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1.3. Double Precision Mathematical Functions

This section describes double precision mathematical functions.

Functions

__device__ ​ double acos ( double  x )
Calculate the arc cosine of the input argument.
__device__ ​ double acosh ( double  x )
Calculate the nonnegative arc hyperbolic cosine of the input argument.
__device__ ​ double asin ( double  x )
Calculate the arc sine of the input argument.
__device__ ​ double asinh ( double  x )
Calculate the arc hyperbolic sine of the input argument.
__device__ ​ double atan ( double  x )
Calculate the arc tangent of the input argument.
__device__ ​ double atan2 ( double  x, double  y )
Calculate the arc tangent of the ratio of first and second input arguments.
__device__ ​ double atanh ( double  x )
Calculate the arc hyperbolic tangent of the input argument.
__device__ ​ double cbrt ( double  x )
Calculate the cube root of the input argument.
__device__ ​ double ceil ( double  x )
Calculate ceiling of the input argument.
__device__ ​ double copysign ( double  x, double  y )
Create value with given magnitude, copying sign of second value.
__device__ ​ double cos ( double  x )
Calculate the cosine of the input argument.
__device__ ​ double cosh ( double  x )
Calculate the hyperbolic cosine of the input argument.
__device__ ​ double cospi ( double  x )
Calculate the cosine of the input argument × π .
__device__ ​ double erf ( double  x )
Calculate the error function of the input argument.
__device__ ​ double erfc ( double  x )
Calculate the complementary error function of the input argument.
__device__ ​ double erfcinv ( double  y )
Calculate the inverse complementary error function of the input argument.
__device__ ​ double erfcx ( double  x )
Calculate the scaled complementary error function of the input argument.
__device__ ​ double erfinv ( double  y )
Calculate the inverse error function of the input argument.
__device__ ​ double exp ( double  x )
Calculate the base e exponential of the input argument.
__device__ ​ double exp10 ( double  x )
Calculate the base 10 exponential of the input argument.
__device__ ​ double exp2 ( double  x )
Calculate the base 2 exponential of the input argument.
__device__ ​ double expm1 ( double  x )
Calculate the base e exponential of the input argument, minus 1.
__device__ ​ double fabs ( double  x )
Calculate the absolute value of the input argument.
__device__ ​ double fdim ( double  x, double  y )
Compute the positive difference between x and y.
__device__ ​ double floor ( double  x )
Calculate the largest integer less than or equal to x.
__device__ ​ double fma ( double  x, double  y, double  z )
Compute x × y + z as a single operation.
__device__ ​ double fmax ( double , double )
Determine the maximum numeric value of the arguments.
__device__ ​ double fmin ( double  x, double  y )
Determine the minimum numeric value of the arguments.
__device__ ​ double fmod ( double  x, double  y )
Calculate the floating-point remainder of x / y.
__device__ ​ double frexp ( double  x, int* nptr )
Extract mantissa and exponent of a floating-point value.
__device__ ​ double hypot ( double  x, double  y )
Calculate the square root of the sum of squares of two arguments.
__device__ ​ int ilogb ( double  x )
Compute the unbiased integer exponent of the argument.
__device__ ​ int isfinite ( double  a )
Determine whether argument is finite.
__device__ ​ int isinf ( double  a )
Determine whether argument is infinite.
__device__ ​ int isnan ( double  a )
Determine whether argument is a NaN.
__device__ ​ double j0 ( double  x )
Calculate the value of the Bessel function of the first kind of order 0 for the input argument.
__device__ ​ double j1 ( double  x )
Calculate the value of the Bessel function of the first kind of order 1 for the input argument.
__device__ ​ double jn ( int  n, double  x )
Calculate the value of the Bessel function of the first kind of order n for the input argument.
__device__ ​ double ldexp ( double  x, int  exp )
Calculate the value of x 2 e x p .
