Using the Intel® Math Library

Example: Using Real Functions

The following examples demonstrate how to use the math library with the Intel® C++ Compiler. After you compile this example and run the program, the program will display the sine value of x.

// real_math.c
#include <stdio.h> 
#include <mathimf.h>

int main() {
 float fp32bits;
 double fp64bits;
 long double fp80bits;
 long double pi_by_four = 3.141592653589793238/4.0;

// pi/4 radians is about 45 degrees
 fp32bits = (float) pi_by_four; // float approximation to pi/4
 fp64bits = (double) pi_by_four; // double approximation to pi/4
 fp80bits = pi_by_four; // long double (extended) approximation to pi/4

// The sin(pi/4) is known to be 1/sqrt(2) or approximately .7071067 
 printf("When x = %8.8f, sinf(x) = %8.8f \n", fp32bits, sinf(fp32bits));
 printf("When x = %16.16f, sin(x) = %16.16f \n", fp64bits, sin(fp64bits));
 printf("When x = %20.20Lf, sinl(x) = %20.20f \n", fp80bits, sinl(fp80bits));

 return 0; 
}

iccreal_math.c 

iccreal_math.c  //with EDG compiler

iclreal_math.c // with CLANG compiler

// real_math.c 
#include <stdio.h> 
#include <mathimf.h>

int main() {
  float fp32bits;
  double fp64bits;

// /Qlong-double compiler option required because, without it, 
// long double types are mapped to doubles. 
  long double fp80bits;
  long double pi_by_four = 3.141592653589793238/4.0;

// pi/4 radians is about 45 degrees
  fp32bits = (float) pi_by_four;

// float approximation to pi/4
  fp64bits = (double) pi_by_four; 

// double approximation to pi/4
  fp80bits = pi_by_four;

// long double (extended) approximation to pi/4 
// The sin(pi/4) is known to be 1/sqrt(2) or approximately .7071067
  printf("When x = %8.8f, sinf(x) = %8.8f \n",
  fp32bits, sinf(fp32bits));

  printf("When x = %16.16f, sin(x) = %16.16f \n", 
  fp64bits, sin(fp64bits));

  printf("When x = %20.20f, sinl(x) = %20.20f \n", 
  (double) fp80bits, (double) sinl(fp80bits));

// printf() does not support the printing of long doubles 
// on Microsoft* Windows*, so fp80bits is cast to double in this example. 
  return 0; 
}

Example Using Complex Functions

After you compile this example and run the program, you should get the following results:

When z = 1.0000000 + 0.7853982 i, cexpf(z) = 1.9221154 + 1.9221156 i

When z = 1.000000000000 + 0.785398163397 i, cexp(z) = 1.922115514080 + 1.922115514080 i

Linux*, OS X*, and Windows*

// complex_math.c
#include <stdio.h> 
#include <complex.h>

int main() {
  float _Complex c32in,c32out;
  double _Complex c64in,c64out;
  double pi_by_four= 3.141592653589793238/4.0;
  c64in = 1.0 + I* pi_by_four;

// Create the double precision complex number 1 + (pi/4) * i 
// where I is the imaginary unit.
  c32in = (float _Complex) c64in;

// Create the float complex value from the double complex value.
  c64out = cexp(c64in);
  c32out = cexpf(c32in);

// Call the complex exponential, 
// cexp(z) = cexp(x+iy) = e^ (x + i y) = e^x * (cos(y) + i sin(y))
 printf("When z = %7.7f + %7.7f i, cexpf(z) = %7.7f + %7.7f i \n"
 ,crealf(c32in),cimagf(c32in),crealf(c32out),cimagf(c32out));
 printf("When z = %12.12f + %12.12f i, cexp(z) = %12.12f + %12.12f i \n"
 ,creal(c64in),cimag(c64in),creal(c64out),cimagf(c64out));

  return 0; 
}

Since this example program includes the _Complex data type, be sure to include the [Q]std=c99 compiler option in the command line.

To compile this example code in Linux*, use the following command:

icc-std=c99complex_math.c

To compile this example code in OS X* use the following commands:

icc-std=c99complex_math.c   //with EDG compiler

icl-std=c99complex_math.c   //with CLANG compiler

To compile this example code in Windows*, use the following command:

icl/Qstd=c99complex_math.c

Exception Conditions

If you call a math function using argument(s) that may produce undefined results, an error number is assigned to the system variable errno. Math function errors are usually domain errors or range errors.

Domain errors result from arguments that are outside the domain of the function. For example, acos is defined only for arguments between -1 and +1 inclusive. Attempting to evaluate acos(-2) or acos(3) results in a domain error, where the return value is QNaN.

Range errors occur when a mathematically valid argument results in a function value that exceeds the range of representable values for the floating-point data type. Attempting to evaluate exp(1000) results in a range error, where the return value is INF.

When domain or range error occurs, the following values are assigned to errno:

• domain error (EDOM): errno = 33

• range error (ERANGE): errno = 34

The following example shows how to read the errno value for an EDOM and ERANGE error.

// errno.c
#include <errno.h> 
#include <mathimf.h> 
#include <stdio.h> 

int main(void) { 
  double neg_one=-1.0;
  double zero=0.0; 

// The natural log of a negative number is considered a domain error - EDOM
  printf("log(%e) = %e and errno(EDOM) = %d \n",neg_one,log(neg_one),errno); 

// The natural log of zero is considered a range error - ERANGE
  printf("log(%e) = %e and errno(ERANGE) = %d \n",zero,log(zero),errno); 
}

The output of errno.c will look like this:

log(-1.000000e+00) = nan and errno(EDOM) = 33

log(0.000000e+00) = -inf and errno(ERANGE) = 34

For the math functions in this section, a corresponding value for errno is listed when applicable.

Other Considerations

Some math functions are inlined automatically by the compiler. The functions actually inlined may vary and may depend on any vectorization or processor-specific compilation options used. You can disable automatic inline expansion of all functions by compiling your program with the -fno-builtin (Linux* and OS X*) option or the /Oi- (Windows*) option.

It is strongly recommended to use the default rounding mode (round-to-nearest-even) when calling math library transcendental functions and compiling with default optimization or higher. Faster implementations— in terms of latency and/or throughput— of these functions are validated under the default round-to-nearest-even mode. Using other rounding modes may make results generated by these faster implementations less accurate, or set unexpected floating-point status flags. This behavior may be avoided by using the -no-fast-transcendentals (Linux* and OS X*) option or /Qfast-transcendentals- (Windows*) option, which disables calls to the faster implementations of math functions, or by using the -fp-model strict (Linux* and OS X*) option or /fp: strict (Windows*) option. This option warns the compiler not to assume default settings for the floating-point environment.

A change of the default precision control or rounding mode may affect the results returned by some of the mathematical functions.