LT4335 integer instructions

LT4335 integer instructions.
Version of 12 July 2011.
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In the instruction descriptions:

u⁸ is an unsigned 8-bit integer (0…255)
s⁹ is a signed 9-bit integer (−255…+255 or null)
s¹² is a signed 12-bit integer (−2047…+2047 or null)

Sometimes the size of a integer is itself represented by a signed integer; an exception will be thrown in response to a requested integer size greater than 255, less than 0, or null.

Many of the get, put, and get-and-put instructions involve an offset. This number, when added to the address of the next physical instruction (which equals the address of the current instruction plus 17), gives the address in genspace whence to read data, or whither to write it. A null offset throws an exception.

Get. (see also float and string) All the integer get instructions trim the result as it is placed into a register. If an untrimmed integer is preferred, the programmer should use a string get instruction.

The first instruction listed, IG_E, pushes a signed integer embedded within its opcode, while the others push a signed integer found in genspace.

IG_E integer get, value embedded s¹²_01_001
Pulled: none
Pushed:
• #0 signed integer: data retrieved
s¹² is the signed integer to be retrived.
IG_AE integer get, absolute address, size embedded u⁸_000_10_1011 IG_AR integer get, absolute address, all operands in registers 0⁸_000_10_1011
Pulled:
• #0 signed integer: address to read in genspace
Pushed:
• #0 signed integer: data retrieved
u⁸ is how many bits to retrieve. If zero, IG_AR is performed instead.
Pulled:
• #0 signed integer: address to read in genspace
• #1 signed integer in 0…255: how many bits to retrieve
Pushed:
• #0 signed integer: data retrieved
IG_AE_Y integer get, absolute address, size embedded, synchronized u⁸_100_10_1011 IG_AR_Y integer get, absolute address, all operands in registers, synchronized 0⁸_100_10_1011
Same as IG_AE, plus synchronization. If u⁸ is zero, IG_AR_Y is performed instead. Same as IG_AR, plus synchronization.
IG_RO integer get, relative address, offset embedded s⁹_01_10_1011
Pulled:
• #0 signed integer 0…255: how many bits to retrieve
Pushed:
• #0 signed integer: data retrieved
s⁹ is the offset.
IG_RS integer get, relative address, size embedded u⁸_010_10_1011 IG_RR integer get, relative address, all operands in registers 0⁸_010_10_1011
Pulled:
• #0 signed integer: offset
Pushed:
• #0 signed integer: data retrieved
If u⁸ is zero, IG_RR is performed instead.
Pulled:
• #0 signed integer: offset
• #1 signed integer in 0…255: how many bits to retrieve
Pushed:
• #0 the signed integer: data retrieved
IG_RO_Y integer get, relative address, offset embedded, synchronized s⁹_11_10_1011
Same as IG_RO, plus synchronization.
IG_RS_Y integer get, relative address, size embedded, synchronized u⁸_110_10_1011 IG_RR_Y integer get, relative address, all operands in registers, synchronized 0⁸_110_10_1011
Same as IG_RS, plus synchronization. If u⁸ is zero, IG_RR_Y is performed instead. Same as IG_RR, plus synchronization.

