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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-----
add_ldoublef-----
add_ldouble-----
add_ldoublel-----
add_ldoublef128-----
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-
cos11-2-
cosl1-1--
cosf128-----
coshf111--
cosh111--
coshl1-1--
coshf128-----
cpowf5 + i 25 + i 25 + 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 21 + i 21 + i 2--
ctan1 + i 21 + i 21 + i 20 + i 1-
ctanl3 + i 3-3 + i 3--
ctanf128-----
ctanhf2 + i 12 + i 22 + i 22 + i 1-
ctanh2 + i 22 + i 22 + i 21 + i 0-
ctanhl3 + i 3-3 + i 3--
ctanhf128-----
div_ldoublef-----
div_ldouble-----
div_ldoublel-----
div_ldoublef128-----
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-----
mul_ldoublef-----
mul_ldouble-----
mul_ldoublel-----
mul_ldoublef128-----
powf111--
pow11---
powl2-2--
powf128-----
sinf111--
sin11---
sinl1-1--
sinf128-----
sincosf1111-
sincos11-1-
sincosl1-1--
sincosf128-----
sinhf222--
sinh222--
sinhl2-2--
sinhf128-----
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
sub_ldoublef-----
sub_ldouble-----
sub_ldoublel-----
sub_ldoublef128-----
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-----
ynf3332-
yn3333-
ynl5-5--
ynf128-----
FunctionHPPAIA64M68kMIPS 32-bitMIPS 64-bit
acosf1--11
acos-1---
acosl----1
acosf128-1---
acoshf2-122
acosh21122
acoshl-11-2
acoshf128-2---
add_ldoublef-----
add_ldouble-----
add_ldoublel-----
add_ldoublef128-----
asinf1--11
asin-----
asinl----1
asinf128-1---
asinhf1-111
asinh11111
asinhl--1-3
asinhf128-3---
atanf1--11
atan-----
atanl----1
atanf128-1---
atan2f1-111
atan2-----
atan2l--1-1
atan2f128-1---
atanhf2--22
atanh2--22
atanhl----3
atanhf128-3---
cabsf-----
cabs1-111
cabsl--1-1
cabsf128-1---
cacosf2 + i 22 + i 22 + i 12 + i 22 + i 2
cacos1 + i 21 + i 21 + i 11 + i 21 + i 2
cacosl-1 + i 21 + i 2-2 + i 2
cacosf128-2 + i 2---
cacoshf2 + i 22 + i 21 + i 22 + i 22 + i 2
cacosh2 + i 12 + i 11 + i 12 + i 12 + i 1
cacoshl-2 + i 12 + i 1-2 + i 2
cacoshf128-2 + i 2---
cargf1-111
carg-----
cargl--1-2
cargf128-2---
casinf1 + i 21 + i 21 + i 11 + i 21 + i 2
casin1 + i 21 + i 21 + i 11 + i 21 + i 2
casinl1 + i 01 + i 21 + i 2-2 + i 2
casinf128-2 + i 2---
casinhf2 + i 12 + i 11 + i 12 + i 12 + i 1
casinh5 + i 32 + i 11 + i 12 + i 12 + i 1
casinhl5 + i 32 + i 12 + i 1-2 + i 2
casinhf128-2 + i 2---
catanf1 + i 10 + i 10 + i 11 + i 11 + i 1
catan1 + i 11 + i 10 + i 11 + i 11 + i 1
catanl0 + i 10 + i 11 + i 1-1 + i 1
catanf128-1 + i 1---
catanhf1 + i 11 + i 01 + i 01 + i 11 + i 1
catanh4 + i 11 + i 11 + i 01 + i 11 + i 1
catanhl4 + i 01 + i 01 + i 1-1 + i 1
catanhf128-1 + i 1---
cbrtf1-111
cbrt3-133
cbrtl1-1-1
cbrtf128-1---
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
ccosf128-1 + i 1---
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
ccoshf128-1 + i 1---
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
cexpf128-1 + i 1---
clogf3 + i 13 + i 02 + i 13 + i 13 + i 1
clog3 + i 02 + i 13 + i 13 + i 03 + i 0
clogl-2 + i 13 + i 1-2 + i 1
clogf128-2 + i 1---
