## IEEE 754 floating point library for BASIC

Questions about the BASICtools and MakeItC
YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### IEEE 754 floating point library for BASIC

Good day folks.

I have uploaded a WIP ARMbasic Math Library, test application, and spreadsheet.

The lib, while being somewhat mature, is indeed of some work. I would encourage
those of you with a math aptitude to download and offer feedback, input, and
code.

While some of the functions are working as expected, with accuracies approaching
the limits of IEEE 754, there are some that are plain humble at best.

I am by no means a mathematician. I actually struggle with higher level maths.
So, this is a call for help.

What is needed is for someone with an SME caliber math aptitude to scrub the
functions and offer feedback on what the domains should be for the various
functions. I have done some of it, but am (honestly) getting burned out on it
all. I've come to far to stop, and am hoping that someone in the group can
pitch in and help round the 4th turn and pour the gas in, to get it across the
finish line.

The function listing follows. Thanks, in advance, for the help.

Have a good one!

-t

*** Common Functions:

fact - factorials for integers 0 to 34 (all that is representable with IEEE 754)

fix - truncates a real number to an integral

int - ditto

floor - returns the largest integer equal to or less then the arg

ceil - returns the smallest integer equal to or above the arg

round - rounds to the nearest integer

sign - returns +1,0,-1 for positive, zero, or negative numbers

fmod - returns the remainder of the division of the denominator into the
numerator

log10i - returns the integer log10 of a number (basically the power of 10)

powi - returns a number raised to an integer power

sci - returns scientific notation of the passed argument. The mantissa is
returned as a real number in the range of 0 to 9.999999 and a byref'd var is set
with the power of 10 of the argument

*** Power/Exp/Log/Sqrt Series:

sqrt - returns the square-root of a number

exp - returns the value of e raised to the power x

logn - returns the exponent to which the base e must be raised to obtain x

pow - raises x to some power p, and returns x^p as output

log - returns the exponent to which the base 10 must be raised to obtain x

log10 - returns the base-10 logarithm of a number

*** Trigonometric Series:

Note all of these are in radians. To use with proper degrees, multiply the

reducerange is a helper function to bring numbers into a range while retaining
the phase angles - see the function's comments. Also, a byref'd var is set with
the multiplier representing the number of reductions required and the the
direction of the reduction.

sin - return the Sine

cos - return the Cosine

tan - return the Tangent

atan - return the arc-tangent

asin - return the arc-sine

acos - return the arc-cosine

atan2 - return the magnitude and angle of a point, with respect to origin.

sec - returns the inverse cosine

csc - returns the inverse sine

ctan - returns the inverse tangent

asec - returns the arc-secant

acsc - return the arc co-secant

acot - returns the arc co-tangent

*** Hyperbolic Functions:

sinh - returns the hyperbolic sine

cosh - returns the hyperbolic cosine

tanh - returns the hyperbolic tangent

sech - returns the hyperbolic secant

csch - returns the hyperbolic cosecant

coth - returns the hyperbolic cotangent

asinh - returns the inverse hyperbolic sine

acosh - returns the inverse hyperbolic cosine

atanh - returns the inverse hyperbolic tangent

asech - returns the inverse hyperbolic secant

ascsh - returns the inverse hyperbolic cosecant

acoth - returns the inverse hyperbolic cotangent

*** Random Functions:

init_globals - this must be done in order for the random function to work

znew, wnew, mwc - these are internal helper functions

rand - returns a random between 0 and 1, not inclusive.

randb - returns a random between the two arguments passed.

*** Miscellaneous Functions:

fabs - returns the absolute of the floating point argument
Attachments
AB_Math.lib
test_AB_Math_Lib1.bas

YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### Re: IEEE 754 floating point library for BASIC

Also, it would be wise, for those folks that may be interested in eventually
getting floats, that they do so sooner vs. later

I overheard a little birdie whispering that the free beta will go away at some
point in the future and that there will be an upgrade fee of \$10 for those who
were not early adopters and didn't help out with the beta.

-t

YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### Re: IEEE 754 floating point library for BASIC

Immediately, I noticed a problem with the defininitions.

integral = integer

int() should be the Greatest integer in X function. Int(-9.5) = -10, int(9.5)
=9 See: http://www.mathnstuff.com/math/spoken/h ... s/g/g6.htm

fix() truncates a number; e.g. fix(-9.5) = -9; fix(+9.5) = 9

They should be different functions. Not ditto.

> fix - truncates a real number to an integral

>

> int - ditto

>

YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### Re: IEEE 754 floating point library for BASIC

Nice. I had made it a synonym of fix when it really is a synonym of floor.

Fixed on my end. I'll update the file in the files section when some more fixes
are identified and incorporated.

Thank you.

-t

YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### Re: IEEE 754 floating point library for BASIC

(bump/nudge,ping/poke) I am looking for feedback and assistance.

Is anyone else planning on using floats on the ARMbasic devices?

-t

YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### Re: IEEE 754 floating point library for BASIC

I'm most definitely going to use floats! I have a bunch of GPS stuff using
Integer math I will convert.

Haven't got started yet though as I'm still trying to load the new firmware on
my Mites and Pros. Only had a day or to to play before going off on vacation for
3 weeks - bad planning on my part.
But I'm sure with Bruce's help I'll be up and running in a couple of days...

Chris

YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### Re: IEEE 754 floating point library for BASIC

Hi Tod,

I'm now up and running on one of my 'Mites. What can I do to help?

I'm moderately proficient with math stuff.

Chris

YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### Re: IEEE 754 floating point library for BASIC

Hey, Chris. Glad to hear you're up and running.

I uploaded a math lib and a test app. It is located here: Files > General
Resources > IEEE 754 Floats

Can you run the code and help to vet the lib's functions?

Please let me know if you have any issues.

Thanks.

-t

YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### Re: IEEE 754 floating point library for BASIC

Unfortunately the test program is too big for the 'mite. I'll extract the funcs
I use most frequently - exp, log, log10, sqrt, sin/cos, tan, atan - and give
them a try.

Should be interesting.

cp

YahooArchive
Posts: 1462
Joined: Fri Oct 19, 2012 5:11 am

### Re: IEEE 754 floating point library for BASIC

Interesting. Is it not a 32K device? I developed it on one. The FW was 12K
and the lib/test app was 19.2K I believe.?. I remember that I had to fight to
get it to compile as it was too large with my initial test app approach (hence
my getting creative therein).

Regardless, I am thankful for any help and will support the vetting efforts
however it works out - iteratively or otherwise.

Thank you.

-t