__device__ ​ double lgamma ( double  x )
Calculate the natural logarithm of the absolute value of the gamma function of the input argument.
__device__ ​ long long int llrint ( double  x )
Round input to nearest integer value.
__device__ ​ long long int llround ( double  x )
Round to nearest integer value.
__device__ ​ double log ( double  x )
Calculate the base e logarithm of the input argument.
__device__ ​ double log10 ( double  x )
Calculate the base 10 logarithm of the input argument.
__device__ ​ double log1p ( double  x )
Calculate the value of l o g e ( 1 + x ) .
__device__ ​ double log2 ( double  x )
Calculate the base 2 logarithm of the input argument.
__device__ ​ double logb ( double  x )
Calculate the floating point representation of the exponent of the input argument.
__device__ ​ long int lrint ( double  x )
Round input to nearest integer value.
__device__ ​ long int lround ( double  x )
Round to nearest integer value.
__device__ ​ double modf ( double  x, double* iptr )
Break down the input argument into fractional and integral parts.
__device__ ​ double nan ( const char* tagp )
Returns "Not a Number" value.
__device__ ​ double nearbyint ( double  x )
Round the input argument to the nearest integer.
__device__ ​ double nextafter ( double  x, double  y )
Return next representable double-precision floating-point value after argument.
__device__ ​ double normcdf ( double  y )
Calculate the standard normal cumulative distribution function.
__device__ ​ double normcdfinv ( double  y )
Calculate the inverse of the standard normal cumulative distribution function.
__device__ ​ double pow ( double  x, double  y )
Calculate the value of first argument to the power of second argument.
__device__ ​ double rcbrt ( double  x )
Calculate reciprocal cube root function.
__device__ ​ double remainder ( double  x, double  y )
Compute double-precision floating-point remainder.
__device__ ​ double remquo ( double  x, double  y, int* quo )
Compute double-precision floating-point remainder and part of quotient.
__device__ ​ double rint ( double  x )
Round to nearest integer value in floating-point.
__device__ ​ double round ( double  x )
Round to nearest integer value in floating-point.
__device__ ​ double rsqrt ( double  x )
Calculate the reciprocal of the square root of the input argument.
__device__ ​ double scalbln ( double  x, long int  n )
Scale floating-point input by integer power of two.
__device__ ​ double scalbn ( double  x, int  n )
Scale floating-point input by integer power of two.
__device__ ​ int signbit ( double  a )
Return the sign bit of the input.
__device__ ​ double sin ( double  x )
Calculate the sine of the input argument.
__device__ ​ void sincos ( double  x, double* sptr, double* cptr )
Calculate the sine and cosine of the first input argument.
__device__ ​ void sincospi ( double  x, double* sptr, double* cptr )
Calculate the sine and cosine of the first input argument × π .
__device__ ​ double sinh ( double  x )
Calculate the hyperbolic sine of the input argument.
__device__ ​ double sinpi ( double  x )
Calculate the sine of the input argument × π .
__device__ ​ double sqrt ( double  x )
Calculate the square root of the input argument.
__device__ ​ double tan ( double  x )
Calculate the tangent of the input argument.
__device__ ​ double tanh ( double  x )
Calculate the hyperbolic tangent of the input argument.
__device__ ​ double tgamma ( double  x )
Calculate the gamma function of the input argument.
__device__ ​ double trunc ( double  x )
Truncate input argument to the integral part.
__device__ ​ double y0 ( double  x )
Calculate the value of the Bessel function of the second kind of order 0 for the input argument.
__device__ ​ double y1 ( double  x )
Calculate the value of the Bessel function of the second kind of order 1 for the input argument.
__device__ ​ double yn ( int  n, double  x )
Calculate the value of the Bessel function of the second kind of order n for the input argument.

