This section lists the known errors of the functions in the math
library. Errors are measured in “units of the last place”. This is a
measure for the relative error. For a number z with the
representation d.d...d·2^e (we assume IEEE
floating-point numbers with base 2) the ULP is represented by
|d.d...d - (z / 2^e)| / 2^(p - 1)
where p is the number of bits in the mantissa of the
floating-point number representation. Ideally the error for all
functions is always less than 0.5ulps. Using rounding bits this is also
possible and normally implemented for the basic operations. To achieve
the same for the complex math functions requires a lot more work and
this has not yet been done.
Therefore many of the functions in the math library have errors. The
table lists the maximum error for each function which is exposed by one
of the existing tests in the test suite. The table tries to cover as much
as possible and list the actual maximum error (or at least a ballpark
figure) but this is often not achieved due to the large search space.
The table lists the ULP values for different architectures. Different
architectures have different results since their hardware support for
floating-point operations varies and also the existing hardware support
is different.
Function
Alpha
ARM
Generic
ix86
IA64
acosf
-
-
-
-
-
acos
-
-
-
-
-
acosl
-
-
-
1150
-
acoshf
-
-
-
-
-
acosh
-
-
-
-
-
acoshl
-
-
-
1
-
asinf
2
2
-
-
-
asin
1
1
-
1
1
asinl
-
-
-
1
-
asinhf
-
-
-
-
-
asinh
-
-
-
-
-
asinhl
-
-
-
656
14
atanf
-
-
-
-
-
atan
-
-
-
-
-
atanl
-
-
-
549
-
atanhf
-
-
-
-
-
atanh
1
1
-
1
-
atanhl
-
-
-
1605
-
atan2f
4
-
-
-
-
atan2
-
-
-
-
-
atan2l
-
-
-
549
-
cabsf
1
1
-
1
1
cabs
1
1
-
1
1
cabsl
-
-
-
560
1
cacosf
1 + i 1
1 + i 1
-
1 + i 2
1 + i 2
cacos
1 + i 0
1 + i 0
-
1 + i 0
1 + i 0
cacosl
-
-
-
151 + i 329
1 + i 1
cacoshf
7 + i 3
7 + i 3
-
4 + i 4
7 + i 0
cacosh
1 + i 1
1 + i 1
-
1 + i 1
1 + i 1
cacoshl
-
-
-
328 + i 151
7 + i 1
cargf
-
-
-
-
-
carg
-
-
-
-
-
cargl
-
-
-
-
-
casinf
2 + i 1
2 + i 1
-
2 + i 2
2 + i 2
casin
