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NextTest("Test arithmetic");
NextTest("Basic calculations");
Verify(3 + 2 , 5);
Verify(3-7, -4);
Verify(1 = 2 , 0 = -1);
Verify(5 ^ 2 , 25);
Verify(IsZero(0.000),True);
Verify(2/5,Hold(2/5));
Verify(IsZero(N(2/5)-0.4));
Verify(IsRational(2),True);
Verify(IsRational(2/5),True);
Verify(IsRational(-2/5),True);
Verify(IsRational(2.0/5),False);
Verify(IsRational(Pi/2),False);
Verify(Numerator(2/5),2);
Verify(Denominator(2/5),5);
VerifyArithmetic(10,5,8);
VerifyArithmetic(10000000000,5,8);
VerifyArithmetic(10,50,80);
VerifyArithmetic(10000,50,88);
Verify(4!,24);
Verify(BinomialCoefficient(2,1),2);
NextTest("Testing math stuff");
Verify(1*a,a);
Verify(a*1,a);
Verify(0*a,0);
Verify(a*0,0);
Verify(aa-aa,0);
Verify(2+3,5);
Verify(2*3,6);
Verify(2+3*4,14);
Verify(3*4+2,14);
Verify(3*(4+2),18);
Verify((4+2)*3,18);
Verify(15/5,3);
Verify(-2+3,1);
Verify(-2.01+3.01,1.);
Verify(0+a,a);
Verify(a+0,a);
Verify(aa-aa,0);
Testing("IntegerOperations");
Verify(1<<10,1024);
Verify(1024>>10,1);
Verify(Modulo(10,3),1);
Verify(Quotient(10,3),3);
Verify(GcdN(55,10),5);
Verify(Modulo(2,Infinity),2);
Verify(Modulo({0,1,2,3,4,5,6},2),{0,1,0,1,0,1,0});
Verify(Modulo({0,1,2,3,4,5,6},{2,2,2,2,2,2,2}),{0,1,0,1,0,1,0});
Testing("PowerN");
// was broken in the gmp version
Verify(PowerN(19, 0), 1);
Verify(PowerN(1, -1), 1);
Verify(PowerN(1, -2), 1);
Verify(IsZero(PowerN(10, -2)- 0.01));
Verify(PowerN(2, 3), 8);
NumericEqual(PowerN(2, -3), 0.125,BuiltinPrecisionGet());
Testing("Rounding");
Verify(Floor(1.2),1);
Verify(Floor(-1.2),-2);
Verify(Ceil(1.2),2);
Verify(Ceil(-1.2),-1);
Verify(Round(1.49),1);
Verify(Round(1.51),2);
Verify(Round(-1.49),-1);
Verify(Round(-1.51),-2);
Testing("Bases");
Verify(ToBase(16,255),"ff");
Verify(FromBase(2,"100"),4);
// conversion between decimal and binary digits
Verify(BitsToDigits(2000, 10), 602);
Verify(DigitsToBits(602, 10), 2000);
LocalSymbols(f,ft)
[
f(x,y):=(Quotient(x,y)*y+Rem(x,y)-x);
ft(x,y):=
[
Verify(f(x,y),0);
Verify(f(-x,y),0);
Verify(f(x,-y),0);
Verify(f(-x,-y),0);
];
ft(10,4);
ft(2.5,1.2);
];
Testing("Factorization");
Verify(
Eval(Factors(447738843))
, {{3,1},{17,1},{2729,1},{3217,1}}
);
//Exponential notation is now supported in the native arithmetic library too...
Verify(2e3+1,2001.);
Verify(2.0e3+1,2001.);
Verify(2.00e3+1,2001.);
Verify(2.000e3+1,2001.);
Verify(2.0000e3+1,2001.);
Verify(1+2e3,2001.);
Verify(1+2.0e3,2001.);
Verify(1+2.00e3,2001.);
Verify(1+2.000e3,2001.);
Verify(1+2.0000e3,2001.);
NumericEqual(N(Sqrt(1e4))-100,0,BuiltinPrecisionGet());
NumericEqual(N(Sqrt(1.0e4))-100,0,BuiltinPrecisionGet());
Verify(2.0000e3-1,1999.);
[
Local(p);
p:=BuiltinPrecisionGet();
BuiltinPrecisionSet(12);//TODO this will fail if you drop precision to below 12, for some reason.
NumericEqual(RoundToPrecision(10e3*1.2e-3,BuiltinPrecisionGet()),12.,BuiltinPrecisionGet());
BuiltinPrecisionSet(p);
];
Verify((10e3*1.2e-4)-1.2,0);
Verify(IsZero(N(Sin(0.1e1)-Sin(1),30)),True);
[
/* In Dutch they have a saying "dit verdient geen schoonheidsprijs" ;-) We need to sort this out.
* But a passable result, for now.
*/
Local(diff);
diff := N(Sin(10e-1)-Sin(1),30);
//BuiltinPrecisionSet(20);
//Echo("diff = ",diff);
//Echo("diff > -0.00001 = ",diff > -0.00001);
//Echo("diff < 0.00001 = ",diff < 0.00001);
Verify(diff > -0.00001 And diff < 0.00001,True);
];
/* Jonathan reported a problem with Simplify(-Sqrt(8)/2), which returned some
* complex expression containing greatest common divisors of square roots.
* This was fixed by adding some rules dealing with taking the gcd of two objects
* where at least one is a square root.
*/
Verify(-Sqrt(8)/2,-Sqrt(2));
Verify(Sqrt(8)/2,Sqrt(2));
Verify(Gcd(Sqrt(2),Sqrt(2)),Sqrt(2));
Verify(Gcd(-Sqrt(2),-Sqrt(2)),Sqrt(2));
Verify(Gcd(Sqrt(2),-Sqrt(2)),Sqrt(2));
Verify(Gcd(-Sqrt(2),Sqrt(2)),Sqrt(2));
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