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头文件<tgmath.h>包含头文件<math.h>和<complex.h>,并定义了几个类型泛型宏,它们根据参数的类型确定哪些实际的或适用的复杂函数。

对于每个宏,参数的相应的实数类型在未被混合的math.h函数中是double的,被称为泛型参数(例如pow的两个参数都是泛型参数,但只有scalbn的第一个参数是泛型参数)。

当使用<tgmath.h>宏时,传递给泛型参数的参数类型决定了如下所述由宏选择哪个函数。 如果参数的类型与所选函数的参数类型不兼容,则行为是未定义的(例如,如果将一个复杂参数传递给实数tgmath宏:float complex fc; ceil(fc)或double complex dc ; double d; fmax(dc,d)是未定义行为的示例)。

注意:类型通用宏在C99中以实现定义的方式实现,但C11关键字_Generic使得可以以便携方式实现这些宏。

复杂/实型通用宏

对于既有真实对象又有复杂对象的所有函数,都存在一个类型通用宏XXX,它调用以下任一项:

  • 实际功能:

    • float 变型 XXXf

    • double 变型 XXX

    • long double 变型 XXXl

  • 复杂功能:

    • float 变型 cXXXf

    • double 变型 cXXX

    • long double 变型 cXXXl

上述规则的一个例外是晶圆厂宏(参见下表)。

要调用的函数如下确定:

  • 如果通用参数的任何参数都是虚构的,则在每个函数参考页面上分别指定行为(特别是,sin,cos,tag,cosh,sinh,tanh,asin,atan,asinh和atanh称为函数, sin,tan,sinh,tanh,asin,atan,asinh和atanh的返回类型是虚构的,cos和cosh的返回类型是实数)

  • 如果通用参数的任何参数都很复杂,则调用复杂函数,否则调用实函数。

  • 如果通用参数的任何参数是long double,则long double调用该变体。否则,如果任何参数是double或整数,则double调用该变体。否则,float调用变体。

类型通用宏如下所示:

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

真正的唯一功能

对于没有复杂对象的所有函数,除了modf之外,还有一个类型通用宏XXX存在,它调用实函数的变体之一:

  • float 变型 XXXf

  • double 变型 XXX

  • long double 变型 XXXl

要调用的函数如下确定:

  • 如果通用参数的任何参数是long double,则调用long double变体。 否则,如果泛型参数的任何参数是双精度型,则调用双精度型。 否则,调用float变量。

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

复杂功能

对于所有没有实际对应项的复数函数,都存在一个类型通用宏cXXX,它调用复杂函数的任何一种变体:

  • float complex 变型 cXXXf

  • double complex 变型 cXXX

  • long double complex 变型 cXXXl

要调用的函数如下确定:

  • 如果通用参数的任何参数是实数,复数或虚数,则调用相应的复数函数。

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

#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}

输出:

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

参考

  • C11标准(ISO / IEC 9899:2011):

    • 7.25类型通用数学<tgmath.h>(p:373-375)

  • C99标准(ISO / IEC 9899:1999):

    • 7.22类型通用数学<tgmath.h>(p:335-337)

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