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19.7 Known Maximum Errors in Math Functions

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 in round-to-nearest mode. Using rounding bits this is also possible and normally implemented for the basic operations. Except for certain functions such as sqrt, fma and rint whose results are fully specified by reference to corresponding IEEE 754 floating-point operations, and conversions between strings and floating point, the GNU C Library does not aim for correctly rounded results for functions in the math library, and does not aim for correctness in whether “inexact” exceptions are raised. Instead, the goals for accuracy of functions without fully specified results are as follows; some functions have bugs meaning they do not meet these goals in all cases. In future, the GNU C Library may provide some other correctly rounding functions under the names such as crsin proposed for an extension to ISO C.

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.

Functionaarch64AlphaARMGenerichppa/fpu
acosf111--
acos-----
acosl11---
acoshf222-1
acosh222-1
acoshl22---
asinf111--
asin-----
asinl11---
asinhf111-1
asinh111-1
asinhl33---
atanf111--
atan1----
atanl11---
atanhf222-1
atanh222-1
atanhl33---
atan2f111-1
atan2-----
atan2l11---
cabsf-----
cabs111--
cabsl11---
cacosf2 + i 22 + i 22 + i 2-2 + i 2
cacos1 + i 11 + i 11 + i 1-1 + i 1
cacosl2 + i 22 + i 2---
cacoshf2 + i 22 + i 22 + i 2-2 + i 2
cacosh1 + i 11 + i 11 + i 1-1 + i 1
cacoshl2 + i 22 + i 2---
cargf111--
carg1----
cargl22---
casinf1 + i 21 + i 21 + i 2-1 + i 2
casin1 + i 11 + i 11 + i 1-1 + i 1
casinl2 + i 22 + i 2--1 + i 0
casinhf2 + i 12 + i 12 + i 1-2 + i 1
casinh1 + i 11 + i 11 + i 1-5 + i 3
casinhl2 + i 22 + i 2--5 + i 3
catanf1 + i 11 + i 11 + i 1-1 + i 1
catan0 + i 10 + i 10 + i 1-0 + i 1
catanl1 + i 11 + i 1--0 + i 1
catanhf1 + i 11 + i 11 + i 1-1 + i 1
catanh1 + i 01 + i 01 + i 0-4 + i 0
catanhl1 + i 11 + i 1--4 + i 0
cbrtf111-1
cbrt333-1
cbrtl11--1
ccosf1 + i 11 + i 11 + i 1-1 + i 1
ccos1 + i 11 + i 11 + i 1-1 + i 1
ccosl1 + i 11 + i 1--1 + i 0
ccoshf1 + i 11 + i 11 + i 1-1 + i 1
ccosh1 + i 11 + i 11 + i 1-1 + i 1
ccoshl1 + i 11 + i 1--1 + i 0
ceilf-----
ceil-----
ceill-----
cexpf1 + i 21 + i 21 + i 2-1 + i 2
cexp2 + i 12 + i 12 + i 1-2 + i 1
cexpl1 + i 11 + i 1---
cimagf-----
cimag-----
cimagl-----
clogf3 + i 13 + i 13 + i 1-1 + i 1
clog3 + i 13 + i 03 + i 0-1 + i 0
clogl2 + i 12 + i 1---
clog10f4 + i 24 + i 24 + i 2-2 + i 1
clog103 + i 13 + i 23 + i 2-2 + i 1
clog10l2 + i 22 + i 2--0 + i 1
conjf-----
conj-----
conjl-----
copysignf-----
