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libm(3lib)
libm(3LIB) Interface Libraries libm(3LIB)
NAME
libm - C math library
SYNOPSIS
c99 [ flag... ] file... -lm [ library... ]
DESCRIPTION
Functions in this library provide common elementary mathematical func‐
tions and floating point environment routines defined by System V, ANSI
C, POSIX, and so on. See standards(7). Additional functions in this
library provide extended support for handling floating point excep‐
tions.
INTERFACES
The shared object libm.so.2 provides the public interfaces defined
below. See intro(3) for additional information on shared object inter‐
faces.
tab(); lw(2.75i) lw(2.75i)
acosacosf acoshacoshf acoshlacosl asinasinf asinhasinhf asinhlasinl
atanatan2 atan2fatan2l atanfatanh atanhfatanhl atanlcabs cabsfcabsl
cacoscacosf cacoshcacoshf cacoshlcacosl cargcargf carglcasin casinfcas‐
inh casinhfcasinhl casinlcatan catanfcatanh catanhfcatanhl catanlcbrt
cbrtfcbrtl ccosccosf ccoshccoshf ccoshlccosl ceilceilf ceillcexp
cexpfcexpl cimagcimagf cimaglclog clogfclogl conjconjf conjlcopysign
copysignfcopysignl coscosf coshcoshf coshlcosl cpowcpowf cpowlcproj
cprojfcprojl crealcrealf creallcsin csinfcsinh csinhfcsinhl csinlcsqrt
csqrtfcsqrtl ctanctanf ctanhctanhf ctanhlctanl erferfc erfcferfcl erf‐
ferfl expexp2 exp2fexp2l expfexpl expm1expm1f expm1lfabs fabsffabsl
fdimfdimf fdimlfeclearexcept fegetenvfegetexceptflag fegetroundfehold‐
except feraiseexceptfesetenv fesetexceptflagfesetround fetestexceptfe‐
updateenv fex_get_handlingfex_get_log fex_get_log_depthfex_getex‐
cepthandler fex_log_entryfex_merge_flags fex_set_handlingfex_set_log
fex_set_log_depthfex_setexcepthandler floorfloorf floorlfma fmaffmal
fmaxfmaxf fmaxlfmin fminffminl fmodfmodf fmodlfrexp frexpffrexpl gam‐
magamma_r gammafgammaf_r gammalgammal_r hypothypotf hypotlilogb ilogb‐
filogbl isnanj0 j0fj0l j1j1f j1ljn jnfjnl ldexpldexpf ldexpllgamma
lgamma_rlgammaf lgammaf_rlgammal lgammal_rllrint llrintfllrintl
llroundllroundf llroundllog log10log10f log10llog1p log1pflog1pl
log2log2f log2llogb logbflogbl logflogl lrintlrintf lrintllround
lroundflroundl matherrmodf modffmodfl nannanf nanlnearbyint nearby‐
intfnearbyintl nextafternextafterf nextafterlnexttoward nextto‐
wardfnexttowardl powpowf powlremainder remainderfremainderl
remquoremquof remquolrint rintfrintl roundroundf roundlscalb scalbfs‐
calbl scalblnscalblnf scalblnlscalbn scalbnfscalbnl signgamsigngamf
signgamlsignificand significandfsignificandl sinsincos sincosfsincosl
sinfsinh sinhfsinhl sinlsqrt sqrtfsqrtl tantanf tanhtanhf tanhltanl
tgammatgammaf tgammaltrunc truncftruncl y0y0f y0ly1 y1fy1l ynynf ynl
The following interfaces are unique to the x86 and x64 versions of this
library:
tab(); lw(2.75i) lw(2.75i)
fegetprecfesetprec
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 accu‐
racy 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 dis‐
abled. 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)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes acosf1.0<
1 acoshf1.0< 1 asinf1.0< 1 asinhf1.0< 1 atanf1.0< 1 atan2f1.0< 1
atanhf1.0< 1 cbrtf1.0< 1 cosf1.0< 1 coshf1.0< 1 erff1.0< 1 erfcf1.0< 1
expf1.0< 1 exp2f1.0< 1 expm1f1.0< 1 hypotf1.0< 1 lgammaf1.0< 1 logf1.0<
1 log10f1.0< 1 log1pf1.0< 1 log2f1.0< 1 powf1.0< 1 sinf1.0< 1 sinhf1.0<
1 sqrtf0.50.500[1] tanf1.0< 1 tanhf1.0< 1 tgammaf1.0< 1
Double precision real functions (SPARC and x64)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes acos1.0<
1 acosh4.01.878 asin1.0< 1 asinh7.01.653 atan1.0<1 atan22.51.475
atanh4.01.960 cbrt1.0< 1 cos1.0< 1 cosh3.01.168 erf4.00.959
erfc6.02.816 exp1.0< 1 exp22.01.050 expm11.0< 1 hypot1.0< 1
lgamma61.55.629[2] log1.0< 1 log103.51.592 log1p1.0< 1 log21.0< 1
pow1.0< 1 sin1.0< 1 sinh4.02.078 sqrt0.50.500[1] tan1.0< 1 tanh3.52.136
tgamma1.0< 1
Double precision real functions (x86)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes acos1.0<
