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7. EXTRACODE INSTRUCTIONS
The basic instructions consist in just those simple operations which the computer has been designed to execute directly. In the Atlas order-code, however, there are many complicated operations which the computer deals with in a special way; these are known as extracodes and are distinguished from the basic instructions by having a 1 in f0, the most-significant bit of the 10-bit function number. Upon encountering an instruction with f = 1, there occurs an automatic entry to one of many built-in subroutines, the choice being determined by the remaining three octal digits of the function number. The exit from the subroutine is again automatic, and the program proceeds in the usual way with the instruction next after the extracode, unless the extracode subroutine has initiated a jump.
7.1.1 Uses of the Extracode Instructions.
As their name implies, the extracodes provide an extension of the basic order-code, including both those complicated operations which are excluded from the basic instructions, and many of the facilities which on previous machines have been obtained by the use of library subroutines.
Amongst the arithmetic instructions provided by extracodes we may instance those in which the address, interpreted as a floating-point number, is used as an operand; double-length operations; and a full range of elementary functions such as logarithm, square-root, sine etc.
An important group of extracodes deals with the special requirements of input and output and also of magnetic tape transfers; the uses of these will be discussed at some length in Chapters 8 and 9.
The organisational extraoodes comprise extensive facilities designed to assist the programmer in making efficient use of the operating system of Atlas. The various aspects of this are described in later Chapters (particularly Chapters 11 and 12).
7.1.2 To the programmer, extracode instructions appear as basic instructions. The two types of instruction can be freely intermixed, and after each instruction control passes sequentially to the next (except for jump instructions). It is therefore not strictly necessary to know how the computer deals with extracode instructions, although this is given for completeness in the next section.
There are 512 function numbers available for extracodes, 1000-1777. Of these, 1000-1477 are singly-modified instructions (B-type) and 1500-1777 are doubly-modified instructions (A-type). In some of the B-type instructions, bm is used as an operand so no modification takes place.
7.2 The Logical Interpretation of Extracode Instructions
When an extracode instruction is encountered the following action place:-
- The content of Main control, b127, is increased by one to the address of the next program instruction.
- The address is modified according to the type (i.e. N + bm for B-type, N + ba + bm for A-type) and the result stored in B119.
- The seven Ba digits are placed in bits 15-21 of B121, unless Ba is B122 in which case B121 is left unchanged; this enables B122 to be used to specify a B-register in extracode functions exactly as in basic functions.
- The function digits f1 - f9 are placed in extracode control,
B126, as shown below.
Bit 0 1-9 10 11 12 13 14 15 16 17 18 19 20 21-23 Value 1 000000000 f1 f2 f3 0 0 f4 f5 f6 f7 f8 f9 000
- Control is switched from Main (B127) to extracode (B126).
The next instruction to be obeyed is now in the fixed store, under extracode control, at a location determined by the function digits. It is in one of 64 registers (given by f4-f9) in one of 8 tables at intervals of 256 words (given by f1-f3). The tables of 64 registers are called jump tables. In general this instruction will be an unconditional jump into a routine which performs the required function. These routines are permanently stored in the fixed-store and written in normal basic instructions. Each routine terminates with an instruction in which f1 = f3 = 1 in the function number. This is obeyed as if f1 = 0 and then control is switched back to main control (e.g. 521 is equivalent to 121 followed by extracode exit). The next instruction to be obeyed is then the one whose address is in B127; if no jump has been initiated by the extracode this instruction will be the one immediately following the extracode instruction.
The routines that perform extracodes can use B-registers 91 to 99 inclusive and always use B119, B126, and B121 (unless Ba = 122).
1. Extracode 1714 is defined as am' = 1/s
Replace the numbers in locations 100 to 105 by their reciprocals.
121 1 0 5 set modifier count 2)1714 0 1 100 am' = 1/s 356 0 1 100 store 203 127 1 A2 count
Each time the extracode instruction is encountered b127' = b127 + 1, b121' = 0, b119' = 100 +b1 + b0, b126' = J40034140 = +1804J4 and control is switched to B126. The instruction in the jump table is
121 126 0 A14
The instructions at A14 are
334 0 0 A96 set am = +1 774 0 119 0 374 division 1/s, then reswitch to main control. 96)+1
2. Extracode 1341 is defined as bat = ba.2n (arithmetic shift up) Shift b16 up by 2 more than the integer in B17
1341 16 17 2
This instruction sets b121' = 16D1, b119' = 2 + b17, etc. (Note that b16 is not added to b119 because 1341 is a singly-modified (B-type) extracode).
