// check/numeric_consist.cpp
/* This test routine creates some numbers and check the result of several
* boolean tests on these numbers like is_integer() etc... */
#include
#include
/* Simple and maybe somewhat pointless consistency tests of assorted tests and
* conversions. */
static unsigned numeric_consist1(void)
{
unsigned result = 0;
numeric test_int1(42);
numeric test_int2(5);
numeric test_rat1 = test_int1; test_rat1 /= test_int2;
test_rat1 = -test_rat1; // -42/5
symbol a("a");
ex e1, e2;
if ( !test_int1.is_integer() ) {
clog << test_int1
<< " erroneously not recognized as integer" << endl;
++result;
}
if ( !test_int1.is_rational() ) {
clog << test_int1
<< " erroneously not recognized as rational" << endl;
++result;
}
if ( !test_rat1.is_rational() ) {
clog << test_rat1
<< " erroneously not recognized as rational" << endl;
++result;
}
if ( test_rat1.is_integer() ) {
clog << test_rat1
<< " erroneously recognized as integer" << endl;
++result;
}
int i = numeric(1984).to_int();
if ( i-1984 ) {
clog << "conversion of " << i
<< " from numeric to int failed" << endl;
++result;
}
e1 = test_int1;
if ( !e1.info(info_flags::posint) ) {
clog << "expression " << e1
<< " erroneously not recognized as positive integer" << endl;
++result;
}
e2 = test_int1 + a;
if ( ex_to_numeric(e2).is_integer() ) {
clog << "expression " << e2
<< " erroneously recognized as integer" << endl;
++result;
}
// The next two were two actual bugs in CLN till June, 12, 1999:
test_rat1 = numeric(3)/numeric(2);
test_rat1 += test_rat1;
if ( !test_rat1.is_integer() ) {
clog << "3/2 + 3/2 erroneously not integer 3 but instead "
<< test_rat1 << endl;
++result;
}
test_rat1 = numeric(3)/numeric(2);
numeric test_rat2 = test_rat1 + numeric(1); // 5/2
test_rat2 -= test_rat1; // 1
if ( !test_rat2.is_integer() ) {
clog << "5/2 - 3/2 erroneously not integer 1 but instead "
<< test_rat2 << endl;
++result;
}
// Check some numerator and denominator calculations:
for (int i=0; i<10; ++i) {
int re_q, im_q;
do { re_q = rand(); } while (re_q == 0);
do { im_q = rand(); } while (im_q == 0);
numeric r(rand()-RAND_MAX/2, re_q);
numeric i(rand()-RAND_MAX/2, im_q);
numeric z = r + I*i;
numeric p = numer(z);
numeric q = denom(z);
numeric res = p/q;
if (res != z) {
clog << z << " erroneously transformed into "
<< p << "/" << q << " by numer() and denom()" << endl;
++result;
}
}
return result;
}
/* We had some fun with a bug in CLN that caused it to loop forever when
* calculating expt(a,b) if b is a rational and a a nonnegative integer.
* Implementing a workaround sadly introduced another bug on May 28th 1999
* that was fixed on May 31st. The workaround turned out to be stupid and
* the bug was finally killed in CLN on September 2nd. */
static unsigned numeric_consist2(void)
{
unsigned result = 0;
ex zero = numeric(0);
ex two = numeric(2);
ex three = numeric(3);
// The hang in this code was the reason for the original workaround
if ( pow(two,two/three) == 42 ) {
clog << "pow(2,2/3) erroneously returned 42" << endl;
++result; // cannot happen
}
// Actually, this used to raise a FPE after introducing the workaround
if ( two*zero != zero ) {
clog << "2*0 erroneously returned " << two*zero << endl;
++result;
}
// And this returned a cl_F due to the implicit call of numeric::power()
ex six = two*three;
if ( !six.info(info_flags::integer) ) {
clog << "2*3 erroneously returned the non-integer " << six << endl;
++result;
}
// The fix in the workaround left a whole which was fixed hours later...
ex another_zero = pow(zero,numeric(1)/numeric(2));
if ( another_zero.compare(exZERO()) ) {
clog << "pow(0,1/2) erroneously returned" << another_zero << endl;
++result;
}
return result;
}
/* Assorted tests to ensure some crucial functions behave exactly as specified
* in the documentation. */
static unsigned numeric_consist3(void)
{
unsigned result = 0;
numeric calc_rem, calc_quo;
numeric a, b;
// check if irem(a, b) and irem(a, b, q) really behave like Maple's
// irem(a, b) and irem(a, b, 'q') as advertised in our documentation.
