Fortran 90 Handbook

13wherei is the integer values is the sign (+1 or –1)r is the radix (integer greater than 1)q is the number of digits (integer greater than 0)d k is the k th digit and is an integer 0 ≤ d k < rThe integer number system model may model the implementation’s integerdata type exactly, but it need not. It does, however, provide accurateinformation about the implementation, such as its largest integer value.13.2.3 The Real Number System ModelThe real number system is modeled bywherepx = sb e f k b – k∑k = 1x is the real values is the sign (+1 or –1)b is the base (real radix) and is an integer greater than 1e is an integer between some minimum and maximum valuep is the number of mantissa digits and is an integer greater than 1f k is the kth digit and is an integer 0 ≤ f k < b,but f 1 may be zero only if all the f k are zeroThe real number system model may model the implementation’s real data typeexactly, but it need not. One common implementation is the IEEE floating pointstandard, which has single precision model numbers:b = 2p = 24– 126 ≤ e ≤ 127This IEEE standard does not represent f 1 , which is presumed to be 1. Thus, themantissa, including its sign, can be represented in 24 bits. The exponent,including sign, takes 8 bits, for a total of 32 bits in the single precisionrepresentation. What normally would be an exponent value of –127 is notIntrinsic Procedures 597Copyright © 1992 J. Adams, W. Brainerd, J. Martin, B. Smith, and J. Wagener