IG_E	integer get, value embedded	s¹²_01_001
Pulled: none Pushed: • #0 signed integer: data retrieved s¹² is the signed integer to be retrived.
IG_AE	integer get, absolute address, size embedded	u⁸_000_10_1011	IG_AR	integer get, absolute address, all operands in registers	0⁸_000_10_1011
Pulled: • #0 signed integer: address to read in genspace Pushed: • #0 signed integer: data retrieved u⁸ is how many bits to retrieve. If zero, IG_AR is performed instead.	Pulled: • #0 signed integer: address to read in genspace • #1 signed integer in 0…255: how many bits to retrieve Pushed: • #0 signed integer: data retrieved
IG_AE_Y	integer get, absolute address, size embedded, synchronized	u⁸_100_10_1011	IG_AR_Y	integer get, absolute address, all operands in registers, synchronized	0⁸_100_10_1011
Same as IG_AE, plus synchronization. If u⁸ is zero, IG_AR_Y is performed instead.	Same as IG_AR, plus synchronization.
IG_RO	integer get, relative address, offset embedded	s⁹_01_10_1011
Pulled: • #0 signed integer 0…255: how many bits to retrieve Pushed: • #0 signed integer: data retrieved s⁹ is the offset.
IG_RS	integer get, relative address, size embedded	u⁸_010_10_1011	IG_RR	integer get, relative address, all operands in registers	0⁸_010_10_1011
Pulled: • #0 signed integer: offset Pushed: • #0 signed integer: data retrieved If u⁸ is zero, IG_RR is performed instead.	Pulled: • #0 signed integer: offset • #1 signed integer in 0…255: how many bits to retrieve Pushed: • #0 the signed integer: data retrieved
IG_RO_Y	integer get, relative address, offset embedded, synchronized	s⁹_11_10_1011
Same as IG_RO, plus synchronization.
IG_RS_Y	integer get, relative address, size embedded, synchronized	u⁸_110_10_1011	IG_RR_Y	integer get, relative address, all operands in registers, synchronized	0⁸_110_10_1011
Same as IG_RS, plus synchronization. If u⁸ is zero, IG_RR_Y is performed instead.	Same as IG_RR, plus synchronization.

Put. (see also float and string) These instructions pull an integer from the stack and write it into genspace. They attempt to convert the integer from the size it assumed in the register to the size requested for genspace, which is likely different from the trimmed size. If the integer will not fit into the requested size, a null is written instead.

IP_AE integer put, absolute address, size embedded u⁸_000_01_1011 IP_AR integer put, absolute address, all operands in registers 0⁸_000_01_1011
Pulled:
• #0 signed integer, the address to write in genspace
• #1 signed integer, data to write
Pushed: none
u⁸ is how many bits to write. If zero, IP_AR is performed instead.
Pulled:
• #0 signed integer: address to write in genspace
• #1 signed integer in 0…255: how many bits to write
• #2 signed integer: data to write
Pushed: none
IP_AE_Y integer put, absolute address, size embedded, synchronized u⁸_100_01_1011 IP_AR_Y integer put, absolute address, all operands in registers, synchronized 0⁸_100_01_1011
Same as IP_AE, plus synchronization. If u⁸ is zero, IP_AR_Y is performed instead. Same as IP_AR, plus synchronization.
IP_RO integer put, relative address, offset embedded s⁹_01_01_1011
Pulled:
• #0 signed integer 0…255: how many bits to write
• #1 signed integer: data to write
Pushed: none
s⁹ is the offset.
IP_RS integer put, relative address, size embedded u⁸_010_01_1011 IP_RR integer put, relative address, all operands in registers 0⁸_010_01_1011
Pulled:
• #0 signed integer: offset
• #1 signed integer: data to write
Pushed: none
u⁸ is how many bits to write. If zero, IP_RR is performed instead.
Pulled:
• #0 signed integer: offset
• #1 signed integer in 0…255: how many bits to write
• #2 signed integer: data to write
Pushed: none
IP_RO_Y integer put, relative address, offset embedded, synchronized s⁹_11_01_1011
Same as IP_RO, plus synchronization. .
IP_RS_Y integer put, relative address, size embedded, synchronized u⁸_110_01_1011 IP_RR_Y integer put, relative address, all operands in registers, synchronized 0⁸_110_01_1011
Same as IP_RE, plus synchronization. If u⁸ is zero, IP_RR_Y is performed instead. Same as IP_RR, plus synchronization.

