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Defined in header <math.h> | ||
float remquof(float x,float y,int*quo); | (1) | (since C99) |
double remquo(double x,double y,int*quo); | (2) | (since C99) |
longdouble remquol(longdouble x,longdouble y,int*quo); | (3) | (since C99) |
Defined in header <tgmath.h> | ||
#define remquo( x, y, quo ) | (4) | (since C99) |
remquol is called. Otherwise, if any non-pointer argument has integer type or has typedouble,remquo is called. Otherwise,remquof is called.Contents |
| x, y | - | floating-point values |
| quo | - | pointer to an integer value to store the sign and some bits ofx/y |
If successful, returns the floating-point remainder of the divisionx/y as defined inremainder, and stores, in*quo, the sign and at least three of the least significant bits ofx/y (formally, stores a value whose sign is the sign ofx/y and whose magnitude is congruentmodulo 2n
to the magnitude of the integral quotient ofx/y, wheren is an implementation-defined integer greater than or equal to3).
Ify is zero, the value stored in*quo is unspecified.
If a domain error occurs, an implementation-defined value is returned (NaN where supported).
If a range error occurs due to underflow, the correct result is returned if subnormals are supported.
Ify is zero, but the domain error does not occur, zero is returned.
Errors are reported as specified inmath_errhandling.
Domain error may occur ify is zero.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
POSIX requires that a domain error occurs ifx is infinite ory is zero.
This function is useful when implementing periodic functions with the period exactly representable as a floating-point value: when calculatingsin(πx) for a very largex, callingsin directly may result in a large error, but if the function argument is first reduced withremquo, the low-order bits of the quotient may be used to determine the sign and the octant of the result within the period, while the remainder may be used to calculate the value with high precision.
On some platforms this operation is supported by hardware (and, for example, on Intel CPU,FPREM1 leaves exactly 3 bits of precision in the quotient).
#include <fenv.h>#include <math.h>#include <stdio.h> #ifndef __GNUC__#pragma STDC FENV_ACCESS ON#endif double cos_pi_x_naive(double x){constdouble pi=acos(-1);returncos(pi* x);} // the period is 2, values are (0;0.5) positive, (0.5;1.5) negative, (1.5,2) positivedouble cos_pi_x_smart(double x){constdouble pi=acos(-1);int extremum;double rem= remquo(x,1,&extremum); extremum=(unsigned)extremum%2;// keep 1 bit to determine nearest extremumreturn extremum?-cos(pi* rem):cos(pi* rem);} int main(void){printf("cos(pi * 0.25) = %f\n", cos_pi_x_naive(0.25));printf("cos(pi * 1.25) = %f\n", cos_pi_x_naive(1.25));printf("cos(pi * 1000000000000.25) = %f\n", cos_pi_x_naive(1000000000000.25));printf("cos(pi * 1000000000001.25) = %f\n", cos_pi_x_naive(1000000000001.25));printf("cos(pi * 1000000000000.25) = %f\n", cos_pi_x_smart(1000000000000.25));printf("cos(pi * 1000000000001.25) = %f\n", cos_pi_x_smart(1000000000001.25)); // error handlingfeclearexcept(FE_ALL_EXCEPT);int quo;printf("remquo(+Inf, 1) = %.1f\n", remquo(INFINITY,1,&quo));if(fetestexcept(FE_INVALID))puts(" FE_INVALID raised");}
Possible output:
cos(pi * 0.25) = 0.707107cos(pi * 1.25) = -0.707107cos(pi * 1000000000000.25) = 0.707123cos(pi * 1000000000001.25) = -0.707117cos(pi * 1000000000000.25) = 0.707107cos(pi * 1000000000001.25) = -0.707107 remquo(+Inf, 1) = -nan FE_INVALID raised
(C99) | computes quotient and remainder of integer division (function)[edit] |
(C99)(C99) | computes remainder of the floating-point division operation (function)[edit] |
(C99)(C99)(C99) | computes signed remainder of the floating-point division operation (function)[edit] |
C++ documentation forremquo | |
