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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.

FunctionAArch64ARCARC soft-floatARMAlpha
acosf11111
acos-1---
acosl1---1
acosf128-----
acoshf22222
acosh23222
acoshl2---2
acoshf128-----
add_ldoublef-----
add_ldouble-----
add_ldoublel-----
add_ldoublef128-----
asinf11111
asin-1---
asinl1---1
asinf128-----
asinhf22222
asinh23222
asinhl3---3
asinhf128-----
atanf11111
atan11---
atanl1---1
atanf128-----
atan2f12111
atan2-7---
atan2l1---1
atan2f128-----
atanhf22222
atanh22222
atanhl3---3
atanhf128-----
cabsf-1---
cabs11111
cabsl1---1
cabsf128-----
cacosf2 + i 22 + i 32 + i 22 + i 22 + i 2
cacos1 + i 22 + i 51 + i 21 + i 21 + i 2
cacosl2 + i 2---2 + i 2
cacosf128-----
cacoshf2 + i 24 + i 22 + i 22 + i 22 + i 2
cacosh2 + i 15 + i 22 + i 12 + i 12 + i 1
cacoshl2 + i 2---2 + i 2
cacoshf128-----
cargf12111
carg17---
cargl2---2
cargf128-----
casinf1 + i 21 + i 41 + i 21 + i 21 + i 2
casin1 + i 23 + i 51 + i 21 + i 21 + i 2
casinl2 + i 2---2 + i 2
casinf128-----
casinhf2 + i 14 + i 22 + i 12 + i 12 + i 1
casinh2 + i 15 + i 32 + i 12 + i 12 + i 1
casinhl2 + i 2---2 + i 2
casinhf128-----
catanf1 + i 11 + i 31 + i 11 + i 11 + i 1
catan1 + i 11 + i 31 + i 11 + i 11 + i 1
catanl1 + i 1---1 + i 1
catanf128-----
catanhf1 + i 14 + i 21 + i 11 + i 11 + i 1
catanh1 + i 14 + i 11 + i 11 + i 11 + i 1
catanhl1 + i 1---1 + i 1
catanhf128-----
cbrtf11111
cbrt44444
cbrtl1---1
cbrtf128-----
ccosf1 + i 13 + i 31 + i 11 + i 11 + i 1
ccos1 + i 13 + i 31 + i 11 + i 11 + i 1
ccosl1 + i 1---1 + i 1
ccosf128-----
ccoshf1 + i 13 + i 31 + i 11 + i 11 + i 1
ccosh1 + i 13 + i 31 + i 11 + i 11 + i 1
ccoshl1 + i 1---1 + i 1
ccoshf128-----
cexpf1 + i 23 + i 31 + i 21 + i 21 + i 2
cexp2 + i 14 + i 42 + i 12 + i 12 + i 1
cexpl1 + i 1---1 + i 1
cexpf128-----
clogf3 + i 14 + i 23 + i 13 + i 13 + i 1
clog3 + i 15 + i 73 + i 03 + i 03 + i 0
clogl2 + i 1---2 + i 1
clogf128-----
clog10f4 + i 25 + i 44 + i 24 + i 24 + i 2
clog103 + i 26 + i 83 + i 23 + i 23 + i 2
clog10l2 + i 2---2 + i 2
clog10f128-----
cosf11111
cos14111
cosl1---1
cosf128-----
coshf23222
cosh23222
coshl1---1
coshf128-----
cpowf5 + i 28 + i 65 + i 25 + i 25 + i 2
cpow2 + i 09 + i 82 + i 02 + i 02 + i 0
cpowl4 + i 1---4 + i 1
cpowf128-----
csinf1 + i 03 + i 31 + i 01 + i 01 + i 0
csin1 + i 03 + i 31 + i 01 + i 01 + i 0
csinl1 + i 1---1 + i 1
csinf128-----
csinhf1 + i 13 + i 31 + i 11 + i 11 + i 1
csinh0 + i 13 + i 30 + i 10 + i 10 + i 1
csinhl1 + i 1---1 + i 1
csinhf128-----
csqrtf2 + i 23 + i 32 + i 22 + i 22 + i 2
csqrt2 + i 24 + i 42 + i 22 + i 22 + i 2
csqrtl2 + i 2---2 + i 2
csqrtf128-----
ctanf1 + i 26 + i 21 + i 21 + i 21 + i 2
ctan1 + i 24 + i 31 + i 21 + i 21 + i 2
ctanl3 + i 3---3 + i 3
ctanf128-----
ctanhf2 + i 12 + i 62 + i 22 + i 22 + i 2
ctanh2 + i 23 + i 42 + i 22 + i 22 + i 2
ctanhl3 + i 3---3 + i 3
ctanhf128-----
div_ldoublef-----
div_ldouble-----
div_ldoublel-----
