RETURN VALUE The acos() function returns the arc cosine in radians and the value is mathematically defined to be between 0 and PI (inclusive).

Transcription

1 ACOS(3) Linux Programmer s Manual ACOS(3) acos, acosf, acosl arc cosine function double acos(double x); float acosf(float x); long double acosl(long double x); The acos() function calculates the arc cosine of x; that is the value whose cosine is x. If x falls outside the range 1 to 1, acos() fails and errno is set. RETURN VALUE The acos() function returns the arc cosine in radians and the value is mathematically defined to be between 0 and PI (inclusive). ERRORS EDOM x is out of range. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and long double variants are C99 requirements. asin(3), atan(3), atan2(3), cos(3), sin(3), tan(3)

2 ACOSH(3) Linux Programmer s Manual ACOSH(3) acosh, acoshf, acoshl inverse hyperbolic cosine function double acosh(double x); float acoshf(float x); long double acoshl(long double x); The acosh() function calculates the inverse hyperbolic cosine of x; that is the value whose hyperbolic cosine is x. Ifx is less than 1.0, acosh() returns not-a-number (NaN) and errno is set. ERRORS EDOM x is out of range. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and long double variants are C99 requirements. asinh(3), atanh(3), cosh(3), sinh(3), tanh(3)

3 ASIN(3) Linux Programmer s Manual ASIN(3) asin, asinf, asinl arc sine function double asin(double x); float asinf(float x); long double asinl(long double x); The asin() function calculates the arc sine of x; that is the value whose sine is x. If x falls outside the range 1 to 1, asin() fails and errno is set. RETURN VALUE The asin() function returns the arc sine in radians and the value is mathematically defined to be between -PI/2 and PI/2 (inclusive). ERRORS EDOM x is out of range. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and long double variants are C99 requirements. acos(3), atan(3), atan2(3), cos(3), sin(3), tan(3)

4 ASINH(3) Linux Programmer s Manual ASINH(3) asinh, asinhf, asinhl inverse hyperbolic sine function double asinh(double x); float asinhf(float x); long double asinhl(long double x); The asinh() function calculates the inverse hyperbolic sine of x; that is the value whose hyperbolic sine is x. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and long double variants are C99 requirements. acosh(3), atanh(3), cosh(3), sinh(3), tanh(3)

5 AT AN(3) Linux Programmer s Manual ATAN(3) atan, atanf, atanl arc tangent function double atan(double x); float atanf(float x); long double atanl( long double x); The atan() function calculates the arc tangent of x; that is the value whose tangent is x. RETURN VALUE The atan() function returns the arc tangent in radians and the value is mathematically defined to be between -PI/2 and PI/2 (inclusive). CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and long double variants are C99 requirements. acos(3), asin(3), atan2(3), cos(3), sin(3), tan(3)

6 AT AN2(3) Linux Programmer s Manual ATAN2(3) atan2, atan2f, atan2l arc tangent function of two variables double atan2(double y, double x); float atan2f(float y, float x); long double atan2l(long double y, long double x); The atan2() function calculates the arc tangent of the two variables x and y. It is similar to calculating the arc tangent of y / x, except that the signs of both arguments are used to determine the quadrant of the result. RETURN VALUE The atan2() function returns the result in radians, which is between -PI and PI (inclusive). CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and long double variants are C99 requirements. acos(3), asin(3), atan(3), cos(3), sin(3), tan(3)

7 AT ANH(3) Linux Programmer s Manual ATANH(3) atanh, atanhf, atanhl inverse hyperbolic tangent function double atanh(double x); float atanhf(float x); long double atanhl(long double x); The atanh() function calculates the inverse hyperbolic tangent of x; that is the value whose hyperbolic tangent is x. If the absolute value of x is greater than 1.0, acosh() returns not-a-number (NaN) and errno is set. ERRORS EDOM x is out of range. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and long double variants are C99 requirements. asinh(3), acosh(3), cosh(3), sinh(3), tanh(3)

8 CBRT(3) Linux Programmer s Manual CBRT(3) cbrt, cbrtf, cbrtl cube root function double cbrt(double x); float cbrtf(float x); long double cbrtl(long double x); The cbrt() function returns the (real) cube root of x. This function cannot fail; every representable real value has a representable real cube root. CONFORMING TO cbrt() was a GNU extension. It is now a C99 requirement. sqrt(3), pow(3) GNU

