Also with this prefix are a series of unusual floating-point arithmetic instructions which are performed using the integer arithmetic unit:

000400 120xxx SFSWH Simple Floating Swap Halfword 000400 121xxx SFCH Simple Floating Compare Halfword 000400 122xxx SFLH Simple Floating Load Halfword 000400 123xxx SFSTH Simple Floating Store Halfword 000400 124xxx SFAH Simple Floating Add Halfword 000400 125xxx SFSH Simple Floating Subtract Halfword 000400 126xxx SFMH Simple Floating Multiply Halfword 000400 127xxx SFDH Simple Floating Divide Halfword 000400 130xxx SFMEUH Simple Floating Multiply Extensibly Unnormalized Halfword 000400 131xxx SFDEUH Simple Floating Divide Extensibly Unnormalized Halfword 000400 132xxx SFLUH Simple Floating Load Unnormalized Halfword 000400 133xxx SFSTUH Simple Floating Store Unnormalized Halfword 000400 134xxx SFAUH Simple Floating Add Unnormalized Halfword 000400 135xxx SFSUH Simple Floating Subtract Unnormalized Halfword 000400 136xxx SFMUH Simple Floating Multiply Unnormalized Halfword 000400 137xxx SFDUH Simple Floating Divide Unnormalized Halfword 000500 100xxx SFSW Simple Floating Swap 000500 101xxx SFC Simple Floating Compare 000500 102xxx SFL Simple Floating Load 000500 103xxx SFST Simple Floating Store 000500 104xxx SFA Simple Floating Add 000500 105xxx SFS Simple Floating Subtract 000500 106xxx SFM Simple Floating Multiply 000500 107xxx SFD Simple Floating Divide 000500 110xxx SFMEU Simple Floating Multiply Extensibly Unnormalized 000500 111xxx SFDEU Simple Floating Divide Extensibly Unnormalized 000500 112xxx SFLU Simple Floating Load Unnormalized 000500 113xxx SFSTU Simple Floating Store Unnormalized 000500 114xxx SFAU Simple Floating Add Unnormalized 000500 115xxx SFSU Simple Floating Subtract Unnormalized 000500 116xxx SFMU Simple Floating Multiply Unnormalized 000500 117xxx SFDU Simple Floating Divide Unnormalized 000500 120xxx SFSWL Simple Floating Swap Long 000500 121xxx SFCL Simple Floating Compare Long 000500 122xxx SFLL Simple Floating Load Long 000500 123xxx SFSTL Simple Floating Store Long 000500 124xxx SFAL Simple Floating Add Long 000500 125xxx SFSL Simple Floating Subtract Long 000500 126xxx SFML Simple Floating Multiply Long 000500 127xxx SFDL Simple Floating Divide Long 000500 130xxx SFMEUL Simple Floating Multiply Extensibly Unnormalized Long 000500 131xxx SFDEUL Simple Floating Divide Extensibly Unnormalized Long 000500 132xxx SFLUL Simple Floating Load Unnormalized Long 000500 133xxx SFSTUL Simple Floating Store Unnormalized Long 000500 134xxx SFAUL Simple Floating Add Unnormalized Long 000500 135xxx SFSUL Simple Floating Subtract Unnormalized Long 000500 136xxx SFMUL Simple Floating Multiply Unnormalized Long 000500 137xxx SFDUL Simple Floating Divide Unnormalized Long

These instructions involve pairs of registers, and operands twice the length of their associated integer type. They work on floating-point numbers represented as pairs of integers.

The first integer is the mantissa, which is a signed two's complement number, and the second integer is the exponent, which is also a signed two's complement number.

In the case of the simple floating long type, since a pair of arithmetic/index registers are required for a 64-bit value, the instructions work on groups of four registers. (Only a pair of registers is required in the case of the 64-bit supplementary arithmetic/index registers; but in that case, due to the arithmetic operations required, a pair of registers is still used in the case of operands of the shorter types as well.)

This allows the computer to match the capabilities of some early computers which used this basic method of achieving the ability to do floating-point arithmetic without adding extensive new logic for performing such arithmetic, most notably the Recomp: this computer, from the Autonetics division of North American Aviation, was the subject of a unique advertisement which turned this particular cost-cutting compromise into a valuable feature, as shown at right.

