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The Newlib Math Library

1. Mathematical Functions (`math.h')  The mathematical functions (`math.h').
2. Reentrancy Properties of libm  The functions in libm are not reentrant by default.
Index  


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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.

  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 section `System Calls' in The Cygnus C Support 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 Version of library  
1.2 acos, acosf---arc cosine  Arccosine
1.3 acosh, acoshf---inverse hyperbolic cosine  Inverse hyperbolic cosine
1.4 asin, asinf---arc sine  Arcsine
1.5 asinh, asinhf---inverse hyperbolic sine  Inverse hyperbolic sine
1.6 atan, atanf---arc tangent  Arctangent
1.7 atan2, atan2f---arc tangent of y/x  Arctangent of y/x
1.8 atanh, atanhf---inverse hyperbolic tangent  Inverse hyperbolic tangent
1.9 jN,jNf,yN,yNf---Bessel functions  Bessel functions (jN, yN)
1.30 cbrt, cbrtf---cube root  Cube root
1.31 copysign, copysignf---sign of y, magnitude of x  Sign of Y, magnitude of X
1.10 cosh, coshf---hyperbolic cosine  Hyperbolic cosine
1.11 erf, erff, erfc, erfcf---error function  Error function (erf, erfc)
1.12 exp, expf---exponential  Exponential
1.32 expm1, expm1f---exponential minus 1  Exponential of x, - 1
1.13 fabs, fabsf---absolute value (magnitude)  Absolute value (magnitude)
1.14 floor, floorf, ceil, ceilf---floor and ceiling  Floor and ceiling (floor, ceil)
1.15 fmod, fmodf---floating-point remainder (modulo)  Floating-point remainder (modulo)
1.16 frexp, frexpf---split floating-point number  Split floating-point number
1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,  Logarithmic gamma function
1.18 hypot, hypotf---distance from origin  Distance from origin
1.33 ilogb, ilogbf---get exponent of floating-point number  Get exponent
1.34 infinity, infinityf---representation of infinity  Floating infinity
1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers  Check type of number
1.20 ldexp, ldexpf---load exponent  Load exponent
1.21 log, logf---natural logarithms  Natural logarithms
1.22 log10, log10f---base 10 logarithms  Base 10 logarithms
1.35 log1p, log1pf---log of 1 + x  Log of 1 + X
1.36 matherr---modifiable math error handler  Modifiable math error handler
1.37 modf, modff---split fractional and integer parts  Split fractional and integer parts
1.38 nan, nanf---representation of "Not a Number"  Floating Not a Number
1.39 nextafter, nextafterf---get next number  Get next representable number
1.23 pow, powf---x to the power y  X to the power Y
1.24 remainder, remainderf---round and remainder  remainder of X divided by Y
1.40 scalbn, scalbnf---scale by power of two  scalbn
1.26 sin, sinf, cos, cosf---sine or cosine  Sine or cosine (sin, cos)
1.27 sinh, sinhf---hyperbolic sine  Hyperbolic sine
1.25 sqrt, sqrtf---positive square root  Positive square root
1.28 tan, tanf---tangent  Tangent
1.29 tanh, tanhf---hyperbolic tangent  Hyperbolic tangent


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1.1 Version of library

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.


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1.2 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.



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1.3 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.



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1.4 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.



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1.5 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.



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1.6 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.



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1.7 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.

If both x and y are 0.0, atan2 causes a DOMAIN error.

You can modify error handling for these functions using matherr.


Portability
atan2 is ANSI C. atan2f is an extension.



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1.8 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.



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1.9 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.



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1.10 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.



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1.11 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.



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1.12 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.



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1.13 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.



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1.14 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.



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1.15 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.



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1.16 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.



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1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,

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);

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).


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.


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1.18 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.


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1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers

Synopsis
 
#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
These functions provide information on the floating-point argument supplied.

