Double concerto for violin, cello, and piano, Beethoven's Triple Concerto for Violin, Cello, Piano and Orchestra being perhaps the most notable, but there have been many; see the list of triple concertos for violin, cello, and piano. A notable quadruple concerto is Olivier Messiaen's incomplete "Concert à quatre". Double concerto A double concerto (Italian: "Doppio concerto"; German: "Doppelkonzert") refers to two distinct variations on the concerto. Most often, it refers to a concerto featuring two performers, as opposed to the usual single performer, in the solo role. These two performers' instruments may be of the same type, as in Bach's, Concerto for
Quadruple-precision floating-point format implement nearly quadruple precision using "pairs" of double-precision values is sometimes called double-double arithmetic. Using pairs of IEEE double-precision values with 53-bit significands, double-double arithmetic can represent operations with at least a 2×53=106-bit significand (actually 107 bits except for some of the largest values, due to the limited exponent range), only slightly less precise than the 113-bit significand of IEEE binary128 quadruple precision. The range of a double-double remains essentially the same as the double-precision format because the exponent has still 11 bits, significantly lower than the 15-bit exponent of IEEE quadruple precision (a range of for double-double versus for