3. Shift the contents of B20 to B47 inclusive up by 5 places.
121 121 0 20D1 set modifier count 1)1341 122 0 5 shift. As Ba = B122, b121 is left unchanged when the extracode is entered. 172 121 0 47D1 bt' = b121 - 47D1 220 127 121 A1 If bt â‰ 0, b121' = b121 + 0.4 and b127' = A1
Example 3 illustrates the use that can be made of B121 and B122 in extracodes; this is the same as their use in basic instructions except that extracodes with Ba â‰ 122 will overwrite B121.
Allocation of Functions
The extracodes are divided into sections as shown below, though there are a few functions which do not fit into this pattern. References are given for those subjects described in this chapter.
|1000-1077||Magnetic tape routines, and Input and Output routines..||--|
|1200-1277||Test instructions and 6-bit character operations||7.6, 7.5.2|
|1400-1477||Complex arithmetic, vector arithmetic and miscellaneous B-type accumulator routines.||7.4.6,7.4.7|
|1500-1577||Double-length arithmetic and accumulator operations using the address as an operand.||7.4.4, 7.4.5|
|1600-1677||Logical accumulator operations and half-word packing.||7.5.3, 7.4.8|
|1700-1777||Arithmetic functions (log, exp, sq.rt., sin, cos, tan, etc.) and miscellaneous A-type accumulator operations.||7.4.1, 7.4.2, 7.4.3|
Not all of the 512 extracode functions have been allocated and, where convenient, constants and extracode programs have been packed into the vacant jump-table locations.
This means that the use of an unallocated extracode function may result in an unassigned function interrupt or may cause some extracode to be entered incorrectly. The latter case would give the programmer wrong results.
In particular, the first location in the fixed store, J4, contains the floating-point number Â½. This causes an unassigned function interrupt if extracode 1000 is encountered, since J4 is the first register of the first jump-table. Note that floating-point zero is equivalent to the instruction
1000 0 0 0
There follows a description of many of the extracodes. Where possible, the actual number of basic instructions obeyed in each extracode routine is given in the right hand column.
Appendix 3 gives an ordered summary of all the extracodes, for easy references.
7.4 The Accumulator Extracodes
7.4.1 The Most Used Arithmetic Functions
The following routines each have two extracode numbers. The first operates on s, which is standardised on entry. The second operates on a, which is standardised, rounded and truncated to a single-length number on entry. For this number we use the notation aq. The results are always standardised rounded numbers in Am.
|1700||Place the logarithm to base e of s in Am||am' = log s|
|1701||Place the logarithm to base e of aq in Am||am' = log aq|
|1702||Place the exponential of s in Am||am' = exp s, 43|
|1703||Place the exponential of aq in Am||am' = exp aq, 42|
|1710||Place the square root of s in Am||am' = +sqrt(s) â‰¤, 42|
|1711||Place the square root of aq in Am||am' = +sqrt(aq) â‰¤, 41|
|1712||Place the sqaure root of (aq2 + s2) and place this in Am||am' = +sqrt(aq2 + s2) â‰¤, 50|
|1720||Place the arc sine of s in Am (am' is in radians, with -Ï€/2 â‰¤ am' â‰¤ +Ï€/2)||am' = arc sin s|
|1721||Place the arc sine of aq in Am (am' is in radians, with -Ï€/2 â‰¤ am' â‰¤ +Ï€/2)||am' = arc sin aq|
|1722||Place the arc cosine of s in Am (am' is in radians, with 0 â‰¤ am' â‰¤ +Ï€)||am' = arc cos s|
|1723||Place the arc cosine of aq in Am (am' is in radians, with 0 â‰¤ am' â‰¤ +Ï€)||am' = arc cos aq|
|1724||Place the arc tangent of s in Am (am' is in radians, with -Ï€/2 < am' < +Ï€/2)||am' = arc tan s|
|1725||Place the arc tangent of aq in Am (am' is in radians, with -Ï€/2 < am' < +Ï€/2)||am' = arc tan aq|
|1726||Divide aq by s and place the arc tangent of this number in Am. am' is in radians and such that -Ï€ < am' â‰¤ +Ï€||am' = arc tan (aq/s)|