9 CEIL(3) Linux Programmer s Manual CEIL(3) ceil, ceilf, ceill ceiling function: smallest integral value not less than argument double ceil(double x); float ceilf(float x); long double ceill(long double x); These functions round x up to the nearest integer. RETURN VALUE The rounded integer value. If x is integral or infinite, x itself is returned. ERRORS No errors other than EDOM and ERANGE can occur. If x is NaN, then NaN is returned and errno may be set to EDOM. NOTES SUSv2 and POSIX contain text about overflow (which might set errno to ERANGE, or raise an exception). In practice, the result cannot overflow on any current machine, so this error-handling stuff is just nonsense. (More precisely, overflow can happen only when the maximum value of the exponent is smaller than the number of mantissa bits. For the IEEE-754 standard 32-bit and 64-bit floating point numbers the maximum value of the exponent is 128 (resp. 1024), and the number of mantissa bits is 24 (resp. 53).) CONFORMING TO The ceil() function conforms to SVID 3, POSIX, BSD 4.3, ISO The other functions are from C99. floor(3), lrint(3), nearbyint(3), rint(3), round(3), trunc(3)

10 COPYSIGN(3) Linux Programmer s Manual COPYSIGN(3) copysign, copysignf, copysignl copy sign of a number double copysign(double x, double y); float copysignf(float x, float y); long double copysignl(long double x, long double y); The copysign() functions return a value whose absolute value matches that of x, but whose sign matches that of y. Ifx is a NaN, then a NaN with the sign of y is returned. NOTES The copysign() functions may treat a negative zero as positive. CONFORMING TO C99, BSD 4.3. This function is defined in IEC 559 (and the appendix with recommended functions in IEEE 754/IEEE 854). signbit(3) GNU

11 COS(3) Linux Programmer s Manual COS(3) cos, cosf, cosl cosine function double cos(double x); float cosf(float x); long double cosl(long double x); The cos() function returns the cosine of x, where x is given in radians. RETURN VALUE The cos() function returns a value between 1 and 1. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. acos(3), asin(3), atan(3), atan2(3), sin(3), tan(3)

12 COSH(3) Linux Programmer s Manual COSH(3) cosh, coshf, coshl hyperbolic cosine function double cosh(double x); float coshf(float x); long double coshl(long double x); The cosh() function returns the hyperbolic cosine of x, which is defined mathematically as (exp(x) + exp(-x)) / 2. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO 9899 (C99). The float and the long double variants are C99 requirements. acosh(3), asinh(3), atanh(3), sinh(3), tanh(3)

13 ERF(3) Linux Programmer s Manual ERF(3) erf, erff, erfl, erfc, erfcf, erfcl error function and complementary error function double erf(double x); float erff(float x); long double erfl(long double x); double erfc(double x); float erfcf(float x); long double erfcl(long double x); The erf() function returns the error function of x; defined as erf(x) = 2/sqrt(pi)* integral from 0 to x of exp(-t*t) dt The erfc() function returns the complementary error function of x, that is erf(x). CONFORMING TO SVID 3, BSD 4.3, C99. The float and long double variants are requirements of C99. exp(3) BSD

14 EXP(3) Linux Programmer s Manual EXP(3) exp, expf, expl base-e exponential function double exp(double x); float expf(float x); long double expl(long double x); The exp() function returns the value of e (the base of natural logarithms) raised to the power of x. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. sqrt(3), cbrt(3) exp10(3), exp2(3)

15 EXPM1(3) Linux Programmer s Manual EXPM1(3) expm1, expm1f, expm1l exponential minus 1 double expm1(double x); float expm1f(float x); long double expm1l(long double x); expm1(x) returns a value equivalent to exp (x) - 1. It is computed in a way that is accurate even if the value of x is near zero--a case where exp (x) - 1 would be inaccurate due to subtraction of two numbers that are nearly equal. CONFORMING TO BSD, C99. The float and the long double variants are C99 requirements. exp(3), log(3), log1p(3)

16 FABS(3) Linux Programmer s Manual FABS(3) fabs, fabsf, fabsl absolute value of floating-point number double fabs(double x); float fabsf(float x); long double fabsl(long double x); The fabs functions return the absolute value of the floating-point number x. ERRORS No errors can occur. CONFORMING TO The fabs() function conforms to SVID 3, POSIX, BSD 4.3, ISO The other functions are from C99. abs(3), ceil(3), floor(3), labs(3), rint(3)

