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Copyright 2020 Joyent, Inc.
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c99 [ flag... ] file... -lm [ library... ]
| acos acosf |
| acosh acoshf |
| acoshl acosl |
| asin asinf |
| asinh asinhf |
| asinhl asinl |
| atan atan2 |
| atan2f atan2l |
| atanf atanh |
| atanhf atanhl |
| atanl cabs |
| cabsf cabsl |
| cacos cacosf |
| cacosh cacoshf |
| cacoshl cacosl |
| carg cargf |
| cargl casin |
| casinf casinh |
| casinhf casinhl |
| casinl catan |
| catanf catanh |
| catanhf catanhl |
| catanl cbrt |
| cbrtf cbrtl |
| ccos ccosf |
| ccosh ccoshf |
| ccoshl ccosl |
| ceil ceilf |
| ceill cexp |
| cexpf cexpl |
| cimag cimagf |
| cimagl clog |
| clogf clogl |
| conj conjf |
| conjl copysign |
| copysignf copysignl |
| cos cosf |
| cosh coshf |
| coshl cosl |
| cpow cpowf |
| cpowl cproj |
| cprojf cprojl |
| creal crealf |
| creall csin |
| csinf csinh |
| csinhf csinhl |
| csinl csqrt |
| csqrtf csqrtl |
| ctan ctanf |
| ctanh ctanhf |
| ctanhl ctanl |
| erf erfc |
| erfcf erfcl |
| erff erfl |
| exp exp2 |
| exp2f exp2l |
| expf expl |
| expm1 expm1f |
| expm1l fabs |
| fabsf fabsl |
| fdim fdimf |
| fdiml feclearexcept |
| fegetenv fegetexceptflag |
| fegetround feholdexcept |
| feraiseexcept fesetenv |
| fesetexceptflag fesetround |
| fetestexcept feupdateenv |
| fex_get_handling fex_get_log |
| fex_get_log_depth fex_getexcepthandler |
| fex_log_entry fex_merge_flags |
| fex_set_handling fex_set_log |
| fex_set_log_depth fex_setexcepthandler |
| floor floorf |
| floorl fma |
| fmaf fmal |
| fmax fmaxf |
| fmaxl fmin |
| fminf fminl |
| fmod fmodf |
| fmodl frexp |
| frexpf frexpl |
| gamma gamma_r |
| gammaf gammaf_r |
| gammal gammal_r |
| hypot hypotf |
| hypotl ilogb |
| ilogbf ilogbl |
| isnan j0 |
| j0f j0l |
| j1 j1f |
| j1l jn |
| jnf jnl |
| ldexp ldexpf |
| ldexpl lgamma |
| lgamma_r lgammaf |
| lgammaf_r lgammal |
| lgammal_r llrint |
| llrintf llrintl |
| llround llroundf |
| llroundl log |
| log10 log10f |
| log10l log1p |
| log1pf log1pl |
| log2 log2f |
| log2l logb |
| logbf logbl |
| logf logl |
| lrint lrintf |
| lrintl lround |
| lroundf lroundl |
| matherr modf |
| modff modfl |
| nan nanf |
| nanl nearbyint |
| nearbyintf nearbyintl |
| nextafter nextafterf |
| nextafterl nexttoward |
| nexttowardf nexttowardl |
| pow powf |
| powl remainder |
| remainderf remainderl |
| remquo remquof |
| remquol rint |
| rintf rintl |
| round roundf |
| roundl scalb |
| scalbf scalbl |
| scalbln scalblnf |
| scalblnl scalbn |
| scalbnf scalbnl |
| signgam signgamf |
| signgaml significand |
| significandf significandl |
| sin sincos |
| sincosf sincosl |
| sinf sinh |
| sinhf sinhl |
| sinl sqrt |
| sqrtf sqrtl |
| tan tanf |
| tanh tanhf |
| tanhl tanl |
| tgamma tgammaf |
| tgammal trunc |
| truncf truncl |
| y0 y0f |
| y0l y1 |
| y1f y1l |
| yn ynf |
| ynl |
The following interfaces are unique to the x86 and amd64 versions of this library:
| fegetprec fesetprec |
The bounds and observed errors listed below apply only in the default floating point modes. Specifically, on SPARC, these bounds assume the rounding direction is round-to-nearest and non-standard mode is disabled. On x86, the bounds assume the rounding direction is round-to-nearest and the rounding precision is round-to-64-bits. Moreover, on x86, floating point function values are returned in a floating point register in extended double precision format, but the bounds below assume that the result value is then stored to memory in the format corresponding to the function's type. On amd64, the bounds assume the rounding direction in both the x87 floating point control word and the MXCSR is round-to-nearest, the rounding precision in the x87 control word is round-to-64-bits, and the FTZ and DAZ modes are disabled.