|1730||Place the sine of s in Am (s in radians)||am' = sin s, 41|
|1731||Place the sine of aq in Am (aq in radians)||am' = sin aq, 40|
|1732||Place the cosine of s in Am (s in radians)||am' = cos s, 42|
|1733||Place the cosine of aq in Am (aq in radians)||am' = cos aq, 41|
|1734||Place the tangent of s in Am (s in radians)||am' = tan s, 34|
|1735||Place the tangent of aq in Am (aq in radians)||am' = tan aq, 33|
7.4.2 Other Floating-Point Arithmetic Functions
|1704||Place the integer part of s in A||a' = int pt s QE||5|
|1705||Place the integer part of a in A||a' = int pt a QE||4|
|1706||Set a' = +1, 0 or -1 as s >, =, or < zero||a' = sign s Q||5-6|
|1707||Set a' = +1, 0 or -1 as a >, =, or < zero||a' = sign a Q||4-5|
|1713||Raise aq to the power s and place the result in am, provided that aq â‰¥ 0, Fault if aq < 0||am' = aqs QRE
aq â‰¥ 0
|1714||Place the reciprocal of s in Am||am' = 1/s QREDO||4|
|1715||Place the reciprocal of am in Am||am' = 1 / am QREDO||4|
|1754||Round am by R+, clear L and standardise||am' = a, l' = 0 QR+||6|
|1756||Interchange the contents of S and Am (with no standardising)||am' = s, s' = am||8|
|1757||Place the result of dividing s by am in Am||am' = s / am QREDO||4|
|1760||Square the contents of Am||am' = am2 QRE||3|
|1774||Divide am by s and place the result in Am. The original numbers need not be standardised||am' = am / s QREDO||10|
|1775||Divide aq by s and place the result in Am. The original numbers need not be standardised||am' = aq / s QREDO||9|
1774 and 1775, besides providing a division instruction which operates on unstandardised numbers, store information which enables extracodes 1776 and 1407 to calculate a quotient and remainder.
|1776||When used after division extracodes
1774, 1775, 1574 or 1575, with no
other extracodes in between and am
unaltered, the definition of 1776 is as follows:
Place the quotient of the previous division in s and the remainder in Am, where the remainder has the sign of the divisor
|s' = quotient QREDO
am' = remainder
|1407||As 1776 except that the quotient is
integral and is adjusted according
to the sign of the remainder, which
is specified by Ba as follows:
Ba Sign of remainder O Same as the denominator 1 Opposite to the denominator 2 Same as the numerator 3 Opposite to the numerator 4 Same as the quotient 5 Opposite to the quotient 6 Positive 7 Negative
|s' = adjusted intregral quotient QEDO
am' = remainder
|1467||Evaluate the polynomial s0 + s1.am + s2.am2 + ... sba.amba where s0 is the number at S, s1 at S+1, etc and the order of the polynomial is given as an integer in Ba.||am' = Î£ sr.amr from r=0 to r=ba
where Sr = S + r QRE
|6 + 3 ba|
|1466||Multiply the two numbers at addresses (N+ba+bm) and (N+bm) and add the double-length result into the full accumulator. Rounding takes place near the least-significant end of L. (In detail, when the double-length product has been formed, its least-significant half is first added in M to the least-significant half of the original contents of A. This addition is rounded. The rest of the product and the original contents of M are then added into A without rounding).||a' = a +
Generate pseudo-random numbers (PRN's) in A and S (or S*) from numbers in S and S*. This extracode may be used in several ways.
- With digit 21 of S equal to 0, the PRN is placed in S and A.
- If s*y = 0, sx > 0 and s*x > 0, then s' will be a PRN in the range 0 to 8sy , rectangularly distributed and fixed-point (i.e. sx' is a fixed-point PRN and sy' = sy). a' will be a PRN in the range 0 to s*x.8sy (with al' = s').
- If s*y = 0, sx < 0 and s*x < 0, then as (a) except that ranges become -8sy to 0 and -s*x.8sy-1 to 0 respectively.
- If s*y = 0 and s*x > 0, then as (a) except that the PRN's alternate in sign.
