LIBM

1 Mathematical Functions (math.h)

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.

1. The representation of infinity as a 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.
2. The structure 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.

1.1 Error Handling

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.

1.2 Standards Compliance And Portability

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.

1.3 acos, acosf—arc cosine

Synopsis

#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.

1.4 acosh, acoshf—inverse hyperbolic cosine

Synopsis

#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.

1.5 asin, asinf—arc sine

Synopsis

#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.

1.6 asinh, asinhf—inverse hyperbolic sine

Synopsis

#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.

1.7 atan, atanf—arc tangent

Synopsis

#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.

1.8 atan2, atan2f—arc tangent of y/x

Synopsis

#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.

1.9 atanh, atanhf—inverse hyperbolic tangent

Synopsis

#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.

1.10 jN, jNf, yN, yNf—Bessel functions

Synopsis

#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.

1.11 cbrt, cbrtf—cube root

Synopsis

#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.

1.12 copysign, copysignf—sign of y, magnitude of x

Synopsis

#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).

1.13 cosh, coshf—hyperbolic cosine

Synopsis

#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.

1.14 erf, erff, erfc, erfcf—error function

Synopsis

#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.

1.15 exp, expf—exponential

Synopsis

#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.

1.16 exp2, exp2f–exponential, base 2

Synopsis

#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.

1.17 expm1, expm1f—exponential minus 1

Synopsis

#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).

1.18 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.

1.19 fdim, fdimf–positive difference

Synopsis

#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.

1.20 floor, floorf, ceil, ceilf—floor and ceiling

Synopsis

#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.

1.21 fma, fmaf–floating multiply add

Synopsis

#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.

1.22 fmax, fmaxf–maximum

Synopsis

#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.

1.23 fmin, fminf–minimum

Synopsis

#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.

1.24 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.

1.25 frexp, frexpf—split floating-point number

Synopsis

#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.

1.26 gamma, gammaf, lgamma, lgammaf, gamma_r, gammaf_r, lgamma_r, lgammaf_r, tgamma, and tgammaf–logarithmic and plain gamma functions

Synopsis

#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.

1.27 hypot, hypotf—distance from origin

Synopsis

#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.

1.28 ilogb, ilogbf—get exponent of floating-point number

Synopsis

#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

1.29 infinity, infinityf–representation of infinity

Synopsis

#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.

1.30 isgreater, isgreaterequal, isless, islessequal, islessgreater, and isunordered–comparison macros

Synopsis

#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.

1.31 fpclassify, isfinite, isinf, isnan, and isnormal–floating-point classification macros; finite, finitef, isinf, isinff, isnan, isnanf–test for exceptional numbers

Synopsis

[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.

1.32 ldexp, ldexpf—load exponent

Synopsis

#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.

1.33 log, logf—natural logarithms

Synopsis

#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.

1.34 log10, log10f—base 10 logarithms

Synopsis

#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.

1.35 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).

1.36 log2, log2f–base 2 logarithm

Synopsis

#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).

1.37 logb, logbf–get exponent of floating-point number

Synopsis

#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

1.38 lrint, lrintf, llrint, llrintf–round to integer

Synopsis

#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

1.39 lround, lroundf, llround, llroundf–round to integer, to nearest

Synopsis

#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

1.40 matherr—modifiable math error handler

Synopsis

#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.

1.41 modf, modff—split fractional and integer parts

Synopsis

#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.

1.42 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.

1.43 nearbyint, nearbyintf–round to integer

Synopsis

#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

1.44 nextafter, nextafterf—get next number

Synopsis

#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).

1.45 pow, powf—x to the power y

Synopsis

#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.

1.46 remainder, remainderf—round and remainder

Synopsis

#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.

1.47 remquo, remquof–remainder and part of quotient

Synopsis

#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.

1.48 rint, rintf–round to integer

Synopsis

#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

1.49 round, roundf–round to integer, to nearest

Synopsis

#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

1.50 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

1.51 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.

1.52 sin, sinf, cos, cosf—sine or cosine

Synopsis

#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.

1.53 sinh, sinhf—hyperbolic sine

Synopsis

#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.

1.54 sqrt, sqrtf—positive square root

Synopsis

#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.

1.55 tan, tanf—tangent

Synopsis

#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.

1.56 tanh, tanhf—hyperbolic tangent

Synopsis

#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.

1.57 trunc, truncf–round to integer, towards zero

Synopsis

#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

2 Mathematical Complex Functions (complex.h)

This chapter groups the complex mathematical functions. The corresponding definitions and declarations are in complex.h. Functions and documentations are taken from NetBSD.

2.1 cabs, cabsf—complex absolute-value

Synopsis

#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

2.2 cacos, cacosf—complex arc cosine

Synopsis

#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

2.3 cacosh, cacoshf—complex arc hyperbolic cosine

Synopsis

#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

2.4 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

2.5 casin, casinf—complex arc sine

Synopsis

#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

2.6 casinh, casinhf—complex arc hyperbolic sine

Synopsis

#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

2.7 catan, catanf—complex arc tangent

Synopsis

#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

2.8 catanh, catanhf—complex arc hyperbolic tangent

Synopsis

#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

2.9 ccos, ccosf—complex cosine

Synopsis

#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

2.10 ccosh, ccoshf—complex hyperbolic cosine

Synopsis

#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

2.11 cexp, cexpf—complex base-e exponential

Synopsis

#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

2.12 cimag, cimagf—imaginary part

Synopsis

#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

2.13 clog, clogf—complex base-e logarithm

Synopsis

#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

2.14 conj, conjf—complex conjugate

Synopsis

#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

2.15 cpow, cpowf—complex power

Synopsis

#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

2.16 cproj, cprojf— Riemann sphere projection

Synopsis

#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

2.17 creal, crealf—real part

Synopsis

#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

2.18 csin, csinf—complex sine

Synopsis

#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

2.19 csinh, csinhf—complex hyperbolic sine

Synopsis

#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

2.20 csqrt, csqrtf—complex square root

Synopsis

#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

2.21 ctan, ctanf—complex tangent

Synopsis

#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

2.22 ctanh, ctanf—complex hyperbolic tangent

Synopsis

#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

3 Reentrancy Properties of 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.

4 The long double function support of 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.

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