Mathematical functions

oleg · November 2019

Is there a better function to get a number sign?

a=-456
anti_abs=math.abs(a)/a 
print(anti_abs)
--> -1
 
a=456
anti_abs=math.abs(a)/a 
print(anti_abs)
--> 1

MoKaLux · November 2019

I found this SO question, in case you haven't seen it. Hope this helps?

https://stackoverflow.com/questions/441893/which-is-faster-math-absvalue-or-value-1

oleg · November 2019

MoKaLux said:
I found this SO question, in case you haven't seen it. Hope this helps?

https://stackoverflow.com/questions/441893/which-is-faster-math-absvalue-or-value-1

I asked about the opposite function, look more closely

 anti_abs=math.abs(a)/a

or

function anti_abs(a) if a<0 then return -1 else return 1 end  end

MoKaLux · November 2019

oops, that didn't help

hgy29 · November 2019

A good question for the profiler

maybe ((a*a)^0.5)/a

keszegh · November 2019

comparing with 0 is slow?

oleg · November 2019

keszegh said:
comparing with 0 is slow?

Not concise

SinisterSoft · November 2019

Here is my version...

a=-456
anti_abs=(a<>-1)><1
print(anti_abs)
 
a=456
anti_abs=(a<>-1)><1
print(anti_abs)
 
a=0
anti_abs=(a<>-1)><1
print(anti_abs)</pre>

oleg · November 2019

SinisterSoft said:
Here is my version...
 
a=0
anti_abs=(a<>-1)><1
print(anti_abs)</pre>

Zero should give +1, not 0

All the examples are wrong with zero ...

Exept this..
if a<0 then return -1 else return 1 end

rrraptor · November 2019

max@1000000
calls @ 10
a @ -458
 
 
local abs=math.abs
function test1()
	for loop=1,max do
		local sign=math.abs(a)/a
	end
end
 
function test2()
	for loop=1,max do
		local sign=1
		if a<0 then sign=-1 end
	end
end
 
function test3()
	for loop=1,max do
		local sign=a < 0 and -1 or 1
	end
end
 
function test4()
	for loop=1,max do
		local sign=abs(a)/a
	end
end
 
function test5()
	for loop=1,max do
		local sign= ~((-a >> 31) - (a >> 31))+1
	end
end
 
function test6()
	for loop=1,max do
		local sign = (((a >> 31 ) + 1) << 1)-1
	end
end
 
Core.profilerReset()
Core.profilerStart()
for loop=1,calls do
	test1()
	test2()
	test3()
	test4()
	test5()
	test6()
end
Core.profilerStop()
 
-- print the results of the profiler
result=Core.profilerReport()
print("Number of tests:",max*calls)
for k,v in pairs(result) do
	local found=false
	for k2,v2 in pairs(v) do
		if found and k2=="time" then print(v1,v2) end
		if k2=="name" and string.sub(v2,1,4)=="test" then v1=v2 found=true end
	end
end

Core i7-8700:

Number of tests: 10000000
test1 2.0068597
test2 0.11249119999957
test3 0.12390259999756
test4 2.1758287000011
test5 0.17857100000037
test6 0.14978380000048

Android Snapdragon 660:

Number of tests: 10000000
test1 11.119264109991
test2 0.3629721889738
test3 0.38107234399649
test4 11.203031454002
test5 0.66782401097589
test6 0.58520260301884

((a*a)^0.5)/a

fastest, but gives incorrect result with 0
I guess, #2 or #3 is ok. Less than a sec., shoud be good

EDIT:
Found one more way:

local sign = ~((-a >> 31) - (a >> 31))+1

It returns -1/0/1 but slower than just

a < 0 and -1 or a > 0 and 1 or 0

EDIT2
Hmm, I wonder why bit operations slower that just "x < y and a or b"?
This give us -1 for neagative and 1 for 0 and positive numbers

(((a >> 31 ) + 1) << 1)-1

But again, slower than

a < 0 and -1 or 1

keszegh · November 2019

wikipedia:
Zero itself is without a sign, or signless.

oleg · November 2019

keszegh said:
wikipedia:
Zero itself is without a sign, or signless.

In our case "-1" and "+1" is not a number - it's a "sign" of the number. 456 * -1 =-456

All other values except "-1" and "+1" will cause errors in the program

keszegh · November 2019

value 0 would be more natural as the sign of 0, and multiplying with 0 won't throw an error.

oleg · November 2019

keszegh said:
wikipedia:
Zero itself is without a sign, or signless.