17 FLOOR(3) Linux Programmer s Manual FLOOR(3) floor, floorf, floorl largest integral value not greater than argument double floor(double x); float floorf(float x); long double floorl(long double x); These functions round x down to the nearest integer. RETURN VALUE The rounded integer value. If x is integral or infinite, x itself is returned. ERRORS No errors other than EDOM and ERANGE can occur. If x is NaN, then NaN is returned and errno may be set to EDOM. NOTES SUSv2 and POSIX contain text about overflow (which might set errno to ERANGE, or raise an exception). In practice, the result cannot overflow on any current machine, so this error-handling stuff is just nonsense. (More precisely, overflow can happen only when the maximum value of the exponent is smaller than the number of mantissa bits. For the IEEE-754 standard 32-bit and 64-bit floating point numbers the maximum value of the exponent is 128 (resp. 1024), and the number of mantissa bits is 24 (resp. 53).) CONFORMING TO The floor() function conforms to SVID 3, POSIX, BSD 4.3, ISO The other functions are from C99. ceil(3), lrint(3), nearbyint(3), rint(3), round(3), trunc(3)

18 FMOD(3) Linux Programmer s Manual FMOD(3) fmod, fmodf, fmodl floating-point remainder function double fmod(double x, double y); float fmodf(float x, float y); long double fmodl(long double x, long double y); The fmod() function computes the remainder of dividing x by y. The return value is x - n * y, where n is the quotient of x / y, rounded towards zero to an integer. RETURN VALUE The fmod() function returns the remainder, unless y is zero, when the function fails and errno is set. ERRORS EDOM The denominator y is zero. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. remainder(3)

19 FREXP(3) Linux Programmer s Manual FREXP(3) frexp, frexpf, frexpl convert floating-point number to fractional and integral components double frexp(double x, int *exp); float frexpf(float x, int *exp); long double frexpl(long double x, int *exp); The frexp() function is used to split the number x into a normalized fraction and an exponent which is stored in exp. RETURN VALUE The frexp() function returns the normalized fraction. If the argument x is not zero, the normalized fraction is x times a power of two, and is always in the range 1/2 (inclusive) to 1 (exclusive). If x is zero, then the normalized fraction is zero and zero is stored in exp. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. EXAMPLE #include <stdio.h> #include <float.h> int main () { double d = 2560; int e; double f = frexp(d, &e); printf("frexp(%g, &e) = %g: %g * %dˆ%d = %g\n", d, f, f, FLT_RADIX, e, d); return 0; } This program prints frexp(2560, &e) = 0.625: * 2ˆ12 = 2560 ldexp(3), modf(3)

20 GAMMA(3) libc math functions GAMMA(3) gamma, gammaf, gammal (logarithm of the) gamma function double gamma(double x); float gammaf(float x); long double gammal(long double x); For the definition of the Gamma function, see tgamma(3). *BSD version 4.4BSD and FreeBSD libm have a gamma() function that computes the Gamma function, as one would expect. glibc version Glibc has a gamma() function that is equivalent to lgamma() and computes the natural logarithm of the Gamma function. (This is for compatibility reasons only. Don t use this function.) HISTORY 4.2BSD had a gamma() that computed ln( Gamma( x ) ), leaving the sign of Gamma( x ) in the external integer signgam. In 4.3BSD the name was changed to lgamma(), and the man page promises "At some time in the future the name gamma will be rehabilitated and used for the Gamma function" This did indeed happen in 4.4BSD, where gamma() computes the Gamma function (with no effect on signgam). However, this came too late, and we now hav e tgamma(), the "true gamma" function. CONFORMING TO 4.2BSD. Compatible with previous mistakes. lgamma(3), signgam(3), tgamma(3) GNU

21 HYPOT(3) Linux Programmer s Manual HYPOT(3) hypot, hypotf, hypotl Euclidean distance function double hypot(double x, double y); float hypotf(float x, float y); long double hypotl (long double x, long double y); The hypot() function returns sqrt(x*x+y*y). This is the length of the hypotenuse of a right-angle triangle with sides of length x and y, or the distance of the point (x,y) from the origin. CONFORMING TO SVID 3, BSD 4.3, C99. The float and the long double variants are C99 requirements. sqrt(3), cabs(3)

22 ISINF(3) Linux Programmer s Manual ISINF(3) isinf, isnan, finite test for infinity or not-a-number (NaN) int isinf(double value); int isnan(double value); int finite(double value); The isinf() function returns 1 if value represents negative infinity, 1 if value represents positive infinity, and 0 otherwise. The isnan() function returns a non-zero value if value is "not-a-number" (NaN), and 0 otherwise. The finite() function returns a non-zero value if value is neither infinite nor a "not-a-number" (NaN) value, and 0 otherwise. NOTE C99 provides additional macros, such as the type-independent fpclassify(), isinf() and isnan(). CONFORMING TO BSD 4.3 fpclassify(3)

