# Type-generic math

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Numerics
 Common mathematical functions Floating-point environment Complex number arithmetics Random number generation Type-generic math

The header `<tgmath.h>` includes the headers `<math.h>` and `<complex.h>` and defines several type-generic macros. These macros determines the actual function to call depending on the types of the parameters.

### Trigonometric, hyperbolic, power and exponential functions (since C99)

A type-generic macro `XXX` calls either of:

• real function:
• float variant `XXXf`
• double variant `XXX`
• long double variant `XXXl`
• complex function:
• float variant `cXXXf`
• double variant `cXXX`
• long double variant `cXXXl`

An exception to the above rule is `exp` (see the table below).

The function to call is determined as follows:

• If any of the parameters is complex, then the complex function is called, otherwise the real function is called.
• If any of the parameters is long double, then the long double variant is called. Otherwise, if any of the parameters is double, then the double variant is called. Otherwise, float variant is called.
• The behavior is undefined if any of the parameters are incompatible with the corresponding argument of the function.  This section is incompleteReason: what's meant by incompatible?

The type-generic macros are as follows:

Type-generic macro Real function
variants
Complex function
variants

float
double
long double
float
double
long double
asin asinf asin asinl casinf casin casinl
acos acosf acos acosl cacosf cacos cacosl
atan atanf atan atanl catanf catan catanl
asinh asinhf asinh asinhl casinhf casinh casinhl
acosh acoshf acosh acoshl cacoshf cacosh cacoshl
atanh atanhf atanh atanhl catanhf catanh catanhl
sin sinf sin sinl csinf csin csinl
cos cosf cos cosl ccosf ccos ccosl
tan tanf tan tanl ctanf ctan ctanl
sinh sinhf sinh sinhl csinhf csinh csinhl
cosh coshf cosh coshl ccoshf ccosh ccoshl
tanh tanhf tanh tanhl ctanhf ctanh ctanhl
exp expf exp expl cexpf cexp cexpl
log logf log logl clogf clog clogl
pow powf pow powl cpowf cpow cpowl
sqrt sqrtf sqrt sqrtl csqrtf csqrt csqrtl
abs fabsf fabs fabsl cabsf cabs cabsl
exp expf exp expl cexpf cexp cexpl

### Miscellaneous functions (since C99)

A type-generic macro `XXX` calls either of the variants of a real function:

• float variant `XXXf`
• double variant `XXX`
• long double variant `XXXl`

Note, there's no `modf` type-generic macro.

The function to call is determined as follows:

• If any of the parameters is long double, then the long double variant is called. Otherwise, if any of the parameters is double, then the double variant is called. Otherwise, float variant is called.
• The behavior is undefined is any of the parameters is incompatible with the corresponding argument of the function.  This section is incompleteReason: what's meant by incompatible?
Type-generic macro Real function
variants

float
double
long double
atan2 atan2f atan2 atan2l
cbrt cbrtf cbrt cbrtl
ceil ceilf ceil ceill
copysign copysignf copysign copysignl
erf erff erf erfl
erfc erfcf erfc erfcl
exp2 exp2f exp2 exp2l
expm1 expm1f expm1 expm1l
fdim fdimf fdim fdiml
floor floorf floor floorl
fma fmaf fma fmal
fmax fmaxf fmax fmaxl
fmin fminf fmin fminl
fmod fmodf fmod fmodl
frexp frexpf frexp frexpl
hypot hypotf hypot hypotl
ilogb ilogbf ilogb ilogbl
ldexp ldexpf ldexp ldexpl
lgamma lgammaf lgamma lgammal
llrint llrintf llrint llrintl
llround llroundf llround llroundl
log10 log10f log10 log10l
log1p log1pf log1p log1pl
log2 log2f log2 log2l
logb logbf logb logbl
lrint lrintf lrint lrintl
lround lroundf lround lroundl
nearbyint nearbyintf nearbyint nearbyintl
nextafter nextafterf nextafter nextafterl
nexttoward nexttowardf nexttoward nexttowardl
remainder remainderf remainder remainderl
remquo remquof remquo remquol
rint rintf rint rintl
round roundf round roundl
scalbln scalblnf scalbln scalblnl
scalbn scalbnf scalbn scalbnl
tgamma tgammaf tgamma tgammal
trunc truncf trunc truncl

###  Example

```int i;
float f;
double d;
long double ld;
float complex fc;
double complex dc;
long double complex ldc;

// macro -> function call
cos(i);   // -> cos(i)
sin(f);   // -> sinf(f)
acos(d);  // -> acos(d)
sqrt(dc); // -> csqrt(dc);```