IP_AE	integer put, absolute address, size embedded	u⁸_000_01_1011	IP_AR	integer put, absolute address, all operands in registers	0⁸_000_01_1011
Pulled: • #0 signed integer, the address to write in genspace • #1 signed integer, data to write Pushed: none u⁸ is how many bits to write. If zero, IP_AR is performed instead.	Pulled: • #0 signed integer: address to write in genspace • #1 signed integer in 0…255: how many bits to write • #2 signed integer: data to write Pushed: none
IP_AE_Y	integer put, absolute address, size embedded, synchronized	u⁸_100_01_1011	IP_AR_Y	integer put, absolute address, all operands in registers, synchronized	0⁸_100_01_1011
Same as IP_AE, plus synchronization. If u⁸ is zero, IP_AR_Y is performed instead.	Same as IP_AR, plus synchronization.
IP_RO	integer put, relative address, offset embedded	s⁹_01_01_1011
Pulled: • #0 signed integer 0…255: how many bits to write • #1 signed integer: data to write Pushed: none s⁹ is the offset.
IP_RS	integer put, relative address, size embedded	u⁸_010_01_1011	IP_RR	integer put, relative address, all operands in registers	0⁸_010_01_1011
Pulled: • #0 signed integer: offset • #1 signed integer: data to write Pushed: none u⁸ is how many bits to write. If zero, IP_RR is performed instead.	Pulled: • #0 signed integer: offset • #1 signed integer in 0…255: how many bits to write • #2 signed integer: data to write Pushed: none
IP_RO_Y	integer put, relative address, offset embedded, synchronized	s⁹_11_01_1011
Same as IP_RO, plus synchronization. .
IP_RS_Y	integer put, relative address, size embedded, synchronized	u⁸_110_01_1011	IP_RR_Y	integer put, relative address, all operands in registers, synchronized	0⁸_110_01_1011
Same as IP_RE, plus synchronization. If u⁸ is zero, IP_RR_Y is performed instead.	Same as IP_RR, plus synchronization.

Get-and-(conditional)-put. (see also float and string) The machine first compares the integer in genspace to the "old value" integer:

If they both have values, and they are equal: the "new value" integer is written to genspace in place of the old value, and the one-bit string 1 is pushed.
If either is null, or they are unequal: genspace is not changed, and the one-bit string 0 is pushed.

To test as equal, it is not necessary that the two integers have been trimmed to the same number of bits. For instance, the 6-bit integer 100_110 equals the 9-bit integer 100_110_000. (If an exact match of bit patterns is desired, the string version of get-and-put should be used.) If the "new value" integer is of such large magnitude that it will not fit into the indicated region of genspace, a null will be written instead.

IGP_AE integer get-and-put, absolute address, size embedded u⁸_000_11_1011 IGP_AR integer get-and-put, absolute address, all operands in registers 0⁸_000_11_1011
Pulled:
• #0 signed integer: the address to examine in genspace
• #1 signed integer: the old value
• #2 signed integer: the new value
Pushed:
• #0 one-bit string: result
u⁸ is how many bits of genspace to examine. If zero, IGP_AR is performed instead.
Pulled:
• #0 signed integer: address to examine in genspace
• #1 signed integer in 0…255: how many bits of genspace to examine
• #2 signed integer: the old value
• #3 signed integer: the new value
Pushed:
• #0 one-bit string: result
IGP_AE_Y integer get-and-put, absolute address, size embedded, synchronized u⁸_100_11_1011 IGP_AR_Y integer get-and-put, absolute address, all operands in registers, synchronized 0⁸_100_11_1011
Same as IGP_AE, plus synchronization. If u⁸ is zero, IGP_AR_Y is performed instead. Same as IGP_AR, plus synchronization.
IGP_RO integer get-and-put, relative address, offset embedded s⁹_01_11_1011
Pulled:
• #0 signed integer 0…255: how many bits of genspace to examine
• #1 signed integer: the old value
• #2 signed integer: the new value
Pushed:
• #0 one-bit string: result
s⁹ is the offset.
IGP_RS integer get-and-put, relative address, size embedded u⁸_010_11_1011 IGP_RR integer get-and-put, relative address, all operands in registers 0⁸_010_11_1011
Pulled:
• #0 signed integer: offset
• #1 signed integer: the old value
• #2 signed integer: the new value
Pushed:
• #0 one-bit string: result
u⁸ is how many bits of genspace to examine. If zero, IGP_RR is performed instead.
Pulled:
• #0 signed integer: offset
• #1 signed integer in 0…255: how many bits of genspace to examine
• #2 signed integer: the old value
• #3 signed integer: the new value
Pushed:
• #0 one-bit string: result
IGP_RO_Y integer get-and-put, relative address, offset embedded, synchronized s⁹_11_11_1011
Same as IGP_RO, plus synchronization.
IGP_RS_Y integer get-and-put, relative address, size embedded, synchronized u⁸_110_11_1011 IGP_RR_Y integer get-and-put, relative address, all operands in registers, synchronized 0⁸_110_11_1011
Same as IGP_RS, plus synchronization. If u⁸ is zero, IGP_RR_Y is performed instead. Same as IGP_RR, plus synchronization.