23 J0(3) Linux Programmer s Manual J0(3) j0, j0f, j0l, j1, j1f, j1l, jn, jnf, jnl, y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl Bessel functions double j0(double x); double j1(double x); double jn(int n, double x); double y0(double x); double y1(double x); double yn(int n, double x); float j0f(float x); float j1f(float x); float jnf(int n, float x); float y0f(float x); float y1f(float x); float ynf(int n, float x); long double j0l(long double x); long double j1l(long double x); long double jnl(int n, long double x); long double y0l(long double x); long double y1l(long double x); long double ynl(int n, long double x); The j0() and j1() functions return Bessel functions of x of the first kind of orders 0 and 1, respectively. The jn() function returns the Bessel function of x of the first kind of order n. The y0() and y1() functions return Bessel functions of x of the second kind of orders 0 and 1, respectively. The yn() function returns the Bessel function of x of the second kind of order n. For the functions y0(), y1() and yn(), the value of x must be positive. For negative values of x, these functions return HUGE_VAL. The j0f() etc. and j0l() etc. functions are versions that take and return float and long double values, respectively. CONFORMING TO The functions returning double conform to SVID 3, BSD 4.3, XPG4, POSIX The other functions are C99 requirements. BUGS There are errors of up to 2e 16 in the values returned by j0(), j1() and jn() for values of x between 8 and

24 LDEXP(3) Linux Programmer s Manual LDEXP(3) ldexp, ldexpf, ldexpl multiply floating-point number by integral power of 2 double ldexp(double x, int exp); float ldexp(float x, int exp); long double ldexp(long double x, int exp); The ldexp() function returns the result of multiplying the floating-point number x by 2 raised to the power exp. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. frexp(3), modf(3)

25 LGAMMA(3) Linux Programmer s Manual LGAMMA(3) lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r log gamma function double lgamma(double x); float lgammaf(float x); long double lgammal(long double x); double lgamma_r(double x, int *signp); float lgammaf_r(float x, int *signp); long double lgammal_r(long double x, int *signp); For the definition of the Gamma function, see tgamma(3). The lgamma() function returns the natural logarithm of the absolute value of the Gamma function. The sign of the Gamma function is returned in the external integer signgam declared in <math.h>. It is 1 when the Gamma function is positive or zero, 1 when it is negative. Since using a constant location signgam is not thread-safe, the functions lgamma_r() etc. have been introduced; they return this sign via the parameter signp. For nonpositive integer values of x, lgamma() returns HUGE_VAL, sets errno to ERANGE and raises the zero divide exception. (Similarly, lgammaf() returns HUGE_VALF and lgammal() returns HUGE_VALL.) ERRORS An application wishing to check for error situations should set errno to zero and call feclearexcept(fe_all_except) before calling these functions. On return, if errno is non-zero or fetestexcept(fe_invalid FE_DIVBYZERO FE_OVERFLOW FE_UNDERFLOW) is non-zero, an error has occurred. A range error occurs if x is too large. A pole error occurs if x is a negative integer or zero. CONFORMING TO C99, SVID 3, BSD 4.3 tgamma(3)

26 EXP(3) Linux Programmer s Manual EXP(3) log, logf, logl natural logarithmic function double log(double x); float logf(float x); long double logl(long double x); The log() function returns the natural logarithm of x. ERRORS The log() function can return the following errors: EDOM The argument x is negative. ERANGE The argument x is zero. The log of zero is not defined (minus infinity). CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. sqrt(3), cbrt(3)

27 EXP(3) Linux Programmer s Manual EXP(3) log10, log10f, log10l base-10 logarithmic function double log10(double x); float log10f(float x); long double log10l(long double x); The log10() function returns the base 10 logarithm of x. ERRORS The log10() function can return the following errors: EDOM The argument x is negative. ERANGE The argument x is zero. The log of zero is not defined. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. sqrt(3), cbrt(3)

28 LOG1P(3) Linux Programmer s Manual LOG1P(3) log1p logarithm of 1 plus argument double log1p(double x); float log1pf(float x); long double log1pl(long double x); log1p(x) returns a value equivalent to log (1 + x). It is computed in a way that is accurate even if the value of x is near zero. CONFORMING TO BSD, C99. The float and the long double variants are C99 requirements. exp(3), log(3), expm1(3)

29 MODF(3) Linux Programmer s Manual MODF(3) modf, modff, modfl extract signed integral and fractional values from floating-point number double modf(double x, double *iptr); float modff(float x, float *iptr); long double modfl(long double x, long double *iptr); The modf() function breaks the argument x into an integral part and a fractional part, each of which has the same sign as x. The integral part is stored in iptr. RETURN VALUE The modf() function returns the fractional part of x. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. frexp(3), ldexp(3)

