HLASM: V1R6 Language Ref

Binary floating-point constants—EB, DB, LBBinary floating-point numbers may be represented in any of three formats: short,long or extended. The short format is 4 bytes with a sign of one bit, an exponent of8 bits and a fraction of 23 bits. The long format is 8 bytes with a sign of one bit, anexponent of 11 bits and a fraction of 52 bits. The extended format is 16 bytes witha sign of one bit, an exponent of 15 bits and a fraction of 112 bits.There are five classes of binary floating-point data, including numeric and relatednonnumeric entities. Each data item consists of a sign, an exponent and asignificand. The exponent is biased such that all exponents are nonnegativeunsigned numbers, and the minimum biased exponent is zero. The significandconsists of an explicit fraction and an implicit unit bit to the left of the binarypoint. The sign bit is zero for plus and one for minus values.All finite nonzero numbers within the range permitted by a given format arenormalized and have a unique representation. There are no unnormalizednumbers, which might allow multiple representations for the same value, and thereare no unnormalized arithmetic operations. Tiny numbers of a magnitude belowthe minimum normalized number in a given format are represented as denormalizednumbers, because they imply a leading zero bit, but those values are alsorepresented uniquely.The classes are:DC instruction—Binary floating-point constants1. Zeros have a biased exponent of zero, a zero fraction and a sign. The impliedunit bit is zero.2. Denormalized numbers have a biased exponent of zero and a nonzero fraction.The implied unit bit is zero.The smallest denormalized numbers have approximate magnitudes 1.4 10**-45(short format), 4.94 10**-324 (long format) and 6.5 10**-4966 (extended format).3. Normalized numbers have a biased exponent greater than zero but less than allones. The implied unit bit is one and the fraction may have any value. Thelargest normalized numbers have approximate magnitudes 3.4 10**38 (shortformat), 1.8 10**308 (long format), and 1.2 10**4932 (extended format). Thesmallest normalized numbers have approximate magnitudes 1.18 10**-38 (shortformat), 2.23 10**-308 (long format), and 3.4 10**-4392 (extended format).4. An infinity is represented by a biased exponent of all ones and a zero fraction.5. A NaN (Not-a-Number) entity is represented by a biased exponent of all onesand a nonzero fraction. NaNs are produced in place of a numeric result after aninvalid operation when there is no interruption. NaNs may also be used by theprogram to flag special operands, such as the contents of an uninitializedstorage area. There are two types of NaNs, signaling and quiet. A signalingNaN (SNaN) is distinguished from the corresponding quiet NaN (QNaN) bythe leftmost fraction bit: zero for the SNaN and one for QNaN. A special QNaNis supplied as the default result for an invalid-operation condition; it has a plussign and a leftmost fraction bit of one, with the remaining fraction bits beingset to zeros. Normally, QNaNs are just propagated during computations, sothat they remain visible at the end. An SNaN operand causes an invalidoperation exception.Chapter 5. Assembler instruction statements 165