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 fmaf( float x, float y, float z ); | (1) | (自C99) |
double fma( double x, double y, double z ); | (2) | (自 C99) |
long double fmal( long double x, long double y, long double z ); | (3) | (自 C99) |
#define FP_FAST_FMA /* implementation-defined */ | (4) | (自C99) |
#define FP_FAST_FMAF /* implementation-defined */ | (5) | (自C99) |
#define FP_FAST_FMAL /* implementation-defined */ | (6) | (自C99) |
Defined in header <tgmath.h> | ||
#define fma( x, y, z ) | (7) | (自C99) |
1-3）计算（x * y）+ z，就像无限精度一样，只舍入一次以适应结果类型。
4-6）如果定义了宏常量FP_FAST_FMAF，FP_FAST_FMA或FP_FAST_FMAL，则相应函数fmaf，fma或fmal的计算速度（除了更精确之外）的计算结果要高于float，double和x * y + z的表达式 长双重论点，分别。 如果定义，这些宏评估为整数1。
7）类型泛型宏：如果任何参数的类型为long double，则调用fmal。 否则，如果任何参数具有整数类型或类型为double，则调用fma。 否则，调用fmaf。
参数
x, y, z | - | floating point values |
|---|
返回值
如果成功，则返回（x * y）+ z的值，如同计算为无限精度一样，并舍入一次以适合结果类型（或者，也可以计算为单个三元浮点运算）。
如果发生由溢出引起的范围错误，则返回±HUGE_VAL，±HUGE_VALF或±HUGE_VALL。
如果发生由于下溢导致的范围错误，则返回正确的值（舍入后）。
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x是零并且y是无限的或者如果x是无限的并且y是零并且z不是NaN，则返回NaN并且引发FE_INVALID
如果x是零并且y是无限的或者如果x是无限的并且y是零并且z是NaN，则返回NaN并且可以提升FE_INVALID
如果x * y是一个精确的无穷大而z是一个具有相反符号的无穷大，则返回NaN并且引发FE_INVALID
如果x或y是NaN，则返回NaN
如果z是NaN，并且x * y不是0 * Inf或Inf * 0，则返回NaN（不含FE_INVALID）
注意
这种操作通常以硬件实现为融合乘加CPU指令。 如果硬件支持，则应该定义适当的FP_FAST_FMA *宏，但是即使未定义宏，许多实现也会使用CPU指令。
POSIX指定值x * y无效且z是NaN的情况是域错误。
由于其无限的中间精度，fma是其他正确舍入的数学运算的常见构建模块，例如sqrt或甚至除CPU之外的分区（例如Itanium）。
与所有浮点表达式一样，除非#pragma STDC FP_CONTRACT处于关闭状态，否则表达式（x * y）+ z可能会编译为已融合的多重加法。
例
#include <stdio.h>#include <math.h>#include <float.h>#include <fenv.h>#pragma STDC FENV_ACCESS ON
int main(void){ // demo the difference between fma and built-in operators
double in = 0.1; printf("0.1 double is %.23f (%a)\n", in, in); printf("0.1*10 is 1.0000000000000000555112 (0x8.0000000000002p-3)," " or 1.0 if rounded to double\n");
double expr_result = 0.1 * 10 - 1; printf("0.1 * 10 - 1 = %g : 1 subtracted after " "intermediate rounding to 1.0\n", expr_result);
double fma_result = fma(0.1, 10, -1); printf("fma(0.1, 10, -1) = %g (%a)\n", fma_result, fma_result);
// fma use in double-double arithmetic printf("\nin double-double arithmetic, 0.1 * 10 is representable as ");
double high = 0.1 * 10;
double low = fma(0.1, 10, -high); printf("%g + %g\n\n", high, low);
//error handling feclearexcept(FE_ALL_EXCEPT); printf("fma(+Inf, 10, -Inf) = %f\n", fma(INFINITY, 10, -INFINITY)); if(fetestexcept(FE_INVALID)) puts(" FE_INVALID raised");}可能的输出：
0.1 double is 0.10000000000000000555112 (0x1.999999999999ap-4)0.1*10 is 1.0000000000000000555112 (0x8.0000000000002p-3), or 1.0 if rounded to double0.1 * 10 - 1 = 0 : 1 subtracted after intermediate rounding to 1.0fma(0.1, 10, -1) = 5.55112e-17 (0x1p-54) in double-double arithmetic, 0.1 * 10 is representable as 1 + 5.55112e-17 fma(+Inf, 10, -Inf) = -nan FE_INVALID raised
参考
C11标准（ISO / IEC 9899：2011）：
7.12.13.1 fma函数（p：258）
7.25类型通用数学<tgmath.h>（p：373-375）
F.10.10.1 fma函数（p：530）
C99标准（ISO / IEC 9899：1999）：
7.12.13.1 fma函数（p：239）
7.22类型通用数学<tgmath.h>（p：335-337）
F.9.10.1 fma函数（p：466）
扩展内容
remainderremainderfremainderl (C99)(C99)(C99) | 计算浮点除法运算的有符号余数（函数） |
|---|---|
remquoremquofremquol（C99）（C99）（C99） | 计算带符号的余数以及除法操作（函数）的最后三位 |
| fma的C ++文档 |