div_ldoublef128-----
erff11111
erf11111
erfl1---1
erff128-----
erfcf25333
erfc25555
erfcl2---2
erfcf128-----
expf11111
exp11111
expl1---1
expf128-----
exp10f11111
exp1024222
exp10l2---2
exp10f128-----
exp2f11-11
exp211111
exp2l1---1
exp2f128-----
expm1f12111
expm112111
expm1l1---1
expm1f128-----
fmaf-----
fma-----
fmal-----
fmaf128-----
fmodf-----
fmod-----
fmodl-----
fmodf128-----
gammaf46777
gamma37444
gammal5---5
gammaf128-----
hypotf-1---
hypot12111
hypotl1---1
hypotf128-----
j0f86888
j024222
j0l2---2
j0f128-----
j1f89999
j125222
j1l4---4
j1f128-----
jnf48444
jn49444
jnl7---7
jnf128-----
lgammaf46777
lgamma37444
lgammal5---5
lgammaf128-----
logf11-11
log11---
logl1---1
logf128-----
log10f23222
log1022222
log10l1---1
log10f128-----
log1pf11111
log1p11111
log1pl2---2
log1pf128-----
log2f11111
log212222
log2l2---2
log2f128-----
mul_ldoublef-----
mul_ldouble-----
mul_ldoublel-----
mul_ldoublef128-----
powf11-11
pow11111
powl2---2
powf128-----
pow10f-----
pow10-----
pow10l-----
pow10f128-----
sinf11111
sin17111
sinl1---1
sinf128-----
sincosf11111
sincos11111
sincosl1---1
sincosf128-----
sinhf23222
sinh23222
sinhl2---2
sinhf128-----
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
sub_ldoublef-----
sub_ldouble-----
sub_ldoublel-----
sub_ldoublef128-----
tanf11111
tan-1---
tanl1---1
tanf128-----
tanhf22222
tanh23222
tanhl2---2
tanhf128-----
tgammaf89888
tgamma99999
tgammal4---4
tgammaf128-----
y0f66888
y023333
y0l3---3
y0f128-----
y1f26222
y137333
y1l2---2
y1f128-----
ynf39333
yn39333
ynl5---5
ynf128-----
FunctionCSKYCSKY soft-floatColdFireGenericHPPA
acosf11--1
acos-----
acosl-----
acosf128-----
acoshf22--2
acosh22--2
acoshl-----
acoshf128-----
add_ldoublef-----
add_ldouble-----
add_ldoublel-----
add_ldoublef128-----
asinf11--1
asin-----
asinl-----
asinf128-----
asinhf22--2
asinh22--2
asinhl-----
asinhf128-----
atanf11--1
atan-----
atanl-----
atanf128-----
atan2f111-1
atan2-----
atan2l-----
atan2f128-----
atanhf221-2
atanh22--2
atanhl-----
atanhf128-----
cabsf-----
cabs11--1
cabsl-----
cabsf128-----
cacosf2 + i 22 + i 2--2 + i 2
cacos1 + i 21 + i 2--1 + i 2
cacosl-----
cacosf128-----
cacoshf2 + i 22 + i 20 + i 1-2 + i 2
cacosh2 + i 12 + i 1--2 + i 1
cacoshl-----
cacoshf128-----
cargf11--1
carg-----
cargl-----
cargf128-----
casinf1 + i 21 + i 21 + i 0-1 + i 2
casin1 + i 21 + i 21 + i 0-1 + i 2
casinl----1 + i 0
casinf128-----
casinhf2 + i 12 + i 11 + i 6-2 + i 1
casinh2 + i 12 + i 15 + i 3-5 + i 3
casinhl----5 + i 3
casinhf128-----
catanf1 + i 11 + i 10 + i 1-1 + i 1
catan1 + i 11 + i 10 + i 1-1 + i 1
catanl----0 + i 1
catanf128-----
catanhf1 + i 11 + i 1--1 + i 1
catanh1 + i 11 + i 14 + i 0-4 + i 1
catanhl----4 + i 0
catanhf128-----
cbrtf11--1
cbrt441-4
cbrtl----1
cbrtf128-----
ccosf1 + i 11 + i 11 + i 1-1 + i 1
ccos1 + i 11 + i 11 + i 0-1 + i 1
ccosl----1 + i 0
ccosf128-----
ccoshf1 + i 11 + i 11 + i 1-1 + i 1
ccosh1 + i 11 + i 11 + i 0-1 + i 1
ccoshl----1 + i 0
