horners_method.txt

https://www.ti.com/lit/an/slaa329a/slaa329a.pdf
https://www.ti.com/en/download/mcu/Digital-filtering-methodoliges-for-MSP430-systems.pdf
https://www.allaboutcircuits.com/technical-articles/an-introduction-to-canonical-signed-digit-representation/


bring into form:

x * m

where m < 1

x / 45
x * (1/45)
x * 0.02222222222

convert mantissa of m to 0b
speedcrunch
	0,02222 =
	F6
	0,000001011011
	truncate at desired bit-depth
		12 bit
		16 bit
		less bits = less steps for horners method!



horners method

count distances between 1s of 0b-formatted m, right-most to left-most
	= dn (0...)
count distance to decimal point
	= dpoint
next one = 1

xtemp = x >> d0 + x
xtemp = xtemp >> d1 + x
...
result = xtemp >> dpoint



canonical signed digit representation

first: convert mantissa of m to 0b

convert to CSDr
right-to-left

single 1 = 1
group consecutive 1s
	right-most 1 becomes (-1)
	all other 1s become 0
	left-most 1 is pre-pended by 1
		0b0.00011111 1001 (space added for alignment)
		0b0.00100000-1001
	iterative
		only one grouping at a time
		still right to left
		0b011 011 1001
		0b011 100-1001
		b0100-100-1001

now apply horners method
	if next 1 is (-1) "+ x" becomes "- x"





x = 512

binary *< 1
x / 4.44
= x * (1/ 4.44)
= x * 0.224224
= x * 0b0.0011100110101000

CSD
 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 0
 0 0 1 1 1 0 1 0-1 0 1 0 1 0 0 0
 0 1 0 0-1 0 1 0-1 0 1 0 1 0 0 0
distances
  2     3   2   2   2   2       

horner
xtemp = x >> 2 + x
xtemp = xtemp >> 2 - x
xtemp = xtemp >> 2 + x
xtemp = xtemp >> 2 - x
xtemp = xtemp >> 3 + x
result = xtemp >> 2