Type-generic math

 

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Type-generic math (C99)

 

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.h>'s 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:

• float complex variant cXXXf
• double complex variant cXXX
• long double complex variant cXXXl

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

Run this code

#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

• C17 standard (ISO/IEC 9899:2018):

• 7.25 Type-generic math <tgmath.h> (p: 272-273)

• 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)