HLASM Language Reference

DC Instruction—Binary Floating-Point Constants
FLOAT DC DE+4'+46,–3.729,+473'
Binary Floating-Point Constants—EB, DB, LB
Binary 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 of
8 bits and a fraction of 23 bits. The long format is 8 bytes with a sign of one bit, an
exponent of 11 bits and a fraction of 52 bits. The extended format is 16 bytes with
a 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 related
nonnumeric entities. Each data item consists of a sign, an exponent and a
significand. The exponent is biased such that all exponents are nonnegative
unsigned numbers, and the minimum biased exponent is zero. The significand
consists of an explicit fraction and an implicit unit bit to the left of the binary point.
The sign bit is zero for plus and one for minus values.
All finite nonzero numbers within the range permitted by a given format are
normalized and have a unique representation. There are no unnormalized
numbers, which might allow multiple representations for the same value, and there
are no unnormalized arithmetic operations. Tiny numbers of a magnitude below the
minimum normalized number in a given format are represented as denormalized
numbers, because they imply a leading zero bit, but those values are also
represented uniquely.
The classes are:
1. Zeros have a biased exponent of zero, a zero fraction and a sign. The implied
unit 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
| all ones. The implied unit bit is one and the fraction may have any value. The
| largest normalized numbers have approximate magnitudes 3.4 10**38 (short
| format), 1.8 10**308 (long format), and 1.2 10**4932 (extended format). The
| smallest normalized numbers have approximate magnitudes 1.18 10**-38 (short
| format), 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 ones
and a nonzero fraction. NaNs are produced in place of a numeric result after
an invalid operation when there is no interruption. NaNs may also be used by
the program to flag special operands, such as the contents of an uninitialized
storage area. There are two types of NaNs, signaling and quiet. A signaling
NaN (SNaN) is distinguished from the corresponding quiet NaN (QNaN) by the
leftmost fraction bit: zero for the SNaN and one for QNaN. A special QNaN is
supplied as the default result for an invalid-operation condition; it has a plus
sign and a leftmost fraction bit of one, with the remaining fraction bits being set
to zeros. Normally, QNaNs are just propagated during computations, so that
they remain visible at the end. An SNaN operand causes an invalid operation
exception.
Chapter 5. Assembler Instruction Statements 167