Functions

__device__ ​ double acos ( double  x )

Calculate the arc cosine of the input argument. Calculate the principal value of the arc cosine of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Result will be in radians, in the interval [0, π ] for x inside [-1, +1].

  • acos(1) returns +0.
  • acos(x) returns NaN for x outside [-1, +1].

__device__ ​ double acosh ( double  x )

Calculate the nonnegative arc hyperbolic cosine of the input argument. Calculate the nonnegative arc hyperbolic cosine of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Result will be in the interval [0, + ].

  • acosh(1) returns 0.
  • acosh(x) returns NaN for x in the interval [ , 1).

__device__ ​ double asin ( double  x )

Calculate the arc sine of the input argument. Calculate the principal value of the arc sine of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Result will be in radians, in the interval [- π /2, + π /2] for x inside [-1, +1].

  • asin(0) returns +0.
  • asin(x) returns NaN for x outside [-1, +1].

__device__ ​ double asinh ( double  x )

Calculate the arc hyperbolic sine of the input argument. Calculate the arc hyperbolic sine of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • asinh(0) returns 1.

__device__ ​ double atan ( double  x )

Calculate the arc tangent of the input argument. Calculate the principal value of the arc tangent of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Result will be in radians, in the interval [- π /2, + π /2].

  • atan(0) returns +0.

__device__ ​ double atan2 ( double  x, double  y )

Calculate the arc tangent of the ratio of first and second input arguments. Calculate the principal value of the arc tangent of the ratio of first and second input arguments x / y. The quadrant of the result is determined by the signs of inputs x and y.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Result will be in radians, in the interval [- π /, + π ].

  • atan2(0, 1) returns +0.

__device__ ​ double atanh ( double  x )

Calculate the arc hyperbolic tangent of the input argument. Calculate the arc hyperbolic tangent of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • atanh( ± 0 ) returns ± 0 .
  • atanh( ± 1 ) returns ± .
  • atanh(x) returns NaN for x outside interval [-1, 1].

__device__ ​ double cbrt ( double  x )

Calculate the cube root of the input argument. Calculate the cube root of x, x 1 / 3 .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns x 1 / 3 .

  • cbrt( ± 0 ) returns ± 0 .
  • cbrt( ± ) returns ± .

__device__ ​ double ceil ( double  x )

Calculate ceiling of the input argument. Compute the smallest integer value not less than x.

Returns

Returns x expressed as a floating-point number.

  • ceil( ± 0 ) returns ± 0 .
  • ceil( ± ) returns ± .

__device__ ​ double copysign ( double  x, double  y )

Create value with given magnitude, copying sign of second value. Create a floating-point value with the magnitude x and the sign of y.

Returns

Returns a value with the magnitude of x and the sign of y.

__device__ ​ double cos ( double  x )

Calculate the cosine of the input argument. Calculate the cosine of the input argument x (measured in radians).

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • cos( ± 0 ) returns 1.
  • cos( ± ) returns NaN.

__device__ ​ double cosh ( double  x )

Calculate the hyperbolic cosine of the input argument. Calculate the hyperbolic cosine of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • cosh(0) returns 1.
  • cosh( ± ) returns + .

__device__ ​ double cospi ( double  x )

Calculate the cosine of the input argument × π . Calculate the cosine of x × π (measured in radians), where x is the input argument.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • cospi( ± 0 ) returns 1.
  • cospi( ± ) returns NaN.

__device__ ​ double erf ( double  x )

Calculate the error function of the input argument. Calculate the value of the error function for the input argument x, 2 π 0 x e t 2 d t .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • erf( ± 0 ) returns ± 0 .
  • erf( ± ) returns ± 1 .

__device__ ​ double erfc ( double  x )

Calculate the complementary error function of the input argument. Calculate the complementary error function of the input argument x, 1 - erf(x).

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • erfc( ) returns 2.
  • erfc( + ) returns +0.

__device__ ​ double erfcinv ( double  y )

Calculate the inverse complementary error function of the input argument. Calculate the inverse complementary error function of the input argument y, for y in the interval [0, 2]. The inverse complementary error function find the value x that satisfies the equation y = erfc(x), for 0 y 2 , and x .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • erfcinv(0) returns + .
  • erfcinv(2) returns .

__device__ ​ double erfcx ( double  x )

Calculate the scaled complementary error function of the input argument. Calculate the scaled complementary error function of the input argument x, e x 2 erfc ( x ) .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • erfcx( - ) returns +
  • erfcx( + ) returns +0
  • erfcx(x) returns + if the correctly calculated value is outside the double floating point range.