- With digit 21 of S = 1, the PRN's are generated in S* and A instead of S and A. The cases are as for 1, interchanging S and S* throughout.
- 3. Two successive uses of the extracode, with digit 21 of S first = 0 and then = 1, and with sy = s*y = 0, will set PRN's in S end S*, both rectangularly distributed in the range 0 to 1. A will contain the product of two PRN's and so will be distributed in the range 0 to 1 with the probability -log xdx of being in the neighbourhood dx of x.
In all cases the generation process must be started with Sx Iand S*x containing numbers with a random mixture of binary digits, but with their least-significant bits set to 1.
7.4.3 Accumulator functions suitable for Fixed-Point Working
|1752||Shift ax up 12 octal places and subtract 12 from ay||m' = ax.8-12
ay' = ay -12 AO
|1753||Shift m down 12 octal places in ax and increase ay by 12||ax' = m.8-12
ay' = ay +12 AO
|1755||Force ay to the number ny given in bits 0-8 of n, shifting ax up or down accordingly||ax' = ax.8ay - ny
ay' = ny AO
|1762||Shift ax up 12 octal places leaving ay unchanged||m' = ax.812
ay' = ay AO
|1763||Shift m down 12 octal places in ax leaving ay unchanged||ax' = m.8-12
ay' = ay AO
|1764||Shift ax up n octal places leaving ay unchanged. If n is negative, shift ax in the opposite direction.||ax' = ax.8n
ay' = ay AO
|1765||Shift ax down n octal places leaving ay unchanged. If n is negative, shift ax in the opposite direction.||ax' = ax.8-n
ay' = ay AO
|1766||Place the modulus of s in Am, without standardising. Accumulator overflow will occur if s is -1.0||am' = |s| AO||4|
|1767||Place the modulus of am in Am, without standardising. AO will occur if am is -1.0||am' = |am| AO||3|
|1772||Multiply m by sx, shifting the result up by 12 octal places to be in M, and subtracting 12 from ay||m' = (m.sx)812
ay' = ay + sy -12 AO
|1773||Divide a by s, and force ay equal to 12, shifting the result, which is in M, if necessary||m' = (ax/sx).8ay - sy - 12
ay' = 12 AO
|1452||Multiply am by s, forming the answer in Ax. Force ay to the number given in digits 0-8 of ba, and shift ax accordingly||ax' = m.sx.8ay + sy - bay
ay' = bay AO
|1473||Divide ax by sx, forming the answer in Ax. Force ay to the number given in digits 0-8 of ba, and shift ax accordingly||ax' = (ax / sx).8ay - sy - bay
ay' = bay AO
Fixed-Point Divisions with remainder
The three extracodes 1474, 1475 and 1476 each divide some part of the accumulator by the contents of store location S, placing an unstandardised quotient q in the location whose address is ba and leaving an unstandardised remainder r in Am. In all cases, r retains the original sign of am and has a mantissa in the range 0 â‰¤ |rx| < |sx|. The quotient is rounded towards zero. Division overflow is set if sx = 0 or -1.0 or if |sx| â‰¤ |mantissa of dividend|. Both DO and AO are set when the mantissa of the dividend is equal to -1.0.
If only the remainder is required, one can avoid the need to set ba by putting Ba = B126 in the extracode instruction.
|1474||Divide am by s. The exponent of q and r are given by qy = ay - sy and ry = ay -13||C(ba)' = quotient (am/s)
am' = remainder (am/s) DO AO E
|1475||Divide a by s. The exponent of q and r are given by qy = ay - sy and ry = ay -13||C(ba)' = quotient (a/s)
am' = remainder (a/s) DO AO E
|1476||Divide the integral part of am by s. The exponents of q and r are forced to qy = 24 -sy and ry = 12. the condition |am| < 824 |sx| must be observed, otherwise division overflow will occur and the results will be meaningless. The least-significant octal digit of q is always zero, and it is intended that usually sy = 12 so that qy = 12 also and one is working with integers. In the case ay â‰¤ -6 and am < 0, this extracode must be preceded by 217, 124, 124, 0 to ensure the true integral part is used.)||C(ba)' = (q int pt am)/s
am' = r (int pt am / s)
AO DO E
7.4.4 Double-Length Arithmetic
The double-length number s: is stored in two consecutive locations s and s + 1 as two standardised floating-point numbers, where sy â‰¥ s*y. s* and al are assumed to be always positive. All arithmetic is standardised, rounded and checked for exponent overflow.
