8. Convergence Comparison
nsqrt() is Newton's method, and gsqrt() is Goldschmidt algorithm.Digits which are correct are shown in blue.
initialized using: x/2 minmax error quadratic nsqrt(2): nsqrt(2): nsqrt: y = 1.000000000000000000 nsqrt: y = 1.424665705758743739 nsqrt: y = 1.500000000000000000 nsqrt: y = 1.414251903754133677 nsqrt: y = 1.416666666666666741 nsqrt: y = 1.414213562892826292 nsqrt: y = 1.414215686274509887 nsqrt: y = 1.414213562373095145 nsqrt: y = 1.414213562374689870 nsqrt: y = 1.414213562373095145 nsqrt: y = 1.414213562373095145 nsqrt: y = 1.414213562373095145 sqrt = 1.414213562373095145 sqrt = 1.414213562373095145 diff = 0.000000000000000000 diff = 0.000000000000000000 gsqrt(2): gsqrt(2): gsqrt: y = 1.000000000000000000 gsqrt: y = 1.389286512067859469 gsqrt: y = 1.250000000000000000 gsqrt: y = 1.413558385017565699 gsqrt: y = 1.386718750000000000 gsqrt: y = 1.414213107147212156 gsqrt: y = 1.413416936993598938 gsqrt: y = 1.414213562372875321 gsqrt: y = 1.414212889391814221 gsqrt: y = 1.414213562373095145 gsqrt: y = 1.414213562372614641 gsqrt: y = 1.414213562373095145 sqrt = 1.414213562373095145 sqrt = 1.414213562373095145 diff = 0.000000000000480505 diff = 0.000000000000000000 nsqrt(10): nsqrt(10): nsqrt: y = 5.000000000000000000 nsqrt: y = 3.153223854021278694 nsqrt: y = 3.500000000000000000 nsqrt: y = 3.162290658199845783 nsqrt: y = 3.178571428571428381 nsqrt: y = 3.162277660195092377 nsqrt: y = 3.162319422150882797 nsqrt: y = 3.162277660168379523 nsqrt: y = 3.162277660444136274 nsqrt: y = 3.162277660168379523 nsqrt: y = 3.162277660168379523 nsqrt: y = 3.162277660168379523 sqrt = 3.162277660168379523 sqrt = 3.162277660168379523 diff = 0.000000000000000000 diff = 0.000000000000000000 gsqrt(10): gsqrt(10): gsqrt: y = 5.000000000000000000 gsqrt: y = 3.199176626212654195 gsqrt: y = 1.250000000000000000 gsqrt: y = 3.161629316070945883 gsqrt: y = 1.777343750000000000 gsqrt: y = 3.162277460792461525 gsqrt: y = 2.385288551449775696 gsqrt: y = 3.162277660168360427 gsqrt: y = 2.899365764300943393 gsqrt: y = 3.162277660168379523 gsqrt: y = 3.130398559817640258 gsqrt: y = 3.162277660168379523 sqrt = 3.162277660168379523 sqrt = 3.162277660168379523 diff = 0.031879100350739265 diff = 0.000000000000000000