30 NEXTAFTER(3) libc math functions NEXTAFTER(3) nextafter, nextafterf, nextafterl, nexttoward, nexttowardf, nexttowardl floating point number manipulation double nextafter(double x, double y); float nextafterf(float x, float y); long double nextafterl(long double x, long double y); double nexttoward(double x, long double y); float nexttowardf(float x, long double y); long double nexttowardl(long double x, long double y); The nextafter() functions return the next representable neighbor of x in the direction towards y. The size of the step between x and the result depends on the type of the result. If x = y the function simply returns y. If either value is NaN, then NaN is returned. Otherwise a value corresponding to the value of the least significant bit in the mantissa is added or subtracted, depending on the direction. The nexttoward() functions do the same as the nextafter() functions, except that they hav e a long double second argument. These functions will signal overflow or underflow if the result goes outside of the range of normalized numbers. CONFORMING TO C99. This function is defined in IEC 559 (and the appendix with recommended functions in IEEE 754/IEEE 854). nearbyint(3) GNU

31 POW(3) Linux Programmer s Manual POW(3) pow, powf, powl power functions double pow(double x, double y); float powf(float x, float y); long double powl(long double x, long double y); The pow() function returns the value of x raised to the power of y. ERRORS The pow() function can return the following error: EDOM The argument x is negative and y is not an integral value. This would result in a complex number. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. sqrt(3), cbrt(3)

32 REMAINDER(3) Linux Programmer s Manual REMAINDER(3) drem, dremf, dreml, remainder, remainderf, remainderl floating-point remainder function /* The C99 versions */ double remainder(double x, double y); float remainderf(float x, float y); long double remainderl(long double x, long double y); /* Obsolete synonyms */ double drem(double x, double y); float dremf(float x, float y); long double dreml(long double x, long double y); Link with lm. The remainder() function computes the remainder of dividing x by y. The return value is x - n * y, where n is the value x / y, rounded to the nearest integer. If this quotient is 1/2, it is rounded to the nearest even number (independent of the current rounding mode). If the return value is 0, it has the sign of x. The drem() function does precisely the same thing. RETURN VALUE The remainder() function returns the remainder, unless y is zero, when the function fails and errno is set. ERRORS EDOM The denominator y is zero. CONFORMING TO IEC The three remainder*() functions are from C99. The function drem() is from BSD 4.3. The float and long double variants dremf() and dreml() exist on some systems, such as Tru64 and glibc2. EXAMPLE The call "remainder(29.0, 3.0)" returns 1. fmod(3)

33 RINT(3) Linux Programmer s Manual RINT(3) nearbyint, nearbyintf, nearbyintl, rint, rintf, rintl round to nearest integer double nearbyint(double x); float nearbyintf(float x); long double nearbyintl(long double x); double rint(double x); float rintf(float x); long double rintl(long double x); The nearbyint functions round their argument to an integer value in floating point format, using the current rounding direction and without raising the inexact exception. The rint functions do the same, but will raise the inexact exception when the result differs in value from the argument. RETURN VALUE The rounded integer value. If x is integral or infinite, x itself is returned. ERRORS No errors other than EDOM and ERANGE can occur. If x is NaN, then NaN is returned and errno may be set to EDOM. NOTES SUSv2 and POSIX contain text about overflow (which might set errno to ERANGE, or raise an exception). In practice, the result cannot overflow on any current machine, so this error-handling stuff is just nonsense. (More precisely, overflow can happen only when the maximum value of the exponent is smaller than the number of mantissa bits. For the IEEE-754 standard 32-bit and 64-bit floating point numbers the maximum value of the exponent is 128 (resp. 1024), and the number of mantissa bits is 24 (resp. 53).) CONFORMING TO The rint() function conforms to BSD 4.3. The other functions are from C99. ceil(3), floor(3), lrint(3), nearbyint(3), round(3), trunc(3)

34 SIN(3) Linux Programmer s Manual SIN(3) sin, sinf, sinl sine function double sin(double x); float sinf(float x); long double sinl(long double x); The sin() function returns the sine of x, where x is given in radians. RETURN VALUE The sin() function returns a value between 1 and 1. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. acos(3), asin(3), atan(3), atan2(3), cos(3), tan(3)

35 SINH(3) Linux Programmer s Manual SINH(3) sinh, sinhf, sinhl hyperbolic sine function double sinh(double x); float sinhf(float x); long double sinhl(long double x); The sinh() function returns the hyperbolic sine of x, which is defined mathematically as (exp(x) - exp(-x)) / 2. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO 9899 (C99). The float and the long double variants are C99 requirements. acosh(3), asinh(3), atanh(3), cosh(3), tanh(3)

36 SQRT(3) Linux Programmer s Manual SQRT(3) sqrt, sqrtf, sqrtl square root function double sqrt(double x); float sqrtf(float x); long double sqrtl(long double x); The sqrt() function returns the non-negative square root of x. It fails and sets errno to EDOM, if x is negative. ERRORS EDOM x is negative. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. hypot(3)