|1500||Add s: to a||a' = a + s:||10|
|1501||Subtract s: from a||a' = a - s:||10|
|1502||Negate a and add s:||a' = -a + s:||14|
|1504||Copy s: into a||a' = s:||4|
|1505||Copy s: negatively into a||a' = -s:||3|
|1542||Multiply a by s:||a' = a.s:||15|
|1543||Multiply a negatively by s:||a' = -a.s:||19|
|1556||Store a at S:||s:' = a||5|
|1565||Negate a||a' = -a||5|
|1566||Form the modulus of a||a' = |a|||4-6|
|1567||Copy the modulus of s: into A||a' = |s:|||5|
|1576||Divide a by s:||a' = a/s:||19|
7.4.5 Arithmetic Using the Address as an Operand
The modified address is taken as a 21-bit integer with an octal fraction. Fixed-point operations imply an exponent of 12.
|1441||Store ba in S as a fixed-point number||sx' = ba, sy' = 12||5|
|1520||Add n to am||am' = am + n QRE||10|
|1521||Subtract n to am||am' = am - n QRE||9|
|1524||Place n into a||a' = n Q||8|
|1525||Place n negatively into a||a' = -n Q||7|
|1534||Place n into a, without standardising||a' = n||10|
|1535||Place n negatively into a, without standardising||a' = -n||9|
|1562||Multiply am by n||am' = am.n QRE||8|
|1574||Divide am by n||am' = am/n QRE||16|
|1575||Divide aq by n||am' = aq/n QRE||15|
After 1574 and 1575, the extracodes 1776 and 1407 can be used to give a remainder and adjusted integral quotient. See section 7.4.2.
7.4.6 Complex Arithmetic
The complex accumulator Ca is taken as a pair of consecutive registers, the address of the first one given by the contents of Ba in the instruction. If Ba is B0, Ca will be locations 0 and 1. As with the double-length arithmetic, s: is a number pair consisting of the two numbers at addresses S and S + 1. For Ca and S:, the real part of the number is in the first location, the imaginary part in the second. Ca may coincide with S: if desired, but the two must not partially overlap, i.e. the difference between ba and S must not equal 1. The accumulator is used for the arithmetic so its original contents on entry are spoiled. All arithmetic is standardised, rounded and checked for exponent overflow.
|1400||Place the logarithm of s: in Ca||ca' = log s:|
|1402||Place the exponential of s: in Ca||ca' = exp s:||140|
|1403||Place the conjugate of s: in Ca||ca' = conj s:||5|
|1410||Place the square root of s: in ca||ca' = +sqrt(s:)||â‰¤117|
|1411||Place the argument of s: (radians) in Am||am' = arg s:|
|1412||Place the modulus of s: in Am||am' = mod s:||â‰¤53|
|1413||Form the number s cos s*, s sin s* and place these in Ca. (s* is in radians.)||ca' = s.cos s*, s.sin s*||95|
|1414||Place the reciprocal of s: in Ca||ca' = 1 / s:||15|
|1420||Add s: to ca||ca' = ca + s:||8|
|1421||Subtract s: from ca||ca' = ca - s:||8|
|1424||Copy s: into Ca||ca' = s:||6|
|1425||Copy s: negatively into Ca||ca' = -s:||6|
|1456||Copy ca into S:||s:' = ca||5|
|1462||Multiply ca by s:||ca' = ca.s:||18|
Note: 1400 - the imaginary part of the complex logarithm will lie in the range - Ï€ (not inclusive) to Ï€ (inclusive).
1410 - of the two possible values of the complex square root, the one computed here has a non-negative real part; the remaining ambiguity about the square roots of negative real numbers is removed by computing the one whose imaginary part is positive.
7.4.7 Vector Arithmetic
The following instructions operate on two vectors s1 and s2. Both vectors consist of lists of floating-point numbers stored in successive locations. In each instruction the singly-modified address n gives the number of terms in the vectors (i.e. the order) and Ba gives the starting address of s1. The next B-register after Ba, Ba*, gives the starting address of s2. Address n must be a positive integer.
Besides their uses in vector and matrix arithmetic, these instructions can be used to manipulate lists of numbers in the store.