clog10f4 + i 24 + i 12 + i 14 + i 24 + i 2
clog103 + i 23 + i 22 + i 13 + i 23 + i 2
clog10l0 + i 12 + i 13 + i 2-2 + i 2
clog10f128-2 + i 2---
cosf1--11
cos21111
cosl2---1
cosf128-1---
coshf1--11
cosh1--11
coshl----1
coshf128-1---
cpowf5 + i 25 + i 23 + i 55 + i 25 + i 2
cpow2 + i 22 + i 01 + i 02 + i 02 + i 0
cpowl2 + i 23 + i 43 + i 1-4 + i 1
cpowf128-4 + i 1---
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
csinf128-1 + i 1---
csinhf1 + i 11 + i 1-1 + i 11 + i 1
csinh0 + i 11 + i 1-0 + i 10 + i 1
csinhl0 + i 11 + i 11 + i 0-1 + i 1
csinhf128-1 + i 1---
csqrtf2 + i 22 + i 21 + i 12 + i 22 + i 2
csqrt2 + i 22 + i 21 + i 12 + i 22 + i 2
csqrtl-2 + i 22 + i 2-2 + i 2
csqrtf128-2 + i 2---
ctanf1 + i 21 + i 11 + i 11 + i 21 + i 2
ctan1 + i 21 + i 21 + i 11 + i 21 + i 2
ctanl0 + i 12 + i 22 + i 2-3 + i 3
ctanf128-3 + i 3---
ctanhf2 + i 21 + i 11 + i 22 + i 22 + i 2
ctanh2 + i 22 + i 21 + i 12 + i 22 + i 2
ctanhl1 + i 01 + i 22 + i 2-3 + i 3
ctanhf128-3 + i 3---
div_ldoublef-----
div_ldouble-----
div_ldoublel-----
div_ldoublef128-----
erff1-111
erf1--11
erfl1-1-1
erff128-1---
erfcf2-122
erfc3--33
erfcl1-2-2
erfcf128-2---
expf11-11
exp-----
expl----1
expf128-1---
exp10f2----
exp106--22
exp10l6---2
exp10f128-2---
exp2f1--11
exp211111
exp2l-1--1
exp2f128-1---
expm1f1--11
expm111-11
expm1l11--1
expm1f128-1---
fmaf-----
fma-----
fmal-----
fmaf128-----
fmodf-----
fmod-----
fmodl-----
fmodf128-----
gammaf41144
gamma4--44
gammal--2-5
gammaf128-----
hypotf1----
hypot1-111
hypotl--1-1
hypotf128-1---
j0f22222
j022122
j0l222-2
j0f128-2---
j1f22222
j111-11
j1l111-4
j1f128-4---
jnf54244
jn44244
jnl444-7
jnf128-7---
lgammaf41144
lgamma4--44
lgammal1-2-5
lgammaf128-5---
logf1--11
log-----
logl----1
logf128-1---
log10f2--22
log102--22
log10l1---1
log10f128-1---
log1pf1--11
log1p1--11
log1pl----2
log1pf128-2---
log2f1--11
log22--22
log2l----2
log2f128-2---
mul_ldoublef-----
mul_ldouble-----
mul_ldoublel-----
mul_ldoublef128-----
powf1-711
pow1-111
powl--9-2
powf128-2---
sinf1--11
sin11111
sinl----1
sinf128-1---
sincosf1--11
sincos11-11
sincosl1---1
sincosf128-1---
sinhf2--22
sinh2--22
sinhl----2
sinhf128-2---
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
sub_ldoublef-----
sub_ldouble-----
sub_ldoublel-----
sub_ldoublef128-----
tanf1--11
tan1----
tanl11--1
tanf128-1---
tanhf2--22
tanh2--22
tanhl----2
tanhf128-2---
tgammaf4-444
tgamma5-155
tgammal119-4
tgammaf128-4---
y0f11111
y022122
y0l211-3
y0f128-3---
y1f22322
y133133
y1l322-2
y1f128-2---
ynf33333
yn33233
ynl334-5
ynf128-5---
FunctionMicroBlazeNios IIPowerPCPowerPC soft-floatRISC-V
acosf11111
acos-----
acosl--111
acosf128--1--
acoshf22222
acosh22222
acoshl--212
acoshf128--2--
add_ldoublef--11-
add_ldouble--11-
add_ldoublel-----
add_ldoublef128-----
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--
cosf1131-
cos-111-
cosl--441
cosf128--1--
coshf11111
cosh11111
coshl--331
coshf128--1--
cpowf4 + i 25 + i 25 + i 25 + 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 1--