copysign-----
copysignl-----
cosf111-1
cos----2
cosl11--2
coshf111-1
cosh111-1
coshl11---
cpowf5 + i 24 + i 24 + i 2-4 + i 2
cpow2 + i 02 + i 02 + i 0-2 + i 2
cpowl4 + i 14 + i 1--2 + i 2
cprojf-----
cproj-----
cprojl-----
crealf-----
creal-----
creall-----
csinf1 + i 01 + i 01 + i 0-1 + i 0
csin1 + i 01 + i 01 + i 0-1 + i 0
csinl1 + i 11 + i 1---
csinhf1 + i 11 + i 11 + i 1-1 + i 1
csinh0 + i 10 + i 10 + i 1-0 + i 1
csinhl1 + i 11 + i 1--0 + i 1
csqrtf2 + i 22 + i 22 + i 2-1 + i 1
csqrt2 + i 22 + i 22 + i 2-1 + i 1
csqrtl2 + i 22 + i 2---
ctanf1 + i 11 + i 11 + i 1-1 + i 1
ctan1 + i 21 + i 21 + i 2-1 + i 2
ctanl3 + i 33 + i 3--0 + i 1
ctanhf2 + i 11 + i 21 + i 2-1 + i 2
ctanh2 + i 22 + i 22 + i 2-2 + i 2
ctanhl3 + i 33 + i 3--1 + i 0
erff111--
erf111-1
erfl11--1
erfcf222-1
erfc233-1
erfcl22--1
expf111--
exp-----
expl11---
exp10f----2
exp10222-6
exp10l22--6
exp2f111--
exp2111--
exp2l11---
expm1f111-1
expm1111-1
expm1l11--1
fabsf-----
fabs-----
fabsl-----
fdimf-----
fdim-----
fdiml-----
floorf-----
floor-----
floorl-----
fmaf-----
fma-----
fmal-----
fmaxf-----
fmax-----
fmaxl-----
fminf-----
fmin-----
fminl-----
fmodf-----
fmod-----
fmodl-----
frexpf-----
frexp-----
frexpl-----
gammaf444-2
gamma344-1
gammal55---
hypotf----1
hypot111-1
hypotl11---
ilogbf-----
ilogb-----
ilogbl-----
j0f222-2
j0222-2
j0l22--2
j1f222-2
j1111-1
j1l44--1
jnf444-5
jn444-4
jnl77--4
lgammaf444-2
lgamma344-1
lgammal55--1
lrintf-----
lrint-----
lrintl-----
llrintf-----
llrint-----
llrintl-----
logf111-1
log-----
logl11---
log10f222-2
log10222-1
log10l11--1
log1pf111-1
log1p111--
log1pl22---
log2f111--
log2122--
log2l22---
logbf-----
logb-----
logbl-----
lroundf-----
lround-----
lroundl-----
llroundf-----
llround-----
llroundl-----
modff-----
modf-----
modfl-----
nearbyintf-----
nearbyint-----
nearbyintl-----
nextafterf-----
nextafter-----
nextafterl-----
nexttowardf-----
nexttoward-----
nexttowardl-----
powf111-1
pow-----
powl22---
remainderf-----
remainder-----
remainderl-----
remquof-----
remquo-----
remquol-----
rintf-----
rint-----
rintl-----
roundf-----
round-----
roundl-----
scalbf-----
scalb-----
scalbl-----
scalbnf-----
scalbn-----
scalbnl-----
scalblnf-----
scalbln-----
scalblnl-----
sinf111-1
sin-----
sinl11---
sincosf111-1
sincos----1
sincosl11--1
sinhf222--
sinh222--
sinhl22---
sqrtf-----
sqrt-----
sqrtl-----
tanf111--
tan----1
tanl11--1
tanhf222--
tanh222--
tanhl22---
tgammaf444-3
tgamma555-4
tgammal44--1
truncf-----
trunc-----
truncl-----
y0f111-1
y0222-2
y0l33--2
y1f222-2
y1333-3
y1l22--3
ynf222-2
yn333-3
ynl55--3
Functionix86i386/i686/fpu/multiarchIA64m68k/coldfire/fpum68k/m680x0/fpu