__device__ ​ double erfinv ( double  y )

Calculate the inverse error function of the input argument. Calculate the inverse error function of the input argument y, for y in the interval [-1, 1]. The inverse error function finds the value x that satisfies the equation y = erf(x), for 1 y 1 , and x .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • erfinv(1) returns + .
  • erfinv(-1) returns .

__device__ ​ double exp ( double  x )

Calculate the base e exponential of the input argument. Calculate the base e exponential of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns e x .

__device__ ​ double exp10 ( double  x )

Calculate the base 10 exponential of the input argument. Calculate the base 10 exponential of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns 10 x .

__device__ ​ double exp2 ( double  x )

Calculate the base 2 exponential of the input argument. Calculate the base 2 exponential of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns 2 x .

__device__ ​ double expm1 ( double  x )

Calculate the base e exponential of the input argument, minus 1. Calculate the base e exponential of the input argument x, minus 1.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns e x 1 .

__device__ ​ double fabs ( double  x )

Calculate the absolute value of the input argument. Calculate the absolute value of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the absolute value of the input argument.

  • fabs( ± ) returns + .
  • fabs( ± 0 ) returns 0.

__device__ ​ double fdim ( double  x, double  y )

Compute the positive difference between x and y. Compute the positive difference between x and y. The positive difference is x - y when x > y and +0 otherwise.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-1.

Returns

Returns the positive difference between x and y.

  • fdim(x, y) returns x - y if x > y.
  • fdim(x, y) returns +0 if x y.

__device__ ​ double floor ( double  x )

Calculate the largest integer less than or equal to x. Calculates the largest integer value which is less than or equal to x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns l o g e ( 1 + x ) expressed as a floating-point number.

  • floor( ± ) returns ± .
  • floor( ± 0 ) returns ± 0 .

__device__ ​ double fma ( double  x, double  y, double  z )

Compute x × y + z as a single operation. Compute the value of x × y + z as a single ternary operation. After computing the value to infinite precision, the value is rounded once.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the rounded value of x × y + z as a single operation.

  • fma( ± , ± 0 , z) returns NaN.
  • fma( ± 0 , ± , z) returns NaN.
  • fma(x, y, ) returns NaN if x × y is an exact + .
  • fma(x, y, + ) returns NaN if x × y is an exact .

__device__ ​ double fmax ( double , double )

Determine the maximum numeric value of the arguments. Determines the maximum numeric value of the arguments x and y. Treats NaN arguments as missing data. If one argument is a NaN and the other is legitimate numeric value, the numeric value is chosen.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the maximum numeric values of the arguments x and y.

  • If both arguments are NaN, returns NaN.
  • If one argument is NaN, returns the numeric argument.

__device__ ​ double fmin ( double  x, double  y )

Determine the minimum numeric value of the arguments. Determines the minimum numeric value of the arguments x and y. Treats NaN arguments as missing data. If one argument is a NaN and the other is legitimate numeric value, the numeric value is chosen.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the minimum numeric values of the arguments x and y.

  • If both arguments are NaN, returns NaN.
  • If one argument is NaN, returns the numeric argument.

__device__ ​ double fmod ( double  x, double  y )

Calculate the floating-point remainder of x / y. Calculate the floating-point remainder of x / y. The absolute value of the computed value is always less than y's absolute value and will have the same sign as x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • Returns the floating point remainder of x / y.
  • fmod( ± 0 , y) returns ± 0 if y is not zero.
  • fmod(x, y) returns NaN and raised an invalid floating point exception if x is ± or y is zero.
  • fmod(x, y) returns zero if y is zero or the result would overflow.
  • fmod(x, ± ) returns x if x is finite.
  • fmod(x, 0) returns NaN.

__device__ ​ double frexp ( double  x, int* nptr )

Extract mantissa and exponent of a floating-point value. Decompose the floating-point value x into a component m for the normalized fraction element and another term n for the exponent. The absolute value of m will be greater than or equal to 0.5 and less than 1.0 or it will be equal to 0; x = m 2 n . The integer exponent n will be stored in the location to which nptr points.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the fractional component m.

