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) |
long double remquol( long double x, long double y, int *quo ); | (3) | (since C99) |
Defined in header <tgmath.h> | ||
#define remquo( x, y, quo ) | (4) | (since C99) |
x/y
as the remainder()
function does. Additionally, the sign and at least the three of the last bits of x/y
will be stored in quo
, sufficient to determine the octant of the result within a period.long double
, remquol
is called. Otherwise, if any non-pointer argument has integer type or has type double
, remquo
is called. Otherwise, remquof
is called.x, y | - | floating point values |
quo | - | pointer to an integer value to store the sign and some bits of x/y |
If successful, returns the floating-point remainder of the division x/y
as defined in remainder
, and stores, in *quo
, the sign and at least three of the least significant bits of x/y
(formally, stores a value whose sign is the sign of x/y
and whose magnitude is congruent modulo 2n
to the magnitude of the integral quotient of x/y
, where n is an implementation-defined integer greater than or equal to 3).
If y
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.
If y
is zero, but the domain error does not occur, zero is returned.
Errors are reported as specified in math_errhandling
.
Domain error may occur if y
is zero.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
FE_INEXACT
is never raised x
is ±∞ and y
is not NaN, NaN is returned and FE_INVALID
is raised y
is ±0 and x
is not NaN, NaN is returned and FE_INVALID
is raised x
or y
is NaN, NaN is returned POSIX requires that a domain error occurs if x
is infinite or y
is zero.
This function is useful when implementing periodic functions with the period exactly representable as a floating-point value: when calculating sin(πx) for a very large x
, calling sin
directly may result in a large error, but if the function argument is first reduced with remquo
, 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 <stdio.h> #include <math.h> #include <fenv.h> #ifndef __GNUC__ #pragma STDC FENV_ACCESS ON #endif double cos_pi_x_naive(double x) { const double pi = acos(-1); return cos(pi * x); } // the period is 2, values are (0;0.5) positive, (0.5;1.5) negative, (1.5,2) positive double cos_pi_x_smart(double x) { const double pi = acos(-1); int extremum; double rem = remquo(x, 1, &extremum); extremum = (unsigned)extremum % 2; // keep 1 bit to determine nearest extremum return 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 handling feclearexcept(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) = 0.707107 cos(pi * 1.25) = -0.707107 cos(pi * 1000000000000.25) = 0.707123 cos(pi * 1000000000001.25) = -0.707117 cos(pi * 1000000000000.25) = 0.707107 cos(pi * 1000000000001.25) = -0.707107 remquo(+Inf, 1) = -nan FE_INVALID raised
(C99) | computes quotient and remainder of integer division (function) |
(C99)(C99) | computes remainder of the floating-point division operation (function) |
(C99)(C99)(C99) | computes signed remainder of the floating-point division operation (function) |
C++ documentation for remquo |
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