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 21 + i 21 + i 21 + i 2
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 22 + i 22 + i 12 + 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--
div_ldoublef--11-
div_ldouble-----
div_ldoublel-----
div_ldoublef128-----
erff11111
erf11111
erfl--111
erff128--1--
erfcf22222
erfc33232
erfcl--332
erfcf128--2--
expf11-1-
exp--1--
expl--111
expf128--1--
exp10f-----
exp1022222
exp10l--112
exp10f128--2--
exp2f11-1-
exp211111
exp2l--211
exp2f128--1--
expm1f11111
expm111111
expm1l--111
expm1f128--1--
fmaf-----
fma-----
fmal--11-
fmaf128-----
fmodf-----
fmod-----
fmodl--11-
fmodf128-----
gammaf44443
gamma44343
gammal--335
gammaf128-----
hypotf-----
hypot11111
hypotl--111
hypotf128--1--
j0f22222
j022222
j0l--222
j0f128--2--
j1f22222
j111111
j1l--214
j1f128--4--
jnf44444
jn44444
jnl--447
jnf128--7--
lgammaf44443
lgamma44343
lgammal--335
lgammaf128--5--
logf1111-
log-----
logl--111
logf128--1--
log10f22222
log1022222
log10l--111
log10f128--1--
log1pf11111
log1p11111
log1pl--222
log1pf128--2--
log2f11111
log222121
log2l--112
log2f128--2--
mul_ldoublef--11-
mul_ldouble--11-
mul_ldoublel-----
mul_ldoublef128-----
powf1311-
pow-111-
powl--112
powf128--2--
sinf1111-
sin-111-
sinl--111
sinf128--1--
sincosf1111-
sincos-111-
sincosl--111
sincosf128--1--
sinhf22222
sinh22222
sinhl--332
sinhf128--2--
sqrtf-----
sqrt-----
sqrtl--11-
sqrtf128-----
sub_ldoublef--11-
sub_ldouble--11-
sub_ldoublel-----
sub_ldoublef128-----
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--
ynf23333
yn33333
ynl--225
ynf128--5--
FunctionRISC-V soft-floatS/390SHSparci686
acosf1111-
acos----1
acosl11-11
acosf128----1
acoshf2222-
acosh22221
acoshl22-22
acoshf128----2
add_ldoublef-----
add_ldouble-----
add_ldoublel-----
add_ldoublef128-----
asinf1111-
asin----1
asinl11-11
asinf128----1
asinhf1111-
asinh11111
asinhl33-33
asinhf128----3
atanf1111-
atan----1
atanl11-11
atanf128----1
atan2f1111-
atan2----1
atan2l11-11
atan2f128----1
atanhf2222-
atanh22221
atanhl33-33
atanhf128----3
cabsf-----
cabs11111
cabsl11-11
cabsf128----1
cacosf2 + i 22 + i 22 + i 22 + i 22 + i 2
cacos1 + i 21 + i 21 + i 21 + i 21 + i 2
cacosl2 + i 22 + i 2-2 + i 21 + 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
cacoshl2 + i 22 + i 2-2 + i 22 + i 1
cacoshf128----2 + i 2
cargf1111-
carg----1
cargl22-21
cargf128----2
casinf1 + i 21 + i 21 + i 21 + i 21 + i 2
casin1 + i 21 + i 21 + i 21 + i 21 + i 2
casinl2 + i 22 + i 2-2 + i 21 + 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
casinhl2 + i 22 + i 2-2 + i 22 + i 1
casinhf128----2 + i 2
catanf1 + i 11 + i 11 + i 11 + i 10 + i 1
catan1 + i 11 + i 11 + i 11 + i 11 + i 1
catanl1 + i 11 + i 1-1 + i 11 + i 1
catanf128----1 + i 1
catanhf1 + i 11 + i 11 + i 11 + i 11 + i 0
catanh1 + i 11 + i 11 + i 11 + i 11 + i 1
catanhl1 + i 11 + i 1-1 + i 11 + i 1
catanhf128----1 + i 1
cbrtf11111
cbrt33331
cbrtl11-13
cbrtf128----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 11 + i 1-1 + i 11 + 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
