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characters

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)

在头文件<tgmath.h>中定义



#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的情况为: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。

#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

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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 |

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