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# Mandelbrot set using fixed-point numbers.
#
# To build:
# $ ./translate mandelbrot-fixed.mu
# To run:
# $ qemu-system-i386 code.img
fn main screen: (addr screen), keyboard: (addr keyboard), data-disk: (addr disk) {
mandelbrot screen
}
# Since they still look like int types, we'll append a '-f' suffix to variable
# names to designate fixed-point numbers.
fn int-to-fixed in: int -> _/eax: int {
var result-f/eax: int <- copy in
result-f <- shift-left 8/fixed-precision
{
break-if-not-overflow
abort "int-to-fixed: overflow"
}
return result-f
}
fn fixed-to-int in-f: int -> _/eax: int {
var result/eax: int <- copy in-f
result <- shift-right-signed 8/fixed-precision
return result
}
# The process of throwing bits away always adjusts a number towards -infinity.
fn test-fixed-conversion {
# 0
var f/eax: int <- int-to-fixed 0
var result/eax: int <- fixed-to-int f
check-ints-equal result, 0, "F - test-fixed-conversion - 0"
# 1
var f/eax: int <- int-to-fixed 1
var result/eax: int <- fixed-to-int f
check-ints-equal result, 1, "F - test-fixed-conversion - 1"
# -1
var f/eax: int <- int-to-fixed -1
var result/eax: int <- fixed-to-int f
check-ints-equal result, -1, "F - test-fixed-conversion - -1"
# 0.5 = 1/2
var f/eax: int <- int-to-fixed 1
f <- shift-right-signed 1
var result/eax: int <- fixed-to-int f
check-ints-equal result, 0, "F - test-fixed-conversion - 0.5"
# -0.5 = -1/2
var f/eax: int <- int-to-fixed -1
f <- shift-right-signed 1
var result/eax: int <- fixed-to-int f
check-ints-equal result, -1, "F - test-fixed-conversion - -0.5"
# 1.5 = 3/2
var f/eax: int <- int-to-fixed 3
f <- shift-right-signed 1
var result/eax: int <- fixed-to-int f
check-ints-equal result, 1, "F - test-fixed-conversion - 1.5"
# -1.5 = -3/2
var f/eax: int <- int-to-fixed -3
f <- shift-right-signed 1
var result/eax: int <- fixed-to-int f
check-ints-equal result, -2, "F - test-fixed-conversion - -1.5"
# 1.25 = 5/4
var f/eax: int <- int-to-fixed 5
f <- shift-right-signed 2
var result/eax: int <- fixed-to-int f
check-ints-equal result, 1, "F - test-fixed-conversion - 1.25"
# -1.25 = -5/4
var f/eax: int <- int-to-fixed -5
f <- shift-right-signed 2
var result/eax: int <- fixed-to-int f
check-ints-equal result, -2, "F - test-fixed-conversion - -1.25"
}
# special routines for multiplying and dividing fixed-point numbers
fn multiply-fixed a: int, b: int -> _/eax: int {
var result/eax: int <- copy a
result <- multiply b
{
break-if-not-overflow
abort "multiply-fixed: overflow"
}
result <- shift-right-signed 8/fixed-precision
return result
}
fn divide-fixed a-f: int, b-f: int -> _/eax: int {
var result-f/eax: int <- copy a-f
result-f <- shift-left 8/fixed-precision
{
break-if-not-overflow
abort "divide-fixed: overflow"
}
var dummy-remainder/edx: int <- copy 0
result-f, dummy-remainder <- integer-divide result-f, b-f
return result-f
}
# multiplying or dividing by an integer can use existing instructions.
# adding and subtracting two fixed-point numbers can use existing instructions.
fn mandelbrot screen: (addr screen) {
var a/eax: int <- copy 0
var b/ecx: int <- copy 0
a, b <- screen-size screen
var width-f/esi: int <- copy a
width-f <- shift-left 0xb/log2-font-width-and-fixed-precision # 3 + 8 = 11
var height-f/edi: int <- copy b
height-f <- shift-left 0xc/log2-font-height-and-fixed-precision # 4 + 8 = 12
var y/ecx: int <- copy 0
{
compare y, height-f
break-if->=
var imaginary-f/ebx: int <- viewport-to-imaginary-f y, width-f, height-f
var x/eax: int <- copy 0
{
compare x, width-f
break-if->=
var real-f/edx: int <- viewport-to-real-f x, width-f
var iterations/esi: int <- mandelbrot-iterations-for-point real-f, imaginary-f, 0x400/max
compare iterations, 0x400/max
{
break-if->=
pixel screen, x, y, 0xf/white
}
compare iterations, 0x400/max
{
break-if-<
pixel screen, x, y, 0/black
}
x <- increment
loop
}
y <- increment
loop
}
}
fn mandelbrot-iterations-for-point real-f: int, imaginary-f: int, max: int -> _/esi: int {
var x-f/esi: int <- copy 0
var y-f/edi: int <- copy 0
var iterations/ecx: int <- copy 0
{
var done?/eax: boolean <- mandelbrot-done? x-f, y-f
compare done?, 0/false
break-if-!=
compare iterations, max
break-if->=
var x2-f/edx: int <- mandelbrot-x x-f, y-f, real-f
var y2-f/ebx: int <- mandelbrot-y x-f, y-f, imaginary-f
x-f <- copy x2-f
y-f <- copy y2-f
iterations <- increment
loop
}
return iterations
}
fn mandelbrot-done? x-f: int, y-f: int -> _/eax: boolean {
# x*x + y*y > 4
var tmp-f/eax: int <- multiply-fixed x-f, x-f
var result-f/ecx: int <- copy tmp-f
tmp-f <- multiply-fixed y-f, y-f
result-f <- add tmp-f
compare result-f, 0x400/4
{
break-if->
return 0/false
}
return 1/true
}
fn mandelbrot-x x-f: int, y-f: int, real-f: int -> _/edx: int {
# x*x - y*y + real
var tmp-f/eax: int <- multiply-fixed x-f, x-f
var result-f/ecx: int <- copy tmp-f
tmp-f <- multiply-fixed y-f, y-f
result-f <- subtract tmp-f
result-f <- add real-f
return result-f
}
fn mandelbrot-y x-f: int, y-f: int, imaginary-f: int -> _/ebx: int {
# 2*x*y + imaginary
var result-f/eax: int <- copy x-f
result-f <- shift-left 1/log2
result-f <- multiply-fixed result-f, y-f
result-f <- add imaginary-f
return result-f
}
# Scale (x, y) pixel coordinates to a complex plane where the viewport width
# ranges from -2 to +2. Viewport height just follows the viewport's aspect
# ratio.
fn viewport-to-real-f x: int, width-f: int -> _/edx: int {
# (x - width/2)*4/width
var result-f/eax: int <- int-to-fixed x
var half-width-f/ecx: int <- copy width-f
half-width-f <- shift-right-signed 1/log2
result-f <- subtract half-width-f
result-f <- shift-left 2/log4
result-f <- divide-fixed result-f, width-f
return result-f
}
fn viewport-to-imaginary-f y: int, width-f: int, height-f: int -> _/ebx: int {
# (y - height/2)*4/width
var result-f/eax: int <- int-to-fixed y
shift-right-signed height-f, 1/log2
result-f <- subtract height-f
result-f <- shift-left 2/log4
result-f <- divide-fixed result-f, width-f
return result-f
}
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