There are five major number formats -

zero
a number which contains all zero bits.
subnormal
Is used to represent 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 perform the same operations as their isnan, isinf and finite counterparts, but on single-precision floating-point numbers.



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1.20 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.



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1.21 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 -HUGE_VAL and errno is set to EDOM. You can control the error behavior via matherr.


Portability
log is ANSI, logf is an extension.



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1.22 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.



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1.23 pow, powf---x to the power y

Synopsis
 
#include <math.h>
double pow(double x, double y);
float pow(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.


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1.24 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.



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1.25 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.



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1.26 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.



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1.27 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.



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1.28 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.



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1.29 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.



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1.30 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.



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1.31 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).



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1.32 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).



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1.33 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 - INT_MAX (INT_MAX is defined in limits.h). If val is infinite, or NaN, they return INT_MAX.


Portability
Neither ilogb nor ilogbf is required by ANSI C or by the System V Interface Definition (Issue 2).


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1.34 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.



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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).



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1.36 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.



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1.37 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.



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1.38 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.



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1.39 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).



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1.40 scalbn, scalbnf---scale by power of two

Synopsis
 
#include <math.h>
double scalbn(double x, int y);
float scalbnf(float x, int y);

Description
scalbn and scalbnf scale x by n, returning x times 2 to the power n. The result is computed by manipulating the exponent, rather than by actually performing an exponentiation or multiplication.


Returns
x times 2 to the power n.


Portability
Neither scalbn nor scalbnf is required by ANSI C or by the System V Interface Definition (Issue 2).



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2. 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.


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Index

Jump to:   A   C   E   F   G   H   I   J   L   M   N   O   P   R   S   T   Y  

Index Entry Section

A
acos1.2 acos, acosf---arc cosine
acosf1.2 acos, acosf---arc cosine
acosh1.3 acosh, acoshf---inverse hyperbolic cosine
acoshf1.3 acosh, acoshf---inverse hyperbolic cosine
asin1.4 asin, asinf---arc sine
asinf1.4 asin, asinf---arc sine
asinh1.5 asinh, asinhf---inverse hyperbolic sine
asinhf1.5 asinh, asinhf---inverse hyperbolic sine
atan1.6 atan, atanf---arc tangent
atan21.7 atan2, atan2f---arc tangent of y/x
atan2f1.7 atan2, atan2f---arc tangent of y/x
atanf1.6 atan, atanf---arc tangent
atanh1.8 atanh, atanhf---inverse hyperbolic tangent
atanhf1.8 atanh, atanhf---inverse hyperbolic tangent

C
cbrt1.30 cbrt, cbrtf---cube root
cbrtf1.30 cbrt, cbrtf---cube root
ceil1.14 floor, floorf, ceil, ceilf---floor and ceiling
ceilf1.14 floor, floorf, ceil, ceilf---floor and ceiling
copysign1.31 copysign, copysignf---sign of y, magnitude of x
copysignf1.31 copysign, copysignf---sign of y, magnitude of x
cos1.26 sin, sinf, cos, cosf---sine or cosine
cosf1.26 sin, sinf, cos, cosf---sine or cosine

E
erf1.11 erf, erff, erfc, erfcf---error function
erfc1.11 erf, erff, erfc, erfcf---error function
erfcf1.11 erf, erff, erfc, erfcf---error function
erff1.11 erf, erff, erfc, erfcf---error function
exp1.12 exp, expf---exponential
expf1.12 exp, expf---exponential
expm11.32 expm1, expm1f---exponential minus 1
expm1f1.32 expm1, expm1f---exponential minus 1

F
fabs1.13 fabs, fabsf---absolute value (magnitude)
fabsf1.13 fabs, fabsf---absolute value (magnitude)
finite1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers
finitef1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers
floor1.14 floor, floorf, ceil, ceilf---floor and ceiling
floorf1.14 floor, floorf, ceil, ceilf---floor and ceiling
fmod1.15 fmod, fmodf---floating-point remainder (modulo)
fmodf1.15 fmod, fmodf---floating-point remainder (modulo)
frexp1.16 frexp, frexpf---split floating-point number
frexpf1.16 frexp, frexpf---split floating-point number