ccoshf128-----
cexpf1 + i 21 + i 21 + i 1-1 + i 2
cexp2 + i 12 + i 1--2 + i 1
cexpl-----
cexpf128-----
clogf3 + i 13 + i 11 + i 0-3 + i 1
clog3 + i 03 + i 0--3 + i 0
clogl-----
clogf128-----
clog10f4 + i 24 + i 21 + i 1-4 + i 2
clog103 + i 23 + i 20 + i 1-3 + i 2
clog10l----0 + i 1
clog10f128-----
cosf111-1
cos112-2
cosl----2
cosf128-----
coshf22--2
cosh22--2
coshl-----
coshf128-----
cpowf5 + i 25 + i 24 + i 2-5 + i 2
cpow2 + i 02 + i 02 + i 2-2 + i 2
cpowl----2 + i 2
cpowf128-----
csinf1 + i 01 + i 0--1 + i 0
csin1 + i 01 + i 0--1 + i 0
csinl-----
csinf128-----
csinhf1 + i 11 + i 11 + i 1-1 + i 1
csinh0 + i 10 + i 10 + i 1-0 + i 1
csinhl----0 + i 1
csinhf128-----
csqrtf2 + i 22 + i 21 + i 0-2 + i 2
csqrt2 + i 22 + i 2--2 + i 2
csqrtl-----
csqrtf128-----
ctanf1 + i 21 + i 2--1 + i 2
ctan1 + i 21 + i 20 + i 1-1 + i 2
ctanl----0 + i 1
ctanf128-----
ctanhf2 + i 22 + i 22 + i 1-2 + i 2
ctanh2 + i 22 + i 21 + i 0-2 + i 2
ctanhl----1 + i 0
ctanhf128-----
div_ldoublef-----
div_ldouble-----
div_ldoublel-----
div_ldoublef128-----
erff11--1
erf111-1
erfl----1
erff128-----
erfcf33--3
erfc551-5
erfcl----1
erfcf128-----
expf11--1
exp11--1
expl-----
expf128-----
exp10f--2-2
exp10226-6
exp10l----6
exp10f128-----
exp2f-1--1
exp211--1
exp2l-----
exp2f128-----
expm1f111-1
expm1111-1
expm1l----1
expm1f128-----
fmaf-----
fma-----
fmal-----
fmaf128-----
fmodf-----
fmod-----
fmodl-----
fmodf128-----
gammaf77--7
gamma44--4
gammal-----
gammaf128-----
hypotf--1-1
hypot11--1
hypotl-----
hypotf128-----
j0f882-8
j0222-2
j0l----2
j0f128-----
j1f992-9
j1221-2
j1l----1
j1f128-----
jnf444-5
jn444-4
jnl----4
jnf128-----
lgammaf772-7
lgamma441-4
lgammal----1
lgammaf128-----
logf-1--1
log-----
logl-----
logf128-----
log10f222-2
log10221-2
log10l----1
log10f128-----
log1pf111-1
log1p11--1
log1pl-----
log1pf128-----
log2f11--1
log222--2
log2l-----
log2f128-----
mul_ldoublef-----
mul_ldouble-----
mul_ldoublel-----
mul_ldoublef128-----
powf-1--1
pow11--1
powl-----
powf128-----
pow10f-----
pow10-2---
pow10l-----
pow10f128-----
sinf11--1
sin11--1
sinl-----
sinf128-----
sincosf-11-1
sincos111-1
sincosl----1
sincosf128-----
sinhf22--2
sinh22--2
sinhl-----
sinhf128-----
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
sub_ldoublef-----
sub_ldouble-----
sub_ldoublel-----
sub_ldoublef128-----
tanf11--1
tan--1-1
tanl----1
tanf128-----
tanhf22--2
tanh22--2
tanhl-----
tanhf128-----
tgammaf881-8
tgamma991-9
tgammal----1
tgammaf128-----
y0f881-8
y0332-3
y0l----2
y0f128-----
y1f222-2
y1333-3
y1l----3
y1f128-----
ynf332-3
yn333-3
ynl----3
ynf128-----
FunctionIA64M68kMIPS 32-bitMIPS 64-bitMicroBlaze
acosf--111
acos1----
acosl---1-
acosf1281----
acoshf-1222
acosh11222
acoshl11-2-
acoshf1282----
add_ldoublef-----
add_ldouble-----
add_ldoublel-----
add_ldoublef128-----
asinf--111
asin-----
asinl---1-
asinf1281----
asinhf-1221
asinh11221
asinhl-1-3-
asinhf1283----
atanf--111
atan-----
atanl---1-
atanf1281----