IGP_AE	integer get-and-put, absolute address, size embedded	u⁸_000_11_1011	IGP_AR	integer get-and-put, absolute address, all operands in registers	0⁸_000_11_1011
Pulled: • #0 signed integer: the address to examine in genspace • #1 signed integer: the old value • #2 signed integer: the new value Pushed: • #0 one-bit string: result u⁸ is how many bits of genspace to examine. If zero, IGP_AR is performed instead.	Pulled: • #0 signed integer: address to examine in genspace • #1 signed integer in 0…255: how many bits of genspace to examine • #2 signed integer: the old value • #3 signed integer: the new value Pushed: • #0 one-bit string: result
IGP_AE_Y	integer get-and-put, absolute address, size embedded, synchronized	u⁸_100_11_1011	IGP_AR_Y	integer get-and-put, absolute address, all operands in registers, synchronized	0⁸_100_11_1011
Same as IGP_AE, plus synchronization. If u⁸ is zero, IGP_AR_Y is performed instead.	Same as IGP_AR, plus synchronization.
IGP_RO	integer get-and-put, relative address, offset embedded	s⁹_01_11_1011
Pulled: • #0 signed integer 0…255: how many bits of genspace to examine • #1 signed integer: the old value • #2 signed integer: the new value Pushed: • #0 one-bit string: result s⁹ is the offset.
IGP_RS	integer get-and-put, relative address, size embedded	u⁸_010_11_1011	IGP_RR	integer get-and-put, relative address, all operands in registers	0⁸_010_11_1011
Pulled: • #0 signed integer: offset • #1 signed integer: the old value • #2 signed integer: the new value Pushed: • #0 one-bit string: result u⁸ is how many bits of genspace to examine. If zero, IGP_RR is performed instead.	Pulled: • #0 signed integer: offset • #1 signed integer in 0…255: how many bits of genspace to examine • #2 signed integer: the old value • #3 signed integer: the new value Pushed: • #0 one-bit string: result
IGP_RO_Y	integer get-and-put, relative address, offset embedded, synchronized	s⁹_11_11_1011
Same as IGP_RO, plus synchronization.
IGP_RS_Y	integer get-and-put, relative address, size embedded, synchronized	u⁸_110_11_1011	IGP_RR_Y	integer get-and-put, relative address, all operands in registers, synchronized	0⁸_110_11_1011
Same as IGP_RS, plus synchronization. If u⁸ is zero, IGP_RR_Y is performed instead.	Same as IGP_RR, plus synchronization.

Versus. (see also float, string, and branch) Two integers may be compared with each other. The result is a string at #0, which contains 20 bits. Its contents are:

Address of bit within #0_new With IV_R, bit equals 1 when … Comments
0 #0_old and #1_old both have values, and #0_old > #1_old never both 1 analogous to float and string
1 #0_old and #1_old both have values, and #0_old ≤ #1_old
2 #0_old and #1_old both have values, and #0_old ≠ #1_old never both 1
3 #0_old and #1_old both have values, and #0_old = #1_old
4 #0_old and #1_old both have values, and #0_old < #1_old never both 1
5 #0_old and #1_old both have values, and #0_old ≥ #1_old
6 #0_old is null never the same analogous to float
7 #0_old has a value
8 #1_old is null never the same
9 #1_old has a value
10 #0_old and #1_old are similar never the same
11 #0_old and #1_old are dissimilar
12 #0_old has a value, and #1_old is null never the same
13 #0_old is null, or #1_old has a value
14 #0_old is null, and #1_old has a value never the same
15 #0_old has a value, or #1_old is null
16 #0_old has a value, and #1_old has a value never the same
17 #0_old is null, or #1_old is null
18 #0_old is null, and #1_old is null never the same
19 #0_old has a value, or #1_old has a value

