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NAME

libm - C math library
 

SYNOPSIS

c99 [ flag... ] file... -lm [ library... ] 

DESCRIPTION

Functions in this library provide common elementary mathematical functions and floating point environment routines defined by System V, ANSI C, POSIX, and so on. See standards(5). Additional functions in this library provide extended support for handling floating point exceptions.  

INTERFACES

The shared object libm.so.2 provides the public interfaces defined below. See Intro(3) for additional information on shared object interfaces.

acos	acosf
acosh	acoshf
acoshl
asin
asinh
asinhl
atan
atan2f
atanf
atanhf
atanl
cabsf
cacos
cacosh
cacoshl
carg
cargl
casinf
casinhf
casinl
catanf
catanhf
catanl
cbrtf
ccos
ccosh
ccoshl
ceil
ceill
cexpf
cimag
cimagl
clogf
conj
conjl
copysignf
cos
cosh
coshl
cpow
cpowl
cprojf
creal
creall
csinf
csinhf
csinl
csqrtf
ctan
ctanh
ctanhl
erf
erfcf
erff
exp
exp2f
expf
expm1
expm1l
fabsf
fdim
fdiml
fegetenv
fegetround
feraiseexcept
fesetexceptflag
fetestexcept
fex_get_handling
fex_get_log_depth
fex_log_entry
fex_set_handling
fex_set_log_depth
floor
floorl
fmaf
fmax
fmaxl
fminf
fmod
fmodl
frexpf
gamma
gammaf
gammal
hypot
hypotl
ilogbf
isnan
j0f
j1
j1l
jnf
ldexp
ldexpl
lgamma_r
lgammaf_r
lgammal_r
llrintf
llround
llroundl
log10
log10l
log1pf
log2
log2l
logbf
logf
lrint
lrintl
lroundf
matherr
modff
nan
nanl
nearbyintf
nextafter
nextafterl
nexttowardf
pow
powl
remainderf
remquo
remquol
rintf
round
roundl
scalbf
scalbln
scalblnl
scalbnf
signgam
signgaml
significandf
sin
sincosf
sinf
sinhf
sinl
sqrtf
tan
tanh
tanhl
tgamma
tgammal
truncf
y0
y0l
y1f
yn
ynl

The following interfaces are unique to the x86 and x64 versions of this library:

fegetprec

fesetprec

ACCURACY

ISO/IEC 9899:1999, also known as C99, specifies the functions listed in the following tables and states that the accuracy of these functions is "implementation-defined". The information below characterizes the accuracy of these functions as implemented in libm.so.2. For each function, the tables provide an upper bound on the largest error possible for any argument and the largest error actually observed among a large sample of arguments. Errors are expressed in "units in the last place", or ulps, relative to the exact function value for each argument (regarding the argument as exact). Ulps depend on the precision of the floating point format: if y is the exact function value, x and x' are adjacent floating point numbers such that x < y < x', and x'' is the computed function value, then provided x, x', and x'' all lie in the same binade, the error in x'' is |y - x''| / |x - x'| ulps. In particular, when the error is less than one ulp, the computed value is one of the two floating point numbers adjacent to the exact value.

The bounds and observed errors listed below apply only in the default floating point modes. Specifically, on SPARC, these bounds assume the rounding direction is round-to-nearest and non-standard mode is disabled. On x86, the bounds assume the rounding direction is round-to-nearest and the rounding precision is round-to-64-bits. Moreover, on x86, floating point function values are returned in a floating point register in extended double precision format, but the bounds below assume that the result value is then stored to memory in the format corresponding to the function's type. On x64, the bounds assume the rounding direction in both the x87 floating point control word and the MXCSR is round-to-nearest, the rounding precision in the x87 control word is round-to-64-bits, and the FTZ and DAZ modes are disabled.

The error bounds listed below are believed to be correct, but smaller bounds might be proved later. The observed errors are the largest ones currently known, but larger errors might be discovered later. Numbers in the notes column refer to the notes following the tables.  

Real Functions

Single precision real functions (SPARC, x86, and x64)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
acosf
acoshf
asinf
asinhf
atanf
atan2f
atanhf
cbrtf
cosf
coshf
erff
erfcf
expf
exp2f
expm1f
hypotf
lgammaf
logf
log10f
log1pf
log2f
powf
sinf
sinhf
sqrtf
tanf
tanhf
tgammaf

Double precision real functions (SPARC and x64)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
acos
acosh
asin
asinh
atan
atan2
atanh
cbrt
cos
cosh
erf
erfc
exp
exp2
expm1
hypot
lgamma
log
log10
log1p
log2
pow
sin
sinh
sqrt
tan
tanh
tgamma

Double precision real functions (x86)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
acos
acosh
asin
asinh
atan
atan2
atanh
cbrt
cos
cosh
erf
erfc
exp
exp2
expm1
hypot
lgamma
log
log10
log1p
log2
pow
sin
sinh
sqrt
tan
tanh
tgamma