atan2f-1111
atan2-----
atan2l-1-1-
atan2f1281----
atanhf--222
atanh--222
atanhl---3-
atanhf1283----
cabsf-----
cabs-1111
cabsl-1-1-
cabsf1281----
cacosf2 + i 22 + i 12 + i 22 + i 22 + i 2
cacos1 + i 21 + i 11 + i 21 + i 21 + i 2
cacosl1 + i 21 + i 2-2 + i 2-
cacosf1282 + i 2----
cacoshf2 + i 21 + i 22 + i 22 + i 22 + i 2
cacosh2 + i 11 + i 12 + i 12 + i 12 + i 1
cacoshl2 + i 12 + i 1-2 + i 2-
cacoshf1282 + i 2----
cargf-1111
carg-----
cargl-1-2-
cargf1282----
casinf1 + i 21 + i 11 + i 21 + i 21 + i 2
casin1 + i 21 + i 11 + i 21 + i 21 + i 2
casinl1 + i 21 + i 2-2 + i 2-
casinf1282 + i 2----
casinhf2 + i 11 + i 12 + i 12 + i 12 + i 1
casinh2 + i 11 + i 12 + i 12 + i 12 + i 1
casinhl2 + i 12 + i 1-2 + i 2-
casinhf1282 + i 2----
catanf0 + i 10 + i 11 + i 11 + i 11 + i 1
catan1 + i 10 + i 11 + i 11 + i 11 + i 1
catanl0 + i 11 + i 1-1 + i 1-
catanf1281 + i 1----
catanhf1 + i 01 + i 01 + i 11 + i 11 + i 1
catanh1 + i 11 + i 01 + i 11 + i 11 + i 1
catanhl1 + i 01 + i 1-1 + i 1-
catanhf1281 + i 1----
cbrtf-1111
cbrt-1443
cbrtl-1-1-
cbrtf1281----
ccosf0 + i 1-1 + i 11 + i 11 + i 1
ccos1 + i 1-1 + i 11 + i 11 + i 1
ccosl1 + i 11 + i 1-1 + i 1-
ccosf1281 + i 1----
ccoshf1 + i 1-1 + i 11 + i 11 + i 1
ccosh1 + i 1-1 + i 11 + i 11 + i 1
ccoshl0 + i 10 + i 1-1 + i 1-
ccoshf1281 + i 1----
cexpf1 + i 2-1 + i 21 + i 21 + i 2
cexp2 + i 1-2 + i 12 + i 12 + i 1
cexpl1 + i 11 + i 1-1 + i 1-
cexpf1281 + i 1----
clogf3 + i 02 + i 13 + i 13 + i 13 + i 1
clog2 + i 13 + i 13 + i 03 + i 03 + i 0
clogl2 + i 13 + i 1-2 + i 1-
clogf1282 + i 1----
clog10f4 + i 12 + i 14 + i 24 + i 24 + i 2
clog103 + i 22 + i 13 + i 23 + i 23 + i 2
clog10l2 + i 13 + i 2-2 + i 2-
clog10f1282 + i 2----
cosf1-111
cos1111-
cosl---1-
cosf1281----
coshf--221
cosh--221
coshl---1-
coshf1281----
cpowf5 + i 23 + i 55 + i 25 + i 24 + i 2
cpow2 + i 01 + i 02 + i 02 + i 02 + i 0
cpowl3 + i 43 + i 1-4 + i 1-
cpowf1284 + i 1----
csinf1 + i 1-1 + i 01 + i 01 + i 0
csin1 + i 0-1 + i 01 + i 01 + i 0
csinl1 + i 01 + i 0-1 + i 1-
csinf1281 + i 1----
csinhf1 + i 1-1 + i 11 + i 11 + i 1
csinh1 + i 1-0 + i 10 + i 10 + i 1
csinhl1 + i 11 + i 0-1 + i 1-
csinhf1281 + i 1----
csqrtf2 + i 21 + i 12 + i 22 + i 22 + i 2
csqrt2 + i 21 + i 12 + i 22 + i 22 + i 2
csqrtl2 + i 22 + i 2-2 + i 2-
csqrtf1282 + i 2----
ctanf1 + i 11 + i 11 + i 21 + i 21 + i 1
ctan1 + i 21 + i 11 + i 21 + i 21 + i 2
ctanl2 + i 22 + i 2-3 + i 3-
ctanf1283 + i 3----
ctanhf1 + i 11 + i 22 + i 22 + i 21 + i 2
ctanh2 + i 21 + i 12 + i 22 + i 22 + i 2
ctanhl1 + i 22 + i 2-3 + i 3-
ctanhf1283 + i 3----
div_ldoublef-----
div_ldouble-----
div_ldoublel-----
div_ldoublef128-----
erff-1111
erf--111
erfl-1-1-
erff1281----
erfcf-1332
erfc--553
erfcl-2-2-
erfcf1282----
expf1-111
exp--11-
expl---1-
expf1281----
exp10f1-11-
exp10--222
exp10l---2-
exp10f1282----
exp2f--111
exp211111
exp2l1--1-
exp2f1281----
expm1f--111
expm11-111
expm1l1--1-
expm1f1281----
fmaf-----
fma-----
fmal-----