acosf-----
acos11---
acosl11---
acoshf----1
acosh11--1
acoshl22--1
asinf-----
asin11---
asinl11---
asinhf----1
asinh11--1
asinhl33--1
atanf-----
atan11---
atanl11---
atanhf---1-
atanh11---
atanhl33---
atan2f---11
atan211---
atan2l11--1
cabsf-----
cabs11--1
cabsl11--1
cacosf1 + i 11 + i 12 + i 2-2 + i 1
cacos1 + i 11 + i 11 + i 1-1 + i 1
cacosl1 + i 21 + i 21 + i 2-1 + i 2
cacoshf1 + i 11 + i 12 + i 20 + i 11 + i 2
cacosh1 + i 11 + i 11 + i 1-1 + i 1
cacoshl2 + i 12 + i 12 + i 1-2 + i 1
cargf----1
carg11---
cargl11--1
casinf1 + i 11 + i 11 + i 21 + i 01 + i 1
casin1 + i 11 + i 11 + i 11 + i 01 + i 1
casinl1 + i 21 + i 21 + i 2-1 + i 2
casinhf1 + i 11 + i 12 + i 11 + i 61 + i 1
casinh1 + i 11 + i 11 + i 15 + i 31 + i 1
casinhl2 + i 12 + i 12 + i 1-2 + i 1
catanf0 + i 10 + i 10 + i 10 + i 10 + i 1
catan0 + i 10 + i 10 + i 10 + i 10 + i 1
catanl0 + i 10 + i 10 + i 1-1 + i 1
catanhf1 + i 01 + i 01 + i 0-1 + i 0
catanh1 + i 01 + i 01 + i 04 + i 01 + i 0
catanhl1 + i 01 + i 01 + i 0-1 + i 1
cbrtf11--1
cbrt11-11
cbrtl33--1
ccosf1 + i 11 + i 10 + i 11 + i 1-
ccos1 + i 11 + i 11 + i 11 + i 0-
ccosl1 + i 11 + i 11 + i 1-1 + i 1
ccoshf1 + i 11 + i 11 + i 11 + i 1-
ccosh1 + i 11 + i 11 + i 11 + i 0-
ccoshl1 + i 11 + i 10 + i 1-0 + i 1
ceilf-----
ceil-----
ceill-----
cexpf1 + i 21 + i 21 + i 21 + i 1-
cexp2 + i 12 + i 12 + i 1--
cexpl1 + i 11 + i 11 + i 1-1 + i 1
cimagf-----
cimag-----
cimagl-----
clogf1 + i 01 + i 01 + i 01 + i 02 + i 1
clog2 + i 12 + i 11 + i 1-3 + i 1
clogl3 + i 13 + i 11 + i 1-3 + i 1
clog10f2 + i 02 + i 02 + i 11 + i 12 + i 1
clog102 + i 12 + i 12 + i 10 + i 12 + i 1
clog10l4 + i 24 + i 21 + i 1-3 + i 2
conjf-----
conj-----
conjl-----
copysignf-----
copysign-----
copysignl-----
cosf1--1-
cos--121
cosl11---
coshf11---
cosh11---
coshl22---
cpowf5 + i 25 + i 25 + i 24 + i 23 + i 5
cpow2 + i 02 + i 12 + i 02 + i 21 + i 0
cpowl3 + i 43 + i 43 + i 4-3 + i 1
cprojf-----
cproj-----
cprojl-----
crealf-----
creal-----
creall-----
csinf1 + i 11 + i 11 + i 1--
csin1 + i 01 + i 11 + i 0--
csinl1 + i 01 + i 01 + i 0-1 + i 0
csinhf0 + i 11 + i 11 + i 11 + i 1-
csinh0 + i 11 + i 11 + i 10 + i 1-
csinhl1 + i 11 + i 11 + i 0-1 + i 0
csqrtf0 + i 10 + i 11 + i 11 + i 01 + i 1
csqrt1 + i 11 + i 11 + i 1-1 + i 1
csqrtl2 + i 22 + i 21 + i 1-2 + i 2
ctanf1 + i 11 + i 11 + i 1-1 + i 1
ctan1 + i 11 + i 11 + i 20 + i 11 + i 1
ctanl2 + i 12 + i 12 + i 2-2 + i 2
ctanhf1 + i 11 + i 11 + i 12 + i 11 + i 2
ctanh1 + i 11 + i 12 + i 21 + i 01 + i 1
ctanhl1 + i 21 + i 21 + i 2-2 + i 2
erff11--1
erf11-1-
erfl11--1
erfcf11--1
erfc11-1-
erfcl33--2
expf-----
exp11---
