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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 the 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. Only the round-to-nearest rounding mode is covered by this table, and vector versions of functions are not covered. Functions not listed do not have known errors.

FunctionAArch64ARMAlphaColdFireGeneric
acosf111--
acos-----
acosl1-1--
acosf128-----
acoshf222--
acosh222--
acoshl2-2--
acoshf128-----
asinf111--
asin-----
asinl1-1--
asinf128-----
asinhf111--
asinh111--
asinhl3-3--
asinhf128-----
atanf111--
atan1----
atanl1-1--
atanf128-----
atan2f1111-
atan2-----
atan2l1-1--
atan2f128-----
atanhf2221-
atanh222--
atanhl3-3--
atanhf128-----
cabsf-----
cabs111--
cabsl1-1--
cabsf128-----
cacosf2 + i 22 + i 22 + i 2--
cacos1 + i 21 + i 21 + i 2--
cacosl2 + i 2-2 + i 2--
cacosf128-----
cacoshf2 + i 22 + i 22 + i 20 + i 1-
cacosh2 + i 12 + i 12 + i 1--
cacoshl2 + i 2-2 + i 2--
cacoshf128-----
cargf111--
carg1----
cargl2-2--
cargf128-----
casinf1 + i 21 + i 21 + i 21 + i 0-
casin1 + i 21 + i 21 + i 21 + i 0-
casinl2 + i 2-2 + i 2--
casinf128-----
casinhf2 + i 12 + i 12 + i 11 + i 6-
casinh2 + i 12 + i 12 + i 15 + i 3-
casinhl2 + i 2-2 + i 2--
casinhf128-----
catanf1 + i 11 + i 11 + i 10 + i 1-
catan1 + i 11 + i 11 + i 10 + i 1-
catanl1 + i 1-1 + i 1--
catanf128-----
catanhf1 + i 11 + i 11 + i 1--
catanh1 + i 11 + i 11 + i 14 + i 0-
catanhl1 + i 1-1 + i 1--
catanhf128-----
cbrtf111--
cbrt3331-
cbrtl1-1--
cbrtf128-----
ccosf1 + i 11 + i 11 + i 11 + i 1-
ccos1 + i 11 + i 11 + i 11 + i 0-
ccosl1 + i 1-1 + i 1--
ccosf128-----
ccoshf1 + i 11 + i 11 + i 11 + i 1-
ccosh1 + i 11 + i 11 + i 11 + i 0-
ccoshl1 + i 1-1 + i 1--
ccoshf128-----
cexpf1 + i 21 + i 21 + i 21 + i 1-
cexp2 + i 12 + i 12 + i 1--
cexpl1 + i 1-1 + i 1--
cexpf128-----
clogf3 + i 13 + i 13 + i 11 + i 0-
clog3 + i 13 + i 03 + i 0--
clogl2 + i 1-2 + i 1--
clogf128-----
clog10f4 + i 24 + i 24 + i 21 + i 1-
clog103 + i 23 + i 23 + i 20 + i 1-
clog10l2 + i 2-2 + i 2--
clog10f128-----
cosf1111-
cos---2-
cosl1-1--
cosf128-----
coshf111--
cosh111--
coshl1-1--
coshf128-----
cpowf5 + i 24 + i 24 + i 24 + i 2-
cpow2 + i 02 + i 02 + i 02 + i 2-
cpowl4 + i 1-4 + i 1--
cpowf128-----
csinf1 + i 01 + i 01 + i 0--
csin1 + i 01 + i 01 + i 0--
csinl1 + i 1-1 + i 1--
csinf128-----
csinhf1 + i 11 + i 11 + i 11 + i 1-
csinh0 + i 10 + i 10 + i 10 + i 1-
csinhl1 + i 1-1 + i 1--
csinhf128-----
csqrtf2 + i 22 + i 22 + i 21 + i 0-
csqrt2 + i 22 + i 22 + i 2--
csqrtl2 + i 2-2 + i 2--
csqrtf128-----
ctanf1 + i 11 + i 11 + i 1--
ctan1 + i 21 + i 21 + i 20 + i 1-
ctanl3 + i 3-3 + i 3--
ctanf128-----
ctanhf2 + i 11 + i 21 + i 22 + i 1-
ctanh2 + i 22 + i 22 + i 21 + i 0-
ctanhl3 + i 3-3 + i 3--
ctanhf128-----
erff111--
erf1111-