fmaf128-----
fmodf-----
fmod-----
fmodl-----
fmodf128-----
gammaf11774
gamma--444
gammal-2-5-
gammaf128-----
hypotf-----
hypot-1111
hypotl-1-1-
hypotf1281----
j0f82882
j021222
j0l22-2-
j0f1282----
j1f82992
j12-221
j1l51-4-
j1f1284----
jnf42444
jn42444
jnl44-7-
jnf1287----
lgammaf11774
lgamma--444
lgammal-2-5-
lgammaf1285----
logf--111
log-----
logl---1-
logf1281----
log10f--222
log10--222
log10l---1-
log10f1281----
log1pf--111
log1p--111
log1pl---2-
log1pf1282----
log2f--111
log2--222
log2l---2-
log2f1282----
mul_ldoublef-----
mul_ldouble-----
mul_ldoublel-----
mul_ldoublef128-----
powf-7111
pow-111-
powl-9-2-
powf1282----
pow10f-----
pow10-----
pow10l-----
pow10f128-----
sinf--111
sin1111-
sinl---1-
sinf1281----
sincosf--111
sincos1-11-
sincosl---1-
sincosf1281----
sinhf--222
sinh--222
sinhl---2-
sinhf1282----
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
sub_ldoublef-----
sub_ldouble-----
sub_ldoublel-----
sub_ldoublef128-----
tanf--111
tan-----
tanl1--1-
tanf1281----
tanhf--222
tanh--222
tanhl---2-
tanhf1282----
tgammaf-4884
tgamma-1995
tgammal19-4-
tgammaf1284----
y0f61881
y021332
y0l11-3-
y0f1283----
y1f23222
y131333
y1l22-2-
y1f1282----
ynf33332
yn32333
ynl34-5-
ynf1285----
FunctionNios IIPowerPCPowerPC soft-floatRISC-VRISC-V soft-float
acosf11111
acos-----
acosl-1111
acosf128-1---
acoshf22222
acosh22222
acoshl-2122
acoshf128-2---
add_ldoublef-11--
add_ldouble-11--
add_ldoublel-----
add_ldoublef128-----
asinf11111
asin-----
asinl-2211
asinf128-1---
asinhf22221
asinh12211
asinhl-2233
asinhf128-3---
atanf11111
atan-1---
atanl-1111
atanf128-1---
atan2f11111
atan2-----
atan2l-2211
atan2f128-1---
atanhf22222
atanh22222
atanhl-2233
atanhf128-3---
cabsf-----
cabs11111
cabsl-1111
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 22 + 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 22 + i 2
cacoshf128-2 + i 2---
cargf11111
carg-1---
cargl-2222
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 22 + 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 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 11 + 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 11 + i 1
catanhf128-1 + i 1---
cbrtf11111
cbrt34433
cbrtl-1111
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 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
ccoshl-1 + i 21 + i 21 + 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
cexpl-2 + i 21 + i 11 + i 11 + i 1
cexpf128-1 + i 1---
clogf3 + i 13 + i 13 + i 13 + i 13 + i 1
clog3 + i 03 + i 13 + i 03 + i 03 + i 0
clogl-5 + i 22 + i 22 + i 12 + 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 22 + i 2
clog10f128-2 + i 2---
cosf1311-
cos11111
cosl-4411
cosf128-1---
coshf22221
cosh12211
coshl-3311
coshf128-1---
cpowf5 + 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 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 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 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