  • frexp(0, nptr) returns 0 for the fractional component and zero for the integer component.
  • frexp( ± 0 , nptr) returns ± 0 and stores zero in the location pointed to by nptr.
  • frexp( ± , nptr) returns ± and stores an unspecified value in the location to which nptr points.
  • frexp(NaN, y) returns a NaN and stores an unspecified value in the location to which nptr points.

__device__ ​ double hypot ( double  x, double  y )

Calculate the square root of the sum of squares of two arguments. Calculate the length of the hypotenuse of a right triangle whose two sides have lengths x and y without undue overflow or underflow.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the length of the hypotenuse x 2 + y 2 . If the correct value would overflow, returns + . If the correct value would underflow, returns 0.

__device__ ​ int ilogb ( double  x )

Compute the unbiased integer exponent of the argument. Calculates the unbiased integer exponent of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • If successful, returns the unbiased exponent of the argument.
  • ilogb(0) returns INT_MIN.
  • ilogb(NaN) returns NaN.
  • ilogb(x) returns INT_MAX if x is or the correct value is greater than INT_MAX.
  • ilogb(x) return INT_MIN if the correct value is less than INT_MIN.

__device__ ​ int isfinite ( double  a )

Determine whether argument is finite. Determine whether the floating-point value a is a finite value (zero, subnormal, or normal and not infinity or NaN).

Returns

Returns a nonzero value if and only if a is a finite value.

__device__ ​ int isinf ( double  a )

Determine whether argument is infinite. Determine whether the floating-point value a is an infinite value (positive or negative).

Returns

Returns a nonzero value if and only if a is a infinite value.

__device__ ​ int isnan ( double  a )

Determine whether argument is a NaN. Determine whether the floating-point value a is a NaN.

Returns

Returns a nonzero value if and only if a is a NaN value.

__device__ ​ double j0 ( double  x )

Calculate the value of the Bessel function of the first kind of order 0 for the input argument. Calculate the value of the Bessel function of the first kind of order 0 for the input argument x, J 0 ( x ) .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the value of the Bessel function of the first kind of order 0.

  • j0( ± ) returns +0.
  • j0(NaN) returns NaN.

__device__ ​ double j1 ( double  x )

Calculate the value of the Bessel function of the first kind of order 1 for the input argument. Calculate the value of the Bessel function of the first kind of order 1 for the input argument x, J 1 ( x ) .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the value of the Bessel function of the first kind of order 1.

  • j1( ± 0 ) returns ± 0 .
  • j1( ± ) returns +0.
  • j1(NaN) returns NaN.

__device__ ​ double jn ( int  n, double  x )

Calculate the value of the Bessel function of the first kind of order n for the input argument. Calculate the value of the Bessel function of the first kind of order n for the input argument x, J n ( x ) .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the value of the Bessel function of the first kind of order n.

  • jn(n, NaN) returns NaN.
  • jn(n, x) returns NaN for n < 0.
  • jn(n, + ) returns +0.

__device__ ​ double ldexp ( double  x, int  exp )

Calculate the value of x 2 e x p . Calculate the value of x 2 e x p of the input arguments x and exp.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • ldexp(x) returns ± if the correctly calculated value is outside the double floating point range.

__device__ ​ double lgamma ( double  x )

Calculate the natural logarithm of the absolute value of the gamma function of the input argument. Calculate the natural logarithm of the absolute value of the gamma function of the input argument x, namely the value of log e 0 e t t x 1 d t

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • lgamma(1) returns +0.
  • lgamma(2) returns +0.
  • lgamma(x) returns ± if the correctly calculated value is outside the double floating point range.
  • lgamma(x) returns + if x 0.
  • lgamma( ) returns .
  • lgamma( + ) returns + .

__device__ ​ long long int llrint ( double  x )

Round input to nearest integer value. Round x to the nearest integer value, with halfway cases rounded towards zero. If the result is outside the range of the return type, the result is undefined.

Returns

Returns rounded integer value.

__device__ ​ long long int llround ( double  x )

Round to nearest integer value. Round x to the nearest integer value, with halfway cases rounded away from zero. If the result is outside the range of the return type, the result is undefined.

Note:

This function may be slower than alternate rounding methods. See llrint().