1 acosh4.01.694 asin1.0< 1 asinh7.01.493 atan1.0< 1 atan21.0< 1
atanh4.01.445 cbrt1.0< 1 cos1.0< 1 cosh3.01.001 erf4.00.932
erfc6.02.728 exp1.0< 1 exp21.0< 1 expm11.0< 1 hypot1.0< 1
lgamma61.52.654[2] log1.0< 1 log101.0< 1 log1p1.0< 1 log21.0< 1 pow1.0<
1 sin1.0< 1 sinh4.01.458 sqrt0.50030.500[1] tan1.0< 1 tanh3.51.592
tgamma1.0< 1
Quadruple precision real functions (SPARC)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes
acosl3.51.771 acoshl8.01.275 asinl4.02.007 asinhl9.01.823 atanl1.0< 1
atan2l2.51.102 atanhl4.01.970 cbrtl1.0< 1 cosl1.0< 1 coshl3.50.985
erfl2.00.779 erfcl68.513.923 expl1.0< 1 exp2l2.00.714 expm1l2.01.020
hypotl1.0< 1 lgammal18.52.916[2] logl1.0< 1 log10l3.51.156
log1pl2.01.216 log2l3.51.675 powl1.0< 1 sinl1.0< 1 sinhl4.51.589
sqrtl0.50.500[1] tanl4.52.380 tanhl4.51.692 tgammal1.0< 1
Extended precision real functions (x86 and x64)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes
acosl3.01.868 acoshl8.02.352 asinl3.01.716 asinhl9.02.346 atanl1.0< 1
atan2l1.0< 1 atanhl4.02.438 cbrtl1.0< 1 cosl1.0< 1 coshl3.51.288
erfl1.0< 1 erfcl78.513.407 expl3.51.291 exp2l1.50.807 expm1l4.01.936
hypotl3.52.087 lgammal22.54.197[2] logl2.00.881 log10l2.01.284
log1pl5.02.370 log2l1.0< 1 powl32770.04478.132 sinl1.0< 1 sinhl4.52.356
sqrtl0.50.500[1] tanl4.52.366 tanhl4.52.417 tgammal1.0< 1
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 cor‐
rectly 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 func‐
tion, the error bound shown applies separately to both the real and
imaginary parts of the result. (For example, both the real and imagi‐
nary 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)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes cacosf,
cacoshf1< 1[1] casinf, casinhf1< 1 catanf, catanhf6< 1 ccosf,
ccoshf102.012 cexpf32.239 clogf3< 1 cpowf—< 1[2] csinf, csinhf102.009
csqrtf4< 1 ctanf, ctanhf136.987
Single precision complex functions (x86)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes cacosf,
cacoshf1< 1[1] casinf, casinhf1< 1 catanf, catanhf6< 1 ccosf,
ccoshf101.984 cexpf31.984 clogf3< 1 cpowf—< 1[2] csinf, csinhf101.973
csqrtf4< 1 ctanf, ctanhf134.657
Double precision complex functions (SPARC and x64)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes cacos,
cacosh93.831[1] casin, casinh93.732 catan, catanh64.179 ccos,
ccosh103.832 cexp32.255 clog32.870 cpow--[2] csin, csinh103.722
csqrt43.204 ctan, ctanh137.143
Double precision complex functions (x86)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes cacos,
cacosh93.624[1] casin, casinh93.624 catan, catanh62.500 ccos,
ccosh102.929 cexp32.147 clog31.927 cpow--[2] csin, csinh102.918
csqrt41.914 ctan, ctanh134.630
Quadruple precision complex functions (SPARC)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes cacosl,
cacoshl93[1] casinl, casinhl93 catanl, catanhl63 ccosl, ccoshl103
cexpl32 clogl32 cpowl--[2] csinl, csinhl103 csqrtl43 ctanl, ctanhl135
Extended precision complex functions (x86 and x64)
tab(); lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i) lw(1.38i)
error boundlargest error function (ulps)observed (ulps) notes cacosl,
cacoshl92[1] casinl, casinhl92 catanl, catanhl62 ccosl, ccoshl103
cexpl32.699 clogl31 cpowl--[2] csinl, csinhl103 csqrtl41.452 ctanl,
ctanhl135
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(7) for descriptions of the following attributes:
tab() box; cw(2.75i) |cw(2.75i) lw(2.75i) |lw(2.75i)
ATTRIBUTE TYPEATTRIBUTE VALUE _ Availabilitysystem/library/math MT-Lev‐
elSafe with exceptions _ Interface StabilityCommitted
As described on the lgamma(3M) manual page, gamma() and lgamma() and
their float and long double counterparts are Unsafe. All other func‐
tions in libm.so.2 are MT-Safe.
SEE ALSO
math.h(3HEAD), lgamma(3M), intro(3), attributes(7), standards(7)
Solaris 11.4 27 Sept 2016 libm(3LIB)