G
gamma1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,
gamma_r1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,
gammaf1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,
gammaf_r1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,

H
hypot1.18 hypot, hypotf---distance from origin
hypotf1.18 hypot, hypotf---distance from origin

I
ilogb1.33 ilogb, ilogbf---get exponent of floating-point number
ilogbf1.33 ilogb, ilogbf---get exponent of floating-point number
infinity1.34 infinity, infinityf---representation of infinity
infinityf1.34 infinity, infinityf---representation of infinity
isinf1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers
isinff1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers
isnan1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers
isnanf1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers

J
j01.9 jN,jNf,yN,yNf---Bessel functions
j0f1.9 jN,jNf,yN,yNf---Bessel functions
j11.9 jN,jNf,yN,yNf---Bessel functions
j1f1.9 jN,jNf,yN,yNf---Bessel functions
jn1.9 jN,jNf,yN,yNf---Bessel functions
jnf1.9 jN,jNf,yN,yNf---Bessel functions

L
ldexp1.20 ldexp, ldexpf---load exponent
ldexpf1.20 ldexp, ldexpf---load exponent
lgamma1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,
lgamma_r1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,
lgammaf1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,
lgammaf_r1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,
log1.21 log, logf---natural logarithms
log101.22 log10, log10f---base 10 logarithms
log10f1.22 log10, log10f---base 10 logarithms
log1p1.35 log1p, log1pf---log of 1 + x
log1pf1.35 log1p, log1pf---log of 1 + x
logf1.21 log, logf---natural logarithms

M
matherr1.36 matherr---modifiable math error handler
matherr and reentrancy2. Reentrancy Properties of libm
modf1.37 modf, modff---split fractional and integer parts
modff1.37 modf, modff---split fractional and integer parts

N
nan1.38 nan, nanf---representation of "Not a Number"
nanf1.38 nan, nanf---representation of "Not a Number"
nextafter1.39 nextafter, nextafterf---get next number
nextafterf1.39 nextafter, nextafterf---get next number

O
OS stubs1. Mathematical Functions (`math.h')

P
pow1.23 pow, powf---x to the power y
powf1.23 pow, powf---x to the power y

R
reentrancy2. Reentrancy Properties of libm
remainder1.24 remainder, remainderf---round and remainder
remainderf1.24 remainder, remainderf---round and remainder

S
scalbn1.40 scalbn, scalbnf---scale by power of two
scalbnf1.40 scalbn, scalbnf---scale by power of two
sin1.26 sin, sinf, cos, cosf---sine or cosine
sinf1.26 sin, sinf, cos, cosf---sine or cosine
sinh1.27 sinh, sinhf---hyperbolic sine
sinhf1.27 sinh, sinhf---hyperbolic sine
sqrt1.25 sqrt, sqrtf---positive square root
sqrtf1.25 sqrt, sqrtf---positive square root
stubs1. Mathematical Functions (`math.h')
support subroutines1. Mathematical Functions (`math.h')
system calls1. Mathematical Functions (`math.h')

T
tan1.28 tan, tanf---tangent
tanf1.28 tan, tanf---tangent
tanh1.29 tanh, tanhf---hyperbolic tangent
tanhf1.29 tanh, tanhf---hyperbolic tangent

Y
y01.9 jN,jNf,yN,yNf---Bessel functions
y0f1.9 jN,jNf,yN,yNf---Bessel functions
y11.9 jN,jNf,yN,yNf---Bessel functions
y1f1.9 jN,jNf,yN,yNf---Bessel functions
yn1.9 jN,jNf,yN,yNf---Bessel functions
ynf1.9 jN,jNf,yN,yNf---Bessel functions

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Table of Contents


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Short Table of Contents

1. Mathematical Functions (`math.h')
2. Reentrancy Properties of libm
Index

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