csqrtl-1 + i 11 + i 12 + 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
ctanl-3 + i 23 + i 23 + i 33 + i 3
ctanf128-3 + i 3---
ctanhf2 + i 22 + i 12 + i 22 + i 12 + i 2
ctanh2 + i 22 + i 22 + i 22 + i 22 + i 2
ctanhl-3 + i 32 + i 33 + i 33 + i 3
ctanhf128-3 + i 3---
div_ldoublef-11--
div_ldouble-----
div_ldoublel-----
div_ldoublef128-----
erff11111
erf11111
erfl-1111
erff128-1---
erfcf32322
erfc32523
erfcl-3322
erfcf128-2---
expf1111-
exp-11--
expl-1111
expf128-1---
exp10f-1---
exp1022222
exp10l-1122
exp10f128-2---
exp2f1-1--
exp211111
exp2l-2111
exp2f128-1---
expm1f11111
expm111111
expm1l-1111
expm1f128-1---
fmaf-----
fma-----
fmal-11--
fmaf128-----
fmodf-----
fmod-----
fmodl-11--
fmodf128-----
gammaf74733
gamma43434
gammal-3355
gammaf128-5---
hypotf-----
hypot11111
hypotl-1111
hypotf128-1---
j0f88882
j022222
j0l-2222
j0f128-2---
j1f98982
j122221
j1l-3344
j1f128-4---
jnf44444
jn44444
jnl-4477
jnf128-7---
lgammaf74733
lgamma43434
lgammal-3355
lgammaf128-5---
logf111--
log-1---
logl-1111
logf128-1---
log10f22222
log1022222
log10l-1111
log10f128-1---
log1pf11111
log1p11111
log1pl-2222
log1pf128-2---
log2f11111
log221212
log2l-1122
log2f128-2---
mul_ldoublef-11--
mul_ldouble-11--
mul_ldoublel-----
mul_ldoublef128-----
powf311--
pow11111
powl-1122
powf128-2---
pow10f-----
pow10-----
pow10l-----
pow10f128-----
sinf1111-
sin11111
sinl-1111
sinf128-1---
sincosf111--
sincos11111
sincosl-1111
sincosf128-1---
sinhf22222
sinh22222
sinhl-3322
sinhf128-2---
sqrtf-----
sqrt-----
sqrtl-11--
sqrtf128-----
sub_ldoublef-11--
sub_ldouble-11--
sub_ldoublel-----
sub_ldoublef128-----
tanf13111
tan-----
tanl-2211
tanf128-1---
tanhf22222
tanh22222
tanhl-1122
tanhf128-2---
tgammaf88884
tgamma59955
tgammal-5444
tgammaf128-4---
y0f86861
y032322
y0l-1233
y0f128-3---
y1f22222
y133333
y1l-2222
y1f128-2---
ynf33333
yn33333
ynl-2255
ynf128-5---
FunctionS/390SHSparci686ix86
acosf111--
acos---11
acosl1-111
acosf128---11
acoshf222--
acosh22211
acoshl2-222
acoshf128---22
add_ldoublef-----
add_ldouble-----
add_ldoublel-----
add_ldoublef128-----
asinf111--
asin---11
asinl1-111
asinf128---11
asinhf222--
asinh22211
asinhl3-333
asinhf128---33
atanf111--
atan---11
atanl1-111
atanf128---11
atan2f111--
atan2---11
atan2l1-111
atan2f128---11
atanhf222--
atanh22211
atanhl3-333
atanhf128---33
cabsf-----
cabs11111
cabsl1-111
cabsf128---11
cacosf2 + i 22 + i 22 + i 22 + i 22 + i 2
cacos1 + i 21 + i 21 + i 21 + i 21 + i 2
cacosl2 + i 2-2 + i 21 + i 21 + i 2
cacosf128---2 + i 22 + 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 2-2 + i 22 + i 12 + i 1
cacoshf128---2 + i 22 + i 2
cargf111--
carg---11
cargl2-211
cargf128---22
casinf1 + i 21 + i 21 + i 21 + i 21 + i 2
casin1 + i 21 + i 21 + i 21 + i 21 + i 2
casinl2 + i 2-2 + i 21 + i 21 + i 2
casinf128---2 + i 22 + 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 2-2 + i 22 + i 12 + i 1
casinhf128---2 + i 22 + i 2
