Infix operators

NOTE: similar to operations on BigInt -- see BigIntOps

1. normal arithmetic (potentially inefficient because of temporaries)
   • + the sum
   • - the difference
   • * the product
   • / quotient
   • = assignment

2. arithmetic and assignment
   • +=, -=, *=, /= -- definitions as expected; LHS must be of type BigRat

3. arithmetic ordering
   • ==, !=
   • <, <=, >, >= -- comparison (using the normal arithmetic ordering) -- see also the cmp function below.

4. increment/decrement
   • ++, -- (prefix, e.g. ++a) use these if you can
   • ++, -- (postfix, e.g. a++) avoid these if you can, as they create temporaries

More functions

1. query functions (all take 1 argument)
   • IsZero(q) -- true iff q is zero
   • IsOne(q) -- true iff q is 1
   • IsMinusOne(q) -- true iff q is -1
   • IsOneNum(q) -- true iff num(q) is 1
   • IsOneDen(q) -- true iff den(q) is 1
   • IsPowerOf2(q) -- true iff q is a power of 2
   • sign(q) -- gives -1 (machine integer) to mean q is negative, 0 (machine integer) to mean q is zero, +1 (machine integer) to mean q is positive.

2. Exponentiation
   • power(a, b) -- returns a to the power b (result is always a BigRat)

3. The cmp function (three way comparison)
   • cmp(a,b) -- returns an int which is < 0 if a < b, or == 0 if a == b, or > 0 if a > b.
   • CmpAbs(a,b) -- equivalent to cmp(abs(a),abs(b))

4. Other functions
   • abs(q) -- gives the absolute value of q
   • floor(q) -- returns a BigInt for the greatest integer <= q
   • ceil(q) -- returns a BigInt for the least integer >= q
   • round(q) -- returns a BigInt which is the nearest to q (halves round the same way as in RoundDiv, see BigIntOps)
   • num(q) -- returns a BigInt which is the numerator of q
   • den(q) -- returns a positive BigInt which is the denominator of q
   • CommonDenom(v) -- returns least (positive) common denominator for a vector of BigRat
   • log(q) -- returns a double whose value is (approx) the natural logarithm of q; error if `` q <= 0``.
   • LogAbs(q) -- equiv to log(abs(q))
   • FloorLog2(q) -- same as ``FloorLogBase(q,2)
   • FloorLog10(q) -- same as ``FloorLogBase(q,10)
   • FloorLogBase(q,base) -- returns largest integer k such that power(base,k) <= abs(q); error if base < 2
   • mantissa(q) -- returns a double between 0.5 and 1 (excluded)
   • exponent(q) --

Conversion functions

Only for BigInt

• mantissa(N) -- N represented as a floating-point number. If N is zero, produces 0.0. If N>0, produces a value between 0.5 and 0.999...; otherwise (when N<0) a value between -0.5 and -0.999... The bits of the floating point result are the topmost bits of the binary representation of N.
• exponent(N) -- result is a long whose value is the least integer e such that 2^e > abs(n). If N is zero, result is zero.

Miscellany

Only for BigInt

• SizeInBase(N, b) -- (returns long) the number of digits N has when written in base b. Very fast! WARNING the result may sometimes to be too large by 1; use 1+FloorLogBase(N) to get the exact result.