Returns

Returns rounded integer value.

__device__ ​ double log ( double  x )

Calculate the base e logarithm of the input argument. Calculate the base e logarithm of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • log( ± 0 ) returns .
  • log(1) returns +0.
  • log(x) returns NaN for x < 0.
  • log( + ) returns +

__device__ ​ double log10 ( double  x )

Calculate the base 10 logarithm of the input argument. Calculate the base 10 logarithm of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • log10( ± 0 ) returns .
  • log10(1) returns +0.
  • log10(x) returns NaN for x < 0.
  • log10( + ) returns + .

__device__ ​ double log1p ( double  x )

Calculate the value of l o g e ( 1 + x ) . Calculate the value of l o g e ( 1 + x ) of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • log1p( ± 0 ) returns .
  • log1p(-1) returns +0.
  • log1p(x) returns NaN for x < -1.
  • log1p( + ) returns + .

__device__ ​ double log2 ( double  x )

Calculate the base 2 logarithm of the input argument. Calculate the base 2 logarithm of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • log2( ± 0 ) returns .
  • log2(1) returns +0.
  • log2(x) returns NaN for x < 0.
  • log2( + ) returns + .

__device__ ​ double logb ( double  x )

Calculate the floating point representation of the exponent of the input argument. Calculate the floating point representation of the exponent of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • logb ± 0 returns
  • logb ± returns +

__device__ ​ long int lrint ( double  x )

Round input to nearest integer value. Round x to the nearest integer value, with halfway cases rounded towards zero. If the result is outside the range of the return type, the result is undefined.

Returns

Returns rounded integer value.

__device__ ​ long int lround ( double  x )

Round to nearest integer value. Round x to the nearest integer value, with halfway cases rounded away from zero. If the result is outside the range of the return type, the result is undefined.

Note:

This function may be slower than alternate rounding methods. See lrint().

Returns

Returns rounded integer value.

__device__ ​ double modf ( double  x, double* iptr )

Break down the input argument into fractional and integral parts. Break down the argument x into fractional and integral parts. The integral part is stored in the argument iptr. Fractional and integral parts are given the same sign as the argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • modf( ± x , iptr) returns a result with the same sign as x.
  • modf( ± , iptr) returns ± 0 and stores ± in the object pointed to by iptr.
  • modf(NaN, iptr) stores a NaN in the object pointed to by iptr and returns a NaN.

__device__ ​ double nan ( const char* tagp )

Returns "Not a Number" value. Return a representation of a quiet NaN. Argument tagp selects one of the possible representations.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • nan(tagp) returns NaN.

__device__ ​ double nearbyint ( double  x )

Round the input argument to the nearest integer. Round argument x to an integer value in double precision floating-point format.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • nearbyint( ± 0 ) returns ± 0 .
  • nearbyint( ± ) returns ± .

__device__ ​ double nextafter ( double  x, double  y )

Return next representable double-precision floating-point value after argument. Calculate the next representable double-precision floating-point value following x in the direction of y. For example, if y is greater than x, nextafter() returns the smallest representable number greater than x

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • nextafter( ± , y) returns ± .

__device__ ​ double normcdf ( double  y )

Calculate the standard normal cumulative distribution function. Calculate the cumulative distribution function of the standard normal distribution for input argument y, Φ ( y ) .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • normcdf( + ) returns 1
  • normcdf( ) returns +0

__device__ ​ double normcdfinv ( double  y )

Calculate the inverse of the standard normal cumulative distribution function. Calculate the inverse of the standard normal cumulative distribution function for input argument y, Φ 1 ( y ) . The function is defined for input values in the interval ( 0 , 1 ) .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • normcdfinv(0) returns .
  • normcdfinv(1) returns + .
  • normcdfinv(x) returns NaN if x is not in the interval [0,1].