erfl1-1--
erff128-----
erfcf222--
erfc2331-
erfcl2-2--
erfcf128-----
expf111--
exp-----
expl1-1--
expf128-----
exp10f---2-
exp102226-
exp10l2-2--
exp10f128-----
exp2f111--
exp2111--
exp2l1-1--
exp2f128-----
expm1f1111-
expm11111-
expm1l1-1--
expm1f128-----
fmaf-----
fma-----
fmal-----
fmaf128-----
fmodf-----
fmod-----
fmodl-----
fmodf128-----
gammaf444--
gamma344--
gammal5-5--
gammaf128-----
hypotf---1-
hypot111--
hypotl1-1--
hypotf128-----
j0f2222-
j02222-
j0l2-2--
j0f128-----
j1f2222-
j11111-
j1l4-4--
j1f128-----
jnf4444-
jn4444-
jnl7-7--
jnf128-----
lgammaf4442-
lgamma3441-
lgammal5-5--
lgammaf128-----
logf111--
log-----
logl1-1--
logf128-----
log10f2222-
log102221-
log10l1-1--
log10f128-----
log1pf1111-
log1p111--
log1pl2-2--
log1pf128-----
log2f111--
log2122--
log2l2-2--
log2f128-----
powf111--
pow-----
powl2-2--
powf128-----
pow10f-----
pow10222--
pow10l2-2--
pow10f128-----
sinf111--
sin-----
sinl1-1--
sinf128-----
sincosf1111-
sincos---1-
sincosl1-1--
sincosf128-----
sinhf222--
sinh222--
sinhl2-2--
sinhf128-----
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
tanf111--
tan---1-
tanl1-1--
tanf128-----
tanhf222--
tanh222--
tanhl2-2--
tanhf128-----
tgammaf4441-
tgamma5551-
tgammal4-4--
tgammaf128-----
y0f1111-
y02222-
y0l3-3--
y0f128-----
y1f2222-
y13333-
y1l2-2--
y1f128-----
ynf2222-
yn3333-
ynl5-5--
ynf128-----
FunctionHPPAIA64M68kMIPS 32-bitMIPS 64-bit
acosf1--11
acos-----
acosl----1
acosf128-----
acoshf2-122
acosh2-122
acoshl--1-2
acoshf128-----
asinf1--11
asin-----
asinl----1
asinf128-----
asinhf1-111
asinh1-111
asinhl--1-3
asinhf128-----
atanf1--11
atan-----
atanl----1
atanf128-----
atan2f1-111
atan2-----
atan2l--1-1
atan2f128-----
atanhf2--22
atanh2--22
atanhl----3
atanhf128-----
cabsf-----
cabs1-111
cabsl--1-1
cabsf128-----
cacosf2 + i 22 + i 22 + i 12 + i 22 + i 2
cacos1 + i 21 + i 11 + i 11 + i 21 + i 2
cacosl-1 + i 21 + i 2-2 + i 2
cacosf128-----
cacoshf2 + i 22 + i 21 + i 22 + i 22 + i 2
cacosh2 + i 11 + i 11 + i 12 + i 12 + i 1
cacoshl-2 + i 12 + i 1-2 + i 2
cacoshf128-----
cargf1-111
carg-----
cargl--1-2
cargf128-----
casinf1 + i 21 + i 21 + i 11 + i 21 + i 2
casin1 + i 21 + i 11 + i 11 + i 21 + i 2
casinl1 + i 01 + i 21 + i 2-2 + i 2
casinf128-----
casinhf2 + i 12 + i 11 + i 12 + i 12 + i 1
casinh5 + i 31 + i 11 + i 12 + i 12 + i 1
casinhl5 + i 32 + i 12 + i 1-2 + i 2
casinhf128-----
catanf1 + i 10 + i 10 + i 11 + i 11 + i 1
catan1 + i 10 + i 10 + i 11 + i 11 + i 1
catanl0 + i 10 + i 11 + i 1-1 + i 1
catanf128-----
catanhf1 + i 11 + i 01 + i 01 + i 11 + i 1
catanh4 + i 11 + i 01 + i 01 + i 11 + i 1
catanhl4 + i 01 + i 01 + i 1-1 + i 1
catanhf128-----
cbrtf1-111
cbrt3-133
cbrtl1-1-1
cbrtf128-----
ccosf1 + i 10 + i 1-1 + i 11 + i 1
ccos1 + i 11 + i 1-1 + i 11 + i 1
ccosl1 + i 01 + i 11 + i 1-1 + i 1
