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Algorithms Algorithms(算法) bsearch bsearch_s qsort qsort_s Atomic operations Atomic operations library(原子操作库) ATOMIC_*_LOCK_FREE atomic_compare_exchange_strong atomic_compare_exchange_strong_explicit atomic_compare_exchange_weak atomic_compare_exchange_weak_explicit atomic_exchange atomic_exchange_explicit atomic_fetch_add atomic_fetch_add_explicit atomic_fetch_and atomic_fetch_and_explicit atomic_fetch_or atomic_fetch_or_explicit atomic_fetch_sub atomic_fetch_sub_explicit atomic_fetch_xor atomic_fetch_xor_explicit atomic_flag atomic_flag_clear atomic_flag_clear_explicit ATOMIC_FLAG_INIT atomic_flag_test_and_set atomic_flag_test_and_set_explicit atomic_init atomic_is_lock_free atomic_load atomic_load_explicit atomic_signal_fence atomic_store atomic_store_explicit atomic_thread_fence(线程围栏) ATOMIC_VAR_INIT kill_dependency memory_order(内存排序) C keywords auto(自动存储) break(跳出循环) C keywords(关键词) case char const(常量修饰符) continue default(预设运算式) do double(双精度浮点型) else enum(枚举类型) extern(全局变量) float(浮点数) for fortran goto(goto语句) if(if语句) inline(行内函式) int long(长整型) register(寄存器变量) restrict( restrict类型限定符) return short signed sizeof(sizeof运算符) static(静态变量) struct(结构体) switch(switch语句) typedef(typedef关键字) union(联合体) unsigned(无符号) void(空类型) volatile(volatile变量) while(while语句) _Alignas _Alignof _Atomic _Bool _Complex _Generic _Imaginary _Noreturn _Static_assert _Thread_local C language #define directive #elif directive #else directive #endif directive #error directive #if directive #ifdef directive #ifndef directive #include directive #line directive #pragma directive alignas(对齐指定符) Alternative operators and tokens(替代运算符和令牌) Analyzability Arithmetic operators Arithmetic types Array declaration(数组声明) Array initialization(阵列初始化) ASCII Chart Assignment operators(赋值运算符) types(atomic类型限定符) Basic concepts Bit fields(位域) break statement C language C Operator Precedence cast operator character constant(字符字面量) Comments(注释符) Comparison operators(比较运算符) compound literals(符合字面量) Conditional inclusion(条件包含) Conformance(一致性) const type qualifier(const 限定符) Constant expressions(常量表达) continue statement Declarations(声明) do-while loop Enumerations(枚举类型) Escape sequences(转义字符) Expressions(表达式) External and tentative definitions(外部和暂定的定义) File scope(文件范围) floating constant(浮点常量) for loop Function declarations(函数声明) Function definitions(函数声明) Functions Generic selection泛型选择 goto statement Identifier(标示符) if statement Implicit conversions(隐式转换) Increment/decrement operators(前置/后置操作符) Initialization(初始化) inline function specifier(内联函式) integer constant Lifetime(生命期) Logical operators(逻辑运算符) Lookup and name spaces Main function(主函式) Member access operators(会员接入运营商) Memory model Objects and alignment(字节对齐) Order of evaluation(评估顺序) Other operators Phases of translation(翻译阶段) Pointer declaration Preprocessor(预处理) restrict type qualifier(restrict类型限定符) return statement Scalar initialization(标量类型初始化) Scope(范围) sizeof operator(sizeof运算符) Statements(陈述) static assert declaration(静态断言声明) Static storage duration(静态存储周期) Storage-class specifiers(存储类说明符) string literals(字符串字面量) Struct and union initialization(结构体与联合体初始化) Struct declaration(结构体声明) switch statement Thread storage duration(线程存储时间) Type Type(类型) Typedef declaration(Typedef声明) Undefined behavior(未定义行为) Union declaration(联合体声明) Value categories(值类别) Variadic arguments(变长参数宏) volatile type qualifier(volatile 类型限定符) while loop _Alignof operator _Noreturn function specifier Date and time asctime(asctime函数) asctime_s clock CLOCKS_PER_SEC clock_t ctime(ctime函数) ctime_s Date and time utilities(日期和时间库) difftime(计算两个时间的间隔) gmtime gmtime_s localtime localtime_s mktime(将时间结构数据转换成经过的秒数的函数) strftime(格式化输出时间函数) time timespec timespec_get time_t tm wcsftime(格式化时间宽字符) Dynamic memory management aligned_alloc C memory management library(内存管理库) calloc free(释放动态分配空间的函数) malloc(动态分配内存空间的函数) realloc(重新分配内存空间的函数) Error handling abort_handler_s assert(断言) constraint_handler_t errno(错误报告) Error handling(错误处理) Error numbers(错误个数) ignore_handler_s set_constraint_handler_s static_assert File input/output clearerr(清除/复位) fclose feof ferror fflush(清空文件缓冲区) fgetc fgetpos fgets fgetwc fgetws File input/output fopen fopen_s fprintf