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Updated: Thursday, June 13, 2019
 
 

libm(3LIB)

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(7). 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
acosl
asin
asinf
asinh
asinhf
asinhl
asinl
atan
atan2
atan2f
atan2l
atanf
atanh
atanhf
atanhl
atanl
cabs
cabsf
cabsl
cacos
cacosf
cacosh
cacoshf
cacoshl
cacosl
carg
cargf
cargl
casin
casinf
casinh
casinhf
casinhl
casinl
catan
catanf
catanh
catanhf
catanhl
catanl
cbrt
cbrtf
cbrtl
ccos
ccosf
ccosh
ccoshf
ccoshl
ccosl
ceil
ceilf
ceill
cexp
cexpf
cexpl
cimag
cimagf
cimagl
clog
clogf
clogl
conj
conjf
conjl
copysign
copysignf
copysignl
cos
cosf
cosh
coshf
coshl
cosl
cpow
cpowf
cpowl
cproj
cprojf
cprojl
creal
crealf
creall
csin
csinf
csinh
csinhf
csinhl
csinl
csqrt
csqrtf
csqrtl
ctan
ctanf
ctanh
ctanhf
ctanhl
ctanl
erf
erfc
erfcf
erfcl
erff
erfl
exp
exp2
exp2f
exp2l
expf
expl
expm1
expm1f
expm1l
fabs
fabsf
fabsl
fdim
fdimf
fdiml
feclearexcept
fegetenv
fegetexceptflag
fegetround
feholdexcept
feraiseexcept
fesetenv
fesetexceptflag
fesetround
fetestexcept
feupdateenv
fex_get_handling
fex_get_log
fex_get_log_depth
fex_getexcepthandler
fex_log_entry
fex_merge_flags
fex_set_handling
fex_set_log
fex_set_log_depth
fex_setexcepthandler
floor
floorf
floorl
fma
fmaf
fmal
fmax
fmaxf
fmaxl
fmin
fminf
fminl
fmod
fmodf
fmodl
frexp
frexpf
frexpl
gamma
gamma_r
gammaf
gammaf_r
gammal
gammal_r
hypot
hypotf
hypotl
ilogb
ilogbf
ilogbl
isnan
j0
j0f
j0l
j1
j1f
j1l
jn
jnf
jnl
ldexp
ldexpf
ldexpl
lgamma
lgamma_r
lgammaf
lgammaf_r
lgammal
lgammal_r
llrint
llrintf
llrintl
llround
llroundf
llroundl
log
log10
log10f
log10l
log1p
log1pf
log1pl
log2
log2f
log2l
logb
logbf
logbl
logf
logl
lrint
lrintf
lrintl
lround
lroundf
lroundl
matherr
modf
modff
modfl
nan
nanf
nanl
nearbyint
nearbyintf
nearbyintl
nextafter
nextafterf
nextafterl
nexttoward
nexttowardf
nexttowardl
pow
powf
powl
remainder
remainderf
remainderl
remquo
remquof
remquol
rint
rintf
rintl
round
roundf
roundl
scalb
scalbf
scalbl
scalbln
scalblnf
scalblnl
scalbn
scalbnf
scalbnl
signgam
signgamf
signgaml
significand
significandf
significandl
sin
sincos
sincosf
sincosl
sinf
sinh
sinhf
sinhl
sinl
sqrt
sqrtf
sqrtl
tan
tanf
tanh
tanhf
tanhl
tanl
tgamma
tgammaf
tgammal
trunc
truncf
truncl
y0
y0f
y0l
y1
y1f
y1l
yn
ynf
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
1.0
< 1
acoshf
1.0
< 1
asinf
1.0
< 1
asinhf
1.0
< 1
atanf
1.0
< 1
atan2f
1.0
< 1
atanhf
1.0
< 1
cbrtf
1.0
< 1
cosf
1.0
< 1
coshf
1.0
< 1
erff
1.0
< 1
erfcf
1.0
< 1
expf
1.0
< 1
exp2f
1.0
< 1
expm1f
1.0
< 1
hypotf
1.0
< 1
lgammaf
1.0
< 1
logf
1.0
< 1
log10f
1.0
< 1
log1pf
1.0
< 1
log2f
1.0
< 1
powf
1.0
< 1
sinf
1.0
< 1
sinhf
1.0
< 1
sqrtf
0.5
0.500
[1]
tanf
1.0
< 1
tanhf
1.0
< 1
tgammaf
1.0
< 1
Double precision real functions (SPARC and x64)
error bound
largest error
function
(ulps)
observed (ulps)
notes
acos
1.0
< 1
acosh
4.0
1.878
asin
1.0
< 1
asinh
7.0
1.653
atan
1.0
<1
atan2
2.5
1.475
atanh
4.0
1.960
cbrt
1.0
< 1
cos
1.0
< 1
cosh
3.0
1.168
erf
4.0
0.959
erfc
6.0
2.816
exp
1.0
< 1
exp2
2.0
1.050
expm1
1.0
< 1
hypot
1.0
< 1
lgamma
61.5
5.629
[2]
log
1.0
< 1
log10
3.5
1.592
log1p
1.0
< 1
log2
1.0
< 1
pow
1.0
< 1
sin
1.0
< 1
sinh
4.0
2.078
sqrt
0.5
0.500
[1]
tan
1.0
< 1
tanh
3.5
2.136
tgamma
1.0
< 1
Double precision real functions (x86)
error bound
largest error
function
(ulps)
observed (ulps)
notes
acos
1.0
< 1
acosh
4.0
1.694
asin
1.0
< 1
asinh
7.0
1.493
atan
1.0
< 1
atan2
1.0
< 1
atanh
4.0
1.445
