4.5 Comparisons

Each of the classes cl_N, cl_R, cl_RA, cl_I, cl_F, cl_SF, cl_FF, cl_DF, cl_LF defines the following operations:

bool operator == (const type&, const type&)

bool operator != (const type&, const type&)

Comparison, as in C and C++.

uint32 equal_hashcode (const type&)

Returns a 32-bit hash code that is the same for any two numbers which are the same according to ==. This hash code depends on the number’s value, not its type or precision.

bool zerop (const type& x)

Compare against zero: x == 0

Each of the classes cl_R, cl_RA, cl_I, cl_F, cl_SF, cl_FF, cl_DF, cl_LF defines the following operations:

cl_signean compare (const type& x, const type& y)

Compares x and y. Returns +1 if x>y, -1 if x<y, 0 if x=y.

bool operator <= (const type&, const type&)

bool operator < (const type&, const type&)

bool operator >= (const type&, const type&)

bool operator > (const type&, const type&)

Comparison, as in C and C++.

bool minusp (const type& x)

Compare against zero: x < 0

bool plusp (const type& x)

Compare against zero: x > 0

type max (const type& x, const type& y)

Return the maximum of x and y.

type min (const type& x, const type& y)

Return the minimum of x and y.

When a floating point number and a rational number are compared, the float is first converted to a rational number using the function rational. Since a floating point number actually represents an interval of real numbers, the result might be surprising. For example, (cl_F)(cl_R)"1/3" == (cl_R)"1/3" returns false because there is no floating point number whose value is exactly 1/3.

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