All microcomputers use operating languages that support such elementary functions as square root, exponential, log, sin, and cos. With the coming of coprocessor chips such as the INTEL 80x87 and the definition of the IEEE 734 arithmetic standard, it has become important to develop computational algorithms that are both fast and accurate.

Traditional methods using optimized or Remez polynomials go some way toward satisfying this need, but current work is aimed both at standardization and at the establishment of precise, and verifiable, error bounds. This paper considers, in detail, procedures for the functions log and log1p (that is, log(1+x)). Tang gives precise specifications and analyzes errors. Tables (in hex) should make the hardware or software implementation simple. This paper is a useful addition to the literature.