Post by Josh Goebel in Utilities/Libraries

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If you’re referring to my thread Jack (as defined by the course) doesn’t support floats, only int16/bool/array objects that contain those things. You could of course write a floating point library in Jack, but it doesn’t have operator overloading and such niceties… or you could add it to the language/compiler itself and write it in Jack VM opcodes (or even Chip8 instructions). I haven’t gotten that far - I’m still finishing the VM.

Fixed floats would be easily compatible with 16-bit math, right? The fastest code to run natively would be code that just treated it as one big 16 bit number with a virtual decimal. If so then all the 16-bit math in the Jack VM (and the OS multiply/divide routines) would “just work” out of the box…

The only trick would come at the edges when you needed strings or just the integer or fractional components. You could potentially even use a lookup table for converting the fractional remainder to a base10 number, then feed it into the existing BCD to font stuff.

Where were people imagining the fixed point being?

Kouzerumatsukite1 year ago (1 edit)

Fixed floats, ehm, fixed points, is fractional numbers, which is being stored as integer.

Let's say, in currency, to represent 0.99, just store it as 99; or 1.25, just store it as 125.
Divide them by 100 when you want to display it, or when doing multiplication on them.
And you don't need to divide them when doing addition or subtraction on them.

The same principle applied to binary:
storing 0b1010.101 (10.625) as 0b1010101 (85),
which later divided by 0b1000 (8) since 3 bits are the fraction parts. or
storing 0b111.1111 (7.9375) as 0b1111111 (127),
which is later divided by 0b10000 (16) since 4 bits are the fractions.

In here, you have to determine how much bits you gonna sacrifice to store fractions,
in this case, you gonna have 8 bits integers, 8 bits of fractions, totaling of 16bits number
you gonna have the granularity of 1/256 (0.00390625) which in binary 0b00000000.00000001
and the largest number you can represent with this would be
65535/256 (255.99609375) a.k.a 0b11111111.11111111

Kouzerumatsukite1 year ago (2 edits)

Any how, you don't need look up table to convert 16-bit fixed points into decimal 😄

The shortest and fastest code for 16-bit fixed points to decimal conversion
that I had come up with would be:

: zeroes
  0 0 0 0 0 0 0 0 0 0 0 0
: decimal_result
  0 0 0
: decimal_fractional_part
  0 0 0 0 0 0 0 0 0
: convert_16_bit_fixed_point_to_decimal
# v0 : Hi-byte
# v1 : Lo-byte
  i := decimal_result  bcd v0
  vF := v1  i := zeroes  load v8  v0 := vF
  # extract decimal of the whole 8-bits
  decimal_extract_bit
  decimal_extract_bit
  decimal_extract_bit
  decimal_extract_bit
  decimal_extract_bit
  decimal_extract_bit
  decimal_extract_bit
  decimal_extract_bit
  # what font index is a dot point
  v0 := DOT_POINT
  # store the result
  i := decimal_fractional_part
  save v8
return
: decimal_extract_bit
# performs reverse double-dabble
  v0 >>= v0  if vF != 0 then  v1 += 10 
  v1 >>= v1  if vF != 0 then  v2 += 10 
  v2 >>= v2  if vF != 0 then  v3 += 10 
  v3 >>= v3  if vF != 0 then  v4 += 10 
  v4 >>= v4  if vF != 0 then  v5 += 10
  v5 >>= v5  if vF != 0 then  v6 += 10
  v6 >>= v6  if vF != 0 then  v7 += 10
  v7 >>= v7  if vF != 0 then  v8 += 10
  v8 >>= v8
return

itch.io

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