// These overloaded routines indeed need to be checked separately since
// internally they might be doing something completely different:
a = 23; b = 4; calc_rem = irem(a, b);
if ( calc_rem != 3 ) {
clog << "irem(" << a << "," << b << ") erroneously returned "
<< calc_rem << endl;
++result;
}
a = 23; b = -4; calc_rem = irem(a, b);
if ( calc_rem != 3 ) {
clog << "irem(" << a << "," << b << ") erroneously returned "
<< calc_rem << endl;
++result;
}
a = -23; b = 4; calc_rem = irem(a, b);
if ( calc_rem != -3 ) {
clog << "irem(" << a << "," << b << ") erroneously returned "
<< calc_rem << endl;
++result;
}
a = -23; b = -4; calc_rem = irem(a, b);
if ( calc_rem != -3 ) {
clog << "irem(" << a << "," << b << ") erroneously returned "
<< calc_rem << endl;
++result;
}
// and now the overloaded irem(a,b,q):
a = 23; b = 4; calc_rem = irem(a, b, calc_quo);
if ( calc_rem != 3 || calc_quo != 5 ) {
clog << "irem(" << a << "," << b << ",q) erroneously returned "
<< calc_rem << " with q=" << calc_quo << endl;
++result;
}
a = 23; b = -4; calc_rem = irem(a, b, calc_quo);
if ( calc_rem != 3 || calc_quo != -5 ) {
clog << "irem(" << a << "," << b << ",q) erroneously returned "
<< calc_rem << " with q=" << calc_quo << endl;
++result;
}
a = -23; b = 4; calc_rem = irem(a, b, calc_quo);
if ( calc_rem != -3 || calc_quo != -5 ) {
clog << "irem(" << a << "," << b << ",q) erroneously returned "
<< calc_rem << " with q=" << calc_quo << endl;
++result;
}
a = -23; b = -4; calc_rem = irem(a, b, calc_quo);
if ( calc_rem != -3 || calc_quo != 5 ) {
clog << "irem(" << a << "," << b << ",q) erroneously returned "
<< calc_rem << " with q=" << calc_quo << endl;
++result;
}
// check if iquo(a, b) and iquo(a, b, r) really behave like Maple's
// iquo(a, b) and iquo(a, b, 'r') as advertised in our documentation.
// These overloaded routines indeed need to be checked separately since
// internally they might be doing something completely different:
a = 23; b = 4; calc_quo = iquo(a, b);
if ( calc_quo != 5 ) {
clog << "iquo(" << a << "," << b << ") erroneously returned "
<< calc_quo << endl;
++result;
}
a = 23; b = -4; calc_quo = iquo(a, b);
if ( calc_quo != -5 ) {
clog << "iquo(" << a << "," << b << ") erroneously returned "
<< calc_quo << endl;
++result;
}
a = -23; b = 4; calc_quo = iquo(a, b);
if ( calc_quo != -5 ) {
clog << "iquo(" << a << "," << b << ") erroneously returned "
<< calc_quo << endl;
++result;
}
a = -23; b = -4; calc_quo = iquo(a, b);
if ( calc_quo != 5 ) {
clog << "iquo(" << a << "," << b << ") erroneously returned "
<< calc_quo << endl;
++result;
}
// and now the overloaded iquo(a,b,r):
a = 23; b = 4; calc_quo = iquo(a, b, calc_rem);
if ( calc_quo != 5 || calc_rem != 3 ) {
clog << "iquo(" << a << "," << b << ",r) erroneously returned "
<< calc_quo << " with r=" << calc_rem << endl;
++result;
}
a = 23; b = -4; calc_quo = iquo(a, b, calc_rem);
if ( calc_quo != -5 || calc_rem != 3 ) {
clog << "iquo(" << a << "," << b << ",r) erroneously returned "
<< calc_quo << " with r=" << calc_rem << endl;
++result;
}
a = -23; b = 4; calc_quo = iquo(a, b, calc_rem);
if ( calc_quo != -5 || calc_rem != -3 ) {
clog << "iquo(" << a << "," << b << ",r) erroneously returned "
<< calc_quo << " with r=" << calc_rem << endl;
++result;
}
a = -23; b = -4; calc_quo = iquo(a, b, calc_rem);
if ( calc_quo != 5 || calc_rem != -3 ) {
clog << "iquo(" << a << "," << b << ",r) erroneously returned "
<< calc_quo << " with r=" << calc_rem << endl;
++result;
}
return result;
}
/* Now we perform some less trivial checks about several functions which should
* return exact numbers if possible. */
static unsigned numeric_consist4(void)
{
unsigned result = 0;
bool passed;
// square roots of squares of integers:
passed = true;
for (int i=0; i<42; ++i) {
if ( !sqrt(numeric(i*i)).is_integer() ) {
passed = false;
}
}
if ( !passed ) {
clog << "One or more square roots of squares of integers did not return exact integers" << endl;
++result;
}
// square roots of squares of rationals:
passed = true;
for (int num=0; num<41; ++num) {
for (int den=1; den<42; ++den) {
if ( !sqrt(numeric(num*num)/numeric(den*den)).is_rational() ) {
passed = false;
}
}
}
if ( !passed ) {
clog << "One or more square roots of squares of rationals did not return exact integers" << endl;
++result;
}
return result;
}
unsigned numeric_consist(void)
{
unsigned result = 0;
cout << "checking consistency of numeric types..." << flush;
clog << "---------consistency of numeric types:" << endl;
result += numeric_consist1();
result += numeric_consist2();
result += numeric_consist3();
result += numeric_consist4();
if ( !result ) {
cout << " passed ";
clog << "(no output)" << endl;
} else {
cout << " failed ";
}
return result;
}