' test sequence of several math commands and functions

'math function tests defines
score=0
tests=0
accuracy = 1e-10

'check used basic functions to ensure the basic math is OK
if abs(-3)<>3 then print "basic function ABS fail":end
if abs(exp(1)-2.718281828459045) > accuracy then print "basic function EXP fail":end
if abs(log(exp(3))-3) > accuracy then print "basic function LOG fail":end
if abs(sin(pi/4)-sqr(1/2)) > accuracy then print "basic function SIN fail":end



'test hyperbolic functions
'check the numerical difference between the hyperbolic function an it's mathmatical formula

dim float x=3 'just any value

tests=tests+1
' test WIKI definition of sinh
if abs(math(sinh x) - (exp(x)-exp(-x))/2) < accuracy then
 score=score+1
else
 ? "MATH(SINH x) function fault"
endif

tests=tests+1
' test WIKI definition of cosh
if abs(math(cosh x) - (exp(x)+exp(-x))/2) < accuracy then
 score=score+1
else
 ? "MATH(COSH x) function fault"
endif

tests=tests+1
' test WIKI definition of tanh
if abs(math(tanh x) - (exp(x)-exp(-x))/(exp(x)+exp(-x))) < accuracy then
 score=score+1
else
 ? "MATH(TANH x) function fault"
endif

tests=tests+1
' log10 of 1000 is 3
if abs(math(log10 1000) - 3) < accuracy then
 score=score+1
else
 ? "MATH(LOG10 x) function fault"
endif

'no test for MATH(ATAN3 x,y) because I only ATAN2 is described in literature



'Simple statistics: a mix of functions ans commands
'use a linear array a size n filled with samples of a sine wave
'a second array b same size is needed.
option base 0
n=512
dim float a(n-1):for i=0 to n-1: a(i)=sin(2*pi*i/n):next i
dim float b(n-1)

tests=tests+1
' standard deviation of a sine wave is equal to the square root of 1/2 (0.707)
if abs(math(sd a()) - sqr(1/2)) < accuracy then
 score=score+1
else
 ? "MATH(SD a()) function fault"
endif

tests=tests+1
' set all values in a array to 3, and sum up all values in normal basic code.
' compare if array size * value
x=0
math set 3,b()
for i=0 to n-1: x=x+b(i) : next i
if abs(x - 3*n) < accuracy then
 score=score+1
else
 ? "MATH SET x,a() command fault"
endif

tests=tests+1
' calculate the mean of an array of identical values. should be equal to that value
if abs(math(mean b()) - 3) < accuracy then
 score=score+1
else
 ? "MATH(MEAN a()) function fault"
endif

tests=tests+1
' add a fixed value to each cell, and redo the mean test. The mean should be equal to
' previous result added to the fixed value
math add b(),3,b()
if abs(math(mean b()) - 3 - 3) < accuracy then
 score=score+1
else
 ? "MATH ADD a(),x,a() command fault"
endif

tests=tests+1
' calculate the sum in the MATH SUM function, should be previous value * array size
if abs(math(sum b()) - 6*n) < accuracy then
 score=score+1
else
 ? "MATH(SUM a()) function fault"
endif

tests=tests+1
' multiply each value in the sine wave array with 2, amplitude should be equal to
' 2x the square root of 1/2 (that is equal to the square root of 2)
math scale a(),2,a()
if abs(math(sd a()) - sqr(2)) < accuracy then
 score=score+1
else
 ? "MATH SCALE a(),x,a() command fault"
endif

tests=tests+1
' a sine wave with amplitude 2 has a peak of +2, find it with MATH MAX
if abs(math(max a()) - 2) < accuracy then
 score=score+1
else
 ? "MATH(MAX a()) function fault"
endif

tests=tests+1
' a sine wave with amplitude 2 has a lowest value of -2, find it with MATH MIN
if abs(math(min a()) + 2) < accuracy then
 score=score+1
else
 ? "MATH(MIN a()) function fault"
endif

tests=tests+1
' perform an FFT on the sine wave array.
dim float dft(1,n-1)
math fft a(),dft()
' to test the FFT a pure sine wave amplitude 2 is converted with 512 samples
' the output spectrum should contain 2 peaks (symetrical spectrum) each containing
' half the samples summed = 512 * 2 / 2 = 512. Other spectral components
' should be rounding errors. The phase part of the array has values between -pi and pi
' and these will be far lower than the peaks in the amplitude section of the dft array
if abs(math(max dft()) - n) < accuracy then
 score=score+1
else
 ? "MATH FFT a(),b() command fault"
endif

tests=tests+1
math fft inverse dft(),b()
' this test uses the output of FFT and converts it back to a signal array b(). The
' array should be a copy of a(), so contain a sine wave amplitude 2.
if abs(math(max b()) - 2) < accuracy then
 score=score+1
else
 ? "MATH FFT INVERSE a(),b() command fault"
endif

tests=tests+1
' check how much a() and b() are alike through correlation
if abs(math(correl b(),a()) - 1) < accuracy then
 score=score+1
else
 ? "MATH(CORREL a(),b()) function fault"
endif

tests=tests+1
' check how much a() and b() are alike through correlation when a fault is introduced
b(123)=10
'? math(correl a(),b())
if math(correl b(),a()) <> 1 then
 score=score+1
else
 ? "MATH(CORREL a(),b()) function fault"
endif

tests=tests+1
dim float c(n-1)
math interpolate b(),a(),1,c()
' the elements in a() and b() (should be identical) are subtracted, resulting in zero
' multiplied by 1, and a() is added, resulting in c() being a copy of a() if b() is
' a copy of a(). So the amplitude should still be 2.
if abs(math(max c()) - 2) < accuracy then
 score=score+1
else
 ? "MATH INTERPOLATE a(),b() command fault"
endif

tests=tests+1
math set 0,dft()
math insert dft(),0,,a()
' zero the dft(1,n-1), the insert array b() into dft(0,n-1)
' then test if values have arrived
if abs(math(max dft()) - 2) < accuracy then
 score=score+1
else
 ? "MATH INSERT a(),,,,b() command fault"
endif

tests=tests+1
math set 0,c()
math slice dft(),0,,c()
' zero the c(), the slice data from array dft(0,n-1) into c()
' then test if values have arrived
if abs(math(max c()) - 2) < accuracy then
 score=score+1
else
 ? "MATH SLICE a(),,,,b() command fault"
endif

tests=tests+1
math set 0,c()
c(123)=1
' all samples are 0 except one that is 1. The mean value will be 1/n
' the median value will be 0 (most samples are 0)
if abs(math(median c())) < accuracy then
 score=score+1
else
 ? "MATH(MEDIAN a()) function fault"
endif


? tests;" tests performed, ";score;" where PASS"
if tests=score then print "simple MATH commands and functions are PASS"
end