Table of Contents

1. Mathematical Complex Functions (complex.h)
cabs — complex absolute-value
cacos — complex arc cosine
cacosh — complex arc hyperbolic cosine
carg — argument (phase angle)
casin — complex arc sine
casinh — complex arc hyperbolic sine
catan — complex arc tangent
catanh — complex arc hyperbolic tangent
ccos — complex cosine
ccosh — complex hyperbolic cosine
cexp — complex base-e exponential
cimag — imaginary part
clog — complex base-e logarithm
conj — complex conjugate
cpow — complex power
cproj — Riemann sphere projection
creal — real part
csin — complex sine
csinh — complex hyperbolic sine
csqrt — complex square root
ctan — complex tangent
ctanh — complex hyperbolic tangent
2. Mathematical Functions (math.h)
acos — arc cosine
acosh — inverse hyperbolic cosine
asin — arc sine
asinh — inverse hyperbolic sine
atan — arc tangent
atan2 — arc tangent of y/x
atanh — inverse hyperbolic tangent
jN — Bessel functions
cbrt — cube root
copysign — sign of y, magnitude of x
cosh — hyperbolic cosine
erf — error function
exp — exponential
exp10 — exponential, base 10
exp2 — exponential, base 2
expm1 — exponential minus 1
fabs — absolute value (magnitude)
fdim — positive difference
floor — floor and ceiling
fma — floating multiply add
fmax — maximum
fmin — minimum
fmod — floating-point remainder (modulo)
frexp — split floating-point number
gamma — logarithmic and plain gamma functions
hypot — distance from origin
ilogb — get exponent of floating-point number
infinity — representation of infinity
isgreater — comparison macros
fpclassify — floating-point classification macros, test for exceptional numbers
ldexp — load exponent
log — natural logarithms
log10 — base 10 logarithms
log1p — log of 1 + x
log2 — base 2 logarithm
logb — get exponent of floating-point number
lrint — round to integer
lround — round to integer, to nearest
matherr — modifiable math error handler
modf — split fractional and integer parts
nan — representation of ``Not a Number''
nearbyint — round to integer
nextafter — get next number
pow — x to the power y
pow10 — base 10 power functions
remainder — round and remainder
remquo — remainder and part of quotient
rint — round to integer
round — round to integer, to nearest
scalbn — scale by power of FLT_RADIX (=2)
signbit — Does floating-point number have negative sign?
sin — sine or cosine
sinh — hyperbolic sine
sqrt — positive square root
tan — tangent
tanh — hyperbolic tangent
trunc — round to integer, towards zero
Index

Chapter 1. Mathematical Complex Functions (complex.h)

Table of Contents

cabs — complex absolute-value
cacos — complex arc cosine
cacosh — complex arc hyperbolic cosine
carg — argument (phase angle)
casin — complex arc sine
casinh — complex arc hyperbolic sine
catan — complex arc tangent
catanh — complex arc hyperbolic tangent
ccos — complex cosine
ccosh — complex hyperbolic cosine
cexp — complex base-e exponential
cimag — imaginary part
clog — complex base-e logarithm
conj — complex conjugate
cpow — complex power
cproj — Riemann sphere projection
creal — real part
csin — complex sine
csinh — complex hyperbolic sine
csqrt — complex square root
ctan — complex tangent
ctanh — complex hyperbolic tangent

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

Name

cabs — complex absolute-value

Synopsis

#include <complex.h>
double cabs(double complex z);
 
float cabsf(float complex z);
 
long double cabsl(long double 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 float complex.

cabsl is identical to cabs, except that it performs its calculations on long double complex.

Returns

The cabs* functions return the complex absolute value.

Portability

cabs, cabsf and cabsl are ISO C99


Name

cacos — 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


Name

cacosh — 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


Name

carg — 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


Name

casin — 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


Name

casinh — 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


Name

catan — 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


Name

catanh — 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


Name

ccos — 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


Name

ccosh — 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


Name

cexp — 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


Name

cimag — imaginary part

Synopsis

#include <complex.h>
double cimag(double complex z);
 
float cimagf(float complex z);
 
long double cimagl(long double complex z);
 

Description

These functions compute the imaginary part of z.

cimagf is identical to cimag, except that it performs its calculations on float complex.

cimagl is identical to cimag, except that it performs its calculations on long double complex.

Returns

The cimag* functions return the imaginary part value (as a real).