37 TAN(3) Linux Programmer s Manual TAN(3) tan, tanf, tanl tangent function double tan(double x); float tanf(float x); long double tanl(long double x); The tan() function returns the tangent of x, where x is given in radians. CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO The float and the long double variants are C99 requirements. acos(3), asin(3), atan(3), atan2(3), cos(3), sin(3)

38 TANH(3) Linux Programmer s Manual TANH(3) tanh, tanhf, tanhl hyperbolic tangent function double tanh(double x); float tanhf(float x); long double tanhl(long double x); The tanh() function returns the hyperbolic tangent of x, which is defined mathematically as sinh(x) / cosh(x). CONFORMING TO SVID 3, POSIX, BSD 4.3, ISO 9899 (C99). The float and the long double variants are C99 requirements. acosh(3), asinh(3), atanh(3), cosh(3), sinh(3)

39 acos(p) acos(p) acos, acosf, acosl - arc cosine functions double acos(double x); float acosf(float x); long double acosl(long double x); The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std defers to the ISO C standard. These functions shall compute the principal value of the arc cosine of their argument x. The value of x should be in the range [-1,1]. An application wishing to check for error situations should set errno to zero and call feclearexcept(fe_all_except) before calling these functions. On return, if errno is non-zero or fetestexcept(fe_invalid FE_DIVBYZERO FE_OVERFLOW FE_UNDERFLOW) is non-zero, an error has occurred. RETURN VALUE Upon successful completion, these functions shall return the arc cosine of x, in the range [0,] radians. For finite values of x not in the range [-1,1], a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned. If x is NaN, a NaN shall be returned. If x is +1, +0 shall be returned. If x is ±Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned. ERRORS These functions shall fail if: Domain Error The x argument is finite and is not in the range [-1,1], <img src="../images/opt-start.gif" alt="[option Start]" border="0"> or is ±Inf. [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised. The following sections are informative. EXAMPLES APPLICATION USAGE On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero. RATIONALE FUTURE DIRECTIONS cos(), feclearexcept(), fetestexcept(), isnan(), the Base Definitions volume of IEEE Std , Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h> POSIX

40 acos(p) acos(p) COPYRIGHT Portions of this text are reprinted and reproduced in electronic form from IEEE Std , 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at POSIX

41 acosh(p) acosh(p) acosh, acoshf, acoshl - inverse hyperbolic cosine functions double acosh(double x); float acoshf(float x); long double acoshl(long double x); The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std defers to the ISO C standard. These functions shall compute the inverse hyperbolic cosine of their argument x. An application wishing to check for error situations should set errno to zero and call feclearexcept(fe_all_except) before calling these functions. On return, if errno is non-zero or fetestexcept(fe_invalid FE_DIVBYZERO FE_OVERFLOW FE_UNDERFLOW) is non-zero, an error has occurred. RETURN VALUE Upon successful completion, these functions shall return the inverse hyperbolic cosine of their argument. For finite values of x < 1, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned. If x is NaN, a NaN shall be returned. If x is +1, +0 shall be returned. If x is +Inf, +Inf shall be returned. If x is -Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned. ERRORS These functions shall fail if: Domain Error The x argument is finite and less than +1.0, or is -Inf. [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised. The following sections are informative. EXAMPLES APPLICATION USAGE On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero. RATIONALE FUTURE DIRECTIONS cosh(), feclearexcept(), fetestexcept(), the Base Definitions volume of IEEE Std , Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h> POSIX

42 acosh(p) acosh(p) COPYRIGHT Portions of this text are reprinted and reproduced in electronic form from IEEE Std , 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at POSIX

43 asin(p) asin(p) asin, asinf, asinl - arc sine function double asin(double x); float asinf(float x); long double asinl(long double x); The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std defers to the ISO C standard. These functions shall compute the principal value of the arc sine of their argument x. The value of x should be in the range [-1,1]. An application wishing to check for error situations should set errno to zero and call feclearexcept(fe_all_except) before calling these functions. On return, if errno is non-zero or fetestexcept(fe_invalid FE_DIVBYZERO FE_OVERFLOW FE_UNDERFLOW) is non-zero, an error has occurred. RETURN VALUE Upon successful completion, these functions shall return the arc sine of x, in the range [-/2,/2] radians. For finite values of x not in the range [-1,1], a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned. If x is NaN, a NaN shall be returned. If x is ±0, x shall be returned. If x is ±Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned. If x is subnormal, a range error may occur and x should be returned. ERRORS These functions shall fail if: Domain Error The x argument is finite and is not in the range [-1,1], <img src="../images/opt-start.gif" alt="[option Start]" border="0"> or is ±Inf. [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised. These functions may fail if: Range Error The value of x is subnormal. [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised. The following sections are informative. EXAMPLES APPLICATION USAGE On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero. POSIX