__device__ ​ double pow ( double  x, double  y )

Calculate the value of first argument to the power of second argument. Calculate the value of x to the power of y

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • pow( ± 0 , y) returns ± for y an integer less than 0.
  • pow( ± 0 , y) returns ± 0 for y an odd integer greater than 0.
  • pow( ± 0 , y) returns +0 for y > 0 and not and odd integer.
  • pow(-1, ± ) returns 1.
  • pow(+1, y) returns 1 for any y, even a NaN.
  • pow(x, ± 0 ) returns 1 for any x, even a NaN.
  • pow(x, y) returns a NaN for finite x < 0 and finite non-integer y.
  • pow(x, ) returns + for | x | < 1 .
  • pow(x, ) returns +0 for | x | > 1 .
  • pow(x, + ) returns +0 for | x | < 1 .
  • pow(x, + ) returns + for | x | > 1 .
  • pow( , y) returns -0 for y an odd integer less than 0.
  • pow( , y) returns +0 for y < 0 and not an odd integer.
  • pow( , y) returns for y an odd integer greater than 0.
  • pow( , y) returns + for y > 0 and not an odd integer.
  • pow( + , y) returns +0 for y < 0.
  • pow( + , y) returns + for y > 0.

__device__ ​ double rcbrt ( double  x )

Calculate reciprocal cube root function. Calculate reciprocal cube root function of x

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • rcbrt( ± 0 ) returns ± .
  • rcbrt( ± ) returns ± 0 .

__device__ ​ double remainder ( double  x, double  y )

Compute double-precision floating-point remainder. Compute double-precision floating-point remainder r of dividing x by y for nonzero y. Thus r = x n y . The value n is the integer value nearest x y . In the case when | n x y | = 1 2 , the even n value is chosen.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • remainder(x, 0) returns NaN.
  • remainder( ± , y) returns NaN.
  • remainder(x, ± ) returns x for finite x.

__device__ ​ double remquo ( double  x, double  y, int* quo )

Compute double-precision floating-point remainder and part of quotient. Compute a double-precision floating-point remainder in the same way as the remainder() function. Argument quo returns part of quotient upon division of x by y. Value quo has the same sign as x y and may not be the exact quotient but agrees with the exact quotient in the low order 3 bits.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the remainder.

  • remquo(x, 0, quo) returns NaN.
  • remquo( ± , y, quo) returns NaN.
  • remquo(x, ± , quo) returns x.

__device__ ​ double rint ( double  x )

Round to nearest integer value in floating-point. Round x to the nearest integer value in floating-point format, with halfway cases rounded to the nearest even integer value.

Returns

Returns rounded integer value.

__device__ ​ double round ( double  x )

Round to nearest integer value in floating-point. Round x to the nearest integer value in floating-point format, with halfway cases rounded away from zero.

Note:

This function may be slower than alternate rounding methods. See rint().

Returns

Returns rounded integer value.

__device__ ​ double rsqrt ( double  x )

Calculate the reciprocal of the square root of the input argument. Calculate the reciprocal of the nonnegative square root of x, 1 / x .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns 1 / x .

  • rsqrt( + ) returns +0.
  • rsqrt( ± 0 ) returns ± .
  • rsqrt(x) returns NaN if x is less than 0.

__device__ ​ double scalbln ( double  x, long int  n )

Scale floating-point input by integer power of two. Scale x by 2 n by efficient manipulation of the floating-point exponent.

Returns

Returns x * 2 n .

  • scalbln( ± 0 , n) returns ± 0 .
  • scalbln(x, 0) returns x.
  • scalbln( ± , n) returns ± .

__device__ ​ double scalbn ( double  x, int  n )

Scale floating-point input by integer power of two. Scale x by 2 n by efficient manipulation of the floating-point exponent.

Returns

Returns x * 2 n .

  • scalbn( ± 0 , n) returns ± 0 .
  • scalbn(x, 0) returns x.
  • scalbn( ± , n) returns ± .

__device__ ​ int signbit ( double  a )

Return the sign bit of the input. Determine whether the floating-point value a is negative.

Returns

Returns a nonzero value if and only if a is negative. Reports the sign bit of all values including infinities, zeros, and NaNs.

__device__ ​ double sin ( double  x )

Calculate the sine of the input argument. Calculate the sine of the input argument x (measured in radians).

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • sin( ± 0 ) returns ± 0 .
  • sin( ± ) returns NaN.