Address of bit within #0_new	With IV_R, bit equals 1 when …	Comments
0	#0_old and #1_old both have values, and #0_old > #1_old	never both 1	analogous to float and string
1	#0_old and #1_old both have values, and #0_old ≤ #1_old
2	#0_old and #1_old both have values, and #0_old ≠ #1_old	never both 1
3	#0_old and #1_old both have values, and #0_old = #1_old
4	#0_old and #1_old both have values, and #0_old < #1_old	never both 1
5	#0_old and #1_old both have values, and #0_old ≥ #1_old
6	#0_old is null	never the same	analogous to float
7	#0_old has a value
8	#1_old is null	never the same
9	#1_old has a value
10	#0_old and #1_old are similar	never the same
11	#0_old and #1_old are dissimilar
12	#0_old has a value, and #1_old is null	never the same
13	#0_old is null, or #1_old has a value
14	#0_old is null, and #1_old has a value	never the same
15	#0_old has a value, or #1_old is null
16	#0_old has a value, and #1_old has a value	never the same
17	#0_old is null, or #1_old is null
18	#0_old is null, and #1_old is null	never the same
19	#0_old has a value, or #1_old has a value

The result of a one-register comparison (IV_E) is the same as that of the two-register version (IV_R), except that the signed integer embedded within the opcode is substituted for #1.

IV_E integer versus, one comparand embedded s⁹_1111_0011 IV_R integer versus, both comparands in registers 0⁸1_1111_0011
Pulled:
• #0 signed integer, a comparand
Pushed:
• #0 20-bit string, the result
If s⁹ is null, IV_R is performed instead.
Pulled:
• #0 signed integer: comparand
• #1 signed integer: comparand
Pushed:
• #0 20-bit string: result

IV_E	integer versus, one comparand embedded	s⁹_1111_0011	IV_R	integer versus, both comparands in registers	0⁸1_1111_0011
Pulled: • #0 signed integer, a comparand Pushed: • #0 20-bit string, the result If s⁹ is null, IV_R is performed instead.	Pulled: • #0 signed integer: comparand • #1 signed integer: comparand Pushed: • #0 20-bit string: result

Note that integer comparison is not trichotomous, but is better described by a tetrachotomy. For any two integers m and n:

m > n
m = n
m < n
Comparison fails, because at least one of m and n is null

This fact greatly influences the writing of code. However, the existence of nulls encourages the programmer to consider error conditions that might otherwise be overlooked.

Arithmetic. (see also float) Addition, subtraction and multiplication are nonsurprising. A result is null if either input is null, or if there is positive or negative overflow. All results are trimmed.

IA_E integer add, addend embedded s⁹_0000_0011 IA_R integer add, addend in register 0⁸1_0000_0011
Pulled:
• #0 signed integer: augend
Pushed:
• #0 signed integer: augend plus addend
If s⁹ is null, IA_R is performed instead.
Pulled:
• #0 signed integer: augend
• #1 signed integer: addend
Pushed:
• #0 signed integer: augend plus addend
IM_E integer multiply, multiplier embedded s⁹_1000_0011 IM_R integer multiply, multiplier in register 0⁸1_1000_0011
Pulled:
• #0 signed integer: multiplicand
Pushed:
• #0 signed integer: multiplicand times multiplier
If s⁹ is null, IM_R is performed instead.
Pulled:
• #0 signed integer: multiplicand
• #1 signed integer: multiplier
Pushed:
• #0 signed integer: multiplicand times multiplier
IS_S integer subtract, subtrahend embedded s⁹_0100_0011 IS_R integer subtract, both operands in register 0⁸1_0100_0011
Pulled:
• #0 signed integer: minuend
Pushed:
• #0 signed integer: minuend minus subtrahend
If s⁹ is null, IS_R is performed instead.
Pulled:
• #0 signed integer: minuend
• #1 signed integer: subtrahend
Pushed:
• #0 signed integer: minuend minus subtrahend
IS_M integer subtract, minuend embedded s⁹_1100_0011
Pulled:
• #0 signed integer: subtrahend
Pushed:
• #0 signed integer: minuend minus subtrahend
To negate the integer in #0, use a minuend of zero.
If s⁹ is null, IS_R is performed instead.

