AlgorithmsAlgorithms（算法）bsearchbsearch_sqsortqsort_sAtomic operationsAtomic operations library（原子操作库）ATOMIC_*_LOCK_FREEatomic_compare_exchange_strongatomic_compare_exchange_strong_explicitatomic_compare_exchange_weakatomic_compare_exchange_weak_explicitatomic_exchangeatomic_exchange_explicitatomic_fetch_addatomic_fetch_add_explicitatomic_fetch_andatomic_fetch_and_explicitatomic_fetch_oratomic_fetch_or_explicitatomic_fetch_subatomic_fetch_sub_explicitatomic_fetch_xoratomic_fetch_xor_explicitatomic_flagatomic_flag_clearatomic_flag_clear_explicitATOMIC_FLAG_INITatomic_flag_test_and_setatomic_flag_test_and_set_explicitatomic_initatomic_is_lock_freeatomic_loadatomic_load_explicitatomic_signal_fenceatomic_storeatomic_store_explicitatomic_thread_fence（线程围栏）ATOMIC_VAR_INITkill_dependencymemory_order（内存排序）C keywordsauto（自动存储）break（跳出循环）C 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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 statementThread storage duration（线程存储时间）TypeType（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 specifierDate and timeasctime（asctime函数）asctime_sclockCLOCKS_PER_SECclock_tctime（ctime函数）ctime_sDate and time utilities（日期和时间库）difftime（计算两个时间的间隔）gmtimegmtime_slocaltimelocaltime_smktime（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）timetimespectimespec_gettime_ttmwcsftime（格式化时间宽字符）Dynamic memory managementaligned_allocC memory management library（内存管理库）callocfree（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 handlingabort_handler_sassert（断言）constraint_handler_terrno（错误报告）Error handling（错误处理）Error 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supportsetlocaleNumericsabsacosacosfacoshacoshfacoshlacoslasinasinfasinhasinhfasinhlasinlatanatan2atan2fatan2latanfatanhatanhfatanhlatanlcabscabsfcabslcacoscacosfcacoshcacoshfcacoshlcacoslcargcargfcarglcasincasinfcasinhcasinhfcasinhlcasinlcatancatanfcatanhcatanhfcatanhlcatanlcbrtcbrtfcbrtlccosccosfccoshccoshfccoshlccoslceilceilfceillcexpcexpfcexplcimagcimagfcimaglclogclogfcloglCMPLXCMPLXFCMPLXLCommon mathematical functionscomplexComplex number arithmeticconjconjfconjlcopysigncopysignfcopysignlcoscosfcoshcoshfcoshlcoslcpowcpowfcpowlcprojcprojfcprojlcrealcrealfcreallcsincsinfcsinhcsinhfcsinhlcsinlcsqrtcsqrtfcsqrtlctanctanfctanhctanhfctanhlctanldivdouble_terferfcerfcferfclerfferflexpexp2exp2fexp2lexpfexplexpm1expm1fexpm1lfabsfabsffabslfdimfeclearexceptfegetenvfegetexceptflagfegetroundfeholdexceptferaiseexceptfesetenvfesetexceptflagfesetroundfetestexceptfeupdateenvFE_ALL_EXCEPTFE_DFL_ENVFE_DIVBYZEROFE_DOWNWARDFE_INEXACTFE_INVALIDFE_OVERFLOWFE_TONEARESTFE_TOWARDZEROFE_UNDERFLOWFE_UPWARDFloating-point 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generationrandRAND_MAXremainderremainderfremainderlremquoremquofremquolrintrintfrintlroundroundfroundlscalblnscalblnfscalblnlscalbnscalbnfscalbnlsignbitsinsinfsinhsinhfsinhlsinlsqrtsqrtfsqrtlsrandtantanftanhtanhftanhltanltgammatgammaftgammaltrunctruncftrunclType-generic math_Complex_I_Imaginary_IProgram supportabortatexitat_quick_exitexitEXIT_FAILUREEXIT_SUCCESSgetenvgetenv_sjmp_buflongjmpProgram support utilitiesquick_exitraisesetjmpSIGABRTSIGFPESIGILLSIGINTsignalSIGSEGVSIGTERMsig_atomic_tSIG_DFLSIG_ERRSIG_IGNsystem_ExitStringsatofatoiatolatollbtowcc16rtombc32rtombchar16_tchar32_tisalnumisalphaisblankiscntrlisdigitisgraphislowerisprintispunctisspaceisupperiswalnumiswalphaiswblankiswcntrliswctypeiswdigitiswgraphiswloweriswprintiswpunctiswspaceiswupperiswxdigitisxdigitmblenmbrlenmbrtoc16mbrtoc32mbrtowcmbsinitmbsrtowcsmbsrtowcs_smbstate_tmbstowcsmbstowcs_smbtowcmemchrmemcmpmemcpymemcpy_smemmovememmove_smemsetmemset_sNull-terminated