Arithmetic primitives

TVM Instructions Content List

Opcode	Fift syntax	Stack	Description	Gas
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Arithmetic primitives

Addition, subtraction, multiplication

xxxxxxx Opcode	xxxxxxxxxxxxxxxxxxxxxxxxxxxx Fift syntax	xxxxxxxxxxxxxxxxx Stack	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Description	xxxx Gas
`A0`	`ADD`	`x y - x+y`		`18`
`A1`	`SUB`	`x y - x-y`		`18`
`A2`	`SUBR`	`x y - y-x`	Equivalent to `SWAP` `SUB`.	`18`
`A3`	`NEGATE`	`x - -x`	Equivalent to `-1 MULCONST` or to `ZERO SUBR`. Notice that it triggers an integer overflow exception if `x=-2^256`.	`18`
`A4`	`INC`	`x - x+1`	Equivalent to `1 ADDCONST`.	`18`
`A5`	`DEC`	`x - x-1`	Equivalent to `-1 ADDCONST`.	`18`
`A6cc`	`[cc] ADDCONST` `[cc] ADDINT` `[-cc] SUBCONST` `[-cc] SUBINT`	`x - x+cc`	`-128 <= cc <= 127`.	`26`
`A7cc`	`[cc] MULCONST` `[cc] MULINT`	`x - xcc`*	`-128 <= cc <= 127`.	`26`
`A8`	`MUL`	`x y - xy`*		`18`

Division

xxxxxxx Opcode	xxxxxxxxxxxxxxxxxxxxxxxxxxxx Fift syntax	xxxxxxxxxxxxxxxxx Stack	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Description	xxxx Gas
`A9mscdf`			This is the general encoding of division, with an optional pre-multiplication and an optional replacement of the division or multiplication by a shift. Variable fields are as follows: `0 <= m <= 1` - Indicates whether there is pre-multiplication (`MULDIV` and its variants), possibly replaced by a left shift. `0 <= s <= 2` - Indicates whether either the multiplication or the division have been replaced by shifts: `s=0` - no replacement, `s=1` - division replaced by a right shift, `s=2` - multiplication replaced by a left shift (possible only for `m=1`). `0 <= c <= 1` - Indicates whether there is a constant one-byte argument `tt` for the shift operator (if `s!=0`). For `s=0`, `c=0`. If `c=1`, then `0 <= tt <= 255`, and the shift is performed by `tt+1` bits. If `s!=0` and `c=0`, then the shift amount is provided to the instruction as a top-of-stack Integer in range `0...256`. `1 <= d <= 3` - Indicates which results of division are required: `1` - only the quotient, `2` - only the remainder, `3` - both. `0 <= f <= 2` - Rounding mode: `0` - floor, `1` - nearest integer, `2` - ceiling. All instructions below are variants of this.	`26`
`A904`	`DIV`	`x y - q`	`q=floor(x/y)`, `r=x-y*q`	`26`
`A905`	`DIVR`	`x y - q’`	`q’=round(x/y)`, `r’=x-y*q’`	`26`
`A906`	`DIVC`	`x y - q''`	`q’’=ceil(x/y)`, `r’’=x-y*q’’`	`26`
`A908`	`MOD`	`x y - r`		`26`
`A90C`	`DIVMOD`	`x y - q r`		`26`
`A90D`	`DIVMODR`	`x y - q' r'`		`26`
`A90E`	`DIVMODC`	`x y - q'' r''`		`26`
`A925`	`RSHIFTR`	`x y - round(x/2^y)`		`26`
`A926`	`RSHIFTC`	`x y - ceil(x/2^y)`		`34`
`A935tt`	`[tt+1] RSHIFTR#`	`x y - round(x/2^(tt+1))`		`34`
`A936tt`	`[tt+1] RSHIFTC#`	`x y - ceil(x/2^(tt+1))`		`34`
`A938tt`	`[tt+1] MODPOW2#`	`x - x mod 2^(tt+1)`		`34`
`A98`	`MULDIV`	`x y z - q`	`q=floor(x*y/z)`	`26`
`A985`	`MULDIVR`	`x y z - q'`	`q'=round(x*y/z)`	`26`
`A98C`	`MULDIVMOD`	`x y z - q r`	`q=floor(xy/z)`, `r=xy-z*q`	`26`
`A9A4`	`MULRSHIFT`	`x y z - floor(xy/2^z)`*	`0 <= z <= 256`	`26`
`A9A5`	`MULRSHIFTR`	`x y z - round(xy/2^z)`*	`0 <= z <= 256`	`26`
`A9A6`	`MULRSHIFTC`	`x y z - ceil(xy/2^z)`*	`0 <= z <= 256`	`34`
`A9B4tt`	`[tt+1] MULRSHIFT#`	`x y - floor(xy/2^(tt+1))`*		`34`
`A9B5tt`	`[tt+1] MULRSHIFTR#`	`x y - round(xy/2^(tt+1))`*		`34`
`A9B6tt`	`[tt+1] MULRSHIFTC#`	`x y - ceil(xy/2^(tt+1))`*		`26`
`A9C4`	`LSHIFTDIV`	`x y z - floor(2^zx/y)`*	`0 <= z <= 256`	`26`
`A9C5`	`LSHIFTDIVR`	`x y z - round(2^zx/y)`*	`0 <= z <= 256`	`26`
`A9C6`	`LSHIFTDIVC`	`x y z - ceil(2^zx/y)`*	`0 <= z <= 256`	`34`
`A9D4tt`	`[tt+1] LSHIFT#DIV`	`x y - floor(2^(tt+1)x/y)`*		`34`
`A9D5tt`	`[tt+1] LSHIFT#DIVR`	`x y - round(2^(tt+1)x/y)`*		`34`
`A9D6tt`	`[tt+1] LSHIFT#DIVC`	`x y - ceil(2^(tt+1)x/y)`*		`26`

