.
Portability
cacos
and cacosf
are ISO C99
cacosh
, cacoshf
—complex arc hyperbolic cosineSynopsis
#include <complex.h> double complex cacosh(double complex z); float complex cacoshf(float complex z);
Description
These functions compute the complex arc hyperbolic cosine of z,
with a branch cut at values less than 1 along the real axis.
cacoshf
is identical to cacosh
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex arc hyperbolic cosine value,
in the range of a half-strip of non-negative values along the
real axis and in the interval [-i * pi, +i * pi] along the
imaginary axis.
Portability
cacosh
and cacoshf
are ISO C99
carg
, cargf
—argument (phase angle)Synopsis
#include <complex.h> double carg(double complex z); float cargf(float complex z);
Description
These functions compute the argument (also called phase angle)
of z, with a branch cut along the negative real axis.
cargf
is identical to carg
, except that it performs
its calculations on floats complex
.
Returns
The carg functions return the value of the argument in the
interval [-pi, +pi]
Portability
carg
and cargf
are ISO C99
casin
, casinf
—complex arc sineSynopsis
#include <complex.h> double complex casin(double complex z); float complex casinf(float complex z);
Description
These functions compute the complex arc sine of z,
with branch cuts outside the interval [-1, +1] along the real axis.
casinf
is identical to casin
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex arc sine value, in the range
of a strip mathematically unbounded along the imaginary axis
and in the interval [-pi/2, +pi/2] along the real axis.
Portability
casin
and casinf
are ISO C99
casinh
, casinhf
—complex arc hyperbolic sineSynopsis
#include <complex.h> double complex casinh(double complex z); float complex casinhf(float complex z);
Description
These functions compute the complex arc hyperbolic sine of z,
with branch cuts outside the interval [-i, +i] along the
imaginary axis.
casinhf
is identical to casinh
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex arc hyperbolic sine value,
in the range of a strip mathematically unbounded along the
real axis and in the interval [-i*p/2, +i*p/2] along the
imaginary axis.
Portability
casinh
and casinhf
are ISO C99
catan
, catanf
—complex arc tangentSynopsis
#include <complex.h> double complex catan(double complex z); float complex catanf(float complex z);
Description
These functions compute the complex arc tangent of z,
with branch cuts outside the interval [-i, +i] along the
imaginary axis.
catanf
is identical to catan
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex arc tangent value, in the range
of a strip mathematically unbounded along the imaginary axis
and in the interval [-pi/2, +pi/2] along the real axis.
Portability
catan
and catanf
are ISO C99
catanh
, catanhf
—complex arc hyperbolic tangentSynopsis
#include <complex.h> double complex catanh(double complex z); float complex catanhf(float complex z);
Description
These functions compute the complex arc hyperbolic tan of z,
with branch cuts outside the interval [-1, +1] along the
real axis.
catanhf
is identical to catanh
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex arc hyperbolic tangent value,
in the range of a strip mathematically unbounded along the
real axis and in the interval [-i*p/2, +i*p/2] along the
imaginary axis.
Portability
catanh
and catanhf
are ISO C99
ccos
, ccosf
—complex cosineSynopsis
#include <complex.h> double complex ccos(double complex z); float complex ccosf(float complex z);
Description
These functions compute the complex cosine of z.
ccosf
is identical to ccos
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex cosine value.
Portability
ccos
and ccosf
are ISO C99
ccosh
, ccoshf
—complex hyperbolic cosineSynopsis
#include <complex.h> double complex ccosh(double complex z); float complex ccoshf(float complex z);
Description
These functions compute the complex hyperbolic cosine of z.
ccoshf
is identical to ccosh
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex hyperbolic cosine value.
Portability
ccosh
and ccoshf
are ISO C99
cexp
, cexpf
—complex base-e exponentialSynopsis
#include <complex.h> double complex cexp(double complex z); float complex cexpf(float complex z);
Description
These functions compute the complex base-e exponential of z.
cexpf
is identical to cexp
, except that it performs
its calculations on floats complex
.
Returns
The cexp functions return the complex base-e exponential value.
Portability
cexp
and cexpf
are ISO C99
cimag
, cimagf
—imaginary partSynopsis
#include <complex.h> double cimag(double complex z); float cimagf(float complex z);
Description
These functions compute the imaginary part of z.
cimagf
is identical to cimag
, except that it performs
its calculations on floats complex
.
Returns
The cimag functions return the imaginary part value (as a real).