44 asin(p) asin(p) RATIONALE FUTURE DIRECTIONS feclearexcept(), fetestexcept(), isnan(), sin(), the Base Definitions volume of IEEE Std , Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h> COPYRIGHT Portions of this text are reprinted and reproduced in electronic form from IEEE Std , 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at POSIX

45 asinh(p) asinh(p) asinh, asinhf, asinhl - inverse hyperbolic sine functions double asinh(double x); float asinhf(float x); long double asinhl(long double x); The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std defers to the ISO C standard. These functions shall compute the inverse hyperbolic sine of their argument x. An application wishing to check for error situations should set errno to zero and call feclearexcept(fe_all_except) before calling these functions. On return, if errno is non-zero or fetestexcept(fe_invalid FE_DIVBYZERO FE_OVERFLOW FE_UNDERFLOW) is non-zero, an error has occurred. RETURN VALUE Upon successful completion, these functions shall return the inverse hyperbolic sine of their argument. If x is NaN, a NaN shall be returned. If x is ±0, or ±Inf, x shall be returned. If x is subnormal, a range error may occur and x should be returned. ERRORS These functions may fail if: Range Error The value of x is subnormal. [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised. The following sections are informative. EXAMPLES APPLICATION USAGE On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero. RATIONALE FUTURE DIRECTIONS feclearexcept(), fetestexcept(), sinh(), the Base Definitions volume of IEEE Std , Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h> COPYRIGHT Portions of this text are reprinted and reproduced in electronic form from IEEE Std , 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the POSIX

46 asinh(p) asinh(p) referee document. The original Standard can be obtained online at POSIX

47 atan(p) atan(p) atan, atanf, atanl - arc tangent function double atan(double x); float atanf(float x); long double atanl(long double x); The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std defers to the ISO C standard. These functions shall compute the principal value of the arc tangent of their argument x. An application wishing to check for error situations should set errno to zero and call feclearexcept(fe_all_except) before calling these functions. On return, if errno is non-zero or fetestexcept(fe_invalid FE_DIVBYZERO FE_OVERFLOW FE_UNDERFLOW) is non-zero, an error has occurred. RETURN VALUE Upon successful completion, these functions shall return the arc tangent of x in the range [-/2,/2] radians. If x is NaN, a NaN shall be returned. If x is ±0, x shall be returned. If x is ±Inf, ±/2 shall be returned. If x is subnormal, a range error may occur and x should be returned. ERRORS These functions may fail if: Range Error The value of x is subnormal. [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised. The following sections are informative. EXAMPLES APPLICATION USAGE On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero. RATIONALE FUTURE DIRECTIONS atan2(), feclearexcept(), fetestexcept(), isnan(), tan(), the Base Definitions volume of IEEE Std , Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h> COPYRIGHT Portions of this text are reprinted and reproduced in electronic form from IEEE Std , 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open POSIX

48 atan(p) atan(p) Group Base Specifications Issue 6, Copyright (C) by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at POSIX

49 atan2(p) atan2(p) atan2, atan2f, atan2l - arc tangent functions double atan2(double y, double x); float atan2f(float y, float x); long double atan2l(long double y, long double x); The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std defers to the ISO C standard. These functions shall compute the principal value of the arc tangent of y/ x, using the signs of both arguments to determine the quadrant of the return value. An application wishing to check for error situations should set errno to zero and call feclearexcept(fe_all_except) before calling these functions. On return, if errno is non-zero or fetestexcept(fe_invalid FE_DIVBYZERO FE_OVERFLOW FE_UNDERFLOW) is non-zero, an error has occurred. RETURN VALUE Upon successful completion, these functions shall return the arc tangent of y/ x in the range [-,] radians. If y is ±0 and x is < 0, ± shall be returned. If y is ±0 and x is > 0, ±0 shall be returned. If y is < 0 and x is ±0, -/2 shall be returned. If y is > 0 and x is ±0, /2 shall be returned. If x is 0, a pole error shall not occur. If either x or y is NaN, a NaN shall be returned. If the result underflows, a range error may occur and y/ x should be returned. If y is ±0 and x is -0, ± shall be returned. If y is ±0 and x is +0, ±0 shall be returned. For finite values of ± y >0,ifxis -Inf, ± shall be returned. For finite values of ± y >0,ifxis +Inf, ±0 shall be returned. For finite values of x, ifyis ±Inf, ±/2 shall be returned. If y is ±Inf and x is -Inf, ±3/4 shall be returned. If y is ±Inf and x is +Inf, ±/4 shall be returned. If both arguments are 0, a domain error shall not occur. ERRORS These functions may fail if: Range Error The result underflows. [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised. The following sections are informative. POSIX