Zero sign doesn't matter '+' or '-', but it must be '+1' or '-1'
For my program only 3 ways will not cause an error in the program:

1.@rrraptor
a<0 and -1 or a > 0 and 1 or 0

2.@SinisterSoft
a=0
anti_abs=(a<>-1)><1
print(anti_abs)

3.if a<0 then return -1 else return 1 end

And my example and example @hgy29 will give a value of 'nan' and cause an error

oleg · November 2019

keszegh said:
value 0 would be more natural as the sign of 0, and multiplying with 0 won't throw an error.

If I want to move the sign '-' numbers '-0' to another number '456' multiplication by 0 will return 0 and must return 456.

So there are only '-1' and '+1' and '0' is not allowed

SinisterSoft · November 2019

Technically 0 has no sign. So there are two solutions test7 and test8 ... (pretty old xeon)

test7 results with:
-1 if neg, 0 if 0, +1 if pos

test8 result with:
-1 if neg, 0 if not neg

function test7()
for loop=1,max do
local sign =(a<>-1)><1
end
end

function test8()
for loop=1,max do
local sign =(a<>-1)><0
end
end

test1 4.5261051000002
test2 0.23030710000012
test3 0.25647970000023
test4 4.9691175000003
test5 0.48598210000046
test6 0.3186288000004
test7 0.17589819999989
test8 0.17575890000012

SinisterSoft · November 2019

I also added a test9 in case being -1 or +1 was important, test9 will give -1 if neg and +1 if pos (inc zero)...

function test9()
for loop=1,max do
local sign =((a<>-1)><0)|1
end
end

test2 0.23013360000004
test3 0.25745690000076
test5 0.37778469999967
test6 0.31808180000007
test7 0.17587430000003
test8 0.17580960000032
test9 0.24851379999927

I removed the two crazy slow functions (1 and 4)!

I think the bitwise operators deal with real numbers so they have to do conversions, so they slow down. If they were true bitwise operators then I think 9 would be faster than 2.

SinisterSoft · November 2019

Just noticed because of the order you don't need the brackets so:

test7
sign=a<>-1><1

test8
sign=a<>-1><0

test9
sign=a<>-1><0|1

timings are the same though, just saves typing!

antix · November 2019

Technically 0 has no sign but in some old projects I ended up with -0 sometimes which caused a lot of issues.

oleg · November 2019

antix said:
Technically 0 has no sign but in some old projects I ended up with -0 sometimes which caused a lot of issues.

Technically, the absence of a sign is a '+' sign

-3,, -2, -1, 0, 1 ,2

SinisterSoft · November 2019

If zero has no negative value then it's not negative. If zero has no positive value then it's not positive. So zero has no sign.

oleg · November 2019

SinisterSoft said:
If zero has no negative value then it's not negative. If zero has no positive value then it's not positive. So zero has no sign.

Move the sign (or no sign) from zero to another number.

antix · November 2019

@oleg, technically that is correct but if Lua/Gideros/Whatever returns a -0 you get all kinds of strange behavior

oleg · November 2019

antix said:
@oleg, technically that is correct but if Lua/Gideros/Whatever returns a -0 you get all kinds of strange behavior

Logically, at '-0' the character should return '-1'

Assuming '-0' is an infinite negative number '-0,000000000000001'

antix · November 2019

It doesn't return what you might logically expect. Usually its not hard to remember and you can make corner case code to accommodate for it... it is just annoying

oleg · November 2019

antix said:
It doesn't return what you might logically expect. Usually its not hard to remember and you can make corner case code to accommodate for it... it is just annoying

You can do the right function that will return 0 correctly.

For example, there is a math.atan2 function which correctly returns zero

Instead of the math.atan function

antix · November 2019

Interesting. I've got -0 results doing normal math and think that it is pretty dumb to have to then pass results through another math function just in case they are incorrect? Oh well, it's all fun and games

oleg · November 2019

antix said:
Interesting. I've got -0 results doing normal math and think that it is pretty dumb to have to then pass results through another math function just in case they are incorrect? Oh well, it's all fun and games

My familiar math professor to work around problems with 0, just uses 0.0001 instead of zero. No exact precision is required in mathematics, no one uses the number pi with all signs. - logical to do so that would simplify the calculations with a tolerance in the calculations

ps/ The sign -0 cannot be because:

-0 = x*-0%
-1 = x*-100%
The sign number is always the digit '1'

33*-1=-33
33*-0 =0 error!!

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