3 + i 0
3 + i 0
-
3 + i 0
3 + i 0
casinl
-
-
-
603 + i 329
0 + i 1
casinhf
1 + i 6
1 + i 6
-
1 + i 6
1 + i 6
casinh
5 + i 3
5 + i 3
-
5 + i 3
5 + i 3
casinhl
-
-
-
892 + i 12
5 + i 5
catanf
4 + i 1
4 + i 1
-
0 + i 1
0 + i 1
catan
0 + i 1
0 + i 1
-
0 + i 1
0 + i 1
catanl
-
-
-
251 + i 474
1 + i 0
catanhf
1 + i 6
1 + i 6
-
1 + i 0
-
catanh
4 + i 1
4 + i 1
-
2 + i 0
4 + i 0
catanhl
-
-
-
66 + i 447
1 + i 0
cbrtf
-
-
-
-
-
cbrt
1
1
-
1
1
cbrtl
-
-
-
716
-
ccosf
0 + i 1
0 + i 1
-
1 + i 1
1 + i 1
ccos
1 + i 1
1 + i 1
-
1 + i 1
1 + i 1
ccosl
-
-
-
5 + i 1901
0 + i 1
ccoshf
1 + i 1
1 + i 1
-
1 + i 1
1 + i 1
ccosh
1 + i 1
1 + i 1
-
1 + i 1
1 + i 1
ccoshl
-
-
-
1467 + i 1183
1 + i 1
ceilf
-
-
-
-
-
ceil
-
-
-
-
-
ceill
-
-
-
-
-
cexpf
1 + i 1
1 + i 1
-
1 + i 0
1 + i 1
cexp
1 + i 0
1 + i 0
-
-
1 + i 0
cexpl
-
-
-
940 + i 1067
2 + i 0
cimagf
-
-
-
-
-
cimag
-
-
-
-
-
cimagl
-
-
-
-
-
clogf
0 + i 3
0 + i 3
-
-
-
clog
0 + i 1
0 + i 1
-
-
-
clogl
-
-
-
0 + i 1
-
clog10f
1 + i 5
1 + i 5
-
1 + i 1
1 + i 1
clog10
1 + i 1
1 + i 1
-
2 + i 1
2 + i 1
clog10l
-
-
-
1403 + i 186
1 + i 2
conjf
-
-
-
-
-
conj
-
-
-
-
-
conjl
-
-
-
-
-
copysignf
-
-
-
-
-
copysign
-
-
-
-
-
copysignl
-
-
-
-
-
cosf
1
1
-
1
1
cos
2
2
-
2
2
cosl
-
-
-
529
0.5
coshf
-
-
-
-
-
cosh
-
-
-
-
-
coshl
-
-
-
309
2
cpowf
4 + i 2
4 + i 2
-
4 + i 2.5333
5 + i 2.5333
cpow
1 + i 1.1031
1 + i 1.1031
-
1 + i 1.104
1 + i 1.1031
cpowl
-
-
-
2 + i 9
1 + i 4
cprojf
-
-
-
-
-
cproj
-
-
-
-
-
cprojl
-
-
-
-
-
crealf
-
-
-
-
-
creal
-
-
-
-
-
creall
-
-
-
-
-
csinf
0 + i 1
0 + i 1
-
-
-
csin
-
-
-
-
-
csinl
-
-
-
966 + i 168
0 + i 1
csinhf
1 + i 1
1 + i 1
-
1 + i 1
1 + i 1
csinh
0 + i 1
0 + i 1
-
1 + i 1
1 + i 1
csinhl
-
-
-
413 + i 477
2 + i 2
csqrtf
1 + i 1
1 + i 1
-
-
1 + i 1
csqrt
1 + i 0
1 + i 0
-
1 + i 0
1 + i 0
csqrtl
-
-
-
237 + i 128
-
ctanf
1 + i 1
1 + i 1
-
1 + i 1
1 + i 1
ctan
1 + i 1
1 + i 1
-
1 + i 1
1 + i 1
ctanl
-
-
-
690 + i 367
436 + i 1
ctanhf
2 + i 1
2 + i 1
-
1 + i 1
1 + i 1
ctanh
2 + i 2
2 + i 2
-
0 + i 1
0 + i 1
ctanhl
-
-
-
286 + i 3074
1 + i 24
