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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

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