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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&middot;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