erff
-
-
-
-
-
erf
-
-
-
-
-
erfl
-
-
-
-
-
erfcf
12
12
-
12
12
erfc
24
24
-
24
24
erfcl
-
-
-
36
12
expf
-
-
-
-
-
exp
-
-
-
-
-
expl
-
-
-
754
-
exp10f
2
2
-
-
2
exp10
6
6
-
1
6
exp10l
-
-
-
1182
3
exp2f
-
-
-
-
-
exp2
-
-
-
-
-
exp2l
-
-
-
462
-
expm1f
1
1
-
-
-
expm1
-
-
-
-
-
expm1l
-
-
-
825
1
fabsf
-
-
-
-
-
fabs
-
-
-
-
-
fabsl
-
-
-
-
-
fdimf
-
-
-
-
-
fdim
-
-
-
-
-
fdiml
-
-
-
-
-
floorf
-
-
-
-
-
floor
-
-
-
-
-
floorl
-
-
-
-
-
fmaf
-
-
-
-
-
fma
-
-
-
-
-
fmal
-
-
-
-
-
fmaxf
-
-
-
-
-
fmax
-
-
-
-
-
fmaxl
-
-
-
-
-
fminf
-
-
-
-
-
fmin
-
-
-
-
-
fminl
-
-
-
-
-
fmodf
1
1
-
1
1
fmod
2
2
-
2
2
fmodl
-
-
-
4096
1
frexpf
-
-
-
-
-
frexp
-
-
-
-
-
frexpl
-
-
-
-
-
gammaf
-
-
-
-
-
gamma
-
-
-
1
-
gammal
-
-
-
1
1
hypotf
1
1
-
1
1
hypot
1
1
-
1
1
hypotl
-
-
-
560
1
ilogbf
-
-
-
-
-
ilogb
-
-
-
-
-
ilogbl
-
-
-
-
-
j0f
2
2
-
1
1
j0
2
2
-
2
2
j0l
-
-
-
1
2
j1f
2
2
-
1
2
j1
1
1
-
2
1
j1l
-
-
-
2
-
jnf
4
4
-
2
4
jn
6
6
-
5
6
jnl
-
-
-
2
2
lgammaf
2
2
-
2
2
lgamma
1
1
-
1
1
lgammal
-
-
-
1
1
lrintf
-
-
-
-
-
lrint
-
-
-
-
-
lrintl
-
-
-
-
-
llrintf
-
-
-
-
-
llrint
-
-
-
-
-
llrintl
-
-
-
-
-
logf
1
1
-
1
1
log
1
1
-
1
1
logl
-
-
-
2341
1
log10f
1
1
-
1
1
log10
1
1
-
1
1
log10l
-
-
-
2033
1
log1pf
1
1
-
1
1
log1p
1
1
-
1
1
log1pl
-
-
-
585
1
log2f
1
1
-
1
1
log2
1
1
-
1
1
log2l
-
-
-
1688
-
logbf
-
-
-
-
-
logb
-
-
-
-
-
logbl
-
-
-
-
-
lroundf
-
-
-
-
-
lround
-
-
-
-
-
lroundl
-
-
-
-
-
llroundf
-
-
-
-
-
llround
-
-
-
-
-
llroundl
-
-
-
-
-
modff
-
-
-
-
-
modf
-
-
-
-
-
modfl
-
-
-
-
-
nearbyintf
-
-
-
-
-
nearbyint
-
-
-
-
-
nearbyintl
-
-
-
-
-
nextafterf
-
-
-
-
-
nextafter
-
-
-
-
-
nextafterl
-
-
-
-
-
nexttowardf
-
-
-
-
-
nexttoward
-
-
-
-
-
nexttowardl
-
-
-
-
-
powf
-
-
-
-
-
pow
-
-
-
-
-
powl
-
-
-
725
1
remainderf
-
-
-
-
-
remainder
-
-
-
-
-
remainderl
-
-
-
-
-
remquof
-
-
-
-
-
remquo
-
-
-
-
-
remquol
-
-
-
-
-
rintf
-
-
-
-
-
rint
-
-
-
-
-
rintl
-
-
-
-
-
roundf
-
-
-
-
-
round
-
-
-
-
-
roundl
-
-
-
-
-
scalbf
-
-
-
-
-
scalb
-
-
-
-
-
scalbl
-
-
-
-
-
scalbnf
-
-
-
-
-