ccosf128-----
ccoshf1 + i 11 + i 1-1 + i 11 + i 1
ccosh1 + i 11 + i 1-1 + i 11 + i 1
ccoshl1 + i 00 + i 10 + i 1-1 + i 1
ccoshf128-----
cexpf1 + i 21 + i 2-1 + i 21 + i 2
cexp2 + i 12 + i 1-2 + i 12 + i 1
cexpl-1 + i 11 + i 1-1 + i 1
cexpf128-----
clogf3 + i 11 + i 02 + i 13 + i 13 + i 1
clog3 + i 01 + i 13 + i 13 + i 03 + i 0
clogl-1 + i 13 + i 1-2 + i 1
clogf128-----
clog10f4 + i 22 + i 12 + i 14 + i 24 + i 2
clog103 + i 22 + i 12 + i 13 + i 23 + i 2
clog10l0 + i 11 + i 13 + i 2-2 + i 2
clog10f128-----
cosf1--11
cos211--
cosl2---1
cosf128-----
coshf1--11
cosh1--11
coshl----1
coshf128-----
cpowf4 + i 25 + i 23 + i 54 + i 24 + i 2
cpow2 + i 22 + i 01 + i 02 + i 02 + i 0
cpowl2 + i 23 + i 43 + i 1-4 + i 1
cpowf128-----
csinf1 + i 01 + i 1-1 + i 01 + i 0
csin1 + i 01 + i 0-1 + i 01 + i 0
csinl-1 + i 01 + i 0-1 + i 1
csinf128-----
csinhf1 + i 11 + i 1-1 + i 11 + i 1
csinh0 + i 11 + i 1-0 + i 10 + i 1
csinhl0 + i 11 + i 01 + i 0-1 + i 1
csinhf128-----
csqrtf2 + i 21 + i 11 + i 12 + i 22 + i 2
csqrt2 + i 21 + i 11 + i 12 + i 22 + i 2
csqrtl-1 + i 12 + i 2-2 + i 2
csqrtf128-----
ctanf1 + i 11 + i 11 + i 11 + i 11 + i 1
ctan1 + i 21 + i 21 + i 11 + i 21 + i 2
ctanl0 + i 12 + i 22 + i 2-3 + i 3
ctanf128-----
ctanhf1 + i 21 + i 11 + i 21 + i 21 + i 2
ctanh2 + i 22 + i 21 + i 12 + i 22 + i 2
ctanhl1 + i 01 + i 22 + i 2-3 + i 3
ctanhf128-----
erff1-111
erf1--11
erfl1-1-1
erff128-----
erfcf2-122
erfc3--33
erfcl1-2-2
erfcf128-----
expf1--11
exp-----
expl----1
expf128-----
exp10f2----
exp106--22
exp10l6---2
exp10f128-----
exp2f1--11
exp21-111
exp2l----1
exp2f128-----
expm1f1--11
expm11--11
expm1l11--1
expm1f128-----
fmaf-----
fma-----
fmal-----
fmaf128-----
fmodf-----
fmod-----
fmodl-----
fmodf128-----
gammaf4-144
gamma4--44
gammal--2-5
gammaf128-----
hypotf1----
hypot1-111
hypotl--1-1
hypotf128-----
j0f22222
j022122
j0l222-2
j0f128-----
j1f22222
j111-11
j1l111-4
j1f128-----
jnf54244
jn44244
jnl444-7
jnf128-----
lgammaf4-144
lgamma4--44
lgammal1-2-5
lgammaf128-----
logf1--11
log-----
logl----1
logf128-----
log10f2--22
log102--22
log10l1---1
log10f128-----
log1pf1--11
log1p1--11
log1pl----2
log1pf128-----
log2f1--11
log22--22
log2l----2
log2f128-----
powf1-711
pow--1--
powl--9-2
powf128-----
pow10f-----
pow102--22
pow10l----2
pow10f128-----
sinf1--11
sin-11--
sinl----1
sinf128-----
sincosf1--11
sincos11---
sincosl1---1
sincosf128-----
sinhf2--22
sinh2--22
sinhl----2
sinhf128-----
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
tanf1--11
tan1----
tanl1---1
tanf128-----
tanhf2--22
tanh2--22
tanhl----2
tanhf128-----
tgammaf4-444
tgamma5-155
tgammal119-4
tgammaf128-----
y0f11111
y022122
y0l211-3
y0f128-----
y1f22322
y133133
y1l322-2
y1f128-----
ynf23322
yn33233
ynl324-5
ynf128-----
FunctionMicroBlazeNios IIPowerPCPowerPC soft-floatS/390