Portability

cimag, cimagf and cimagl are ISO C99


Name

clog — 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


Name

conj — 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


Name

cpow — 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


Name

cproj — 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


Name

creal — real part

Synopsis

#include <complex.h>
double creal(double complex z);
 
float crealf(float complex z);
 
double long creall(long double complex z);
 

Description

These functions compute the real part of z.

crealf is identical to creal, except that it performs its calculations on float complex.

creall is identical to creal, except that it performs its calculations on long double complex.

Returns

The creal* functions return the real part value.

Portability

creal, crealf and creall are ISO C99


Name

csin — 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


Name

csinh — 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


Name

csqrt — 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


Name

ctan — 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


Name

ctanh — 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

Chapter 2. Mathematical Functions (math.h)

Table of Contents

acos — arc cosine
acosh — inverse hyperbolic cosine
asin — arc sine
asinh — inverse hyperbolic sine
atan — arc tangent
atan2 — arc tangent of y/x
atanh — inverse hyperbolic tangent
jN — Bessel functions
cbrt — cube root
copysign — sign of y, magnitude of x
cosh — hyperbolic cosine
erf — error function
exp — exponential
exp10 — exponential, base 10
exp2 — exponential, base 2
expm1 — exponential minus 1
fabs — absolute value (magnitude)
fdim — positive difference
floor — floor and ceiling
fma — floating multiply add
fmax — maximum
fmin — minimum
fmod — floating-point remainder (modulo)
frexp — split floating-point number
gamma — logarithmic and plain gamma functions
hypot — distance from origin
ilogb — get exponent of floating-point number
infinity — representation of infinity
isgreater — comparison macros
fpclassify — floating-point classification macros, test for exceptional numbers
ldexp — load exponent
log — natural logarithms
log10 — base 10 logarithms
log1p — log of 1 + x
log2 — base 2 logarithm
logb — get exponent of floating-point number
lrint — round to integer
lround — round to integer, to nearest
matherr — modifiable math error handler
modf — split fractional and integer parts
nan — representation of ``Not a Number''
nearbyint — round to integer
nextafter — get next number
pow — x to the power y
pow10 — base 10 power functions
remainder — round and remainder
remquo — remainder and part of quotient
rint — round to integer
round — round to integer, to nearest
scalbn — scale by power of FLT_RADIX (=2)
signbit — Does floating-point number have negative sign?
sin — sine or cosine
sinh — hyperbolic sine
sqrt — positive square root
tan — tangent
tanh — hyperbolic tangent
trunc — round to integer, towards zero

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. @xref{syscalls,,System Calls, libc.info, 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.

Name

acos — 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.


Name

acosh — 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.


Name

asin — 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.


Name

asinh — 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.


Name

atan — 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.


Name

atan2 — 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.


Name

atanh — 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.


Name

jN — 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.


Name

cbrt — 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.


Name

copysign — 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).


Name

cosh — 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.


Name

erf — 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.


Name

exp — 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.


Name

exp10 — exponential, base 10

Synopsis

#include <math.h>
double exp10(double x);
 
float exp10f(float x);
 

Description

exp10 and exp10f calculate 10 ^ x, that is, 10 raised to the power x.

You can use the (non-ANSI) function matherr to specify error handling for these functions.

Returns

On success, exp10 and exp10f 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

exp10 and exp10f are GNU extensions.


Name

exp2 — 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.


Name

expm1 — 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).


Name

fabs — 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.


Name

fdim — 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.


Name

floor — 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.


Name

fma — 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.


Name

fmax — 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.


Name

fmin — 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.


Name

fmod — 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.


Name

frexp — 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.


Name

gamma — 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.


Name

hypot — 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.


Name

ilogb — 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


Name

infinity — 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.


Name

isgreater — 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.


Name

fpclassify — floating-point classification macros, 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.


Name

ldexp — 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.


Name

log — 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.


Name

log10 — 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.


Name

log1p — 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).


Name

log2 — 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).


Name

logb — 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


Name

lrint — 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


Name

lround — 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


Name

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.


Name

modf — 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.


Name

nan — representation of ``Not a Number''

Synopsis

#include <math.h>
double nan(const char *unused);
 
float nanf(const char *unused);
 

Description

nan and nanf return an IEEE NaN (Not a Number) in double- and single-precision arithmetic respectively. The argument is currently disregarded.


Name

nearbyint — 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


Name

nextafter — 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).


Name

pow — 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.


Name

pow10 — base 10 power functions

Synopsis

#include <math.h>
double pow10(double x);
 
float pow10f(float x);
 

Description

pow10 and pow10f calculate 10 ^ x, that is, 10 raised to the power x.

You can use the (non-ANSI) function matherr to specify error handling for these functions.

Returns

On success, pow10 and pow10f 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

pow10 and pow10f are GNU extensions.


Name

remainder — 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.