scalbn
-
-
-
-
-
scalbnl
-
-
-
-
-
scalblnf
-
-
-
-
-
scalbln
-
-
-
-
-
scalblnl
-
-
-
-
-
sinf
-
-
-
-
-
sin
-
-
-
-
-
sinl
-
-
-
627
1
sincosf
1
1
-
1
1
sincos
1
1
-
1
1
sincosl
-
-
-
627
1
sinhf
1
1
-
1
1
sinh
1
1
-
-
-
sinhl
-
-
-
1029
1
sqrtf
-
-
-
-
-
sqrt
-
-
-
-
-
sqrtl
-
-
-
489
-
tanf
-
-
-
-
-
tan
0.5
0.5
-
0.5
0.5
tanl
-
-
-
1401
1
tanhf
1
1
-
-
1
tanh
1
1
-
-
1
tanhl
-
-
-
521
1
tgammaf
1
1
-
1
1
tgamma
1
1
-
2
1
tgammal
-
-
-
2
1
truncf
-
-
-
-
-
trunc
-
-
-
-
-
truncl
-
-
-
-
-
y0f
1
1
-
1
1
y0
2
2
-
3
2
y0l
-
-
-
2
2
y1f
2
2
-
2
2
y1
3
3
-
3
3
y1l
-
-
-
2
1
ynf
2
2
-
3
2
yn
3
3
-
6
3
ynl
-
-
-
7
7
Function
M68k
MIPS
PowerPC
S/390
SH4
acosf
-
-
-
-
-
acos
-
-
-
-
-
acosl
1
-
-
-
-
acoshf
-
-
-
-
-
acosh
-
-
-
-
-
acoshl
1
-
-
-
-
asinf
-
2
2
2
2
asin
1
1
1
1
1
asinl
1
-
-
-
-
asinhf
-
-
-
-
-
asinh
-
-
-
-
-
asinhl
14
-
-
-
-
atanf
-
-
-
-
-
atan
-
-
-
-
-
atanl
-
-
-
-
-
atanhf
-
-
-
-
-
atanh
1
1
1
1
1
atanhl
-
-
-
-
-
atan2f
-
4
4
4
4
atan2
-
-
-
-
-
atan2l
-
-
-
-
-
cabsf
1
1
1
1
1
cabs
-
1
1
1
1
cabsl
1
-
-
-
-
cacosf
1 + i 2
1 + i 1
1 + i 1
1 + i 1
1 + i 1
cacos
1 + i 0
1 + i 0
1 + i 0
1 + i 0
1 + i 0
cacosl
1 + i 1
-
-
-
-
cacoshf
7 + i 0
7 + i 3
7 + i 3
7 + i 3
7 + i 3
cacosh
1 + i 1
1 + i 1
1 + i 1
1 + i 1
1 + i 1
cacoshl
6 + i 2
-
-
-
-
cargf
-
-
-
-
-
carg
-
-
-
-
-
cargl
-
-
-
-
-
casinf
2 + i 2
2 + i 1
2 + i 1
2 + i 1
2 + i 1
casin
3 + i 0
3 + i 0
3 + i 0
3 + i 0
3 + i 0
casinl
0 + i 1
-
-
-
-
casinhf
19 + i 2
1 + i 6
1 + i 6
1 + i 6
1 + i 6
casinh
6 + i 13
5 + i 3
5 + i 3
5 + i 3
5 + i 3
casinhl
5 + i 6
-
-
-
-
catanf
0 + i 1
4 + i 1
4 + i 1
4 + i 1
4 + i 1
catan
0 + i 1
0 + i 1
0 + i 1
0 + i 1
0 + i 1
catanl
1 + i 0
-
-
-
-
catanhf
-
1 + i 6
0 + i 6
1 + i 6
1 + i 6
catanh
-
4 + i 1
4 + i 1
4 + i 1
4 + i 1
catanhl
1 + i 0
-
-
-
-
cbrtf
-
-
-
-
-
cbrt
1
1
1
1
1
cbrtl
1
-
-
-
-
ccosf
1 + i 1
0 + i 1
0 + i 1
0 + i 1
0 + i 1
ccos
0 + i 1
1 + i 1
1 + i 1
1 + i 1
1 + i 1
ccosl
0 + i 1
-
-
-
-
ccoshf
3 + i 1
1 + i 1
1 + i 1
1 + i 1
1 + i 1
ccosh
1 + i 0
1 + i 1
1 + i 1
1 + i 1
1 + i 1