catanf1 + i 11 + i 11 + i 10 + i 10 + i 1
catan1 + i 11 + i 11 + i 11 + i 11 + i 1
catanl1 + i 1-1 + i 11 + i 11 + i 1
catanf128---1 + i 11 + i 1
catanhf1 + i 11 + i 11 + i 11 + i 01 + i 0
catanh1 + i 11 + i 11 + i 11 + i 11 + i 1
catanhl1 + i 1-1 + i 11 + i 11 + i 1
catanhf128---1 + i 11 + i 1
cbrtf11111
cbrt44411
cbrtl1-133
cbrtf128---11
ccosf1 + i 11 + i 11 + i 11 + i 11 + i 1
ccos1 + i 11 + i 11 + i 11 + i 11 + i 1
ccosl1 + i 1-1 + i 11 + 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
ccoshl1 + i 1-1 + i 11 + 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
cexpl1 + i 1-1 + i 11 + i 11 + i 1
cexpf128---1 + i 11 + i 1
clogf3 + i 13 + i 13 + i 13 + i 03 + i 0
clog3 + i 03 + i 03 + i 02 + i 12 + i 1
clogl2 + i 1-4 + i 13 + i 13 + i 1
clogf128---2 + i 12 + i 1
clog10f4 + i 24 + i 24 + i 24 + i 14 + i 1
clog103 + i 23 + i 23 + i 23 + i 23 + i 2
clog10l2 + i 2-4 + i 24 + i 24 + i 2
clog10f128---2 + i 22 + i 2
cosf111-1
cos11111
cosl1-111
cosf128---11
coshf22222
cosh22211
coshl1-122
coshf128---11
cpowf5 + i 25 + i 25 + i 25 + i 25 + i 2
cpow2 + i 02 + i 02 + i 02 + i 12 + i 0
cpowl4 + i 1-4 + i 13 + 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
csinl1 + i 1-1 + i 11 + i 01 + i 0
csinf128---1 + i 11 + i 1
csinhf1 + i 11 + i 11 + i 11 + i 11 + i 1
csinh0 + i 10 + i 10 + i 11 + i 10 + i 1
csinhl1 + i 1-1 + i 11 + i 11 + i 1
csinhf128---1 + i 11 + 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 2-2 + i 22 + i 22 + i 2
csqrtf128---2 + i 22 + 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 3-3 + i 32 + i 12 + i 1
ctanf128---3 + i 33 + i 3
ctanhf2 + i 12 + i 22 + i 22 + i 22 + i 2
ctanh2 + i 22 + i 22 + i 22 + i 22 + i 2
ctanhl3 + i 3-3 + i 31 + i 21 + i 2
ctanhf128---3 + i 33 + i 3
div_ldoublef-----
div_ldouble-----
div_ldoublel-----
div_ldoublef128-----
erff11111
erf11111
erfl1-111
erff128---11
erfcf22323
erfc25533
erfcl2-233
erfcf128---22
expf11111
exp11111
expl1-111
expf128---11
exp10f1-1--
exp1022211
exp10l2-211
exp10f128---22
exp2f--1--
exp211111
exp2l1-111
exp2f128---11
expm1f111--
expm111111
expm1l1-122
expm1f128---11
fmaf-----
fma-----
fmal-----
fmaf128-----
fmodf-----
fmod-----
fmodl-----
fmodf128-----
gammaf33735
gamma34444
gammal5-544
gammaf128-----
hypotf-----
hypot11111
hypotl1-111
hypotf128---11
j0f88858
j022222
j0l2-222
j0f128---22
j1f88959
j122222
j1l4-455
j1f128---44
jnf44444
jn44444
jnl7-744
jnf128---77
lgammaf33735
lgamma34444
lgammal5-544
lgammaf128---55
logf-11--
log1--11
logl1-111
logf128---11
log10f222--
log1022211
log10l1-111
log10f128---11
log1pf111--
log1p11111
log1pl2-222
log1pf128---22
log2f11111
log2-2211
log2l2-211
log2f128---22
mul_ldoublef-----
mul_ldouble-----
mul_ldoublel-----
mul_ldoublef128-----
powf-13--
pow11111
powl2-211
powf128---22
pow10f-----
pow10-----
pow10l-----
pow10f128-----
sinf111-1
sin11111
sinl1-111
sinf128---11
sincosf-11-1
sincos11111
sincosl1-111
sincosf128---11
sinhf22222
sinh22222
sinhl2-222