byte stringsNull-terminated multibyte stringsNull-terminated wide stringsstrcatstrcat_sstrchrstrcmpstrcollstrcpystrcpy_sstrcspnstrerrorstrerrorlen_sstrerror_sStrings librarystrlenstrncatThread supportcall_oncecnd_broadcastcnd_destroycnd_initcnd_signalcnd_timedwaitcnd_waitmtx_destroymtx_initmtx_lockmtx_plainmtx_recursivemtx_timedmtx_timedlockmtx_trylockmtx_unlockonce_flagONCE_FLAG_INITthrd_busythrd_createthrd_currentthrd_detachthrd_equalthrd_errorthrd_exitthrd_jointhrd_nomemthrd_sleepthrd_successthrd_timedoutthrd_yieldThread support librarythread_localtss_createtss_deleteTSS_DTOR_ITERATIONStss_gettss_setType supportBoolean type support libraryFixed width integer typesFLT_EVAL_METHODFLT_ROUNDSmax_align_tNULLNumeric limitsoffsetofptrdiff_tsize_tType supportVariadic functionsVariadic functionsva_argva_copyva_endva_listva_start
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在头文件<math.h>中定义 | ||
|---|---|---|
float complex catanhf( float complex z ); | (1) | (since C99) |
double complex catanh( double complex z ); | (2) | (since C99) |
long double complex catanhl( long double complex z ); | (3) | (since C99) |
Defined in header <tgmath.h> | ||
#define atanh( z ) | (4) | (since C99) |
1-3）计算z区间-1以外的分支切口的复数双曲正切; +1沿实轴。
4）类型 - 通用宏：如果z有类型long double complex，catanhl被调用。如果z有类型double complex，catanh称为，如果z有类型float complex，catanhf称为。如果z是真实的或整数，则宏调用相应的实函数（atanhf，atanh，atanhl）。如果z是虚构的，那么宏调用相应的真实版本atan，实现公式atanh（iy）= i atan（y），并且返回类型是虚构的。
参数
z | - | 复杂的论点 |
|---|
返回值
如果没有出现错误，z则返回复数圆弧双曲正切值，该值在半径数值范围内沿着实轴且在区间-iπ/ 2中是数学上无界的; +iπ/ 2沿着虚轴。
错误处理和特殊值
报告的错误与math_errhandling一致。
如果实现支持IEEE浮点运算，
catanh(conj(z))==conj(catanh(z))catanh(-z) == -catanh(z)如果
z是+0+0i，结果是+0+0i如果
z是+0+NaNi，结果是+0+NaNi如果
z是+1+0i，结果是+∞+0i并且FE_DIVBYZERO被提出如果
z是x+∞i（对于任何有限的正x），结果是+0+iπ/2如果
z是x+NaNi（对于任何有限的非零x），结果是NaN+NaNi并FE_INVALID可能被提出如果
z是+∞+yi（对于任何有限的正y），结果是+0+iπ/2如果
z是+∞+∞i，结果是+0+iπ/2如果
z是+∞+NaNi，结果是+0+NaNi如果
z是NaN+yi（对于任何有限的y），结果是NaN+NaNi并且FE_INVALID可能会被提出如果
z是NaN+∞i，结果是±0+iπ/2（真实部分的符号未指定）如果
z是NaN+NaNi，结果是NaN+NaNi
笔记
尽管C标准将这个函数命名为“复圆弧双曲正切”，但双曲函数的反函数是区域函数。他们的论点是双曲线领域，而不是弧线。正确的名称是“复反双曲正切”，并且不太常见的是“复曲面双曲正切”。
逆双曲正切是一种多值函数，需要在复平面上进行分支切割。分支切割通常放置在实轴的线段（-∞，-1）和[+ 1，+∞）处。反双曲正弦的主值的数学定义是atanh z =
| ln(1+z)-ln(z-1) |
|:----|
| 2 |
.
For any z, atanh(z) =
| atan(iz) |
|:----|
| i |
例
#include <stdio.h>#include <complex.h>
int main(void){
double complex z = catanh(2); printf("catanh(+2+0i) = %f%+fi\n", creal(z), cimag(z));
double complex z2 = catanh(conj(2)); // or catanh(CMPLX(2, -0.0)) in C11 printf("catanh(+2-0i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));
// for any z, atanh(z) = atan(iz)/i
double complex z3 = catanh(1+2*I); printf("catanh(1+2i) = %f%+fi\n", creal(z3), cimag(z3));
double complex z4 = catan((1+2*I)*I)/I; printf("catan(i * (1+2i))/i = %f%+fi\n", creal(z4), cimag(z4));}输出：
catanh(+2+0i) = 0.549306+1.570796icatanh(+2-0i) (the other side of the cut) = 0.549306-1.570796icatanh(1+2i) = 0.173287+1.178097icatan(i * (1+2i))/i = 0.173287+1.178097i
参考
C11标准（ISO / IEC 9899：2011）：
7.3.6.3函数（p：193）
7.25类型通用数学<tgmath.h>（p：373-375）
G.6.2.3通信功能（p：540-541）
G.7类型 - 通用数学<tgmath.h>（p：545）
C99标准（ISO / IEC 9899：1999）：
7.3.6.3 catanh函数（p：175）
7.22类型通用数学<tgmath.h>（p：335-337）
G.6.2.3通信功能（p：475-476）
G.7类型 - 通用数学<tgmath.h>（p：480）