Hexadecimal floating-point constants—E, EH, D, DH, L, LH, LQ

Floating-point constants let you introduce data that is in the form suitable for the operations of the floating-point feature instructions. These constants have the following advantages over fixed-point constants:

You do not have to consider the fractional portion of a value you specify, nor worry about the position of the decimal point when algebraic operations are to be done.
You can specify both much larger and much smaller values.
You retain greater processing precision; that is, your values are carried in more significant figures.

The nominal value can be a signed (see 1 in Table 1) integer, fraction, or mixed number (see 2 Table 1) followed by a signed exponent (see 3 in Table 1). If a sign is not specified for either the number or exponent, a plus sign is assumed.

If you specify the 'H' type extension you can also specify a rounding mode that is used when the nominal value is converted from decimal to its hexadecimal form. The syntax for nominal values (including the binary floating-point constants) is shown in Figure 1. The valid rounding mode values are:

Figure 1. Rounding mode values

1: Round by adding one in the first lost bit position
4: Unbiased round to nearest, with tie-breaking rule
5: Round towards zero (that is, truncate)
6: Round up towards the maximum positive value
7: Round down towards the minimum negative value

See 4 in Table 1.

The exponent must lie within the permissible range. If an exponent modifier is also specified, the algebraic sum of the exponent and the exponent modifier must lie within the permissible range.

Table 1. Hexadecimal floating-point constants
Subfield	Value	Example
1. Duplication factor	Allowed
2. Type	E, D, and L
3. Type Extension	Omitted or H or Q
4. Program type	Allowed
5. Modifiers
Length:	E-type: 1 to 8 (byte length) .1 to .64 (bit length) EH-type: .12 to .64 (bit length) D-type: 1 to 8 (byte length) .1 to .64 (bit length) DH-type: .12 to .64 (bit length) L-type: 1 to 16 (byte length) .1 to .128 (bit length) LH-type: .12 to .128 (bit length) LQ-type: .12 to .128 (bit length)
Implicit length: (Length modifier not present)	E-type: 4 bytes D-type: 8 bytes L-type: 16 bytes
Alignment: (Length modifier not present)	E-type: Fullword D-type: Doubleword L-type: Doubleword LQ-type: Quadword
Scale:	E-type: 0 to 5 D-type: 0 to 13 L-type: 0 to 27
Exponent:	-85 to +75
6. Nominal value
Represented by:	Decimal digits	E-type: `DC E'+525'` 1 `DC E'5.25'` 2 D-type: `DC D'-525'` 1 `DC D'+.001'` 2 L-type: `DC L'525'` `DC L'3.414'` 2
Enclosed by:	Apostrophes
Exponent allowed:	Yes	E-type: `DC E'1E+60'` 3 D-type: `DC D'-2.5E10'` 3 L-type: `DC L'3.712E-3'` 3
Rounding mode allowed if type extension specified:	Yes (see Figure 1 for values)	E-type: `DC EH'1E+60R1'` 4 D-type: `DC DH'-2.5E10R4'` 4 L-type: `DC LH'3.712E-3R5'` 4
Number of values per operand:	Multiple
Padding:	Correct fraction is extended to the right and rounded
Truncation of assembled value:	Only if rounding mode 5; rounded otherwise.

The format of the constant is shown in Figure 2.

The value of the constant is represented by two parts:

An exponent portion (see 1 in Figure 2), followed by
A fractional portion (see 2 in Figure 2)

A sign bit (see 3 in Figure 2) indicates whether a positive or negative number has been specified. The number specified must first be converted into a hexadecimal fraction before it can be assembled into the correct internal format. The quantity expressed is the product of the fraction (see 4 in Figure 2) and the number 16 raised to a power (see 5 in Figure 2). Figure 2 shows the external format of the three types of floating-point constants.

Here is the range of values that can be assembled into hexadecimal floating-point constants:

Type of Constant	Range of Magnitude (M) of Values (Positive and Negative)
E	16^-65 ≤ M ≤ (1-16^-6) x 16⁶³
D	16^-65 ≤ M ≤ (1-16^-14) x 16⁶³
L	16^-65 ≤ M ≤ (1-16^-28) x 16⁶³
E, D, L	5.4 x 10^-79 ≤ M ≤ 7.2 x 10⁷⁵ (approximate)

If the value specified for a particular constant does not lie within these ranges, the assembled value then depends on these factors:

With type extension H, overflows assemble to the largest magnitude for the specified type, underflows denormalize the value or return zero, depending on the value and rounding mode.
Without type extension H, certain combinations of exponents (modifier and nominal value) might produce invalid results (message ASMA071E). If the exponent is too large it is ignored, and the nominal value of the constant preceding the exponent is assembled instead.

Figure 2. Hexadecimal floating-point external formats

Type │ Called     │ Format
─────┼────────────┼────────────────────────────────────────────────────────────────
E    │ Short      │         1  7 bit Characteristic      2  24 bit Fraction
EH   │ Floating-  │  3    + ┌──────────┴──────────┐ ┌────────────┴────────────┐
     │ Point      │  │  ┌───┬─────────────────────┐ ┌───────────/ /───────────┐
     │ Number     │  └> └───┴─────────────────────┘ └───────────/ /───────────┘
     │            │       -
     │            │ Bits 0   1                 7     8                       31
     │            │
     │            │
     │            │
D    │ Long       │          7 bit Characteristic         56 bit Fraction
DH   │ Floating-  │       + ┌──────────┴──────────┐ ┌────────────┴────────────┐
     │ Point      │     ┌───┬─────────────────────┐ ┌───────────/ /───────────┐
     │ Number     │     └───┴─────────────────────┘ └───────────/ /───────────┘
     │            │       -
     │            │ Bits 0   1                 7     8                       63
     │            │
     │            │
     │            │
     │            │                                     High-order 56 bits
L    │ Extended   │          7 bit Characteristic       of 112 bit Fraction
LH   │ Floating-  │       + ┌──────────┴──────────┐ ┌────────────┴────────────┐
LQ   │ Point      │     ┌───┬─────────────────────┐ ┌───────────/ /───────────┐
     │ Number     │     └───┴─────────────────────┘ └───────────/ /───────────┘───┐
     │            │       -                                                       │
     │            │ Bits 0   1                 7     8                       63   │
     │            │                                                               │
     │            │                                 ┌─────────────────────────────┘
     │            │                                 │
     │            │                                 │   Low-order 56 bits
     │            │          7 bit Characteristic   V   of 112 bit Fraction
     │            │       + ┌──────────┴──────────┐ ┌────────────┴────────────┐
     │            │     ┌───┬─────────────────────┐ ┌───────────/ /───────────┐
     │            │     └───┴─────────────────────┘ └───────────/ /───────────┘
     │            │       -           ∧
     │            │ Bits 0   1        │        7     8                       63
     │            │                   │
     │            │            Set in second half
     │            │            of L-type constant


Characteristic    │ Hexadecimal Fraction
──────────────────┼──────────────────────────────────
                  │    4 
                  │    a     b      c
 5     16^E        X [ ─── + ───  + ───  + … ]
                  │   16    16²    16³
                  │

where a,b,c ... are hexadecimal digits, and E is an exponent that has a positive or negative value indicated by the characteristic