The error bounds listed below are believed to be correct, but smaller bounds might be proved later. The observed errors are the largest ones currently known, but larger errors might be discovered later. Numbers in the notes column refer to the notes following the tables.
| error bound largest error |
| function (ulps) observed (ulps) notes |
| acosf 1.0 < 1 |
| acoshf 1.0 < 1 |
| asinf 1.0 < 1 |
| asinhf 1.0 < 1 |
| atanf 1.0 < 1 |
| atan2f 1.0 < 1 |
| atanhf 1.0 < 1 |
| cbrtf 1.0 < 1 |
| cosf 1.0 < 1 |
| coshf 1.0 < 1 |
| erff 1.0 < 1 |
| erfcf 1.0 < 1 |
| expf 1.0 < 1 |
| exp2f 1.0 < 1 |
| expm1f 1.0 < 1 |
| hypotf 1.0 < 1 |
| lgammaf 1.0 < 1 |
| logf 1.0 < 1 |
| log10f 1.0 < 1 |
| log1pf 1.0 < 1 |
| log2f 1.0 < 1 |
| powf 1.0 < 1 |
| sinf 1.0 < 1 |
| sinhf 1.0 < 1 |
| sqrtf 0.5 0.500 [1] |
| tanf 1.0 < 1 |
| tanhf 1.0 < 1 |
| tgammaf 1.0 < 1 |
| error bound largest error |
| function (ulps) observed (ulps) notes |
| acos 1.0 < 1 |
| acosh 4.0 1.878 |
| asin 1.0 < 1 |
| asinh 7.0 1.653 |
| atan 1.0 <1 |
| atan2 2.5 1.475 |
| atanh 4.0 1.960 |
| cbrt 1.0 < 1 |
| cos 1.0 < 1 |
| cosh 3.0 1.168 |
| erf 4.0 0.959 |
| erfc 6.0 2.816 |
| exp 1.0 < 1 |
| exp2 2.0 1.050 |
| expm1 1.0 < 1 |
| hypot 1.0 < 1 |
| lgamma 61.5 5.629 [2] |
| log 1.0 < 1 |
| log10 3.5 1.592 |
| log1p 1.0 < 1 |
| log2 1.0 < 1 |
| pow 1.0 < 1 |
| sin 1.0 < 1 |
| sinh 4.0 2.078 |
| sqrt 0.5 0.500 [1] |
| tan 1.0 < 1 |
| tanh 3.5 2.136 |
| tgamma 1.0 < 1 |
| error bound largest error |
| function (ulps) observed (ulps) notes |
| acos 1.0 < 1 |
| acosh 4.0 1.694 |
| asin 1.0 < 1 |
| asinh 7.0 1.493 |
| atan 1.0 < 1 |
| atan2 1.0 < 1 |
| atanh 4.0 1.445 |
| cbrt 1.0 < 1 |
| cos 1.0 < 1 |
| cosh 3.0 1.001 |
| erf 4.0 0.932 |
| erfc 6.0 2.728 |
| exp 1.0 < 1 |
| exp2 1.0 < 1 |
| expm1 1.0 < 1 |
| hypot 1.0 < 1 |
| lgamma 61.5 2.654 [2] |
| log 1.0 < 1 |
| log10 1.0 < 1 |
| log1p 1.0 < 1 |
| log2 1.0 < 1 |
| pow 1.0 < 1 |
| sin 1.0 < 1 |
| sinh 4.0 1.458 |
| sqrt 0.5003 0.500 [1] |
| tan 1.0 < 1 |
| tanh 3.5 1.592 |
| tgamma 1.0 < 1 |
| error bound largest error |