Shifts, logical operations

xxxxxxx Opcode	xxxxxxxxxxxxxxxxxxxxxxxxxxxx Fift syntax	xxxxxxxxxxxxxxxxx Stack	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Description	xxxx Gas
`AAcc`	`[cc+1] LSHIFT#`	`x - x2^(cc+1)`*	`0 <= cc <= 255`	`26`
`ABcc`	`[cc+1] RSHIFT#`	`x - floor(x/2^(cc+1))`	`0 <= cc <= 255`	`18`
`AC`	`LSHIFT`	`x y - x2^y`*	`0 <= y <= 1023`	`18`
`AD`	`RSHIFT`	`x y - floor(x/2^y)`	`0 <= y <= 1023`	`18`
`AE`	`POW2`	`y - 2^y`	`0 <= y <= 1023` Equivalent to `ONE` `SWAP` `LSHIFT`.	`18`
`B0`	`AND`	`x y - x&y`	Bitwise and of two signed integers `x` and `y`, sign-extended to infinity.	`18`
`B1`	`OR`	`x y - x\\|y`	Bitwise or of two integers.	`18`
`B2`	`XOR`	`x y - x xor y`	Bitwise xor of two integers.	`18`
`B3`	`NOT`	`x - ~x`	Bitwise not of an integer.	`26`
`B4cc`	`[cc+1] FITS`	`x - x`	Checks whether `x` is a `cc+1`-bit signed integer for `0 <= cc <= 255` (i.e., whether `-2^cc <= x < 2^cc`). If not, either triggers an integer overflow exception, or replaces `x` with a `NaN` (quiet version).	`26/76`
`B400`	`CHKBOOL`	`x - x`	Checks whether `x` is a “boolean value'' (i.e., either 0 or -1).	`26/76`
`B5cc`	`[cc+1] UFITS`	`x - x`	Checks whether `x` is a `cc+1`-bit unsigned integer for `0 <= cc <= 255` (i.e., whether `0 <= x < 2^(cc+1)`).	`26/76`
`B500`	`CHKBIT`	`x - x`	Checks whether `x` is a binary digit (i.e., zero or one).	`26/76`
`B600`	`FITSX`	`x c - x`	Checks whether `x` is a `c`-bit signed integer for `0 <= c <= 1023`.	`26/76`
`B601`	`UFITSX`	`x c - x`	Checks whether `x` is a `c`-bit unsigned integer for `0 <= c <= 1023`.	`26/76`
`B602`	`BITSIZE`	`x - c`	Computes smallest `c >= 0` such that `x` fits into a `c`-bit signed integer (`-2^(c-1) <= c < 2^(c-1)`).	`26`
`B603`	`UBITSIZE`	`x - c`	Computes smallest `c >= 0` such that `x` fits into a `c`-bit unsigned integer (`0 <= x < 2^c`), or throws a range check exception.	`26`
`B608`	`MIN`	`x y - x or y`	Computes the minimum of two integers `x` and `y`.	`26`
`B609`	`MAX`	`x y - x or y`	Computes the maximum of two integers `x` and `y`.	`26`
`B60A`	`MINMAX` `INTSORT2`	`x y - x y or y x`	Sorts two integers. Quiet version of this operation returns two `NaN`s if any of the arguments are `NaN`s.	`26`
`B60B`	`ABS`	`x - \\|x\\|`	Computes the absolute value of an integer `x`.	`26`