Name

remquo — 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.


Name

rint — 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


Name

round — 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


Name

scalbn — 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


Name

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.


Name

sin — 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.


Name

sinh — 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.


Name

sqrt — 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.


Name

tan — 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.


Name

tanh — 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.


Name

trunc — 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

Index

A

acos, acos
acosf, acos
acosh, acosh
acoshf, acosh
asin, asin
asinf, asin
asinh, asinh
asinhf, asinh
atan, atan
atan2, atan2
atan2f, atan2
atanf, atan
atanh, atanh
atanhf, atanh

C

cabs, cabs
cabsf, cabs
cabsl, cabs
cacos, cacos
cacosf, cacos
cacosh, cacosh
cacoshf, cacosh
carg, carg
cargf, carg
casin, casin
casinf, casin
casinh, casinh
casinhf, casinh
catan, catan
catanf, catan
catanh, catanh
catanhf, catanh
cbrt, cbrt
cbrtf, cbrt
ccos, ccos
ccosf, ccos
ccosh, ccosh
ccoshf, ccosh
ceil, floor
ceilf, floor
cexp, cexp
cexpf, cexp
cimag, cimag
cimagf, cimag
cimagl, cimag
clog, clog
clogf, clog
conj, conj
conjf, conj
copysign, copysign
copysignf, copysign
cos, sin
cosf, sin
cpow, cpow
cpowf, cpow
cproj, cproj
cprojf, cproj
creal, creal
crealf, creal
creall, creal
csin, csin
csinf, csin
csinh, csinh
csinhf, csinh
csqrt, csqrt
csqrtf, csqrt
ctan, ctan
ctanf, ctan
ctanh, ctanh
ctanhf, ctanh

E

erf, erf
erfc, erf
erfcf, erf
erff, erf
exp, exp
exp10, exp10
exp10f, exp10
exp2, exp2
exp2f, exp2
expf, exp
expm1, expm1
expm1f, expm1

F

fabs, fabs
fabsf, fabs
fdim, fdim
fdimf, fdim
finite, fpclassify
finitef, fpclassify
floor, floor
floorf, floor
fma, fma
fmaf, fma
fmax, fmax
fmaxf, fmax
fmin, fmin
fminf, fmin
fmod, fmod
fmodf, fmod
fpclassify, fpclassify
frexp, frexp
frexpf, frexp

G

gamma, gamma
gammaf, gamma
gammaf_r, gamma
gamma_r, gamma

H

hypot, hypot
hypotf, hypot

I

ilogb, ilogb
ilogbf, ilogb
infinity, infinity
infinityf, infinity
isfinite, fpclassify
isgreater, isgreater
isgreaterequal, isgreater
isinf, fpclassify
isinff, fpclassify
isless, isgreater
islessequal, isgreater
islessgreater, isgreater
isnan, fpclassify
isnanf, fpclassify
isnormal, fpclassify
isunordered, isgreater

J

j0, jN
j0f, jN
j1, jN
j1f, jN
jn, jN
jnf, jN

L

ldexp, ldexp
ldexpf, ldexp
lgamma, gamma
lgammaf, gamma
lgammaf_r, gamma
lgamma_r, gamma
llrint, lrint
llrintf, lrint
llround, lround
llroundf, lround
log, log
log10, log10
log10f, log10
log1p, log1p
log1pf, log1p
log2, log2
log2f, log2
logb, logb
logbf, logb
logf, log
lrint, lrint
lrintf, lrint
lround, lround
lroundf, lround

M

matherr, matherr
modf, modf
modff, modf

N

nan, nan
nanf, nan
nearbyint, nearbyint
nearbyintf, nearbyint
nextafter, nextafter
nextafterf, nextafter

P

pow, pow
pow10, pow10
pow10f, pow10
powf, pow

R

remainder, remainder
remainderf, remainder
remquo, remquo
remquof, remquo
rint, rint
rintf, rint
round, round
roundf, round

S

scalbln, scalbn
scalblnf, scalbn
scalbn, scalbn
scalbnf, scalbn
signbit, signbit
sin, sin
sinf, sin
sinh, sinh
sinhf, sinh
sqrt, sqrt
sqrtf, sqrt
stubs, Mathematical Functions (math.h)
support subroutines, Mathematical Functions (math.h)
system calls, Mathematical Functions (math.h)

T

tan, tan
tanf, tan
tanh, tanh
tanhf, tanh
tgamma, gamma
tgammaf, gamma
trunc, trunc
truncf, trunc

Y

y0, jN
y0f, jN
y1, jN
y1f, jN
yn, jN
ynf, jN