1: #include <petscsys.h>

  3: /*@C
  4:   PetscIsCloseAtTol - Returns whether the two `PetscReal` numbers
  5:   are close at a given relative and absolute tolerances <https://www.python.org/dev/peps/pep-0485/>.

  7:   Input Parameters:
  8: + a    - first floating point number
  9: . b    - second floating point number
 10: . rtol - relative tolerance
 11: - atol - absolute tolerances

 13:   Level: beginner

 15: .seealso: `PetscIsCloseAtTolScalar()`, `PetscEqualReal()`, `PetscEqualScalar()`
 16: @*/
 17: PetscBool PetscIsCloseAtTol(PetscReal a, PetscReal b, PetscReal rtol, PetscReal atol)
 18: {
 19:   PetscReal diff;
 20:   /* NaN is not considered close to any other value, including NaN */
 21:   if (PetscIsNanReal(a) || PetscIsNanReal(b)) return PETSC_FALSE;
 22:   /* Fast path for exact equality or two infinities of same sign */
 23:   if (a == b) return PETSC_TRUE;
 24:   /* Handle two infinities of opposite sign */
 25:   if (PetscIsInfReal(a) || PetscIsInfReal(b)) return PETSC_FALSE;
 26:   /* Cannot error if tolerances are negative */
 27:   rtol = PetscAbsReal(rtol);
 28:   atol = PetscAbsReal(atol);
 29:   /* The regular check for difference within tolerances */
 30:   diff = PetscAbsReal(b - a);
 31:   return ((diff <= PetscAbsReal(rtol * b)) || (diff <= PetscAbsReal(rtol * a)) || (diff <= atol)) ? PETSC_TRUE : PETSC_FALSE;
 32: }