fprintf_s fputc fputs fputwc fputws fread freopen freopen_s fscanf fscanf_s fseek fsetpos ftell fwide fwprintf fwprintf_s fwrite fwscanf fwscanf_s getc getchar gets gets_s getwchar perror printf printf_s putc putchar puts putwc putwchar remove rename rewind scanf scanf_s setbuf setvbuf snprintf sprintf sscanf sscanf_s swprintf swprintf_s swscanf swscanf_s tmpfile tmpfile_s tmpnam tmpnam_s ungetc ungetwc vfprintf vfprintf_s vfscanf vfscanf_s vfwprintf vfwprintf_s vfwscanf vfwscanf_s vprintf vprintf_s vscanf vscanf_s vsnprintf vsprintf vsscanf vsscanf_s vswprintf vswprintf_s vswscanf vswscanf_s vwprintf vwprintf_s vwscanf vwscanf_s wprintf wprintf_s wscanf wscanf_s Localization support lconv LC_ALL LC_COLLATE LC_CTYPE LC_MONETARY LC_NUMERIC LC_TIME localeconv Localization support setlocale Numerics abs 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 CMPLX CMPLXF CMPLXL Common mathematical functions complex Complex number arithmetic 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 div double_t erf erfc erfcf erfcl erff erfl exp exp2 exp2f exp2l expf expl expm1 expm1f expm1l fabs fabsf fabsl fdim feclearexcept fegetenv fegetexceptflag fegetround feholdexcept feraiseexcept fesetenv fesetexceptflag fesetround fetestexcept feupdateenv FE_ALL_EXCEPT FE_DFL_ENV FE_DIVBYZERO FE_DOWNWARD FE_INEXACT FE_INVALID FE_OVERFLOW FE_TONEAREST FE_TOWARDZERO FE_UNDERFLOW FE_UPWARD Floating-point environment float_t floor floorf floorl fma fmaf fmal fmax fmaxf fmaxl fmin fminf fminl fmod fmodf fmodl fpclassify FP_INFINITE FP_NAN FP_NORMAL FP_SUBNORMAL FP_ZERO frexp frexpf frexpl HUGE_VAL HUGE_VALF HUGE_VALL hypot hypotf hypotl I ilogb ilogbf ilogbl imaginary imaxabs imaxdiv INFINITY isfinite isgreater isgreaterequal isinf isless islessequal islessgreater isnan isnormal isunordered labs ldexp ldexpf ldexpl ldiv lgamma lgammaf lgammal llabs lldiv 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 MATH_ERREXCEPT math_errhandling MATH_ERRNO modf modff modfl nan NAN nanf nanl nearbyint nearbyintf nearbyintl nextafter nextafterf nextafterl nexttoward nexttowardf nexttowardl Numerics pow powf powl Pseudo-random number generation rand RAND_MAX remainder remainderf remainderl remquo remquof remquol rint rintf rintl round roundf roundl scalbln scalblnf scalblnl scalbn scalbnf scalbnl signbit sin sinf sinh sinhf sinhl sinl sqrt sqrtf sqrtl srand tan tanf tanh tanhf tanhl tanl tgamma tgammaf tgammal trunc truncf truncl Type-generic math _Complex_I _Imaginary_I Program support abort atexit at_quick_exit exit EXIT_FAILURE EXIT_SUCCESS getenv getenv_s jmp_buf longjmp Program support utilities quick_exit raise setjmp SIGABRT SIGFPE SIGILL SIGINT signal SIGSEGV SIGTERM sig_atomic_t SIG_DFL SIG_ERR SIG_IGN system _Exit Strings atof atoi atol atoll btowc c16rtomb c32rtomb char16_t char32_t isalnum isalpha isblank iscntrl isdigit isgraph islower isprint ispunct isspace isupper iswalnum iswalpha iswblank iswcntrl iswctype iswdigit iswgraph iswlower iswprint iswpunct iswspace iswupper iswxdigit isxdigit mblen mbrlen mbrtoc16 mbrtoc32 mbrtowc mbsinit mbsrtowcs mbsrtowcs_s mbstate_t mbstowcs mbstowcs_s mbtowc memchr memcmp memcpy memcpy_s memmove memmove_s memset memset_s Null-terminated byte strings Null-terminated multibyte strings Null-terminated wide strings strcat strcat_s strchr strcmp strcoll strcpy strcpy_s strcspn strerror strerrorlen_s strerror_s Strings library strlen strncat Thread support call_once cnd_broadcast cnd_destroy cnd_init cnd_signal cnd_timedwait cnd_wait mtx_destroy mtx_init mtx_lock mtx_plain mtx_recursive mtx_timed mtx_timedlock mtx_trylock mtx_unlock once_flag ONCE_FLAG_INIT thrd_busy thrd_create thrd_current thrd_detach thrd_equal thrd_error thrd_exit thrd_join thrd_nomem thrd_sleep thrd_success thrd_timedout thrd_yield Thread support library thread_local tss_create tss_delete TSS_DTOR_ITERATIONS tss_get tss_set Type support Boolean type support library Fixed width integer types FLT_EVAL_METHOD FLT_ROUNDS max_align_t NULL Numeric limits offsetof ptrdiff_t size_t Type support Variadic functions Variadic functions va_arg va_copy va_end va_list va_start
Figuren

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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