cbrt
1.0
< 1
cos
1.0
< 1
cosh
3.0
1.001
erf
4.0
0.932
erfc
6.0
2.728
exp
1.0
< 1
exp2
1.0
< 1
expm1
1.0
< 1
hypot
1.0
< 1
lgamma
61.5
2.654
[2]
log
1.0
< 1
log10
1.0
< 1
log1p
1.0
< 1
log2
1.0
< 1
pow
1.0
< 1
sin
1.0
< 1
sinh
4.0
1.458
sqrt
0.5003
0.500
[1]
tan
1.0
< 1
tanh
3.5
1.592
tgamma
1.0
< 1
Quadruple precision real functions (SPARC)
error bound
largest error
function
(ulps)
observed (ulps)
notes
acosl
3.5
1.771
acoshl
8.0
1.275
asinl
4.0
2.007
asinhl
9.0
1.823
atanl
1.0
< 1
atan2l
2.5
1.102
atanhl
4.0
1.970
cbrtl
1.0
< 1
cosl
1.0
< 1
coshl
3.5
0.985
erfl
2.0
0.779
erfcl
68.5
13.923
expl
1.0
< 1
exp2l
2.0
0.714
expm1l
2.0
1.020
hypotl
1.0
< 1
lgammal
18.5
2.916
[2]
logl
1.0
< 1
log10l
3.5
1.156
log1pl
2.0
1.216
log2l
3.5
1.675
powl
1.0
< 1
sinl
1.0
< 1
sinhl
4.5
1.589
sqrtl
0.5
0.500
[1]
tanl
4.5
2.380
tanhl
4.5
1.692
tgammal
1.0
< 1
Extended precision real functions (x86 and x64)
error bound
largest error
function
(ulps)
observed (ulps)
notes
acosl
3.0
1.868
acoshl
8.0
2.352
asinl
3.0
1.716
asinhl
9.0
2.346
atanl
1.0
< 1
atan2l
1.0
< 1
atanhl
4.0
2.438
cbrtl
1.0
< 1
cosl
1.0
< 1
coshl
3.5
1.288
erfl
1.0
< 1
erfcl
78.5
13.407
expl
3.5
1.291
exp2l
1.5
0.807
expm1l
4.0
1.936
hypotl
3.5
2.087
lgammal
22.5
4.197
[2]
logl
2.0
0.881
log10l
2.0
1.284
log1pl
5.0
2.370
log2l
1.0
< 1
powl
32770.0
4478.132
sinl
1.0
< 1
sinhl
4.5
2.356
sqrtl
0.5
0.500
[1]
tanl
4.5
2.366
tanhl
4.5
2.417
tgammal
1.0
< 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 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
1
< 1
[1]
casinf, casinhf
1
< 1
catanf, catanhf
6
< 1
ccosf, ccoshf
10
2.012
cexpf
3
2.239
clogf
3
< 1
cpowf
< 1
[2]
csinf, csinhf
10
2.009
csqrtf
4
< 1
ctanf, ctanhf
13
6.987
Single precision complex functions (x86)
error bound
largest error
function
(ulps)
observed (ulps)
notes
cacosf, cacoshf
1
< 1
[1]
casinf, casinhf
1
< 1
catanf, catanhf
6
< 1
ccosf, ccoshf
10
1.984
cexpf
3
1.984
clogf
3
< 1
cpowf
< 1
[2]
csinf, csinhf
10
1.973
csqrtf
4
< 1
ctanf, ctanhf
13
4.657
Double precision complex functions (SPARC and x64)
error bound
largest error
function
(ulps)
observed (ulps)
notes
cacos, cacosh
9
3.831
[1]
casin, casinh
9
3.732
catan, catanh
6
4.179
ccos, ccosh
10
3.832
cexp
3
2.255
clog
3
2.870
cpow
-
-
[2]
csin, csinh
10
3.722
csqrt
4
3.204
ctan, ctanh
13
7.143
Double precision complex functions (x86)
error bound
largest error
function
(ulps)
observed (ulps)
notes
cacos, cacosh
9
3.624
[1]
casin, casinh
9
3.624
catan, catanh
6
2.500
ccos, ccosh
10
2.929
cexp
3
2.147
clog
3
1.927
cpow
-
-
[2]
csin, csinh
10
2.918
csqrt
4
1.914
ctan, ctanh
13
4.630
Quadruple precision complex functions (SPARC)
error bound
largest error
function
(ulps)
observed (ulps)
notes
cacosl, cacoshl
9
3
[1]
casinl, casinhl
9
3
catanl, catanhl
6
3
ccosl, ccoshl
10
3
cexpl
3
2
clogl
3
2
cpowl
-
-
[2]
csinl, csinhl
10
3
csqrtl
4
3
ctanl, ctanhl
13
5
Extended precision complex functions (x86 and x64)
error bound
largest error
function
(ulps)
observed (ulps)
notes
cacosl, cacoshl
9
2
[1]
casinl, casinhl
9
2
catanl, catanhl
6
2
ccosl, ccoshl
10
3
cexpl
3
2.699
clogl
3
1
cpowl
-
-
[2]
csinl, csinhl
10
3
csqrtl
4
1.452
ctanl, ctanhl
13
5
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:

ATTRIBUTE TYPE
ATTRIBUTE VALUE
Availability
system/library/math
MT-Level
Safe with exceptions
Interface Stability
Committed

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

math.h(3HEAD), lgamma(3M), intro(3), attributes(7), standards(7)