expl11---
exp10f---2-
exp1011-6-
exp10l11---
exp2f-----
exp211--1
exp2l11---
expm1f---1-
expm111-1-
expm1l221--
fabsf-----
fabs-----
fabsl-----
fdimf-----
fdim-----
fdiml-----
floorf-----
floor-----
floorl-----
fmaf-----
fma-----
fmal-----
fmaxf-----
fmax-----
fmaxl-----
fminf-----
fmin-----
fminl-----
fmodf-----
fmod-----
fmodl-----
frexpf-----
frexp-----
frexpl-----
gammaf23--1
gamma33---
gammal44--2
hypotf---1-
hypot11--1
hypotl11--1
ilogbf-----
ilogb-----
ilogbl-----
j0f11222
j011221
j0l222-2
j1f11222
j12211-
j1l111-1
jnf33442
jn22442
jnl444-4
lgammaf23-21
lgamma33-1-
lgammal44--2
lrintf-----
lrint-----
lrintl-----
llrintf-----
llrint-----
llrintl-----
logf-----
log11---
logl11---
log10f---2-
log1011-1-
log10l11---
log1pf---1-
log1p11---
log1pl22---
log2f-----
log211---
log2l11---
logbf-----
logb-----
logbl-----
lroundf-----
lround-----
lroundl-----
llroundf-----
llround-----
llroundl-----
modff-----
modf-----
modfl-----
nearbyintf-----
nearbyint-----
nearbyintl-----
nextafterf-----
nextafter-----
nextafterl-----
nexttowardf-----
nexttoward-----
nexttowardl-----
powf----7
pow11--1
powl11--9
remainderf-----
remainder-----
remainderl-----
remquof-----
remquo-----
remquol-----
rintf-----
rint-----
rintl-----
roundf-----
round-----
roundl-----
scalbf-----
scalb-----
scalbl-----
scalbnf-----
scalbn-----
scalbnl-----
scalblnf-----
scalbln-----
scalblnl-----
sinf1----
sin--1-1
sinl11---
sincosf1--1-
sincos--11-
sincosl11---
sinhf-----
sinh11---
sinhl22---
sqrtf-----
sqrt-----
sqrtl-----
tanf11---
tan---1-
tanl22---
tanhf-----
tanh11---
tanhl33---
tgammaf33-14
tgamma33-11
tgammal551-9
truncf-----
trunc-----
truncl-----
y0f11111
y011221
y0l111-1
y1f22223
y122331
y1l222-2
ynf33323
yn22332
ynl442-4
Functionmicroblazemips/mips32mips/mips64nios2PowerPC
acosf-1111
acos-----
acosl--1-1
acoshf-2222
acosh12222
acoshl--2-1
asinf-1111
asin-----
asinl--1-2
asinhf11111
asinh11111
asinhl--3-2
atanf-1111
atan----1
atanl--1-1
atanhf12222
atanh-2222
atanhl--3-2
atan2f11111
atan2-----
atan2l--1-2
cabsf-----
cabs-1111
cabsl--1-1
cacosf2 + i 22 + i 22 + i 22 + i 22 + i 2
cacos1 + i 11 + i 11 + i 11 + i 11 + i 1
cacosl--2 + i 2-1 + i 2
cacoshf2 + i 22 + i 22 + i 22 + i 22 + i 2
cacosh1 + i 11 + i 11 + i 11 + i 11 + i 1
cacoshl--2 + i 2-2 + i 1
cargf-1111
carg----1
cargl--2-2
casinf1 + i 21 + i 21 + i 21 + i 21 + i 2
casin1 + i 11 + i 11 + i 11 + i 11 + i 1
casinl--2 + i 2-1 + i 2
casinhf2 + i 12 + i 12 + i 12 + i 12 + i 1
casinh1 + i 11 + i 11 + i 11 + i 11 + i 1
casinhl--2 + i 2-2 + i 1
catanf1 + i 11 + i 11 + i 11 + i 11 + i 1
catan0 + i 10 + i 10 + i 10 + i 10 + i 1
catanl--1 + i 1-1 + i 1