sinhf128---22
sqrtf-----
sqrt-----
sqrtl-----
sqrtf128-----
sub_ldoublef-----
sub_ldouble-----
sub_ldoublel-----
sub_ldoublef128-----
tanf11111
tan-----
tanl1-122
tanf128---11
tanhf22222
tanh22222
tanhl2-233
tanhf128---22
tgammaf88848
tgamma99966
tgammal4-455
tgammaf128---44
y0f66818
y023323
y0l3-311
y0f128---33
y1f22222
y133333
y1l2-232
y1f128---52
ynf33333
yn33333
ynl5-544
ynf128---55
Functionx86_64
acosf1
acos-
acosl1
acosf1281
acoshf2
acosh2
acoshl2
acoshf1282
add_ldoublef-
add_ldouble-
add_ldoublel-
add_ldoublef128-
asinf1
asin-
asinl1
asinf1281
asinhf2
asinh2
asinhl3
asinhf1283
atanf1
atan-
atanl1
atanf1281
atan2f1
atan2-
atan2l1
atan2f1281
atanhf2
atanh2
atanhl3
atanhf1283
cabsf-
cabs1
cabsl1
cabsf1281
cacosf2 + i 2
cacos1 + i 2
cacosl1 + i 2
cacosf1282 + i 2
cacoshf2 + i 2
cacosh2 + i 1
cacoshl2 + i 1
cacoshf1282 + i 2
cargf1
carg-
cargl1
cargf1282
casinf1 + i 2
casin1 + i 2
casinl1 + i 2
casinf1282 + i 2
casinhf2 + i 1
casinh2 + i 1
casinhl2 + i 1
casinhf1282 + i 2
catanf1 + i 1
catan1 + i 1
catanl1 + i 1
catanf1281 + i 1
catanhf1 + i 1
catanh1 + i 1
catanhl1 + i 1
catanhf1281 + i 1
cbrtf1
cbrt4
cbrtl1
cbrtf1281
ccosf1 + i 1
ccos1 + i 1
ccosl1 + i 1
ccosf1281 + i 1
ccoshf1 + i 1
ccosh1 + i 1
ccoshl1 + i 1
ccoshf1281 + i 1
cexpf1 + i 2
cexp2 + i 1
cexpl1 + i 1
cexpf1281 + i 1
clogf3 + i 1
clog3 + i 0
clogl3 + i 1
clogf1282 + i 1
clog10f4 + i 2
clog103 + i 2
clog10l4 + i 2
clog10f1282 + i 2
cosf1
cos1
cosl1
cosf1281
coshf2
cosh2
coshl2
coshf1281
cpowf5 + i 2
cpow2 + i 0
cpowl3 + i 4
cpowf1284 + i 1
csinf1 + i 0
csin1 + i 0
csinl1 + i 0
csinf1281 + i 1
csinhf1 + i 1
csinh0 + i 1
csinhl1 + i 1
csinhf1281 + i 1
csqrtf2 + i 2
csqrt2 + i 2
csqrtl2 + i 2
csqrtf1282 + i 2
ctanf1 + i 2
ctan1 + i 2
ctanl2 + i 1
ctanf1283 + i 3
ctanhf2 + i 2
ctanh2 + i 2
ctanhl1 + i 2
ctanhf1283 + i 3
div_ldoublef-
div_ldouble-
div_ldoublel-
div_ldoublef128-
erff1
erf1
erfl1
erff1281
erfcf3
erfc5
erfcl3
erfcf1282
expf1
exp1
expl1
expf1281
exp10f1
exp102
exp10l1
exp10f1282
exp2f1
exp21
exp2l1
exp2f1281
expm1f1
expm11
expm1l2
expm1f1281
fmaf-
fma-
fmal-
fmaf128-
fmodf-
fmod-
fmodl-
fmodf128-
gammaf7
gamma4
gammal4
gammaf128-
hypotf-
hypot1
hypotl1
hypotf1281
j0f8
j02
j0l2
j0f1282
j1f9
j12
j1l5
j1f1284
jnf4
jn4
jnl4
jnf1287
lgammaf7
lgamma4
lgammal4
lgammaf1285
logf1
log1
logl1
logf1281
log10f2
log102
log10l1
log10f1281
log1pf1
log1p1
log1pl2
log1pf1282
log2f1
log22
log2l1
log2f1282
mul_ldoublef-
mul_ldouble-
mul_ldoublel-
mul_ldoublef128-
powf1
pow1
powl1
powf1282
pow10f-
pow10-
pow10l-
pow10f128-
sinf1
sin1
sinl1
sinf1281
sincosf-
sincos1
sincosl1
sincosf1281
sinhf2
sinh2
sinhl2
sinhf1282
sqrtf-
sqrt-
sqrtl-
sqrtf128-
sub_ldoublef-
sub_ldouble-
sub_ldoublel-
sub_ldoublef128-
tanf1
tan-
tanl2
tanf1281
tanhf2
tanh2
tanhl3
tanhf1282
tgammaf8
tgamma9
tgammal5
tgammaf1284
y0f8
y03
y0l1
y0f1283
y1f9
y16
y1l3
y1f1285
ynf3
yn3
ynl4
ynf1285

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