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'example code from: ARMBasic.pdf : Runtime Library  / Floating Point Functions/ trig Functions (page 214)
#define include_trig
#include <AB_Math.bas>
for i=0 to 90 step 10
print i,sin(_deg2rad *i),cos(_deg2rad *i),tan((_deg2rad *i)
next i

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const _nan		=	$7fc00000

CONST DivByFact = { 0.0, 1.00000000000000000000000, 0.50000000000000000000000,
					0.16666666666666700000000, 0.04166666666666670000000, 0.00833333333333333000000,
					0.00138888888888889000000, 0.00019841269841269800000, 0.00002480158730158730000,
					0.00000275573192239859000, 0.00000027557319223985900, 0.00000002505210838544170 }


const _2pi 		=	6.283185307179590000
const _halfpi 	=	1.570796326794900000
const _qtrpi 	=	0.785398163397448000

function fix(x as single) as integer
	' fix truncates a floating-point expression to its integer portion, returning an integer
	' print fix(12.49), fix(12.54)    'output is:  12  12
	return x
	endfunction

function floor(x as single) as single
	' floor returns the largest integral single value not greater than fparam
	' floor of 3.8 is 3.0, floor of -2.3 is -3.0
	if(x = fix(x)) or x>=0 then return fix(x) else return fix(x)-1
	endfunction	

function int(x as single) as integer
	return floor(x)
	endfunction
 

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'=== Workaround to use sine function (library AB_Math.bas being too big for the memory of the LPC812 eval board):
'=== 
'=== 1) Do not include AB_Math.bas 
'=== 2) Only include the code between the dashed lines to your program:
'===    The code is taken straight from AB_Math. Except for the constants _rad2deg and _deg2rad everything is essential. 
'=== 
'=== At the end of this file at main: you find a some example code to show it works.
 


'-------------- start of AB_Math code ---------------------------------------------------------------------

const _nan      =   $7fc00000

CONST DivByFact = { 0.0, 1.00000000000000000000000, 0.50000000000000000000000,
               0.16666666666666700000000, 0.04166666666666670000000, 0.00833333333333333000000,
               0.00138888888888889000000, 0.00019841269841269800000, 0.00002480158730158730000,
               0.00000275573192239859000, 0.00000027557319223985900, 0.00000002505210838544170 }


const _2pi       =   6.283185307179590000
const _halfpi    =   1.570796326794900000
const _qtrpi    =   0.785398163397448000

const _rad2deg 	= 57.295779513082320876798154814105		'x*180/pi
const _deg2rad 	= 0.01745329251994329576923690768489	'x*pi/180


function fix(x as single) as integer
   ' fix truncates a floating-point expression to its integer portion, returning an integer
   ' print fix(12.49), fix(12.54)    'output is:  12  12
   return x
   endfunction

function floor(x as single) as single
   ' floor returns the largest integral single value not greater than fparam
   ' floor of 3.8 is 3.0, floor of -2.3 is -3.0
   if(x = fix(x)) or x>=0 then return fix(x) else return fix(x)-1
   endfunction   

function int(x as single) as integer
   return floor(x)
   endfunction
 


function fmod(n as single, d as single) as single
	' returns the floating-point remainder of numerator/denominator.
	if d <> 0 then return n-(fix(n/d)*d) else return _nan
	endfunction

function powi(b as single, e as integer) as single
	' returns the base raised to the integral power of exponent
	dim res as single
	if e = 0 then return 1
	if e = 1 then return b
	res = 1
	while e		' iterate thru the exponent, moving it towards zero while multiplying the base
		res = res*if(e<0,1/b,b)
		e = e+if(e<0,1,-1)
		loop
	return res
	endfunction

function reducerange(x as single, sc as single, byref m as integer) as single

	' this is used to reduce a number to within a range and maintain the phase angles
	' for some gawd awful reason, this kicked my arse for hours over a few nights,
	' i strongly suspect that i got lost as i couldn't see the gd forest 'cause of all of
	' the effin trees. i was, admittedly, buring the candle at both ends too.
	' this is a function that can be optimized a lot i suspect.
	' however, i am still tired and ... it ain't broke, boss...

	dim res as single	
	dim scsign, xsign as integer
	
	xsign=1
	scsign =1
	
	if x < 0 then
		xsign = -1
		x *= -1
		endif
	
	if sc < 0 then
		scsign = -1
		sc *= -1
		endif
		
	res = fmod(x,sc)
	m = (int(x/sc))
	
	if (res = 0) and (m = 1) and (xsign=scsign)
		' print "same side same val - unity"
		m = 0
		return x * xsign
	elseif (res = 0) and (m = 1) and (xsign<>scsign)
		' print "opposite unities"
		m = 2 * if(scsign=-1,-1,1)
		return sc * scsign
	elseif (res = 0) and (m > 1) and (xsign <> scsign)
		' print "opposite side - multiples: ";m
		m = if(scsign=-1,-m-1,m+1)
		return sc * scsign
	elseif (res = 0) and (m > 1) 'and xsign = scsign
		' print "same side - multiples: ";m
		m = if(scsign=1,(m-1)*-1,m-1)
		return sc * scsign
	elseif scsign = 1 and xsign = 1
		m *= -1
		return res
	elseif scsign = 1 and xsign = -1
		m += 1
		return sc - res	
	elseif scsign = -1 and xsign = -1
		return res * -1
	else ' scsign = -1 and xsign = 1
		m += 1
		m *= -1
		return res - sc
	endif
	endfunction



function sin(rad as single) as single		' using polynomial - good
	' domain and range: from the graphs above we see that for both the sin and cos functions the
	' domain is all real numbers and the range is all reals from -1 to +1 inclusive. for the tan
	' function the domain is all real numbers except ±p/2, ±3p/2, ±5p/2, …, 
	' (or in degrees: ±90°, ±270°, ±450°, …), where the tan function is undefined.
	' the range of the tan function is all real numbers.
	
	dim multiple as integer
	dim period, symm as single
	period = reducerange(rad,_2pi,multiple)		' 0-360
	symm = reducerange(period,_halfpi,multiple)	' 0-90
	if multiple = -1 then symm = _halfpi-symm
	if multiple = -3 then symm = _halfpi-symm
	
	if symm <=_qtrpi			' <=45 deg
		return if(multiple<-1,-1,1)*(symm-(powi(symm,3)*divbyfact(3))+(powi(symm,5)*divbyfact(5))-(powi(symm,7)*divbyfact(7)))
	else
		return if(multiple<-1,-1,1)*(1-(powi((_halfpi-symm),2)*divbyfact(2))+(powi((_halfpi-symm),4)*divbyfact(4))-(powi((_halfpi-symm),6)*divbyfact(6)))
	endif
	endfunction

'-------------- end of AB_Math code --------------------------------------------------------------------- 


main:

'=== example from ARMbasic.pdf( Trigonometric Functions) adapted to use only sin(x)

for i=0 to 90 step 10
print i,sin(_deg2rad *i)
next i