| function (ulps) observed (ulps) notes |
| acosl 3.5 1.771 |
| acoshl 8.0 1.275 |
| asinl 4.0 2.007 |
| asinhl 9.0 1.823 |
| atanl 1.0 < 1 |
| atan2l 2.5 1.102 |
| atanhl 4.0 1.970 |
| cbrtl 1.0 < 1 |
| cosl 1.0 < 1 |
| coshl 3.5 0.985 |
| erfl 2.0 0.779 |
| erfcl 68.5 13.923 |
| expl 1.0 < 1 |
| exp2l 2.0 0.714 |
| expm1l 2.0 1.020 |
| hypotl 1.0 < 1 |
| lgammal 18.5 2.916 [2] |
| logl 1.0 < 1 |
| log10l 3.5 1.156 |
| log1pl 2.0 1.216 |
| log2l 3.5 1.675 |
| powl 1.0 < 1 |
| sinl 1.0 < 1 |
| sinhl 4.5 1.589 |
| sqrtl 0.5 0.500 [1] |
| tanl 4.5 2.380 |
| tanhl 4.5 1.692 |
| tgammal 1.0 < 1 |
| error bound largest error |
| function (ulps) observed (ulps) notes |
| acosl 3.0 1.868 |
| acoshl 8.0 2.352 |
| asinl 3.0 1.716 |
| asinhl 9.0 2.346 |
| atanl 1.0 < 1 |
| atan2l 1.0 < 1 |
| atanhl 4.0 2.438 |
| cbrtl 1.0 < 1 |
| cosl 1.0 < 1 |
| coshl 3.5 1.288 |
| erfl 1.0 < 1 |
| erfcl 78.5 13.407 |
| expl 3.5 1.291 |
| exp2l 1.5 0.807 |
| expm1l 4.0 1.936 |
| hypotl 3.5 2.087 |
| lgammal 22.5 4.197 [2] |
| logl 2.0 0.881 |
| log10l 2.0 1.284 |
| log1pl 5.0 2.370 |
| log2l 1.0 < 1 |
| powl 32770.0 4478.132 |
| sinl 1.0 < 1 |
| sinhl 4.5 2.356 |
| sqrtl 0.5 0.500 [1] |
| tanl 4.5 2.366 |
| tanhl 4.5 2.417 |
| tgammal 1.0 < 1 |
[1]
On SPARC and amd64, sqrtf, sqrt, and sqrtl are correctly rounded in accordance with IEEE 754. On x86, sqrtl is correctly rounded, sqrtf is correctly rounded provided the result is narrowed to single precision as discussed above, but sqrt might not be correctly rounded due to "double rounding": when the intermediate value computed to extended precision lies exactly halfway between two representable numbers in double precision, the result of rounding the intermediate value to double precision is determined by the round-ties-to-even rule. If this rule causes the second rounding to round in the same direction as the first, the net rounding error can exceed 0.5 ulps. (The error is bounded instead by 0.5*(1 + 2^-11) ulps.)
[2]
Error bounds for lgamma and lgammal apply only for positive arguments.
