Short Floating-Point Number lsi ____ o 1 8 31
Long Floating-Point NumberS Charactl3ristic 63
Extended Floating-Point NumberI s I Characteristic High-Drder Half of F o 8 ' 63
64 72Low-Order Half 127
In the short and long formats, the first bit is the
sign bit(51). The subsequent seven bit positions are
occupied by the characteristic. The following field
contains the fraction, which, depending on the for
mat, consists of six or 14 hexadecimal digits.
Short floating-point numbers occupy only the
leftmost 32 bit positions of a floating-point register.
When a floating-point register is used as the source
of a short floating-point number, the rightmost 32
bit positions of the register are ignored. When a
floating-point register is used as the destination of a
short floating-point number, the rightmost 32 bit
positionsIOf the register remain unchanged.
Anextended floating-point number has a 28-digit
fraction and consists of two long floating-point num
bers in consecutive floating-point registers. Two
pairs offllDating-point registers can be used as
sources of extended operands or destinations of ex
tended results: registers0, 2 and registers 4, 6 .. The
designation of any other register pair causes the op
eration to be and a program interruption
for a specification exception to occur.
The two long floating-point numbers comprising
an extended floating-point number are called the
high-order and low-order parts. The high-order part
may be allY long floating-point number. If it is nor
malized, the extended number is considered normal
ized. The characteristic of the high-order part is the
characteristic of the extended number, and the sign
of the high-order part is the sign of the extended
number.
The fraction field of the low-order part contains
the 14 low-order hexadecimal digits of the 28-digit
extended fraction. The sign and characteristic of the
low-order part of an extended operand are ignored,
the value of the number being assumed such as if the
158 System/370Principles of Operation sign of the low-order part were the same as that of
the high-order part, and the characteristic of the
low-order part were 14 less than that of the high
order part. In extended results, the sign of the low
order part is made the same as that of the high-order
part, and, unless the result is a true zero, the low
order characteristic is made 14 less than the high
order characteristic. When the subtraction of 14
causes the low-order characteristic to become less
than zero, it is made 128 larger than its correct val
ue. Exponent-underflow is indicated only when the
high-order characteristic underflows.
The entire set of floating-point functions is availa
ble for short and long operands. These instructions
generate a result that has the same format as the
sources, except that in the case of MULTIPLY, a
long product is produced from a short multiplier and
multiplicand. For extended operands, instructions
are provided for normalized addition, subtraction,
and multiplication. Additionally, two multiplication
instructions are provided that generate an extended
product from a long multiplier and multiplicand.
The rounding instructions provide for rounding from
extended to long format and from long to short for-
mat.i Programming Note
A long floating-point number can be extended to the
extended format by appending any long floating
point number having a zero fraction, including a true
zero. Conversion from the extended to the long for
mat can be accomplished by truncation or by means
ofLOAD ROUNDED. In the absence of an exponent overflow or expo
nent underflow, the long floating-point number con
stituting the low-order part of an extended result
correctly expresses the value of the low-order part of
the extended result when the characteristic of the
high-order part is 14 or higher. This relation is true
also when the result is a true zero. When the high
order characteristic is less than 14 but the number is
nota true zero, the low-order part, when addressed
as a long floating-point number, does not have the
correct characteristic value.
Guard Digit
Although final results have six fraction digits in the
short format, 14 fraction digits in the long format,
and 28 fraction digits in the extended format, inter
mediate results in ADDNORMALIZED, SUB TRACT NORMALIZED, ADD UNNORMAL IZED, SUBTRACT UNNORMALIZED, COM- P ARE, HALVE, and MULTIPLY may have one
additional low-order digit. This low-order digit, the
Long Floating-Point Number
Extended Floating-Point Number
64 72
In the short and long formats, the first bit is the
sign bit
occupied by the characteristic. The following field
contains the fraction, which, depending on the for
mat, consists of six or 14 hexadecimal digits.
Short floating-point numbers occupy only the
leftmost 32 bit positions of a floating-point register.
When a floating-point register is used as the source
of a short floating-point number, the rightmost 32
bit positions of the register are ignored. When a
floating-point register is used as the destination of a
short floating-point number, the rightmost 32 bit
positions
An
fraction and consists of two long floating-point num
bers in consecutive floating-point registers. Two
pairs of
sources of extended operands or destinations of ex
tended results: registers
designation of any other register pair causes the op
eration to be
for a specification exception to occur.
The two long floating-point numbers comprising
an extended floating-point number are called the
high-order and low-order parts. The high-order part
may be allY long floating-point number. If it is nor
malized, the extended number is considered normal
ized. The characteristic of the high-order part is the
characteristic of the extended number, and the sign
of the high-order part is the sign of the extended
number.
The fraction field of the low-order part contains
the 14 low-order hexadecimal digits of the 28-digit
extended fraction. The sign and characteristic of the
low-order part of an extended operand are ignored,
the value of the number being assumed such as if the
158 System/370
the high-order part, and the characteristic of the
low-order part were 14 less than that of the high
order part. In extended results, the sign of the low
order part is made the same as that of the high-order
part, and, unless the result is a true zero, the low
order characteristic is made 14 less than the high
order characteristic. When the subtraction of 14
causes the low-order characteristic to become less
than zero, it is made 128 larger than its correct val
ue. Exponent-underflow is indicated only when the
high-order characteristic underflows.
The entire set of floating-point functions is availa
ble for short and long operands. These instructions
generate a result that has the same format as the
sources, except that in the case of MULTIPLY, a
long product is produced from a short multiplier and
multiplicand. For extended operands, instructions
are provided for normalized addition, subtraction,
and multiplication. Additionally, two multiplication
instructions are provided that generate an extended
product from a long multiplier and multiplicand.
The rounding instructions provide for rounding from
extended to long format and from long to short for-
mat.
A long floating-point number can be extended to the
extended format by appending any long floating
point number having a zero fraction, including a true
zero. Conversion from the extended to the long for
mat can be accomplished by truncation or by means
of
nent underflow, the long floating-point number con
stituting the low-order part of an extended result
correctly expresses the value of the low-order part of
the extended result when the characteristic of the
high-order part is 14 or higher. This relation is true
also when the result is a true zero. When the high
order characteristic is less than 14 but the number is
not
as a long floating-point number, does not have the
correct characteristic value.
Guard Digit
Although final results have six fraction digits in the
short format, 14 fraction digits in the long format,
and 28 fraction digits in the extended format, inter
mediate results in ADD
additional low-order digit. This low-order digit, the