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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