C语言中文开发手册
目录搜索
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 keywords（关键词）casecharconst（常量修饰符）continuedefault（预设运算式）dodouble（双精度浮点型）elseenum（枚举类型）extern（全局变量）float（浮点数）forfortrangoto（goto语句）if（if语句）inline（行内函式）intlong（长整型）register（寄存器变量）restrict（ restrict类型限定符）returnshortsignedsizeof（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_localC language#define directive#elif directive#else directive#endif directive#error directive#if directive#ifdef directive#ifndef directive#include directive#line directive#pragma directivealignas（对齐指定符）Alternative operators and tokens（替代运算符和令牌）AnalyzabilityArithmetic operatorsArithmetic typesArray declaration（数组声明）Array initialization（阵列初始化）ASCII ChartAssignment operators（赋值运算符）types（atomic类型限定符）Basic conceptsBit fields（位域）break statementC languageC Operator Precedencecast operatorcharacter 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 statementDeclarations（声明）do-while loopEnumerations（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 loopFunction declarations（函数声明）Function definitions（函数声明）FunctionsGeneric selection泛型选择goto statementIdentifier（标示符）if statementImplicit 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 constantLifetime（生命期）Logical operators（逻辑运算符）Lookup and name spacesMain function（主函式）Member access operators（会员接入运营商）Memory modelObjects and alignment（字节对齐）Order of evaluation（评估顺序）Other operatorsPhases of translation（翻译阶段）Pointer declarationPreprocessor（预处理）restrict type qualifier（restrict类型限定符）return statementScalar 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 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 numbers（错误个数）ignore_handler_sset_constraint_handler_sstatic_assertFile input/outputclearerr（清除/复位）fclosefeofferrorfflush（清空文件缓冲区）fgetcfgetposfgetsfgetwcfgetwsFile input/outputfopenfopen_sfprintffprintf_sfputcfputsfputwcfputwsfreadfreopenfreopen_sfscanffscanf_sfseekfsetposftellfwidefwprintffwprintf_sfwritefwscanffwscanf_sgetcgetchargetsgets_sgetwcharperrorprintfprintf_sputcputcharputsputwcputwcharremoverenamerewindscanfscanf_ssetbufsetvbufsnprintfsprintfsscanfsscanf_sswprintfswprintf_sswscanfswscanf_stmpfiletmpfile_stmpnamtmpnam_sungetcungetwcvfprintfvfprintf_svfscanfvfscanf_svfwprintfvfwprintf_svfwscanfvfwscanf_svprintfvprintf_svscanfvscanf_svsnprintfvsprintfvsscanfvsscanf_svswprintfvswprintf_svswscanfvswscanf_svwprintfvwprintf_svwscanfvwscanf_swprintfwprintf_swscanfwscanf_sLocalization supportlconvLC_ALLLC_COLLATELC_CTYPELC_MONETARYLC_NUMERICLC_TIMElocaleconvLocalization supportsetlocaleNumericsabsacosacosfacoshacoshfacoshlacoslasinasinfasinhasinhfasinhlasinlatanatan2atan2fatan2latanfatanhatanhfatanhlatanlcabscabsfcabslcacoscacosfcacoshcacoshfcacoshlcacoslcargcargfcarglcasincasinfcasinhcasinhfcasinhlcasinlcatancatanfcatanhcatanhfcatanhlcatanlcbrtcbrtfcbrtlccosccosfccoshccoshfccoshlccoslceilceilfceillcexpcexpfcexplcimagcimagfcimaglclogclogfcloglCMPLXCMPLXFCMPLXLCommon mathematical functionscomplexComplex number arithmeticconjconjfconjlcopysigncopysignfcopysignlcoscosfcoshcoshfcoshlcoslcpowcpowfcpowlcprojcprojfcprojlcrealcrealfcreallcsincsinfcsinhcsinhfcsinhlcsinlcsqrtcsqrtfcsqrtlctanctanfctanhctanhfctanhlctanldivdouble_terferfcerfcferfclerfferflexpexp2exp2fexp2lexpfexplexpm1expm1fexpm1lfabsfabsffabslfdimfeclearexceptfegetenvfegetexceptflagfegetroundfeholdexceptferaiseexceptfesetenvfesetexceptflagfesetroundfetestexceptfeupdateenvFE_ALL_EXCEPTFE_DFL_ENVFE_DIVBYZEROFE_DOWNWARDFE_INEXACTFE_INVALIDFE_OVERFLOWFE_TONEARESTFE_TOWARDZEROFE_UNDERFLOWFE_UPWARDFloating-point environmentfloat_tfloorfloorffloorlfmafmaffmalfmaxfmaxffmaxlfminfminffminlfmodfmodffmodlfpclassifyFP_INFINITEFP_NANFP_NORMALFP_SUBNORMALFP_ZEROfrexpfrexpffrexplHUGE_VALHUGE_VALFHUGE_VALLhypothypotfhypotlIilogbilogbfilogblimaginaryimaxabsimaxdivINFINITYisfiniteisgreaterisgreaterequalisinfislessislessequalislessgreaterisnanisnormalisunorderedlabsldexpldexpfldexplldivlgammalgammaflgammalllabslldivllrintllrintfllrintlllroundllroundfllroundlloglog10log10flog10llog1plog1pflog1pllog2log2flog2llogblogbflogbllogflogllrintlrintflrintllroundlroundflroundlMATH_ERREXCEPTmath_errhandlingMATH_ERRNOmodfmodffmodflnanNANnanfnanlnearbyintnearbyintfnearbyintlnextafternextafterfnextafterlnexttowardnexttowardfnexttowardlNumericspowpowfpowlPseudo-random number 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

©
本文档使用 php.cn手册 发布

文字

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 standard (ISO/IEC 9899:2011):

    • 7.3.6.3 The catanh functions (p: 193)

    • 7.25 Type-generic math <tgmath.h> (p: 373-375)

    • G.6.2.3 The catanh functions (p: 540-541)

    • G.7 Type-generic math <tgmath.h> (p: 545)

  • C99 standard (ISO/IEC 9899:1999):

    • 7.3.6.3 The catanh functions (p: 175)

    • 7.22 Type-generic math <tgmath.h> (p: 335-337)

    • G.6.2.3 The catanh functions (p: 475-476)

    • G.7 Type-generic math <tgmath.h> (p: 480)

上一篇：下一篇：