50 atan2(p) atan2(p) EXAMPLES APPLICATION USAGE On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero. RATIONALE FUTURE DIRECTIONS atan(), feclearexcept(), fetestexcept(), isnan(), tan(), the Base Definitions volume of IEEE Std , Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h> COPYRIGHT Portions of this text are reprinted and reproduced in electronic form from IEEE Std , 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at POSIX

51 atanh(p) atanh(p) atanh, atanhf, atanhl - inverse hyperbolic tangent functions double atanh(double x); float atanhf(float x); long double atanhl(long double x); The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std defers to the ISO C standard. These functions shall compute the inverse hyperbolic tangent of their argument x. An application wishing to check for error situations should set errno to zero and call feclearexcept(fe_all_except) before calling these functions. On return, if errno is non-zero or fetestexcept(fe_invalid FE_DIVBYZERO FE_OVERFLOW FE_UNDERFLOW) is non-zero, an error has occurred. RETURN VALUE Upon successful completion, these functions shall return the inverse hyperbolic tangent of their argument. If x is ±1, a pole error shall occur, and atanh(), atanhf(), and atanhl() shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively, with the same sign as the correct value of the function. For finite x >1, a domain error shall occur, and either a NaN (if supported), or an implementationdefined value shall be returned. If x is NaN, a NaN shall be returned. If x is ±0, x shall be returned. If x is ±Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned. If x is subnormal, a range error may occur and x should be returned. ERRORS These functions shall fail if: Domain Error The x argument is finite and not in the range [-1,1], or is ±Inf. [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised. Pole Error The x argument is ±1. [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the divide-by-zero floating-point exception shall be raised. These functions may fail if: Range Error The value of x is subnormal. [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then POSIX

52 atanh(p) atanh(p) the underflow floating-point exception shall be raised. The following sections are informative. EXAMPLES APPLICATION USAGE On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero. RATIONALE FUTURE DIRECTIONS feclearexcept(), fetestexcept(), tanh(), the Base Definitions volume of IEEE Std , Section 4.18, Treatment of Error Conditions for Mathematical Functions, <math.h> COPYRIGHT Portions of this text are reprinted and reproduced in electronic form from IEEE Std , 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at POSIX

53 cbrt(p) cbrt(p) cbrt, cbrtf, cbrtl - cube root functions double cbrt(double x); float cbrtf(float x); long double cbrtl(long double x); The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std defers to the ISO C standard. These functions shall compute the real cube root of their argument x. RETURN VALUE Upon successful completion, these functions shall return the cube root of x. If x is NaN, a NaN shall be returned. If x is ±0 or±inf, x shall be returned. ERRORS No errors are defined. The following sections are informative. EXAMPLES APPLICATION USAGE RATIONALE For some applications, a true cube root function, which returns negative results for negative arguments, is more appropriate than pow( x, 1.0/3.0), which returns a NaN for x less than 0. FUTURE DIRECTIONS The Base Definitions volume of IEEE Std , <math.h> COPYRIGHT Portions of this text are reprinted and reproduced in electronic form from IEEE Std , 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at POSIX

54 ceil(p) ceil(p) ceil, ceilf, ceill - ceiling value function double ceil(double x); float ceilf(float x); long double ceill(long double x); The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std defers to the ISO C standard. These functions shall compute the smallest integral value not less than x. An application wishing to check for error situations should set errno to zero and call feclearexcept(fe_all_except) before calling these functions. On return, if errno is non-zero or fetestexcept(fe_invalid FE_DIVBYZERO FE_OVERFLOW FE_UNDERFLOW) is non-zero, an error has occurred. RETURN VALUE Upon successful completion, ceil(), ceilf(), and ceill() shall return the smallest integral value not less than x, expressed as a type double, float, orlong double, respectively. If x is NaN, a NaN shall be returned. If x is ±0 or±inf, x shall be returned. If the correct value would cause overflow, a range error shall occur and ceil(), ceilf(), and ceill() shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively. ERRORS These functions shall fail if: Range Error The result overflows. [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised. The following sections are informative. EXAMPLES APPLICATION USAGE The integral value returned by these functions need not be expressible as an int or long. The return value should be tested before assigning it to an integer type to avoid the undefined results of an integer overflow. The ceil() function can only overflow when the floating-point representation has DBL_MANT_DIG > DBL_MAX_EXP. On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero. RATIONALE FUTURE DIRECTIONS POSIX