acosf11111
acos-----
acosl--111
acosf128--1--
acoshf22222
acosh22222
acoshl--212
acoshf128--2--
asinf11111
asin-----
asinl--221
asinf128--1--
asinhf11111
asinh11111
asinhl--223
asinhf128--3--
atanf11111
atan--1--
atanl--111
atanf128--1--
atan2f11111
atan2-----
atan2l--221
atan2f128--1--
atanhf22222
atanh22222
atanhl--223
atanhf128--3--
cabsf-----
cabs11111
cabsl--111
cabsf128--1--
cacosf2 + i 22 + i 22 + i 22 + i 22 + i 2
cacos1 + i 21 + i 21 + i 21 + i 21 + i 2
cacosl--1 + i 22 + i 12 + i 2
cacosf128--2 + i 2--
cacoshf2 + i 22 + i 22 + i 22 + i 22 + i 2
cacosh2 + i 12 + i 12 + i 12 + i 12 + i 1
cacoshl--2 + i 11 + i 22 + i 2
cacoshf128--2 + i 2--
cargf11111
carg--1--
cargl--222
cargf128--2--
casinf1 + i 21 + i 21 + i 21 + i 21 + i 2
casin1 + i 21 + i 21 + i 21 + i 21 + i 2
casinl--1 + i 22 + i 12 + i 2
casinf128--2 + i 2--
casinhf2 + i 12 + i 12 + i 12 + i 12 + i 1
casinh2 + i 12 + i 12 + i 12 + i 12 + i 1
casinhl--2 + i 11 + i 22 + i 2
casinhf128--2 + i 2--
catanf1 + i 11 + i 11 + i 11 + i 11 + i 1
catan1 + i 11 + i 11 + i 11 + i 11 + i 1
catanl--3 + i 23 + i 21 + i 1
catanf128--1 + i 1--
catanhf1 + i 11 + i 11 + i 11 + i 11 + i 1
catanh1 + i 11 + i 11 + i 11 + i 11 + i 1
catanhl--2 + i 32 + i 31 + i 1
catanhf128--1 + i 1--
cbrtf11111
cbrt33333
cbrtl--111
cbrtf128--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 21 + i 21 + i 1
ccosf128--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 21 + i 21 + i 1
ccoshf128--1 + i 1--
cexpf1 + i 21 + i 21 + i 21 + i 21 + i 2
cexp2 + i 12 + i 12 + i 12 + i 12 + i 1
cexpl--2 + i 21 + i 11 + i 1
cexpf128--1 + i 1--
clogf3 + i 13 + i 13 + i 13 + i 13 + i 1
clog3 + i 03 + i 03 + i 13 + i 03 + i 0
clogl--5 + i 22 + i 22 + i 1
clogf128--2 + i 1--
clog10f4 + i 24 + i 24 + i 24 + i 24 + i 2
clog103 + i 23 + i 23 + i 23 + i 23 + i 2
clog10l--3 + i 23 + i 22 + i 2
clog10f128--2 + i 2--
cosf11311
cos-----
cosl--441
cosf128--1--
coshf11111
cosh11111
coshl--331
coshf128--1--
cpowf4 + i 24 + i 25 + i 24 + i 25 + i 2
cpow2 + i 02 + i 02 + i 02 + i 02 + i 0
cpowl--4 + i 24 + i 14 + i 1
cpowf128--4 + i 9--
csinf1 + i 01 + i 01 + i 01 + i 01 + i 0
csin1 + i 01 + i 01 + i 01 + i 01 + i 0
csinl--2 + i 12 + i 11 + i 1
csinf128--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 21 + i 21 + i 1
csinhf128--1 + i 1--
csqrtf2 + i 22 + i 22 + i 22 + i 22 + i 2
csqrt2 + i 22 + i 22 + i 22 + i 22 + i 2
csqrtl--1 + i 11 + i 12 + i 2
csqrtf128--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
ctanl--3 + i 23 + i 23 + i 3
ctanf128--3 + i 3--
ctanhf1 + i 21 + i 22 + i 11 + i 22 + i 1
ctanh2 + i 22 + i 22 + i 22 + i 22 + i 2
ctanhl--3 + i 32 + i 33 + i 3
ctanhf128--3 + i 3--
erff11111
erf11111
erfl--111
erff128--1--
erfcf22222
erfc33232
erfcl--332
erfcf128--2--