Portability
cimag
and cimagf
are ISO C99
clog
, clogf
—complex base-e logarithmSynopsis
#include <complex.h> double complex clog(double complex z); float complex clogf(float complex z);
Description
These functions compute the complex natural (base-e) logarithm
of z, with a branch cut along the negative real axis.
clogf
is identical to clog
, except that it performs
its calculations on floats complex
.
Returns
The clog functions return the complex natural logarithm value, in
the range of a strip mathematically unbounded along the real axis
and in the interval [-i*pi , +i*pi] along the imaginary axis.
Portability
clog
and clogf
are ISO C99
conj
, conjf
—complex conjugateSynopsis
#include <complex.h> double complex conj(double complex z); float complex conjf(float complex z);
Description
These functions compute the complex conjugate of z,
by reversing the sign of its imaginary part.
conjf
is identical to conj
, except that it performs
its calculations on floats complex
.
Returns
The conj functions return the complex conjugate value.
Portability
conj
and conjf
are ISO C99
cpow
, cpowf
—complex powerSynopsis
#include <complex.h> double complex cpow(double complex x, double complex y); float complex cpowf(float complex x, float complex y);
Description
The cpow functions compute the complex power function x^y
power, with a branch cut for the first parameter along the
negative real axis.
cpowf
is identical to cpow
, except that it performs
its calculations on floats complex
.
Returns
The cpow functions return the complex power function value.
Portability
cpow
and cpowf
are ISO C99
cproj
, cprojf
— Riemann sphere projectionSynopsis
#include <complex.h> double complex cproj(double complex z); float complex cprojf(float complex z);
Description
These functions compute a projection of z onto the Riemann
sphere: z projects to z except that all complex infinities
(even those with one infinite part and one NaN part) project
to positive infinity on the real axis. If z has an infinite part,
then cproj
(z) is equivalent to
INFINITY + I * copysign(0.0, cimag(z))
cprojf
is identical to cproj
, except that it performs
its calculations on floats complex
.
Returns
The cproj functions return the value of the projection onto
the Riemann sphere.
Portability
cproj
and cprojf
are ISO C99
creal
, crealf
—real partSynopsis
#include <complex.h> double creal(double complex z); float crealf(float complex z);
Description
These functions compute the real part of z.
crealf
is identical to creal
, except that it performs
its calculations on floats complex
.
Returns
The creal functions return the real part value.
Portability
creal
and crealf
are ISO C99
csin
, csinf
—complex sineSynopsis
#include <complex.h> double complex csin(double complex z); float complex csinf(float complex z);
Description
These functions compute the complex sine of z.
csinf
is identical to csin
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex sine value.
Portability
csin
and csinf
are ISO C99
csinh
, csinhf
—complex hyperbolic sineSynopsis
#include <complex.h> double complex csinh(double complex z); float complex csinhf(float complex z);
Description
These functions compute the complex hyperbolic sine of z.
ccoshf
is identical to ccosh
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex hyperbolic sine value.
Portability
csinh
and csinhf
are ISO C99
csqrt
, csqrtf
—complex square rootSynopsis
#include <complex.h> double complex csqrt(double complex z); float complex csqrtf(float complex z);
Description
These functions compute the complex square root of z, with
a branch cut along the negative real axis.
csqrtf
is identical to csqrt
, except that it performs
its calculations on floats complex
.
Returns
The csqrt functions return the complex square root value, in
the range of the right halfplane (including the imaginary axis).
Portability
csqrt
and csqrtf
are ISO C99
ctan
, ctanf
—complex tangentSynopsis
#include <complex.h> double complex ctan(double complex z); float complex ctanf(float complex z);
Description
These functions compute the complex tangent of z.
ctanf
is identical to ctan
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex tangent value.
Portability
ctan
and ctanf
are ISO C99
ctanh
, ctanf
—complex hyperbolic tangentSynopsis
#include <complex.h> double complex ctanh(double complex z); float complex ctanhf(float complex z);
Description
These functions compute the complex hyperbolic tangent of z.
ctanhf
is identical to ctanh
, except that it performs
its calculations on floats complex
.
Returns
These functions return the complex hyperbolic tangent value.
Portability
ctanh
and ctanhf
are ISO C99
Next: Long Double Functions, Previous: Complex, Up: Top [Contents][Index]
libm
When a libm function detects an exceptional case, errno
may be
set, the matherr
function may be called, and a error message
may be written to the standard error stream. This behavior may not
be reentrant.
With reentrant C libraries like the Red Hat newlib C library, errno
is
a macro which expands to the per-thread error value. This makes it thread
safe.
When the user provides his own matherr
function it must be
reentrant for the math library as a whole to be reentrant.
