haroldbot 2

show more parentheses

Examples

Just do some math
    1000 + 15 & -16

Find out whether two expressions are equivalent
    let x = a + b in (x < a) == (x < max(a, b))

Prove that two expressions are equivalent
    a ^ ((a ^ b) & mask) == (a & ~mask) | (b & mask)

Find when two expressions are equal and when they are not
    x == -x

Quantify some variables away to find values that always work
    forall x: -x == (x ^ m) - m

Notes

Tip: a saved copy of this page works offline.

See the table of operators below for operator precedence.

Comparisons result in 0 (false) or -1 (true).

Finding proofs can be slow and often nothing is found at all.

SAT fallback now exists, using MiniSat compiled with Emscripten. This is brand new so expect bugs (not due to MiniSat, but for example I don't entirely trust my circuit builder and circuit-to-SAT converter). haroldbot should now give up early on (some) multiplications that would create a gigantic BDD.

In general, there are many bugs.

Since everything happens client-side, I don't get automatic bug reports. Please open an issue or contact me (eg via email, Mastodon @harold@mastodon.gamedev.place or twitter @HaroldAptroot).

Overview of how haroldbot works.

List of available functions

• min = min_u, min_s
• max = max_u, max_s
• ror, rol bitwise rotate
• addus, addss, subus, subss (un)signed saturating addition and subtraction
• avg, avg_up unsigned average, rounded down or up respectively
• ternlog
• popcnt
• abs
• nlz (alias lzcnt) number of leading zeroes
• ntz (alias tzcnt) number of trailing zeroes
• reverse bit-reversal
• grev generalized bit-reversal (2 arguments)
• hmul = hmul_u, hmul_s high half of product
• blsi, blsr, blsmsk, tzmsk BMI operations
• bzhi, pdep, pext BMI2 operations
• clmul carryless multiplication
• grevmul it's grevmul, whatever that is

Operators

Precedence	Operator	Description
1	let ... in ...	"let" expression
2	~	bitwise complement
	-	negation
3	*	multiplication
	/ /u	unsigned division
	/s	signed division
	/e	Euclidean division
	/p	unsigned division but division by zero yields zero
	% %u	unsigned remainder
	%s	signed remainder
	%e	Euclidean remainder
4	+	addition
	-	subtraction
5	<<	shift left
	>> >>u	shift right (logical)
	>>s	shift right (arithmetic)
6	&	bitwise AND
7	^	bitwise XOR
8	|	bitwise OR
9	==	compare equal
	!=	compare not equal
	< <u	compare unsigned less than
	<s	compare signed less than
	> >u	compare unsigned greater than
	>s	compare signed greater than
	<= <=u	compare unsigned less than or equal
	<=s	compare signed less than or equal
	>= >=u	compare unsigned greater than or equal
	>=s	compare signed greater than or equal
10	&&	Boolean AND, implicitly converts integer operands to Boolean
11	||	Boolean OR, implicitly converts integer operands to Boolean
12	=>	Boolean implication, implicitly converts integer operands to Boolean
13	... ? ... : ...	Ternary operator if the condition is a Boolean, otherwise bitwise MUX