ccoshl
1 + i 2
-
-
-
-
ceilf
-
-
-
-
-
ceil
-
-
-
-
-
ceill
-
-
-
-
-
cexpf
3 + i 2
1 + i 1
1 + i 1
1 + i 1
1 + i 1
cexp
-
1 + i 0
1 + i 0
1 + i 0
1 + i 0
cexpl
2 + i 0
-
-
-
-
cimagf
-
-
-
-
-
cimag
-
-
-
-
-
cimagl
-
-
-
-
-
clogf
-
0 + i 3
0 + i 3
0 + i 3
0 + i 3
clog
-
0 + i 1
0 + i 1
0 + i 1
0 + i 1
clogl
-
-
-
-
-
clog10f
1 + i 1
1 + i 5
1 + i 5
1 + i 5
1 + i 5
clog10
1 + i 1
1 + i 1
1 + i 1
1 + i 1
1 + i 1
clog10l
1 + i 3
-
-
-
-
conjf
-
-
-
-
-
conj
-
-
-
-
-
conjl
-
-
-
-
-
copysignf
-
-
-
-
-
copysign
-
-
-
-
-
copysignl
-
-
-
-
-
cosf
1
1
1
1
1
cos
2
2
2
2
2
cosl
1
-
-
-
-
coshf
-
-
-
-
-
cosh
-
-
-
-
-
coshl
2
-
-
-
-
cpowf
1 + i 6
4 + i 2
4 + i 2
4 + i 2
4 + i 2
cpow
1 + i 2
1 + i 1.1031
1 + i 2
1 + i 1.1031
1 + i 1.1031
cpowl
5 + i 2
-
-
-
-
cprojf
-
-
-
-
-
cproj
-
-
-
-
-
cprojl
-
-
-
-
-
crealf
-
-
-
-
-
creal
-
-
-
-
-
creall
-
-
-
-
-
csinf
1 + i 1
0 + i 1
0 + i 1
0 + i 1
0 + i 1
csin
-
-
-
-
-
csinl
-
-
-
-
-
csinhf
1 + i 1
1 + i 1
1 + i 1
1 + i 1
1 + i 1
csinh
-
0 + i 1
0 + i 1
0 + i 1
0 + i 1
csinhl
1 + i 2
-
-
-
-
csqrtf
1 + i 0
1 + i 1
1 + i 1
1 + i 1
1 + i 1
csqrt
-
1 + i 0
1 + i 0
1 + i 0
1 + i 0
csqrtl
-
-
-
-
-
ctanf
1 + i 0
1 + i 1
1 + i 1
1 + i 1
1 + i 1
ctan
1 + i 0
1 + i 1
1 + i 1
1 + i 1
1 + i 1
ctanl
439 + i 2
-
-
-
-
ctanhf
1 + i 0
2 + i 1
2 + i 1
2 + i 1
2 + i 1
ctanh
0 + i 1
2 + i 2
2 + i 2
2 + i 2
2 + i 2
ctanhl
2 + i 25
-
-
-
-
erff
-
-
-
-
-
erf
-
-
-
-
-
erfl
-
-
-
-
-
erfcf
11
12
12
12
12
erfc
24
24
24
24
24
erfcl
12
-
-
-
-
expf
-
-
-
-
-
exp
-
-
-
-
-
expl
-
-
-
-
-
exp10f
-
2
2
2
2
exp10
1
6
6
6
6
exp10l
1
-
-
-
-
exp2f
-
-
-
-
-
exp2
-
-
-
-
-
exp2l
-
-
-
-
-
expm1f
-
1
1
1
1
expm1
-
-
-
-
-
expm1l
1
-
-
-
-
fabsf
-
-
-
-
-
fabs
-
-
-
-
-
fabsl
-
-
-
-
-
fdimf
-
-
-
-
-
fdim
-
-
-
-
-
fdiml
-
-
-
-
-
floorf
-
-
-
-
-
floor
-
-
-
-
-
floorl
-
-
-
-
-
fmaf
-
-
-
-
-
fma
-
-
-
-
-
fmal
-
-
-
-
-
fmaxf
-
-
-
-
-
fmax
-
-
-
-
-
fmaxl
-
-
-
-
-
fminf
-
-
-
-
-
fmin
-
-
-
-
-
fminl
-
-
-
-
-
fmodf
1
1
1
1
1
fmod
2
2
2
2
2
fmodl
1
-
-
-
-
frexpf
-
-
-
-
-
frexp