The complex functions listed below are complex-valued. For each function, the error bound shown applies separately to both the real and imaginary parts of the result. (For example, both the real and imaginary parts of cacosf(z) are accurate to within 1 ulp regardless of their magnitudes.) Similarly, the largest observed error shown is the largest error found in either the real or the imaginary part of the result.
| error bound largest error |
| function (ulps) observed (ulps) notes |
| cacosf, cacoshf 1 < 1 [1] |
| casinf, casinhf 1 < 1 |
| catanf, catanhf 6 < 1 |
| ccosf, ccoshf 10 2.012 |
| cexpf 3 2.239 |
| clogf 3 < 1 |
| cpowf \(em < 1 [2] |
| csinf, csinhf 10 2.009 |
| csqrtf 4 < 1 |
| ctanf, ctanhf 13 6.987 |
| error bound largest error |
| function (ulps) observed (ulps) notes |
| cacosf, cacoshf 1 < 1 [1] |
| casinf, casinhf 1 < 1 |
| catanf, catanhf 6 < 1 |
| ccosf, ccoshf 10 1.984 |
| cexpf 3 1.984 |
| clogf 3 < 1 |
| cpowf \(em < 1 [2] |
| csinf, csinhf 10 1.973 |
| csqrtf 4 < 1 |
| ctanf, ctanhf 13 4.657 |
| error bound largest error |
| function (ulps) observed (ulps) notes |
| cacos, cacosh 9 3.831 [1] |
| casin, casinh 9 3.732 |
| catan, catanh 6 4.179 |
| ccos, ccosh 10 3.832 |
| cexp 3 2.255 |
| clog 3 2.870 |
| cpow - - [2] |
| csin, csinh 10 3.722 |
| csqrt 4 3.204 |
| ctan, ctanh 13 7.143 |
| error bound largest error |
| function (ulps) observed (ulps) notes |
| cacos, cacosh 9 3.624 [1] |
| casin, casinh 9 3.624 |
| catan, catanh 6 2.500 |
| ccos, ccosh 10 2.929 |
| cexp 3 2.147 |
| clog 3 1.927 |
| cpow - - [2] |
| csin, csinh 10 2.918 |
| csqrt 4 1.914 |
| ctan, ctanh 13 4.630 |
| error bound largest error |
| function (ulps) observed (ulps) notes |
| cacosl, cacoshl 9 3 [1] |
| casinl, casinhl 9 3 |
| catanl, catanhl 6 3 |
| ccosl, ccoshl 10 3 |
| cexpl 3 2 |
| clogl 3 2 |
| cpowl - - [2] |
| csinl, csinhl 10 3 |
| csqrtl 4 3 |
| ctanl, ctanhl 13 5 |
| error bound largest error |
| function (ulps) observed (ulps) notes |
| cacosl, cacoshl 9 2 [1] |
| casinl, casinhl 9 2 |
| catanl, catanhl 6 2 |
| ccosl, ccoshl 10 3 |
| cexpl 3 2.699 |
| clogl 3 1 |
| cpowl - - [2] |
| csinl, csinhl 10 3 |
| csqrtl 4 1.452 |
| ctanl, ctanhl 13 5 |
[1]
The complex hyperbolic trigonometric functions are equivalent by symmetries to their circular trigonometric counterparts. Because the implementations of these functions exploit these symmetries, corresponding functions have the same error bounds and observed errors.
[2]
For large arguments, the results computed by cpowf, cpow, and cpowl can have unbounded relative error. It might be possible to give error bounds for specific domains, but no such bounds are currently available. The observed errors shown are for the domain {(z,w) : max(|Re z|, |Im z|, |Re w|, |Im w|) <= 1}.
shared object
/lib/64/libm.so.2
64-bit shared object
| ATTRIBUTE TYPE ATTRIBUTE VALUE |
| MT-Level Safe with exceptions |
As described on the lgamma(3M) manual page, gamma() and lgamma() and their float and long double counterparts are Unsafe. All other functions in libm.so.2 are MT-Safe.