catanhf1 + i 11 + i 11 + i 11 + i 11 + i 1
catanh1 + i 01 + i 01 + i 01 + i 01 + i 0
catanhl--1 + i 1-1 + i 1
cbrtf11111
cbrt13333
cbrtl--1-1
ccosf1 + i 11 + i 11 + i 11 + i 11 + i 1
ccos1 + i 11 + i 11 + i 11 + i 11 + i 1
ccosl--1 + i 1-1 + i 1
ccoshf1 + i 11 + i 11 + i 11 + i 11 + i 1
ccosh1 + i 11 + i 11 + i 11 + i 11 + i 1
ccoshl--1 + i 1-1 + i 2
ceilf-----
ceil-----
ceill-----
cexpf1 + i 21 + i 21 + i 21 + i 21 + i 2
cexp2 + i 12 + i 12 + i 12 + i 12 + i 1
cexpl--1 + i 1-2 + i 2
cimagf-----
cimag-----
cimagl-----
clogf1 + i 13 + i 13 + i 13 + i 13 + i 1
clog1 + i 03 + i 03 + i 03 + i 03 + i 1
clogl--2 + i 1-5 + i 2
clog10f2 + i 14 + i 24 + i 24 + i 24 + i 2
clog102 + i 13 + i 23 + i 23 + i 23 + i 1
clog10l--2 + i 2-3 + i 2
conjf-----
conj-----
conjl-----
copysignf-----
copysign-----
copysignl-----
cosf11111
cos-----
cosl--1-4
coshf11111
cosh11111
coshl--1-3
cpowf4 + i 24 + i 24 + i 24 + i 25 + i 2
cpow2 + i 02 + i 02 + i 02 + i 02 + i 0
cpowl--4 + i 1-4 + i 2
cprojf-----
cproj-----
cprojl-----
crealf-----
creal-----
creall-----
csinf1 + i 01 + i 01 + i 01 + i 01 + i 0
csin1 + i 01 + i 01 + i 01 + i 01 + i 0
csinl--1 + i 1-1 + i 1
csinhf1 + i 11 + i 11 + i 11 + i 11 + i 1
csinh0 + i 10 + i 10 + i 10 + i 10 + i 1
csinhl--1 + i 1-1 + i 1
csqrtf1 + i 12 + i 22 + i 22 + i 22 + i 2
csqrt1 + i 12 + i 22 + i 22 + i 22 + i 2
csqrtl--2 + i 2-1 + i 1
ctanf1 + i 11 + i 11 + i 11 + i 11 + i 1
ctan1 + i 21 + i 21 + i 21 + i 21 + i 2
ctanl--3 + i 3-2 + i 2
ctanhf1 + i 21 + i 21 + i 21 + i 22 + i 1
ctanh2 + i 22 + i 22 + i 22 + i 22 + i 2
ctanhl--3 + i 3-3 + i 2
erff-1111
erf11111
erfl--1-1
erfcf12222
erfc13332
erfcl--2-2
expf-1111
exp----1
expl--1-1
exp10f-----
exp1012222
exp10l--2-1
exp2f-1111
exp2-1111
exp2l--1-2
expm1f11111
expm111111
expm1l--1-1
fabsf-----
fabs-----
fabsl-----
fdimf-----
fdim-----
fdiml-----
floorf-----
floor-----
floorl-----
fmaf-----
fma-----
fmal----1
fmaxf-----
fmax-----
fmaxl-----
fminf-----
fmin-----
fminl-----
fmodf-----
fmod-----
fmodl----1
frexpf-----
frexp-----
frexpl-----
gammaf14444
gamma14443
gammal--5-3
hypotf-----
hypot11111
hypotl--1-1
ilogbf-----
ilogb-----
ilogbl-----
j0f22222
j022222
j0l--2-2
j1f22222
j111111
j1l--4-1
jnf44444
jn44444
jnl--7-4
lgammaf14444
lgamma14443
lgammal--5-3
lrintf-----
lrint-----
lrintl-----
llrintf-----
llrint-----
llrintl-----
logf11111
log-----
logl--1-1
log10f22222
log1012222
log10l--1-1
log1pf11111
log1p-1111
log1pl--2-2
log2f-1111
log2-2221
log2l--2-1
logbf-----
logb-----
logbl-----
lroundf-----
lround-----
lroundl-----
llroundf-----
llround-----
llroundl-----
modff-----
modf-----
modfl-----