-
-
-
-
-
frexpl
-
-
-
-
-
gammaf
-
-
-
-
-
gamma
-
-
-
-
-
gammal
1
-
-
-
-
hypotf
1
1
1
1
1
hypot
-
1
1
1
1
hypotl
1
-
-
-
-
ilogbf
-
-
-
-
-
ilogb
-
-
-
-
-
ilogbl
-
-
-
-
-
j0f
1
2
1
2
2
j0
1
2
2
2
2
j0l
1
-
-
-
-
j1f
2
2
2
2
2
j1
-
1
1
1
1
j1l
2
-
-
-
-
jnf
11
4
4
4
4
jn
4
6
6
6
6
jnl
2
-
-
-
-
lgammaf
2
2
2
2
2
lgamma
1
1
1
1
1
lgammal
1
-
-
-
-
lrintf
-
-
-
-
-
lrint
-
-
-
-
-
lrintl
-
-
-
-
-
llrintf
-
-
-
-
-
llrint
-
-
-
-
-
llrintl
-
-
-
-
-
logf
1
1
1
1
1
log
1
1
1
1
1
logl
2
-
-
-
-
log10f
1
1
1
1
1
log10
1
1
1
1
1
log10l
1
-
-
-
-
log1pf
1
1
1
1
1
log1p
1
1
1
1
1
log1pl
2
-
-
-
-
log2f
1
1
1
1
1
log2
1
1
1
1
1
log2l
1
-
-
-
-
logbf
-
-
-
-
-
logb
-
-
-
-
-
logbl
-
-
-
-
-
lroundf
-
-
-
-
-
lround
-
-
-
-
-
lroundl
-
-
-
-
-
llroundf
-
-
-
-
-
llround
-
-
-
-
-
llroundl
-
-
-
-
-
modff
-
-
-
-
-
modf
-
-
-
-
-
modfl
-
-
-
-
-
nearbyintf
-
-
-
-
-
nearbyint
-
-
-
-
-
nearbyintl
-
-
-
-
-
nextafterf
-
-
-
-
-
nextafter
-
-
-
-
-
nextafterl
-
-
-
-
-
nexttowardf
-
-
-
-
-
nexttoward
-
-
-
-
-
nexttowardl
-
-
-
-
-
powf
-
-
-
-
-
pow
-
-
-
-
-
powl
1
-
-
-
-
remainderf
-
-
-
-
-
remainder
-
-
-
-
-
remainderl
-
-
-
-
-
remquof
-
-
-
-
-
remquo
-
-
-
-
-
remquol
-
-
-
-
-
rintf
-
-
-
-
-
rint
-
-
-
-
-
rintl
-
-
-
-
-
roundf
-
-
-
-
-
round
-
-
-
-
-
roundl
-
-
-
-
-
scalbf
-
-
-
-
-
scalb
-
-
-
-
-
scalbl
-
-
-
-
-
scalbnf
-
-
-
-
-
scalbn
-
-
-
-
-
scalbnl
-
-
-
-
-
scalblnf
-
-
-
-
-
scalbln
-
-
-
-
-
scalblnl
-
-
-
-
-
sinf
-
-
-
-
-
sin
-
-
-
-
-
sinl
1
-
-
-
-
sincosf
1
1
1
1
1
sincos
1
1
1
1
1
sincosl
1
-
-
-
-
sinhf
1
1
1
1
1
sinh
-
1
1
1
1
sinhl
-
-
-
-
-
sqrtf
-
-
-
-
-
sqrt
-
-
-
-
-
sqrtl
-
-
-
-
-
tanf
-
-
-
-
-
tan
1
0.5
1
0.5
0.5
tanl
1
-
-
-
-
tanhf
-
1
1
1
1
tanh
-
1
1
1
1
tanhl
-
-
-
-
-
tgammaf
1
1
1
1
1
tgamma
1
1
1
1
1
tgammal
1
-
-
-
-
truncf
-
-
-
-
-
trunc
-
-
-
-
-
truncl
-
-
-
-
-
y0f
2
1
1
1
1
y0
2
2
2
2
2
y0l
2
-
-
-
-
y1f
2
2
2
2
2
y1
1
3
3
3
3
y1l
2
-
-
-
-
ynf
2
2
2
2
2
yn
6
3
3
3
3
ynl
7
-
-
-
-
Function
Sparc 32-bit
Sparc 64-bit
x86_64/fpu
acosf
-
-
-
acos
-
