Next | Continued Fraction Arithmetic | 38 |

Instead of evaluating one variable,

*x*, on the range (0, )We evaluate two,

*x*and*y*So we're asking what values

*z*assumes on the entire quarter-planeFortunately, it's enough to know its values only at the four corners [0, 0], [ , 0], [0, ], [ , ]

These values are merely

*a*/*e*,*b*/*f*,*c*/*g*, and*d*/*h*If all four agree on the next term,

*z*can output itOtherwise, input from

*x*or*y*Choose from

*x*if |*b*/*f*-*a*/*e*| > |*c*/*g*-*a*/*e*|

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