ccoshl1 + i 11 + i 1-1 + i 11 + 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
cexpl1 + i 11 + i 1-1 + i 11 + i 1
cexpf128----1 + i 1
clogf3 + i 13 + i 13 + i 13 + i 13 + i 0
clog3 + i 03 + i 03 + i 03 + i 02 + i 1
clogl2 + i 12 + i 1-4 + i 13 + i 1
clogf128----2 + i 1
clog10f4 + i 24 + i 24 + i 24 + i 24 + i 1
clog103 + i 23 + i 23 + i 23 + i 23 + i 2
clog10l2 + i 22 + i 2-4 + i 24 + i 2
clog10f128----2 + i 2
cosf--11-
cos-1111
cosl11-11
cosf128----1
coshf11111
cosh11111
coshl11-12
coshf128----1
cpowf5 + i 25 + i 25 + i 25 + i 25 + i 2
cpow2 + i 02 + i 02 + i 02 + i 02 + i 1
cpowl4 + i 14 + i 1-4 + i 13 + i 4
cpowf128----4 + i 1
csinf1 + i 01 + i 01 + i 01 + i 01 + i 1
csin1 + i 01 + i 01 + i 01 + i 01 + i 1
csinl1 + i 11 + i 1-1 + i 11 + i 0
csinf128----1 + i 1
csinhf1 + i 11 + i 11 + i 11 + i 11 + i 1
csinh0 + i 10 + i 10 + i 10 + i 11 + i 1
csinhl1 + i 11 + i 1-1 + i 11 + 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
csqrtl2 + i 22 + i 2-2 + i 22 + i 2
csqrtf128----2 + i 2
ctanf1 + i 21 + i 21 + i 21 + i 21 + i 2
ctan1 + i 21 + i 21 + i 21 + i 21 + i 2
ctanl3 + i 33 + i 3-3 + i 32 + i 1
ctanf128----3 + i 3
ctanhf2 + i 22 + i 12 + i 22 + i 22 + i 2
ctanh2 + i 22 + i 22 + i 22 + i 22 + i 2
ctanhl3 + i 33 + i 3-3 + i 31 + i 2
ctanhf128----3 + i 3
div_ldoublef-----
div_ldouble-----
div_ldoublel-----
div_ldoublef128-----
erff11111
erf11111
erfl11-11
erff128----1
erfcf22222
erfc32333
erfcl22-23
erfcf128----2
expf---1-
exp----1
expl11-11
expf128----1
exp10f-----
exp1022221
exp10l22-21
exp10f128----2
exp2f---1-
exp211111
exp2l11-11
exp2f128----1
expm1f1111-
expm111111
expm1l11-12
expm1f128----1
fmaf-----
fma-----
fmal-----
fmaf128-----
fmodf-----
fmod-----
fmodl-----
fmodf128-----
gammaf33343
gamma43444
gammal55-54
gammaf128-----
hypotf-----
hypot11111
hypotl11-11
hypotf128----1
j0f22222
j022222
j0l22-22
j0f128----2
j1f22222
j111112
j1l44-41
j1f128----4
jnf44444
jn44444
jnl77-74
jnf128----7
lgammaf33343
lgamma43444
lgammal55-54
lgammaf128----5
logf--11-
log----1
logl11-11
logf128----1
log10f2222-
log1022221
log10l11-11
log10f128----1
log1pf1111-
log1p11111
log1pl22-22
log1pf128----2
log2f11111
log221221
log2l22-21
log2f128----2
mul_ldoublef-----
mul_ldouble-----
mul_ldoublel-----
mul_ldoublef128-----
powf--13-
pow-1111
powl22-21
powf128----2
sinf--11-
sin-1111
sinl11-11
sinf128----1
sincosf--11-
sincos-1111
sincosl11-11
sincosf128----1
sinhf22222
sinh22222
sinhl22-22
sinhf128----2
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
sub_ldoublef-----
sub_ldouble-----
sub_ldoublel-----
sub_ldoublef128-----
tanf11111
tan-----
tanl11-12
tanf128----1
tanhf22222
tanh22222
tanhl22-23
tanhf128----2
tgammaf44454
tgamma55555
tgammal44-45
tgammaf128----4
y0f11111
y022222
y0l33-31
y0f128----3
y1f22222
y133333
y1l22-22
y1f128----2
ynf33333
yn33333
ynl55-54
ynf128----5
Functionix86x86_64
acosf-1
acos1-
acosl11
acosf12811
acoshf-2
acosh12
acoshl22
acoshf12822
add_ldoublef--
add_ldouble--
add_ldoublel--
add_ldoublef128--
asinf-1