-
-
acosl
-
1
-
acoshf
-
-
-
acosh
-
-
-
acoshl
-
-
-
asinf
2
2
-
asin
1
1
1
asinl
-
-
1
asinhf
-
-
-
asinh
-
-
-
asinhl
-
-
15
atanf
-
-
-
atan
-
-
-
atanl
-
1
-
atanhf
-
-
-
atanh
1
1
1
atanhl
-
-
1
atan2f
4.0000
4
4
atan2
-
-
-
atan2l
-
1
-
cabsf
1
1
1
cabs
1
1
1
cabsl
-
-
1
cacosf
1 + i 1
1 + i 1
1 + i 1
cacos
1 + i 0
1 + i 0
1 + i 0
cacosl
-
0 + i 3
1 + i 1
cacoshf
7 + i 3
7 + i 3
7 + i 3
cacosh
1 + i 1
1 + i 1
1 + i 1
cacoshl
-
5 + i 1
6 + i 1
cargf
-
-
-
carg
-
-
-
cargl
-
-
-
casinf
2 + i 1
2 + i 1
2 + i 1
casin
3 + i 0
3 + i 0
3 + i 0
casinl
-
1 + i 3
0 + i 1
casinhf
1 + i 6
1 + i 6
1 + i 6
casinh
5 + i 3
5 + i 3
5 + i 3
casinhl
-
4 + i 2
5 + i 5
catanf
4 + i 1
4 + i 1
4 + i 1
catan
0 + i 1
0 + i 1
0 + i 1
catanl
-
0 + i 1
1 + i 0
catanhf
1 + i 6
1 + i 6
1 + i 6
catanh
4 + i 1
4 + i 1
4 + i 0
catanhl
-
-
1 + i 0
cbrtf
-
-
-
cbrt
1
1
1
cbrtl
-
-
948
ccosf
0 + i 1
0 + i 1
0 + i 1
ccos
1 + i 1
1 + i 1
1 + i 1
ccosl
-
-
0 + i 1
ccoshf
1 + i 1
1 + i 1
1 + i 1
ccosh
1 + i 1
1 + i 1
1 + i 1
ccoshl
-
-
1 + i 1
ceilf
-
-
-
ceil
-
-
-
ceill
-
-
-
cexpf
1 + i 1
1 + i 1
1 + i 1
cexp
1 + i 0
1 + i 0
1 + i 0
cexpl
-
1 + i 1
2 + i 1
cimagf
-
-
-
cimag
-
-
-
cimagl
-
-
-
clogf
0 + i 3
0 + i 3
0 + i 3
clog
0 + i 1
0 + i 1
-
clogl
-
-
-
clog10f
1 + i 5
1 + i 5
1 + i 5
clog10
1 + i 1
1 + i 1
1 + i 1
clog10l
-
-
1 + i 3
conjf
-
-
-
conj
-
-
-
conjl
-
-
-
copysignf
-
-
-
copysign
-
-
-
copysignl
-
-
-
cosf
1
1
1
cos
2
2
2
cosl
-
1
0.5
coshf
-
-
-
cosh
-
-
-
coshl
-
-
2
cpowf
4 + i 2
4 + i 2
4 + i 2
cpow
1 + i 1.1031
1 + i 1.1031
1 + i 1.1031
cpowl
-
3 + i 0.9006
1 + i 2
cprojf
-
-
-
cproj
-
-
-
cprojl
-
-
-
crealf
-
-
-
creal
-
-
-
creall
-
-
-
csinf
0 + i 1
0 + i 1
0 + i 1
csin
-
-
-
csinl
-
-
0 + i 2
csinhf
1 + i 1
1 + i 1
1 + i 1
csinh
0 + i 1
0 + i 1
0 + i 1
csinhl
-
-
2 + i 2
csqrtf
1 + i 1
1 + i 1
1 + i 1
csqrt
1 + i 0
1 + i 0
1 + i 0
csqrtl
-
1 + i 1
-
ctanf
1 + i 1
1 + i 1
1 + i 1
ctan
1 + i 1
1 + i 1
1 + i 1
ctanl
-
-
439 + i 2
ctanhf
2 + i 1
2 + i 1
2 + i 1
ctanh
2 + i 2
2 + i 2
2 + i 2
ctanhl
-
-
5 + i 25