Quiet arithmetic primitives

Quiet operations return NaN instead of throwing exceptions if one of their arguments is a NaN or in the case of an integer overflow. Quiet operations have a prefix Q as shown below. Another way to make an operation quiet is to add QUIET before it (i.e. one can write QUIET ADD instead of QADD). Quiet versions of integer comparison primitives are also available (QUIET SGN, QUIET LESS etc).

xxxxxxx Opcode	xxxxxxxxxxxxxxxxxxxxxxxxxxxx Fift syntax	xxxxxxxxxxxxxxxxx Stack	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Description	xxxx Gas
`B7A0`	`QADD`	`x y - x+y`		`26`
`B7A1`	`QSUB`	`x y - x-y`		`26`
`B7A2`	`QSUBR`	`x y - y-x`		`26`
`B7A3`	`QNEGATE`	`x - -x`		`26`
`B7A4`	`QINC`	`x - x+1`		`26`
`B7A5`	`QDEC`	`x - x-1`		`26`
`B7A8`	`QMUL`	`x y - xy`*		`26`
`B7A904`	`QDIV`	`x y - q`	Division returns `NaN` if `y=0`.	`34`
`B7A905`	`QDIVR`	`x y - q’`		`34`
`B7A906`	`QDIVC`	`x y - q''`		`34`
`B7A908`	`QMOD`	`x y - r`		`34`
`B7A90C`	`QDIVMOD`	`x y - q r`		`34`
`B7A90D`	`QDIVMODR`	`x y - q' r'`		`34`
`B7A90E`	`QDIVMODC`	`x y - q'' r''`		`34`
`B7A985`	`QMULDIVR`	`x y z - q'`		`34`
`B7A98C`	`QMULDIVMOD`	`x y z - q r`		`34`
`B7AC`	`QLSHIFT`	`x y - x2^y`*		`26`
`B7AD`	`QRSHIFT`	`x y - floor(x/2^y)`		`26`
`B7AE`	`QPOW2`	`y - 2^y`		`26`
`B7B0`	`QAND`	`x y - x&y`		`26`
`B7B1`	`QOR`	`x y - x\\|y`		`26`
`B7B2`	`QXOR`	`x y - x xor y`		`26`
`B7B3`	`QNOT`	`x - ~x`		`26`
`B7B4cc`	`[cc+1] QFITS`	`x - x`	Replaces `x` with a `NaN` if x is not a `cc+1`-bit signed integer, leaves it intact otherwise.	`34`
`B7B5cc`	`[cc+1] QUFITS`	`x - x`	Replaces `x` with a `NaN` if x is not a `cc+1`-bit unsigned integer, leaves it intact otherwise.	`34`
`B7B600`	`QFITSX`	`x c - x`	Replaces `x` with a `NaN` if x is not a c-bit signed integer, leaves it intact otherwise.	`34`
`B7B601`	`QUFITSX`	`x c - x`	Replaces `x` with a `NaN` if x is not a c-bit unsigned integer, leaves it intact otherwise.	`34`

Arithmetic primitives

TVM Instructions Content List​

Arithmetic primitives​

Addition, subtraction, multiplication​

Division​

Shifts, logical operations​

Quiet arithmetic primitives​

TVM Instructions Content List​

TVM Instructions Content List

Arithmetic primitives

Addition, subtraction, multiplication

Division

Shifts, logical operations

Quiet arithmetic primitives

TVM Instructions Content List