* tests on these numbers like is_integer() etc... */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
#include "exams.h"
+#include <sstream>
+
/* Simple and maybe somewhat pointless consistency tests of assorted tests and
* conversions. */
static unsigned exam_numeric1(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
- numeric test_crat = test_rat1+I*test_int2; // 5*I-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;
- }
-
- if (!test_crat.is_crational()) {
- clog << test_crat
- << " erroneously not recognized as complex rational" << 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;
- }
-
- return result;
+ 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
+ numeric test_crat = test_rat1+I*test_int2; // 5*I-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;
+ }
+
+ if (!test_crat.is_crational()) {
+ clog << test_crat
+ << " erroneously not recognized as complex rational" << 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 (e2.info(info_flags::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;
+ }
+
+ return result;
}
/* We had some fun with a bug in CLN that caused it to loop forever when
* the original bug in CLN was finally killed on September 2nd. */
static unsigned exam_numeric2(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.is_zero()) {
- clog << "pow(0,1/2) erroneously returned" << another_zero << endl;
- ++result;
- }
-
- return result;
+ 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.is_zero()) {
+ 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 exam_numeric3(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;
+ 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 exam_numeric4(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 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;
+}
+
+/* This test examines that simplifications of the form 5^(3/2) -> 5*5^(1/2)
+ * are carried out properly. */
+static unsigned exam_numeric5(void)
+{
+ unsigned result = 0;
+
+ // A variation of one of Ramanujan's wonderful identities must be
+ // verifiable with very primitive means:
+ ex e1 = pow(1 + pow(3,numeric(1,5)) - pow(3,numeric(2,5)),3);
+ ex e2 = expand(e1 - 10 + 5*pow(3,numeric(3,5)));
+ if (!e2.is_zero()) {
+ clog << "expand((1+3^(1/5)-3^(2/5))^3-10+5*3^(3/5)) returned "
+ << e2 << " instead of 0." << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+/* This test checks whether the numeric output/parsing routines are
+ consistent. */
+static unsigned exam_numeric6(void)
+{
+ unsigned result = 0;
+
+ symbol sym("sym");
+ vector<ex> test_numbers;
+ test_numbers.push_back(numeric(0)); // zero
+ test_numbers.push_back(numeric(1)); // one
+ test_numbers.push_back(numeric(-1)); // minus one
+ test_numbers.push_back(numeric(42)); // positive integer
+ test_numbers.push_back(numeric(-42)); // negative integer
+ test_numbers.push_back(numeric(14,3)); // positive rational
+ test_numbers.push_back(numeric(-14,3)); // negative rational
+ test_numbers.push_back(numeric(3.141)); // positive decimal
+ test_numbers.push_back(numeric(-3.141)); // negative decimal
+ test_numbers.push_back(numeric(0.1974)); // positive decimal, leading zero
+ test_numbers.push_back(numeric(-0.1974)); // negative decimal, leading zero
+ test_numbers.push_back(sym); // symbol
+
+ for (vector<ex>::const_iterator br=test_numbers.begin(); br<test_numbers.end(); ++br) {
+ for (vector<ex>::const_iterator bi=test_numbers.begin(); bi<test_numbers.end(); ++bi) {
+
+ for (vector<ex>::const_iterator er=test_numbers.begin(); er<test_numbers.end(); ++er) {
+ for (vector<ex>::const_iterator ei=test_numbers.begin(); ei<test_numbers.end(); ++ei) {
+
+ // Construct expression, don't test invalid ones
+ ex base = (*br) + (*bi)*I, exponent = (*er) + (*ei)*I, x;
+ try {
+ x = pow(base, exponent);
+ } catch (...) {
+ continue;
+ }
+
+ // Print to string
+ std::ostringstream s;
+ s << x;
+
+ // Read back expression from string
+ string x_as_string = s.str();
+ ex x_again(x_as_string, lst(sym));
+
+ // They should be equal
+ if (!x_again.is_equal(x)) {
+ clog << x << " was read back as " << x_again << endl;
+ ++result;
+ }
+ }
+ }
+ }
+ }
+
+ return result;
}
unsigned exam_numeric(void)
{
- unsigned result = 0;
-
- cout << "examining consistency of numeric types" << flush;
- clog << "----------consistency of numeric types:" << endl;
-
- result += exam_numeric1(); cout << '.' << flush;
- result += exam_numeric2(); cout << '.' << flush;
- result += exam_numeric3(); cout << '.' << flush;
- result += exam_numeric4(); cout << '.' << flush;
-
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
-
- return result;
+ unsigned result = 0;
+
+ cout << "examining consistency of numeric types" << flush;
+ clog << "----------consistency of numeric types:" << endl;
+
+ result += exam_numeric1(); cout << '.' << flush;
+ result += exam_numeric2(); cout << '.' << flush;
+ result += exam_numeric3(); cout << '.' << flush;
+ result += exam_numeric4(); cout << '.' << flush;
+ result += exam_numeric5(); cout << '.' << flush;
+ result += exam_numeric6(); cout << '.' << flush;
+
+ if (!result) {
+ cout << " passed " << endl;
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed " << endl;
+ }
+
+ return result;
}
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