The accumulator is used in the arithmetic so its original contents on entry are lost. All operations are standardised rounded and checked for exponent overflow.
|1430||Add the vector s2, which consists of n successive numbers starting at C(ba*) into the vector s1, which consists of n successive nunbers starting at C(ba).||s1' = s1 + s2||9 + 4n|
|1431||Subtract s2 from s1||s1' = s1 - s2||9 + 4n|
|1432||Multiply each term of s2 by am and store the resultant vector at s1||s1' = am.s2||10 + 4n|
|1433||Multiply s2 by am and add this to s1||s1' = s1 + am.s2||10 + 5n|
|1434||Copy s2 to s1||s1' = s2||10 + 3n|
|1436||Form in Am the scalar product: s1 0.s2 0 + ... + s1 (n-1).s2 (n-1), where s1 0, s1 1 ... s1 (n-1) are the numbers in s1 and s2 0, s2 1 ... s2 (n-1) are the numbers in s2||a' = Î£ s1 i.s2 i, i=0,n-1||10 + 13n|
|1437||As 1436 but forming the scalar product to double-length accuracy in a||a' = Î£ s1 i.s2 i, i=0,n-1||10 + 13n|
7.4.8 Half-Word Packing
Half-word floating-point numbers consisting of 8-bit exponents and 16-bit mantissae are sometimes useful for low-accuracy calculations where it is necessary to reduce store usage.
|1624||Transfer the floating-point number at S into the accumulator, without standardising||a' = s R||6|
|1626||Copy ay and the 16 most-significant digits of ax into S after rounding this number in Am by forcing a one in its lowest bit if the rest of ax is non-zero||s' = am R||8|
7.5 B-Register Arithmetic
7.5.1 General B-Register Operations
|1300||Place in Ba the integral part of the floating-point number s. Place the fractional part in Am.||ba' = int pt of s
am' = frac pt of s
|1301||Place in Ba the integral part of am. Place the fractional part in Am.||ba' = int pt of am
am' = frac pt of am
The following six instructions provide integer multiplications and division of ba by n.
For 1302 - 1304, ba and n are interpreted in the normal way as 21-bit integers with a least-significant octal fraction. In the multiplication instructions octal fractions are rounded away from zero, and overflow of the answer is not detected. The accumulator is used in the calculation, but am is preserved.
|1302||Multiply ba by n and place the result in Ba||ba' = ba Ã— n||23-24|
|1303||Multiply ba negatively by n and place the result in Ba||ba' = - ba Ã— n||22-23|
|1304||Divide ba by n. Place the integer quotient in Ba and the remainder, which has the sign of the dividend, as a 24-bit integer in B97.||ba' = int pt (ba / n)
b97' = remainder
For 1312-1314, ba and n are interpreted as 24-bit integers, and the result is again a 24-bit integer.
|1312||Multiply ba by n and place the result in Ba||ba' = ba Ã— n||23-24|
|1313||Multiply ba negatively by n and place the result in Ba||ba' = - ba Ã— n||22-23|
|1314||Divide ba by n. Place the integer quotient at the least significant end of Ba and the remainder, which has the sign of the dividend, as a 24-bit integer in B97.||ba' = int pt (ba / n)
b97' = remainder
The following six instructions provide general n-place shifts of numbers in B-registers.
In arithmetic shifts, the sign digit is propagated at the most-significant end of the register for shifts to the right (i.e. down).
In logical shifts the sign digit is not propagated.
For both arithmetic and logical shifts the result is unrounded on shifts down. In circular shifts, digits shifted off the most-significant end of the register reappear at the least-significant end and vice-versa. n is an integer in bits 0-20 as usual, with no octal fraction. (If n has an octal fraction the answer may be wrong by a shift of one place). In each case, if n is negative a shift of n places in the opposite direction occurs.
|1340||Shift ba arithmetically to the right by n places||ba' = ba.2-n||10-22|
|1341||Shift ba arithmetically to the left by n places||ba' = ba.2n||9-21|
|1342||Shift ba circularly to the right by n places||ba' = ba.2-n
|1343||Shift ba circularly to the left by n places||ba' = ba.2n
|1344||Shift ba logically to the right by n places||ba' = ba.2-n
|1345||Shift ba logically to the left by n places||ba' = ba.2n
The following are miscellaneous arithmetic instructions on half-words and index registers.