In normal debugged programs, there are usually no math subroutine
errors—and therefore no assignments to errno
and no matherr
calls; in that situation, the math functions behave reentrantly.
Next: Document Index, Previous: Reentrancy, Up: Top [Contents][Index]
libm
Currently, the full set of long double math functions is only provided on platforms where long double equals double. For such platforms, the long double math functions are implemented as calls to the double versions.
Previous: Long Double Functions, Up: Top [Contents][Index]
Jump to: | A C E F G H I J L M N O P R S T Y |
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Jump to: | A C E F G H I J L M N O P R S T Y |
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acos
, acosf
—arc cosineacosh
, acoshf
—inverse hyperbolic cosineasin
, asinf
—arc sineasinh
, asinhf
—inverse hyperbolic sineatan
, atanf
—arc tangentatan2
, atan2f
—arc tangent of y/xatanh
, atanhf
—inverse hyperbolic tangentjN
, jNf
, yN
, yNf
—Bessel functionscbrt
, cbrtf
—cube rootcopysign
, copysignf
—sign of y, magnitude of xcosh
, coshf
—hyperbolic cosineerf
, erff
, erfc
, erfcf
—error functionexp
, expf
—exponentialexp2
, exp2f
–exponential, base 2expm1
, expm1f
—exponential minus 1fabs
, fabsf
—absolute value (magnitude)fdim
, fdimf
–positive differencefloor
, floorf
, ceil
, ceilf
—floor and ceilingfma
, fmaf
–floating multiply addfmax
, fmaxf
–maximumfmin
, fminf
–minimumfmod
, fmodf
—floating-point remainder (modulo)frexp
, frexpf
—split floating-point numbergamma
, gammaf
, lgamma
, lgammaf
, gamma_r
, gammaf_r
, lgamma_r
, lgammaf_r
, tgamma
, and tgammaf
–logarithmic and plain gamma functionshypot
, hypotf
—distance from originilogb
, ilogbf
—get exponent of floating-point numberinfinity
, infinityf
–representation of infinityisgreater
, isgreaterequal
, isless
, islessequal
, islessgreater
, and isunordered
–comparison macrosfpclassify
, isfinite
, isinf
, isnan
, and isnormal
–floating-point classification macros; finite
, finitef
, isinf
, isinff
, isnan
, isnanf
–test for exceptional numbersldexp
, ldexpf
—load exponentlog
, logf
—natural logarithmslog10
, log10f
—base 10 logarithmslog1p
, log1pf
—log of 1 + x
log2
, log2f
–base 2 logarithmlogb
, logbf
–get exponent of floating-point numberlrint
, lrintf
, llrint
, llrintf
–round to integerlround
, lroundf
, llround
, llroundf
–round to integer, to nearestmatherr
—modifiable math error handlermodf
, modff
—split fractional and integer partsnan
, nanf
—representation of “Not a Number”nearbyint
, nearbyintf
–round to integernextafter
, nextafterf
—get next numberpow
, powf
—x to the power yremainder
, remainderf
—round and remainderremquo
, remquof
–remainder and part of quotientrint
, rintf
–round to integerround
, roundf
–round to integer, to nearestscalbn
, scalbnf
, scalbln
, scalblnf
–scale by power of FLT_RADIX (=2)signbit
–Does floating-point number have negative sign?sin
, sinf
, cos
, cosf
—sine or cosinesinh
, sinhf
—hyperbolic sinesqrt
, sqrtf
—positive square roottan
, tanf
—tangenttanh
, tanhf
—hyperbolic tangenttrunc
, truncf
–round to integer, towards zerocabs
, cabsf
—complex absolute-valuecacos
, cacosf
—complex arc cosinecacosh
, cacoshf
—complex arc hyperbolic cosinecarg
, cargf
—argument (phase angle)casin
, casinf
—complex arc sinecasinh
, casinhf
—complex arc hyperbolic sinecatan
, catanf
—complex arc tangentcatanh
, catanhf
—complex arc hyperbolic tangentccos
, ccosf
—complex cosineccosh
, ccoshf
—complex hyperbolic cosinecexp
, cexpf
—complex base-e exponentialcimag
, cimagf
—imaginary partclog
, clogf
—complex base-e logarithmconj
, conjf
—complex conjugatecpow
, cpowf
—complex powercproj
, cprojf
— Riemann sphere projectioncreal
, crealf
—real partcsin
, csinf
—complex sinecsinh
, csinhf
—complex hyperbolic sinecsqrt
, csqrtf
—complex square rootctan
, ctanf
—complex tangentctanh
, ctanf
—complex hyperbolic tangentlibm
libm