erff
-
-
-
erf
-
-
-
erfl
-
-
-
erfcf
12
12
12
erfc
24
24
24
erfcl
-
-
36
expf
-
-
-
exp
-
-
-
expl
-
-
-
exp10f
2
2
2
exp10
6
6
6
exp10l
-
1
3
exp2f
-
-
-
exp2
-
-
-
exp2l
-
-
-
expm1f
1
1
1
expm1
-
1
1
expm1l
-
-
1
fabsf
-
-
-
fabs
-
-
-
fabsl
-
-
-
fdimf
-
-
-
fdim
-
-
-
fdiml
-
-
-
floorf
-
-
-
floor
-
-
-
floorl
-
-
-
fmaf
-
-
-
fma
-
-
-
fmal
-
-
-
fmaxf
-
-
-
fmax
-
-
-
fmaxl
-
-
-
fminf
-
-
-
fmin
-
-
-
fminl
-
-
-
fmodf
1
1
1
fmod
2
2
2
fmodl
-
2
1
frexpf
-
-
-
frexp
-
-
-
frexpl
-
-
-
gammaf
-
-
-
gamma
-
-
-
gammal
-
-
1
hypotf
1
1
1
hypot
1
1
1
hypotl
-
-
1
ilogbf
-
-
-
ilogb
-
-
-
ilogbl
-
-
-
j0f
2
2
2
j0
2
2
2
j0l
-
-
-
j1f
2
2
2
j1
1
1
1
j1l
-
-
2
jnf
4
4
4
jn
6
6
6
jnl
-
-
2
lgammaf
2
2
2
lgamma
1
1
1
lgammal
-
-
1
lrintf
-
-
-
lrint
-
-
-
lrintl
-
-
-
llrintf
-
-
-
llrint
-
-
-
llrintl
-
-
-
logf
1
1
1
log
1
1
1
logl
-
1
1
log10f
1
1
1
log10
1
1
1
log10l
-
-
1
log1pf
1
1
1
log1p
1
1
1
log1pl
-
1
1
log2f
1
1
1
log2
1
1
1
log2l
-
-
-
logbf
-
-
-
logb
-
-
-
logbl
-
-
-
lroundf
-
-
-
lround
-
-
-
lroundl
-
-
-
llroundf
-
-
-
llround
-
-
-
llroundl
-
-
-
modff
-
-
-
modf
-
-
-
modfl
-
-
-
nearbyintf
-
-
-
nearbyint
-
-
-
nearbyintl
-
-
-
nextafterf
-
-
-
nextafter
-
-
-
nextafterl
-
-
-
nexttowardf
-
-
-
nexttoward
-
-
-
nexttowardl
-
-
-
powf
-
-
-
pow
-
-
-
powl
-
-
-
remainderf
-
-
-
remainder
-
-
-
remainderl
-
-
-
remquof
-
-
-
remquo
-
-
-
remquol
-
-
-
rintf
-
-
-
rint
-
-
-
rintl
-
-
-
roundf
-
-
-
round
-
-
-
roundl
-
-
-
scalbf
-
-
-
scalb
-
-
-
scalbl
-
-
-
scalbnf
-
-
-
scalbn
-
-
-
scalbnl
-
-
-
scalblnf
-
-
-
scalbln
-
-
-
scalblnl
-
-
-
sinf
-
-
-
sin
-
-
-
sinl
-
-
1
sincosf
1
1
1
sincos
1
1
1
sincosl
-
1
1
sinhf
1
1
1
sinh
1
1
1
sinhl
-
-
1
sqrtf
-
-
-
sqrt
-
-
-
sqrtl
-
1
-
tanf
-
-
-
tan
0.5
0.5
0.5
tanl
-
1
1
tanhf
1
1
1
tanh
1
1
1
tanhl
-
-
1
tgammaf
1
1
1
tgamma
1
1
1
tgammal
-
-
2
truncf
-
-
-
trunc
-
-
-
truncl
-
-
-
y0f
1
1
1
y0
2
2
2
y0l
-
-
2
y1f
2
2
2
y1
3
3
3
y1l
-
-
2
ynf
2
2
2
yn
3
3
3
ynl
-
-
7
Published under the terms of the GNU General Public License