|1347||Perform the logical OR operation on ba and s and place the result in S||s' = ba or s||5|
|1353||Set B123 by writing n to it, and read the result to Ba. This sets ba equal to the position of the most significant 1 bit in bits 16-23 of n. (B123 is described in Chapter4.)||b123' = n, then ba' = b123||5|
|1356||Set the B-test register as the result of non-equivalencing ba and s||bt' = ba neqv s||7|
|1357||Set the B-test register as the result of non-equivalencing ba and n||bt' = ba neqv n||5|
|1376||Set the B-test register as the result of collating ba and s||bt' = ba & s||5|
|1377||Set the B-test register as the result of collating ba and n||bt' = ba & n|
|1364||Preserve the digits of Ba where there are zeros in n and copy digits from Bm into Ba where there are ones in n||ba' = (ba & z) or (bm & n)
where z is n with bits inverted
[also b119' = (ba neqv bm) & n]
|1371||Dummy extracode to set up b121 and b119||b121' = ba
b119' = N + bm
|1771||Dummy extracode to set up b121 and b119||b121' = Ba
b119' = N + ba + bm
7.5.2 Character Data Processing
|1131||Search for s in table starting at C(ba).
If s can be found, ba' will record its address, otherwise the sign bit of ba' will
be set to 1.
Main control is re-entered at c' = c + 2, and C(c + 1) is used to speoify
parameters k, l, m as shown below.
Up to l + 1 half-words are scanned, starting with C(ba) and continuing at
intervals of k half-words, each being masked with m before comparison with s.
bits 0-9 10-20 21-23 0-23 k l spare m interval count mask
In the following two instructions S is taken as a character address, the octal fraction giving the address of the 6-bit character within the word.
|1250||Place the character s in the least-significant 6 bits of Ba and clear the other digits of Ba.||ba' = char s||7-10|
|1251||Copy the character from the least-significant 6-bits of Ba into the character position at S, leaving the other characters in the word unaltered.||s' = char ba||11-18|
In the following two instructions ba is interpreted as a character address, and the content of the next B-register, ba*, is interpreted as a half-word address. n is used as a count and its octal fraction must be zero.
|1252||Unpack n characters. The n characters, packed in successive character positions starting at C(ba), are placed in the least-significant 6-bits of n successive half-words starting at C(ba*}. The other digits in each half-word are set to zero.||16 + int pt (6.75n)|
|1253||Pack n characters. Take the n characters stored in the least-significant 6-bits of n successive half-words starting at C(ba*) and pack these into n successive character positions starting at C(ba).||18+5n|
7.5.3 Logical Accumulator Instructions
B98 and B99 are used in these instructions as a double-length B-register. This is called the logical accumulator and denoted by G.
|1204||Starting at the most-significant end, count the number of 6-bit characters which are identical in g and s, continuing only until the first dissimilar characters are found. Place the result in Ba.||10-31|
|1265||Shift g up by 6 places, writing overspill to Ba, and add n.||ba' = m.s character of g.
g' = 26g + n
|1601||Copy s into G||g' = s||3|
|1604||Add s into G||g' = g + s||7|
|1605||Add s into G, adding any overflow carry in again at the least-significant end.||g' = g + s with end-around carry||12|
|1606||Non-equivalence s with G||g' = g neqv s||4|
|1607||Collate s with G||g' = g & s||3|
|1611||Replace g by its logical binary complement||g' = z where z is the logical complement of g||3|
|1613||Copy g into S||s' = g||3|
|1615||Copy g into Am, without standardising||am' = g||4|
|1630||Form the logical binary complement of s and collate this with g.||g' = g & z where z is the logical complement of s||5|
|1635||Copy am into G||g' = am||4|
|1646||OR s with G||g' = g or s||3|
|1652||Set Bt by the result of subtracting s from g||bt' = g - s||7-9|
7.6.1 Accumulator test Instructions
|1200||Place n in Ba if the Acoumulator overflow (AO) is set. Clear AO.||ba' = n if AO is set||9|
|1201||Place n in Ba if AO is not set. Clear AO.||ba' = n if AO is not set||7|
|1234||Increase main control by 2 (instead of by 1) if am is approximately equal to s.||c' = c +2 if am nearly equals s||11|
|1235||Increase main control by 2 if am is not approximately equal to s.||c' = c if am not nearly equal to s||11|
For 1234 and 1235, approximate equality is defined as |(am - s) / am| < C(ba)
am must be standardised on entry. By definition, if am = 0 then am is not approximately equal to s.