Quadruple precision real functions (SPARC)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
acosl
acoshl
asinl
asinhl
atanl
atan2l
atanhl
cbrtl
cosl
coshl
erfl
erfcl
expl
exp2l
expm1l
hypotl
lgammal
logl
log10l
log1pl
log2l
powl
sinl
sinhl
sqrtl
tanl
tanhl
tgammal

Extended precision real functions (x86 and x64)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
acosl
acoshl
asinl
asinhl
atanl
atan2l
atanhl
cbrtl
cosl
coshl
erfl
erfcl
expl
exp2l
expm1l
hypotl
lgammal
logl
log10l
log1pl
log2l
powl
sinl
sinhl
sqrtl
tanl
tanhl
tgammal

Notes:

[1]

On SPARC and x64, sqrtf, sqrt, and sqrtl are correctly rounded in accordance with IEEE 754. On x86, sqrtl is correctly rounded, sqrtf is correctly rounded provided the result is narrowed to single precision as discussed above, but sqrt might not be correctly rounded due to "double rounding": when the intermediate value computed to extended precision lies exactly halfway between two representable numbers in double precision, the result of rounding the intermediate value to double precision is determined by the round-ties-to-even rule. If this rule causes the second rounding to round in the same direction as the first, the net rounding error can exceed 0.5 ulps. (The error is bounded instead by 0.5*(1 + 2^-11) ulps.)

[2]

Error bounds for lgamma and lgammal apply only for positive arguments.

Complex functions

The real-valued complex functions cabsf, cabs, cabsl, cargf, carg, and cargl are equivalent to the real functions hypotf, hypot, hypotl, atan2f, atan2, and atan2l, respectively. The error bounds and observed errors given above for the latter functions also apply to the former.

The complex functions listed below are complex-valued. For each function, the error bound shown applies separately to both the real and imaginary parts of the result. (For example, both the real and imaginary parts of cacosf(z) are accurate to within 1 ulp regardless of their magnitudes.) Similarly, the largest observed error shown is the largest error found in either the real or the imaginary part of the result.  

Single precision complex functions (SPARC and x64)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
cacosf, cacoshf
casinf, casinhf
catanf, catanhf
ccosf, ccoshf
cexpf
clogf
cpowf
csinf, csinhf
csqrtf
ctanf, ctanhf

Single precision complex functions (x86)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
cacosf, cacoshf
casinf, casinhf
catanf, catanhf
ccosf, ccoshf
cexpf
clogf
cpowf
csinf, csinhf
csqrtf
ctanf, ctanhf

Double precision complex functions (SPARC and x64)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
cacos, cacosh
casin, casinh
catan, catanh
ccos, ccosh
cexp
clog
cpow
csin, csinh
csqrt
ctan, ctanh

Double precision complex functions (x86)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
cacos, cacosh
casin, casinh
catan, catanh
ccos, ccosh
cexp
clog
cpow
csin, csinh
csqrt
ctan, ctanh

Quadruple precision complex functions (SPARC)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
cacosl, cacoshl
casinl, casinhl
catanl, catanhl
ccosl, ccoshl
cexpl
clogl
cpowl
csinl, csinhl
csqrtl
ctanl, ctanhl

Extended precision complex functions (x86 and x64)

	error bound	largest error
function	(ulps)	observed (ulps)	notes
cacosl, cacoshl
casinl, casinhl
catanl, catanhl
ccosl, ccoshl
cexpl
clogl
cpowl
csinl, csinhl
csqrtl
ctanl, ctanhl

Notes:

[1]

The complex hyperbolic trigonometric functions are equivalent by symmetries to their circular trigonometric counterparts. Because the implementations of these functions exploit these symmetries, corresponding functions have the same error bounds and observed errors.

[2]

For large arguments, the results computed by cpowf, cpow, and cpowl can have unbounded relative error. It might be possible to give error bounds for specific domains, but no such bounds are currently available. The observed errors shown are for the domain {(z,w) : max(|Re z|, |Im z|, |Re w|, |Im w|) <= 1}.

FILES

/lib/libm.so.2

shared object

/lib/64/libm.so.2

64-bit shared object

ATTRIBUTES

See attributes(5) for descriptions of the following attributes:

ATTRIBUTE TYPE ATTRIBUTE VALUE Availability SUNWlibmsr MT-Level

As described on the lgamma(3M) manual page, gamma() and lgamma() and their float and long double counterparts are Unsafe. All other functions in libm.so.2 are MT-Safe.  

SEE ALSO

Intro(3), lgamma(3M), math.h(3HEAD), attributes(5), standards(5)

Index

NAME

SYNOPSIS

DESCRIPTION

INTERFACES

ACCURACY

Real Functions

Single precision real functions (SPARC, x86, and x64)

Double precision real functions (SPARC and x64)

Double precision real functions (x86)

Quadruple precision real functions (SPARC)

Extended precision real functions (x86 and x64)

Notes:

Complex functions

Single precision complex functions (SPARC and x64)

Single precision complex functions (x86)

Double precision complex functions (SPARC and x64)

Double precision complex functions (x86)

Quadruple precision complex functions (SPARC)

Extended precision complex functions (x86 and x64)

Notes:

FILES

ATTRIBUTES

SEE ALSO

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