nearbyintf-----
nearbyint-----
nearbyintl-----
nextafterf-----
nextafter-----
nextafterl-----
nexttowardf-----
nexttoward-----
nexttowardl-----
powf11131
pow-----
powl--2-1
remainderf-----
remainder-----
remainderl-----
remquof-----
remquo-----
remquol-----
rintf-----
rint-----
rintl-----
roundf-----
round-----
roundl-----
scalbf-----
scalb-----
scalbl-----
scalbnf-----
scalbn-----
scalbnl-----
scalblnf-----
scalbln-----
scalblnl-----
sinf11111
sin-----
sinl--1-1
sincosf11111
sincos-----
sincosl--1-1
sinhf-2222
sinh-2222
sinhl--2-3
sqrtf-----
sqrt-----
sqrtl----1
tanf-1111
tan-----
tanl--1-2
tanhf-2222
tanh-2222
tanhl--2-1
tgammaf34454
tgamma45555
tgammal--4-5
truncf-----
trunc-----
truncl-----
y0f11111
y022222
y0l--3-1
y1f22222
y133333
y1l--2-2
ynf22222
yn33333
ynl--5-2
Functionpowerpc/nofpuS/390shsparc/fputile
acosf11-11
acos-----
acosl11-1-
acoshf22-22
acosh22122
acoshl12-2-
asinf11-11
asin-----
asinl21-1-
asinhf11111
asinh11111
asinhl23-3-
atanf11-11
atan-1---
atanl11-1-
atanhf22122
atanh22-22
atanhl23-3-
atan2f11111
atan2-----
atan2l21-1-
cabsf-----
cabs11-11
cabsl11-1-
cacosf2 + i 22 + i 22 + i 22 + i 22 + i 2
cacos1 + i 11 + i 11 + i 11 + i 11 + i 1
cacosl2 + i 12 + i 2-2 + i 2-
cacoshf2 + i 22 + i 22 + i 22 + i 22 + i 2
cacosh1 + i 11 + i 11 + i 11 + i 11 + i 1
cacoshl1 + i 22 + i 2-2 + i 2-
cargf11-11
carg-1---
cargl22-2-
casinf1 + i 21 + i 21 + i 21 + i 21 + i 2
casin1 + i 11 + i 11 + i 11 + i 11 + i 1
casinl2 + i 12 + i 2-2 + i 2-
casinhf2 + i 12 + i 12 + i 12 + i 12 + i 1
casinh1 + i 11 + i 11 + i 11 + i 11 + i 1
casinhl1 + i 22 + i 2-2 + i 2-
catanf1 + i 11 + i 11 + i 11 + i 11 + i 1
catan0 + i 10 + i 10 + i 10 + i 10 + i 1
catanl1 + i 11 + i 1-1 + i 1-
catanhf1 + i 11 + i 11 + i 11 + i 11 + i 1
catanh1 + i 01 + i 01 + i 01 + i 01 + i 0
catanhl1 + i 11 + i 1-1 + i 1-
cbrtf11111
cbrt33133
cbrtl11-1-
ccosf1 + i 11 + i 11 + i 11 + i 11 + i 1
ccos1 + i 11 + i 11 + i 11 + i 11 + i 1
ccosl1 + i 21 + i 1-1 + i 1-
ccoshf1 + i 11 + i 11 + i 11 + i 11 + i 1
ccosh1 + i 11 + i 11 + i 11 + i 11 + i 1
ccoshl1 + i 21 + i 1-1 + i 1-
ceilf-----
ceil-----
ceill-----
cexpf1 + i 21 + i 21 + i 21 + i 21 + i 2
cexp2 + i 12 + i 12 + i 12 + i 12 + i 1
cexpl1 + i 11 + i 1-1 + i 1-
cimagf-----
cimag-----
cimagl-----
clogf3 + i 13 + i 11 + i 13 + i 13 + i 1
clog3 + i 03 + i 11 + i 03 + i 03 + i 0
clogl2 + i 22 + i 1-4 + i 1-
clog10f4 + i 24 + i 22 + i 14 + i 24 + i 2
clog103 + i 23 + i 12 + i 13 + i 23 + i 2
clog10l3 + i 22 + i 2-4 + i 2-
conjf-----
conj-----
conjl-----
copysignf-----
copysign-----
copysignl-----
cosf11111
cos-----
cosl41-1-
coshf11111
cosh11111