expf11111
exp--1--
expl--111
expf128--1--
exp10f-----
exp1022222
exp10l--112
exp10f128--2--
exp2f11111
exp211111
exp2l--211
exp2f128--1--
expm1f11111
expm111111
expm1l--111
expm1f128--1--
fmaf-----
fma-----
fmal--11-
fmaf128-----
fmodf-----
fmod-----
fmodl--11-
fmodf128-----
gammaf44444
gamma44343
gammal--335
gammaf128--9--
hypotf-----
hypot11111
hypotl--111
hypotf128--1--
j0f22222
j022222
j0l--222
j0f128--2--
j1f22222
j111111
j1l--214
j1f128--4--
jnf44444
jn44444
jnl--447
jnf128--7--
lgammaf44444
lgamma44343
lgammal--335
lgammaf128--9--
logf11111
log-----
logl--111
logf128--1--
log10f22222
log1022222
log10l--111
log10f128--1--
log1pf11111
log1p11111
log1pl--222
log1pf128--2--
log2f11111
log222121
log2l--112
log2f128--2--
powf13111
pow-----
powl--112
powf128--2--
pow10f-----
pow1022222
pow10l--112
pow10f128--2--
sinf11111
sin-----
sinl--111
sinf128--1--
sincosf11111
sincos-----
sincosl--111
sincosf128--1--
sinhf22222
sinh22222
sinhl--332
sinhf128--2--
sqrtf-----
sqrt-----
sqrtl--11-
sqrtf128-----
tanf11311
tan-----
tanl--221
tanf128--1--
tanhf22222
tanh22222
tanhl--112
tanhf128--2--
tgammaf45444
tgamma55555
tgammal--534
tgammaf128--4--
y0f11111
y022222
y0l--113
y0f128--3--
y1f22222
y133333
y1l--222
y1f128--2--
ynf22222
yn33333
ynl--225
ynf128--5--
FunctionSHSparcTilei686ix86
acosf-11--
acos---11
acosl-1-11
acosf128---11
acoshf-22--
acosh12211
acoshl-2-22
acoshf128---22
asinf-11--
asin---11
asinl-1-11
asinf128---11
asinhf111--
asinh11111
asinhl-3-33
asinhf128---33
atanf-11--
atan---11
atanl-1-11
atanf128---11
atan2f111--
atan2---11
atan2l-1-11
atan2f128---11
atanhf122--
atanh-2211
atanhl-3-33
atanhf128---33
cabsf-----
cabs-1111
cabsl-1-11
cabsf128---11
cacosf2 + i 22 + i 22 + i 21 + i 11 + i 1
cacos1 + i 11 + i 21 + i 11 + i 11 + i 1
cacosl-2 + i 2-1 + i 21 + i 2
cacosf128---2 + i 22 + i 2
cacoshf2 + i 22 + i 22 + i 21 + i 11 + i 1
cacosh1 + i 12 + i 11 + i 11 + i 11 + i 1
cacoshl-2 + i 2-2 + i 12 + i 1
cacoshf128---2 + i 22 + i 2
cargf-11--
carg---11
cargl-2-11
cargf128---22
casinf1 + i 21 + i 21 + i 21 + i 11 + i 1
casin1 + i 11 + i 21 + i 11 + i 11 + i 1
casinl-2 + i 2-1 + i 21 + i 2
casinf128---2 + i 22 + i 2
casinhf2 + i 12 + i 12 + i 11 + i 11 + i 1
casinh1 + i 12 + i 11 + i 11 + i 11 + i 1
casinhl-2 + i 2-2 + i 12 + i 1
casinhf128---2 + i 22 + i 2
catanf1 + i 11 + i 11 + i 10 + i 10 + i 1
catan0 + i 11 + i 10 + i 11 + i 11 + i 1
catanl-1 + i 1-1 + i 11 + i 1
catanf128---1 + i 11 + i 1
catanhf1 + i 11 + i 11 + i 11 + i 01 + i 0
catanh1 + i 01 + i 11 + i 01 + i 11 + i 1
catanhl-1 + i 1-1 + i 11 + i 1
catanhf128---1 + i 11 + i 1
cbrtf11111
cbrt13311
cbrtl-1-33
cbrtf128---11
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 11 + i 1
ccosf128---1 + i 11 + 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 11 + i 1