A much better copy of this advertisement is on-line here; the image I am using is from a black-and-white scan of an old magazine in which this advertisement appeared (in early 1960), and I restored the coloring by hand in a paint program, so my image may be imperfect.

In addition, versions of the conversion instructions for this floating-point mode are provided here as well, which have this form:

and these opcodes:

000400 1010xx 00xxxx CVPSFH Convert Packed to Simple Floating Halfword 000400 1014xx 00xxxx CVSFHP Convert Simple Floating Halfword to Packed 000400 1020xx 00xxxx CVPSF Convert Packed to Simple Floating 000400 1024xx 00xxxx CVSFP Convert Simple Floating to Packed 000400 1030xx 00xxxx CVPSFL Convert Packed to Simple Floating Long 000400 1034xx 00xxxx CVSFLP Convert Simple Floating Long to Packed

These instructions have the same format as the conversions between packed decimal and floating-point types, consisting of the prefix 000400 preceding the type conversion for the integer type which constitutes the components of the simple floating type in question.

Note that, due to the large magnitudes possible with this floating-point format, execution times for these instructions may be longer than for the corresponding conversions to and from conventional floating-point types.

Simple floating operands in registers always begin with an even-numbered register: where the operand is of long type, since each of the elements occupies a pair of registers, only arithmetic/index registers 0 and 4 can be used as the source or destination of a long simple floating operation.

These operations, unlike the register packed operations,
*can* be performed using the
long vector arithmetic unit as well. This is particularly useful with
the simple floating instructions (for which only long operations require
the use of an even numbered register, since the supplementary arithmetic/index
registers are 64 bits long, not 32 bits long) when the common floating-point format
is selected, as it can increase by
half the amount of floating-point operations that can be concurrent at
a given instant.

This may not lead to the full expected corresponding speed increase, however, since some implementations may apply optimizations to the floating-point arithmetic units that are not applied to the integer arithmetic units. Also, for the long simple floating instructions, since it is envisaged little extra hardware will be added for this relatively little-used function, multiplications will require two steps rather than one, to make use of circuits designed only to multiply numbers of half the width of the complete number; this will be no problem for the ordinary simple floating-point format, but it will affect simple floating-point instructions when the format is modified to be the common floating-point format.

Instructions in the vector register mode that would normally handle up to 64 operands instead would handle up to 32 operands of the simple floating type, and are coded as if each simple floating operand is simply two successive integer operands. However, the start of a range must be even, the end of a range must be odd, and mask bits must be on or off in pairs, so that any simple floating value composed of two integers has both its parts either included or excluded from a given simple floating vector operation, or the results will be undefined.

Although it may appear that the simple floating halfword type is of limited utility, since a signed 16-bit number provides about four and a half decimal digits of precision, this type can be useful under some circumstances:

- when the word length is increased from 32 bits to 36 or 40 bits; a signed 18-bit number provides five decimal digits of precision, and single-precision floating point numbers on the Digital Equipment Corporation PDP-15 computer were of this type (whereas, for double-precision numbers, which occupied three words, the effort was made to split the first word into two halves, only the first of which was used for the exponent, with the result that single-precision floating-point numbers had a larger range than double-precision floating-point numbers);
- when the Common Floating-Point Format bits in the Program Status Block are not both zero, so that the length of the mantissa field is increased at the expense of that of the exponent field.

Because arithmetic on operands of the Simple Floating type is performed
using the hardware primarily intended for integer arithmetic, not only
are no guard bits retained in registers between operations on values of
this type, *but no guard bit or sticky bit is used with a value of this type
during an operation*. Therefore, the results even of simple operations on
values of the Simple Floating type are **not guaranteed** to be the closest
approximation to the correct result expressible in the format.

Only the Simple Floating type has the latter limitation, although the former limitation, of no guard bits retained between operations, is shared by some other floating-point types. The following table summarizes the situation.

Floating-point Type | Guard, Round, and Sticky Bits | Additional Guard Bits |

Floating-Point Shorter than 128 bits in Regular Floating-Point Registers | Yes | Yes |

128-bit Floating-Point | Yes | No |

Floating-Point in Short Vector Registers | Yes | No |

Simple Floating Type | No | No |