IA_E	integer add, addend embedded	s⁹_0000_0011	IA_R	integer add, addend in register	0⁸1_0000_0011
Pulled: • #0 signed integer: augend Pushed: • #0 signed integer: augend plus addend If s⁹ is null, IA_R is performed instead.	Pulled: • #0 signed integer: augend • #1 signed integer: addend Pushed: • #0 signed integer: augend plus addend
IM_E	integer multiply, multiplier embedded	s⁹_1000_0011	IM_R	integer multiply, multiplier in register	0⁸1_1000_0011
Pulled: • #0 signed integer: multiplicand Pushed: • #0 signed integer: multiplicand times multiplier If s⁹ is null, IM_R is performed instead.	Pulled: • #0 signed integer: multiplicand • #1 signed integer: multiplier Pushed: • #0 signed integer: multiplicand times multiplier
IS_S	integer subtract, subtrahend embedded	s⁹_0100_0011	IS_R	integer subtract, both operands in register	0⁸1_0100_0011
Pulled: • #0 signed integer: minuend Pushed: • #0 signed integer: minuend minus subtrahend If s⁹ is null, IS_R is performed instead.	Pulled: • #0 signed integer: minuend • #1 signed integer: subtrahend Pushed: • #0 signed integer: minuend minus subtrahend
IS_M	integer subtract, minuend embedded	s⁹_1100_0011
Pulled: • #0 signed integer: subtrahend Pushed: • #0 signed integer: minuend minus subtrahend To negate the integer in #0, use a minuend of zero. If s⁹ is null, IS_R is performed instead.

Integer division requires further comment. It involves two inputs (numerator N and denominator D) and two outputs (quotient Q and remainder R). Elsewhere in mathematics, the numerator is termed the dividend, and the denominator is called the divisor, but here those words are avoided because both begin with the letter d.

Here are the specifications:

If D = 0, R and Q will be null.
N − R will equal Q × D.
The magnitude of R will be less than the magnitude of D.
R will be of the same sign (positive, negative, zero) as D.

Examples (in decimal):

If N = +23 and D = +7, then Q = +3 and R = +2.
If N = −23 and D = +7, then Q = −4 and R = +5.
If N = +23 and D = −7, then Q = −4 and R = −5.
If N = −23 and D = −7, then Q = +3 and R = −2.

Whatever the signs of N and D, Q is rounded toward negative infinity; no attempt is made to round Q to the nearest integer. Other rounding policies could reasonably have been chosen, as there is no consensus in computer science or mathematics on this matter. In any case, −∞ is simple to remember.

A result is null if either of the inputs is null, or if there is division by zero; in particular, null divided by zero is null. All results are trimmed.

IQ_D integer quotient, denominator embedded s⁹_0010_0011 IQ_R integer quotient, both operands in registers 0⁸1_0010_0011
Pulled:
• #0 signed integer: numerator
Pushed:
• #0 signed integer: quotient
If s⁹ is null, IQ_R is performed instead.
Pulled:
• #0 signed integer: numerator
• #1 signed integer: denominator
Pushed:
• #0 signed integer: quotient
IQ_N integer quotient, numerator embedded s⁹_1010_0011
Pulled:
• #0 signed integer: denominator
Pushed:
• #0 signed integer: quotient
If s⁹ is null, IQ_R is performed instead.
IR_D integer remainder, denominator embedded s⁹_0110_0011 IR_R integer remainder, both operands in registers 0⁸1_0110_0011
Pulled:
• #0 signed integer: numerator
Pushed:
• #0 signed integer: remainder
If s⁹ is null, IR_R is performed instead.
Pulled:
• #0 signed integer: numerator
• #1 signed integer: denominator
Pushed:
• #0 signed integer: remainder
IR_N integer remainder, numerator embedded s⁹_1110_0011
Pulled:
• #0 signed integer: denominator
Pushed:
• #0 signed integer: remainder
If s⁹ is null, IR_R is performed instead.
IQR_D integer quotient and remainder, denominator embedded s⁹_0001_0011 IQR_R integer quotient and remainder, both operands in registers 0⁸1_0001_0011
Pulled:
• #0 signed integer: numerator
Pushed:
• #0 signed integer: quotient
• #1 signed integer: remainder
If s⁹ is null, IQR_R is performed instead.
Pulled:
• #0 signed integer: numerator
• #1 signed integer: denominator
Pushed:
• #0 signed integer: quotient
• #1 signed integer: remainder
IQR_N integer quotient and remainder, numerator embedded s⁹_1001_0011
Pulled:
• #0 signed integer: denominator
Pushed:
• #0 signed integer: quotient
• #1 signed integer: remainder
If s⁹ is null, IQR_R is performed instead.