asin1-
asinl11
asinf12811
asinhf-1
asinh11
asinhl33
asinhf12833
atanf-1
atan1-
atanl11
atanf12811
atan2f-1
atan21-
atan2l11
atan2f12811
atanhf-2
atanh12
atanhl33
atanhf12833
cabsf--
cabs11
cabsl11
cabsf12811
cacosf2 + i 22 + i 2
cacos1 + i 21 + i 2
cacosl1 + i 21 + i 2
cacosf1282 + i 22 + i 2
cacoshf2 + i 22 + i 2
cacosh2 + i 12 + i 1
cacoshl2 + i 12 + i 1
cacoshf1282 + i 22 + i 2
cargf-1
carg1-
cargl11
cargf12822
casinf1 + i 21 + i 2
casin1 + i 21 + i 2
casinl1 + i 21 + i 2
casinf1282 + i 22 + i 2
casinhf2 + i 12 + i 1
casinh2 + i 12 + i 1
casinhl2 + i 12 + i 1
casinhf1282 + i 22 + i 2
catanf0 + i 11 + i 1
catan1 + i 11 + i 1
catanl1 + i 11 + i 1
catanf1281 + i 11 + i 1
catanhf1 + i 01 + i 1
catanh1 + i 11 + i 1
catanhl1 + i 11 + i 1
catanhf1281 + i 11 + i 1
cbrtf11
cbrt13
cbrtl31
cbrtf12811
ccosf1 + i 11 + i 1
ccos1 + i 11 + i 1
ccosl1 + i 11 + i 1
ccosf1281 + i 11 + i 1
ccoshf1 + i 11 + i 1
ccosh1 + i 11 + i 1
ccoshl1 + i 11 + i 1
ccoshf1281 + i 11 + i 1
cexpf1 + i 21 + i 2
cexp2 + i 12 + i 1
cexpl1 + i 11 + i 1
cexpf1281 + i 11 + i 1
clogf3 + i 03 + i 1
clog2 + i 13 + i 0
clogl3 + i 13 + i 1
clogf1282 + i 12 + i 1
clog10f4 + i 14 + i 2
clog103 + i 23 + i 2
clog10l4 + i 24 + i 2
clog10f1282 + i 22 + i 2
cosf1-
cos11
cosl11
cosf12811
coshf11
cosh11
coshl22
coshf12811
cpowf5 + i 25 + i 2
cpow2 + i 02 + i 0
cpowl3 + i 43 + i 4
cpowf1284 + i 14 + i 1
csinf1 + i 11 + i 0
csin1 + i 01 + i 0
csinl1 + i 01 + i 0
csinf1281 + i 11 + i 1
csinhf1 + i 11 + i 1
csinh0 + i 10 + i 1
csinhl1 + i 11 + i 1
csinhf1281 + i 11 + i 1
csqrtf2 + i 22 + i 2
csqrt2 + i 22 + i 2
csqrtl2 + i 22 + i 2
csqrtf1282 + i 22 + i 2
ctanf1 + i 21 + i 2
ctan1 + i 21 + i 2
ctanl2 + i 12 + i 1
ctanf1283 + i 33 + i 3
ctanhf2 + i 22 + i 2
ctanh2 + i 22 + i 2
ctanhl1 + i 21 + i 2
ctanhf1283 + i 33 + i 3
div_ldoublef--
div_ldouble--
div_ldoublel--
div_ldoublef128--
erff11
erf11
erfl11
erff12811
erfcf22
erfc33
erfcl33
erfcf12822
expf--
exp1-
expl11
expf12811
exp10f--
exp1012
exp10l11
exp10f12822
exp2f-1
exp211
exp2l11
exp2f12811
expm1f-1
expm111
expm1l22
expm1f12811
fmaf--
fma--
fmal--
fmaf128--
fmodf--
fmod--
fmodl--
fmodf128--
gammaf34
gamma44
gammal44
gammaf128--
hypotf--
hypot11
hypotl11
hypotf12811
j0f22
j022
j0l22
j0f12822
j1f22
j121
j1l11
j1f12844
jnf44
jn44
jnl44
jnf12877
lgammaf34
lgamma44
lgammal44
lgammaf12855
logf-1
log1-
logl11
logf12811
log10f-2
log1012
log10l11
log10f12811
log1pf-1
log1p11
log1pl22
log1pf12822
log2f11
log212
log2l11
log2f12822
mul_ldoublef--
mul_ldouble--
mul_ldoublel--
mul_ldoublef128--
powf-1
pow11
powl11
powf12822
sinf1-
sin11
sinl11
sinf12811
sincosf1-
sincos11
sincosl11
sincosf12811
sinhf22
sinh22
sinhl22
sinhf12822
sqrtf--
sqrt--
sqrtl--
sqrtf128--
sub_ldoublef--
sub_ldouble--
sub_ldoublel--
sub_ldoublef128--
tanf11
tan--
tanl22
tanf12811
tanhf22
tanh22
tanhl33
tanhf12822
tgammaf45
tgamma55
tgammal55
tgammaf12844
y0f11
y022
y0l11
y0f12833
y1f22
y133
y1l22
y1f12822
ynf33
yn33
ynl44
ynf12855

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