ccoshf128---1 + i 11 + i 1
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 1-1 + i 11 + i 1
cexpf128---1 + i 11 + i 1
clogf1 + i 13 + i 13 + i 11 + i 01 + i 0
clog1 + i 03 + i 03 + i 02 + i 12 + i 1
clogl-4 + i 1-3 + i 13 + i 1
clogf128---2 + i 12 + i 1
clog10f2 + i 14 + i 24 + i 22 + i 02 + i 0
clog102 + i 13 + i 23 + i 22 + i 12 + i 1
clog10l-4 + i 2-4 + i 24 + i 2
clog10f128---2 + i 22 + i 2
cosf111-1
cos-----
cosl-1-11
cosf128---11
coshf11111
cosh11111
coshl-1-22
coshf128---11
cpowf4 + i 24 + i 24 + i 25 + i 25 + i 2
cpow2 + i 02 + i 02 + i 02 + i 12 + i 0
cpowl-4 + i 1-3 + i 43 + i 4
cpowf128---4 + i 14 + i 1
csinf1 + i 01 + i 01 + i 01 + i 11 + i 1
csin1 + i 01 + i 01 + i 01 + i 11 + i 0
csinl-1 + i 1-1 + i 01 + i 0
csinf128---1 + i 11 + i 1
csinhf1 + i 11 + i 11 + i 11 + i 10 + i 1
csinh0 + i 10 + i 10 + i 11 + i 10 + i 1
csinhl-1 + i 1-1 + i 11 + i 1
csinhf128---1 + i 11 + i 1
csqrtf1 + i 12 + i 22 + i 20 + i 10 + i 1
csqrt1 + i 12 + i 22 + i 21 + i 11 + i 1
csqrtl-2 + i 2-2 + i 22 + i 2
csqrtf128---2 + i 22 + i 2
ctanf1 + i 11 + i 11 + i 11 + i 11 + i 1
ctan1 + i 21 + i 21 + i 21 + i 11 + i 1
ctanl-3 + i 3-2 + i 12 + i 1
ctanf128---3 + i 33 + i 3
ctanhf1 + i 21 + i 21 + i 21 + i 11 + i 1
ctanh2 + i 22 + i 22 + i 21 + i 11 + i 1
ctanhl-3 + i 3-1 + i 21 + i 2
ctanhf128---3 + i 33 + i 3
erff-1111
erf11111
erfl-1-11
erff128---11
erfcf12211
erfc13311
erfcl-2-33
erfcf128---22
expf-11--
exp---11
expl-1-11
expf128---11
exp10f-----
exp1012211
exp10l-2-11
exp10f128---22
exp2f-11--
exp2-1111
exp2l-1-11
exp2f128---11
expm1f111--
expm111111
expm1l-1-22
expm1f128---11
fmaf-----
fma-----
fmal-----
fmaf128-----
fmodf-----
fmod-----
fmodl-----
fmodf128-----
gammaf14432
gamma14433
gammal-5-44
gammaf128-----
hypotf-----
hypot11111
hypotl-1-11
hypotf128---11
j0f22211
j022222
j0l-2-22
j0f128---22
j1f22211
j111122
j1l-4-11
j1f128---44
jnf44433
jn44422
jnl-7-44
jnf128---77
lgammaf14432
lgamma14433
lgammal-5-44
lgammaf128---55
logf111--
log---11
logl-1-11
logf128---11
log10f222--
log1012211
log10l-1-11
log10f128---11
log1pf111--
log1p-1111
log1pl-2-22
log1pf128---22
log2f-11--
log2-2211
log2l-2-11
log2f128---22
powf133--
pow---11
powl-2-11
powf128---22
pow10f-----
pow1012211
pow10l-2-11
pow10f128-----
sinf111-1
sin-----
sinl-1-11
sinf128---11
sincosf111-1
sincos-----
sincosl-1-11
sincosf128---11
sinhf-22--
sinh-2211
sinhl-2-22
sinhf128---22
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
tanf-1111
tan-----
tanl-1-22
tanf128---11
tanhf-22--
tanh-2211
tanhl-2-33
tanhf128---22
tgammaf35533
tgamma45533
tgammal-4-55
tgammaf128---44
y0f11111
y022211
y0l-3-11
y0f128---33
y1f22222
y133322
y1l-2-22
y1f128---22
ynf22233
yn33322
ynl-5-44
ynf128---55

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