IQ_D	integer quotient, denominator embedded	s⁹_0010_0011	IQ_R	integer quotient, both operands in registers	0⁸1_0010_0011
Pulled: • #0 signed integer: numerator Pushed: • #0 signed integer: quotient If s⁹ is null, IQ_R is performed instead.	Pulled: • #0 signed integer: numerator • #1 signed integer: denominator Pushed: • #0 signed integer: quotient
IQ_N	integer quotient, numerator embedded	s⁹_1010_0011
Pulled: • #0 signed integer: denominator Pushed: • #0 signed integer: quotient If s⁹ is null, IQ_R is performed instead.
IR_D	integer remainder, denominator embedded	s⁹_0110_0011	IR_R	integer remainder, both operands in registers	0⁸1_0110_0011
Pulled: • #0 signed integer: numerator Pushed: • #0 signed integer: remainder If s⁹ is null, IR_R is performed instead.	Pulled: • #0 signed integer: numerator • #1 signed integer: denominator Pushed: • #0 signed integer: remainder
IR_N	integer remainder, numerator embedded	s⁹_1110_0011
Pulled: • #0 signed integer: denominator Pushed: • #0 signed integer: remainder If s⁹ is null, IR_R is performed instead.
IQR_D	integer quotient and remainder, denominator embedded	s⁹_0001_0011	IQR_R	integer quotient and remainder, both operands in registers	0⁸1_0001_0011
Pulled: • #0 signed integer: numerator Pushed: • #0 signed integer: quotient • #1 signed integer: remainder If s⁹ is null, IQR_R is performed instead.	Pulled: • #0 signed integer: numerator • #1 signed integer: denominator Pushed: • #0 signed integer: quotient • #1 signed integer: remainder
IQR_N	integer quotient and remainder, numerator embedded	s⁹_1001_0011
Pulled: • #0 signed integer: denominator Pushed: • #0 signed integer: quotient • #1 signed integer: remainder If s⁹ is null, IQR_R is performed instead.

Format. (see also float) When an integer is stored into a register, it is by default trimmed so as to use the fewest bits. However, the programmer can change it to something different. Requesting a size smaller than the minimum will result in a null, still with the requested number of bits.

IF_TE integer format trim, size embedded u⁸_0101_0011 IF_TR integer format trim, size in register 0⁸_0101_0011
Pulled:
• #0 signed integer: to be resized
Pushed:
• #0 signed integer: in its new size
If u⁸ is zero, IF_TR is performed instead.
Pulled:
• #0 signed integer: to be resized
• #1 signed integer in 0…255: new size
Pushed:
• #0 signed integer: in its new size
IF_TQ integer format trim, query ?_0_1101_0011 IF_TM integer format trim, minimum ?_1_1101_0011
Pulled:
• #0 signed integer: that would be resized
Pushed:
• #0 signed integer: minimum size of #0_old
#0_new contains the size that #0_old would become if it were supplied to IF_TM.
Pulled:
• #0 signed integer: to be resized
Pushed:
• #0 signed integer: in the smallest legal size

IF_TE	integer format trim, size embedded	u⁸_0101_0011	IF_TR	integer format trim, size in register	0⁸_0101_0011
IF_TE	Pulled: • #0 signed integer: to be resized Pushed: • #0 signed integer: in its new size If u⁸ is zero, IF_TR is performed instead.		IF_TR	Pulled: • #0 signed integer: to be resized • #1 signed integer in 0…255: new size Pushed: • #0 signed integer: in its new size
IF_TQ	integer format trim, query	?_0_1101_0011	IF_TM	integer format trim, minimum	?_1_1101_0011
IF_TQ	Pulled: • #0 signed integer: that would be resized Pushed: • #0 signed integer: minimum size of #0_old #0_new contains the size that #0_old would become if it were supplied to IF_TM.		IF_TM	Pulled: • #0 signed integer: to be resized Pushed: • #0 signed integer: in the smallest legal size