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
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在头文件<math.h>中定义 | ||
|---|---|---|
float nextafterf( float from, float to ); | (1) | (since C99) |
double nextafter( double from, double to ); | (2) | (since C99) |
long double nextafterl( long double from, long double to ); | (3) | (since C99) |
float nexttowardf( float from, long double to ); | (4) | (since C99) |
double nexttoward( double from, long double to ); | (5) | (since C99) |
long double nexttowardl( long double from, long double to ); | (6) | (since C99) |
Defined in header <tgmath.h> | ||
#define nextafter(from, to) | (7) | (since C99) |
#define nexttoward(from, to) | (8) | (since C99) |
1-3）首先，将两个参数都转换为函数的类型，然后返回下一个可表示值from的方向to。如果from等于to，to则返回。
4-6）首先，将第一个参数转换为函数的类型，然后返回下一个可表示值from的方向to。如果from等于to，to则返回，转换long double为函数的返回类型，但不会丢失范围或精度。
7）类型 - 通用宏：如果任何参数具有类型long double，nextafterl则被调用。否则，如果任何参数具有整数类型或具有类型double，nextafter则被调用。否则，nextafterf被调用。
8）类型 - 通用宏：如果参数from具有类型long double，nexttowardl则被调用。否则，如果from有整数类型或类型double，nexttoward则调用。否则，nexttowardf被调用。
参数
from, to | - | 浮点值 |
|---|
返回值
如果没有错误发生，下一个可表示值from的方向to。返回。如果from等于to，则to返回，转换为函数的类型。
如果范围误差由于发生溢出，±HUGE_VAL，±HUGE_VALF，或±HUGE_VALL被返回（与相同的符号from）。
如果由于下溢而发生范围错误，则返回正确的结果。
错误处理
按照math_errhandling中的指定报告错误。
如果实现支持IEEE浮点运算（IEC 60559），
如果
from是有限的，但预期的结果是无穷大，提高FE_INEXACT和FE_OVERFLOW如果
from不相等to，结果是低于正常或零，则引发FE_INEXACT和FE_UNDERFLOW在任何情况下，返回值都与当前舍入模式无关
如果是
from或者to是NaN，则返回NaN
笔记
POSIX指定溢出和下溢条件是范围错误（可能会设置错误）。
IEC 60559建议from每当返回from==to。这些函数会返回to，这会使零之间的行为保持一致：nextafter(-0.0, +0.0)返回+0.0并nextafter(+0.0, -0.0)返回–0.0。
例
#include <math.h>#include <stdio.h>#include <float.h>#include <fenv.h>
int main(void){
float from1 = 0, to1 = nextafterf(from1, 1); printf("The next representable float after %.2f is %.20g (%a)\n", from1, to1, to1);
float from2 = 1, to2 = nextafterf(from2, 2); printf("The next representable float after %.2f is %.20f (%a)\n", from2, to2, to2);
double from3 = nextafter(0.1, 0), to3 = 0.1; printf("The number 0.1 lies between two valid doubles:\n" " %.56f (%a)\nand %.55f (%a)\n", from3, from3, to3, to3);
// difference between nextafter and nexttoward:
long double dir = nextafterl(from1, 1); // first subnormal long double
float x = nextafterf(from1, dir); // first converts dir to float, giving 0 printf("Using nextafter, next float after %.2f (%a) is %.20g (%a)\n",
from1, from1, x, x);
x = nexttowardf(from1, dir); printf("Using nexttoward, next float after %.2f (%a) is %.20g (%a)\n",
from1, from1, x, x);
// special values {
#pragma STDC FENV_ACCESS ON feclearexcept(FE_ALL_EXCEPT);
double from4 = DBL_MAX, to4 = nextafter(from4, INFINITY); printf("The next representable double after %.2g (%a) is %.23f (%a)\n",
from4, from4, to4, to4); if(fetestexcept(FE_OVERFLOW)) puts(" raised FE_OVERFLOW"); if(fetestexcept(FE_INEXACT)) puts(" raised FE_INEXACT"); } // end FENV_ACCESS block
float from5 = 0.0, to5 = nextafter(from5, -0.0); printf("nextafter(+0.0, -0.0) gives %.2g (%a)\n", to5, to5);}输出：
The next representable float after 0.00 is 1.4012984643248170709e-45 (0x1p-149)The next representable float after 1.00 is 1.00000011920928955078 (0x1.000002p+0)The number 0.1 lies between two valid doubles: 0.09999999999999999167332731531132594682276248931884765625 (0x1.9999999999999p-4)and 0.1000000000000000055511151231257827021181583404541015625 (0x1.999999999999ap-4)Using nextafter, next float after 0.00 (0x0p+0) is 0 (0x0p+0)Using nexttoward, next float after 0.00 (0x0p+0) is 1.4012984643248170709e-45 (0x1p-149)The next representable double after 1.8e+308 (0x1.fffffffffffffp+1023) is inf (inf) raised FE_OVERFLOW raised FE_INEXACTnextafter(+0.0, -0.0) gives -0 (-0x0p+0)
参考
C11标准（ISO / IEC 9899：2011）：
7.12.11.3 nextafter函数（p：256）
7.12.11.4 nexttoward函数（p：257）
7.25类型通用数学<tgmath.h>（p：373-375）
F.10.8.3 nextafter函数（p：529）
F.10.8.4 nexttoward函数（p：529）
C99标准（ISO / IEC 9899：1999）：
7.12.11.3 nextafter函数（p：237）
7.12.11.4 nexttoward函数（p：238）
7.22类型通用数学<tgmath.h>（p：335-337）
F.9.8.3 nextafter函数（p：466）
F.9.8.4 nexttoward函数（p：466）