__device__ ​ void sincos ( double  x, double* sptr, double* cptr )

Calculate the sine and cosine of the first input argument. Calculate the sine and cosine of the first input argument x (measured in radians). The results for sine and cosine are written into the second argument, sptr, and, respectively, third argument, cptr.

See also:

sin() and cos().

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • none

__device__ ​ void sincospi ( double  x, double* sptr, double* cptr )

Calculate the sine and cosine of the first input argument × π . Calculate the sine and cosine of the first input argument, x (measured in radians), × π . The results for sine and cosine are written into the second argument, sptr, and, respectively, third argument, cptr.

See also:

sinpi() and cospi().

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • none

__device__ ​ double sinh ( double  x )

Calculate the hyperbolic sine of the input argument. Calculate the hyperbolic sine of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • sinh( ± 0 ) returns ± 0 .

__device__ ​ double sinpi ( double  x )

Calculate the sine of the input argument × π . Calculate the sine of x × π (measured in radians), where x is the input argument.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • sinpi( ± 0 ) returns ± 0 .
  • sinpi( ± ) returns NaN.

__device__ ​ double sqrt ( double  x )

Calculate the square root of the input argument. Calculate the nonnegative square root of x, x .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns x .

  • sqrt( ± 0 ) returns ± 0 .
  • sqrt( + ) returns + .
  • sqrt(x) returns NaN if x is less than 0.

__device__ ​ double tan ( double  x )

Calculate the tangent of the input argument. Calculate the tangent of the input argument x (measured in radians).

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • tan( ± 0 ) returns ± 0 .
  • tan( ± ) returns NaN.

__device__ ​ double tanh ( double  x )

Calculate the hyperbolic tangent of the input argument. Calculate the hyperbolic tangent of the input argument x.

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • tanh( ± 0 ) returns ± 0 .

__device__ ​ double tgamma ( double  x )

Calculate the gamma function of the input argument. Calculate the gamma function of the input argument x, namely the value of 0 e t t x 1 d t .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

  • tgamma( ± 0 ) returns ± .
  • tgamma(2) returns +0.
  • tgamma(x) returns ± if the correctly calculated value is outside the double floating point range.
  • tgamma(x) returns NaN if x < 0.
  • tgamma( ) returns NaN.
  • tgamma( + ) returns + .

__device__ ​ double trunc ( double  x )

Truncate input argument to the integral part. Round x to the nearest integer value that does not exceed x in magnitude.

Returns

Returns truncated integer value.

__device__ ​ double y0 ( double  x )

Calculate the value of the Bessel function of the second kind of order 0 for the input argument. Calculate the value of the Bessel function of the second kind of order 0 for the input argument x, Y 0 ( x ) .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the value of the Bessel function of the second kind of order 0.

  • y0(0) returns .
  • y0(x) returns NaN for x < 0.
  • y0( + ) returns +0.
  • y0(NaN) returns NaN.

__device__ ​ double y1 ( double  x )

Calculate the value of the Bessel function of the second kind of order 1 for the input argument. Calculate the value of the Bessel function of the second kind of order 1 for the input argument x, Y 1 ( x ) .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the value of the Bessel function of the second kind of order 1.

  • y1(0) returns .
  • y1(x) returns NaN for x < 0.
  • y1( + ) returns +0.
  • y1(NaN) returns NaN.

__device__ ​ double yn ( int  n, double  x )

Calculate the value of the Bessel function of the second kind of order n for the input argument. Calculate the value of the Bessel function of the second kind of order n for the input argument x, Y n ( x ) .

Note:

For accuracy information for this function see the CUDA C Programming Guide, Appendix C, Table C-2.

Returns

Returns the value of the Bessel function of the second kind of order n.

  • yn(n, x) returns NaN for n < 0.
  • yn(n, 0) returns .
  • yn(n, x) returns NaN for x < 0.
  • yn(n, + ) returns +0.
  • yn(n, NaN) returns NaN.


CUDA Math API (PDF) - CUDA Toolkit v5.5 (older) - Last updated May 11, 2013 - Send Feedback