# Type-generic math

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 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 that determine which real or, when applicable, complex function to call based on the types of the arguments.

For each macro, the parameters whose corresponding real type in the unsuffixed math.h function is double are known as generic parameters (for example, both parameters of pow are generic parameters, but only the first parameter of scalbn is a generic parameter)

When a <tgmath.h> macro is used the types of the arguments passed to the generic parameters determine which function is selected by the macro as described below. If the types of the arguments are not compatible with the parameter types of the selected function, the behavior is undefined (e.g. if a complex argument is passed into a real-only tgmath macro: float complex fc; ceil(fc) or double complex dc; double d; fmax(dc, d) are examples of undefined behavior)

Note: type-generic macros were implemented in implementation-defined manner in C99, but C11 keyword _Generic makes it possible to implement these macros in portable manner.

### Complex/real type-generic macros

For all functions that have both real and complex counterparts, a type-generic macro XXX exists, which 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 the fabs macro (see the table below).

The function to call is determined as follows:

• If any of the arguments for the generic parameters is imaginary, the behavior is specified on each function reference page individually (in particular, sin, cos, tag, cosh, sinh, tanh, asin, atan, asinh, and atanh call real functions, the return types of sin, tan, sinh, tanh, asin, atan, asinh, and atanh are imaginary, and the return types of cos and cosh are real)
• If any of the arguments for the generic parameters is complex, then the complex function is called, otherwise the real function is called.
• If any of the arguments for the generic parameters is long double, then the long double variant is called. Otherwise, if any of the parameters is double or integer, then the double variant is called. Otherwise, float variant is called.

The type-generic macros are as follows:

Type-generic macro Real function
variants
Complex function
variants

float
double
long double
float
double
long double
fabs fabsf fabs fabsl cabsf cabs cabsl
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
sin sinf sin sinl csinf csin csinl
cos cosf cos cosl ccosf ccos ccosl
tan tanf tan tanl ctanf ctan ctanl
asin asinf asin asinl casinf casin casinl
acos acosf acos acosl cacosf cacos cacosl
atan atanf atan atanl catanf catan catanl
sinh sinhf sinh sinhl csinhf csinh csinhl
cosh coshf cosh coshl ccoshf ccosh ccoshl
tanh tanhf tanh tanhl ctanhf ctanh ctanhl
asinh asinhf asinh asinhl casinhf casinh casinhl
acosh acoshf acosh acoshl cacoshf cacosh cacoshl
atanh atanhf atanh atanhl catanhf catanh catanhl

### Real-only functions

For all functions that do not have complex counterparts, with the exception of modf, a type-generic macro XXX exists, which calls either of the variants of a real function:

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

The function to call is determined as follows:

• If any of the arguments for the generic parameters is long double, then the long double variant is called. Otherwise, if any of the arguments for the generic parameters is double, then the double variant is called. Otherwise, float variant is called.
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

### Complex-only functions

For all complex number functions that do not have real counterparts, a type-generic macro cXXX exists, which calls either of the variants of a complex function:

The function to call is determined as follows:

• If any of the arguments for the generic parameters is real, complex, or imaginary, then the appropriate complex function is called.
Type-generic macro Complex function
variants

float
double
long double
carg cargf carg cargl
conj conjf conj conjl
creal crealf creal creall
cimag cimagf cimag cimagl
cproj cprojf cproj cprojl

### Example

#include <stdio.h>
#include <tgmath.h>

int main(void)
{
int i = 2;
printf("sqrt(2) = %f\n", sqrt(i)); // argument type is int, calls sqrt

float f = 0.5;
printf("sin(0.5f) = %f\n", sin(f));   // argument type is float, calls sinf

float complex dc = 1 + 0.5*I;
float complex z = sqrt(dc);      // argument type is float complex, calls csqrtf
printf("sqrt(1 + 0.5i) = %f+%fi\n",
creal(z),  // argument type is float complex, calls crealf
cimag(z)); // argument type is float complex, calls cimagf
}

Output:

sqrt(2) = 1.414214
sin(0.5f) = 0.479426
sqrt(1 + 0.5i) = 1.029086+0.242934i

### References

• C11 standard (ISO/IEC 9899:2011):
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• C99 standard (ISO/IEC 9899:1999):
• 7.22 Type-generic math <tgmath.h> (p: 335-337)