coshl31-1-
cpowf4 + i 25 + i 24 + i 24 + i 24 + i 2
cpow2 + i 02 + i 02 + i 02 + i 02 + i 0
cpowl4 + i 14 + i 1-4 + i 1-
cprojf-----
cproj-----
cprojl-----
crealf-----
creal-----
creall-----
csinf1 + i 01 + i 01 + i 01 + i 01 + i 0
csin1 + i 01 + i 01 + i 01 + i 01 + i 0
csinl2 + i 11 + i 1-1 + i 1-
csinhf1 + i 11 + i 11 + i 11 + i 11 + i 1
csinh0 + i 10 + i 10 + i 10 + i 10 + i 1
csinhl1 + i 21 + i 1-1 + i 1-
csqrtf2 + i 22 + i 21 + i 12 + i 22 + i 2
csqrt2 + i 22 + i 21 + i 12 + i 22 + i 2
csqrtl1 + i 12 + i 2-2 + i 2-
ctanf1 + i 11 + i 11 + i 11 + i 11 + i 1
ctan1 + i 21 + i 21 + i 21 + i 21 + i 2
ctanl3 + i 23 + i 3-3 + i 3-
ctanhf1 + i 22 + i 11 + i 21 + i 21 + i 2
ctanh2 + i 22 + i 22 + i 22 + i 22 + i 2
ctanhl2 + i 33 + i 3-3 + i 3-
erff11-11
erf11111
erfl11-1-
erfcf22122
erfc32133
erfcl32-2-
expf11-11
exp-----
expl11-1-
exp10f-----
exp1022122
exp10l12-2-
exp2f11-11
exp211-11
exp2l11-1-
expm1f11111
expm111111
expm1l11-1-
fabsf-----
fabs-----
fabsl-----
fdimf-----
fdim-----
fdiml-----
floorf-----
floor-----
floorl-----
fmaf-----
fma-----
fmal1----
fmaxf-----
fmax-----
fmaxl-----
fminf-----
fmin-----
fminl-----
fmodf-----
fmod-----
fmodl1----
frexpf-----
frexp-----
frexpl-----
gammaf44144
gamma43144
gammal35-5-
hypotf-----
hypot11111
hypotl11-1-
ilogbf-----
ilogb-----
ilogbl-----
j0f22222
j022222
j0l22-2-
j1f22222
j111111
j1l14-4-
jnf44444
jn44444
jnl47-7-
lgammaf44144
lgamma43144
lgammal35-5-
lrintf-----
lrint-----
lrintl-----
llrintf-----
llrint-----
llrintl-----
logf11111
log-----
logl11-1-
log10f22222
log1022122
log10l11-1-
log1pf11111
log1p11-11
log1pl22-2-
log2f11-11
log221-22
log2l12-2-
logbf-----
logb-----
logbl-----
lroundf-----
lround-----
lroundl-----
llroundf-----
llround-----
llroundl-----
modff-----
modf-----
modfl-----
nearbyintf-----
nearbyint-----
nearbyintl-----
nextafterf-----
nextafter-----
nextafterl-----
nexttowardf-----
nexttoward-----
nexttowardl-----
powf11133
pow-----
powl12-2-
remainderf-----
remainder-----
remainderl-----
remquof-----
remquo-----
remquol-----
rintf-----
rint-----
rintl-----
roundf-----
round-----
roundl-----
scalbf-----
scalb-----
scalbl-----
scalbnf-----
scalbn-----
scalbnl-----
scalblnf-----
scalbln-----
scalblnl-----
sinf11111
sin-----
sinl11-1-
sincosf11111
sincos-----
sincosl11-1-
sinhf22-22
sinh22-22
sinhl32-2-
sqrtf-----
sqrt-----
sqrtl1----
tanf11-11
tan-----
tanl21-1-
tanhf22-22
tanh22-22
tanhl12-2-
tgammaf44355
tgamma55455
tgammal34-4-
truncf-----
trunc-----
truncl-----
y0f11111
y022222
y0l13-3-
y1f22222
y133333
y1l22-2-
ynf22222
yn33333
ynl25-5-

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