|1236||Place n in Ba if am is greater than zero.||ba' = n if am > 0||4-6|
|1237||Place n in Ba if am is less than or equal to zero.||am â‰¤ 0||3-5|
|1255||Place n in Ba if m is neither zero nor all ones.||ba' = n if m neqv all 1's or all 0's|
|1727||Depending on whether am is greater than, equal to, or less than s, increase main control by 1, 2 or 3.||c' = c + 1, 2, 3 as am >, =, < s||7|
|1736||Increase main control by 2 if the modulus of am is greater than or equal to s.||c' = c+ 2 if |am| â‰¥ s|
|1737||Increase main oontrol by 2 if the modulus of am is less than s.||c' = c + 2 if |am| < s|
In 1234, 1235, 1727, 1736 and 1737 am is preserved but l is not.
7.6.2 B-register Test Instructions
|1206||Place n in Ba if the most significant 6-bit character in G is zero||4|
|1216||Place n in Ba if bm is greater than zero||ba' = n if bm > 0|
|1217||Place n in Ba if bm is less than or equal to zero||ba' = n if bm â‰¤ 0|
|1226||Place n in Ba if bt is lgreater than zero||ba' = n if bt > 0||4-6|
|1227||Place n in Ba if bt is less than or equal to zero||ba' = n if bt â‰¤ 0||3-5|
|1223||Place n in Ba if the B-carry digit is set||ba' = n if bc = 1||4|
The B-carry digit (Bc) is set to 0 or a 1 in the following basic instructions.
100 102 104 110 112 114 120 122 124 150 152 164 170 172
Bc records the final carry or borrow generated after the addition or subtraction of the most significant digits of the operands.
When the most-significant digit is taken as a sign bit, which is usually the case, Bc is not a true overflow digit. For example, adding -1 or +1 gives 0 and also sets Bc = 1 as there is a final carry. (See Chapter 4).
7.7 Subroutine Entry
|1100||Set link in Ba and enter subroutine at s||ba' = c + 1, c' = s||6|
|1101||Set link in Ba and enter subroutine at n||ba' = c + 1, c' = n||5|
|1100||Set link in Ba and enter subroutine at bm||ba' = c + 1, c' = bm||6|
|1362||Set link in B90 and enter subroutine at n. On completion of this extracode, b121' = ba, so that Ba or ba may be used to carry information into the subroutine.||b90' = c + 1, c' =n||3|
The link set in Ba can be picked up as an exit from the subroutine by the instruction
121 127 B% 0
where B% is the address of the B-register (Ba) in which the link was set. It is conventional to use B90 for this purpose, and 1362 was provided for that reason.
7.8 Miscellaneous Operations
|1117||End program. This extracode is used to end a program unless it is monitored by the Supervisor. Certain information about the program is output, and the program cleared from the computer. (see Chapter 11.)|
|1120||Record the time in Ba, with hours, minutes and seconds
each given by two decimal digits specified in four bits apieoe, as follows:-
bits 0-3 4-7 8-11 12-15 16-19 20-23 tens units tens units tens units HOURS MINUTES SECONDS
|ba' = clock|
|1121||Record the date in Ba, with the day, month and year each given
by two decimal digits specified in four bits apiece, as follows:-
bits 0-3 4-7 8-11 12-15 16-19 20-23 tens units tens units tens units DAY MONTH YEAR
|1124||Set the central computer V-store line 6 to n.
The least-significant six bits of V-line 6 are used as follows:-
bit Set to 0 Set to 1 18 13 shift 12 shift on division; needed to adjust remainder for 376, 377 instructions 19 Qs â‰¥ 0 Qs < 0 Sign of quotient in basic division orders 20 AO clear AO set 21 bt â‰¥ 0 bt < 0 22 bt = 0 bt â‰ 0 23 Bc clear Bc set
|1125||Collate the contents of the central computer V-store line 6 with n, placing the result in Ba. Any digits of v6 may thus be read.||ba' = v6 & n|