1. A printer for printing onto a print medium by moving a carriage having a print head alternately in a main scanning direction and a sub scanning direction, comprising: image processing means for generating bit image data by executing predetermined image processing on digital image data inputted from outside; first image data storing means for storing said bit image data; data volume determining means for determining whether or not the volume of said bit image data corresponding to images printed during one main scanning of said carriage exceeds the maximum memory capacity of said first image data storing means; and storage control means for storing said bit image data in said first image data storage means when said data volume determining means determine that the volume of said bit image data corresponding to images printed during one main scanning of said carriage does not exceed the maximum memory capacity of said first image data storing means, and for providing a part of said digital image data necessary for (printing) to said image processing means without using said first image data storage means when said data volume determining means determine that the volume of said bit image data corresponding to images printed during one main scanning of said carriage exceeds the maximum memory capacity of said first image data storing means.