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# Mandelbrot set
#
# Install:
# $ git clone https://github.com/akkartik/mu
# $ cd mu
# Build on Linux:
# $ ./translate apps/mandelbrot.mu
# Build on other platforms (slow):
# $ ./translate_emulated apps/mandelbrot.mu
# Run:
# $ qemu-system-i386 code.img
fn main screen: (addr screen), keyboard: (addr keyboard), data-disk: (addr disk) {
# Initially the viewport is centered at 0, 0 in the scene.
var zero: float
var scene-cx/xmm1: float <- copy zero
var scene-cy/xmm2: float <- copy zero
# Initially the viewport shows a section of the scene 4 units wide.
# scene-width-scale = 0.5
var scene-width-scale: float
var dest/eax: (addr float) <- address scene-width-scale
fill-in-rational dest, 1, 2
# scene-width = 4
var four: float
var dest/eax: (addr float) <- address four
fill-in-rational dest, 4, 1
var scene-width/xmm3: float <- copy four
{
mandelbrot screen scene-cx, scene-cy, scene-width
# move the center some % of the current screen-width
var adj/xmm0: float <- rational 2, 0x1c/28
adj <- multiply scene-width
scene-cx <- subtract adj
scene-cy <- add adj
# slowly shrink the scene width to zoom in
scene-width <- multiply scene-width-scale
loop
}
}
fn mandelbrot screen: (addr screen), scene-cx: float, scene-cy: float, scene-width: float {
var a/eax: int <- copy 0
var b/ecx: int <- copy 0
a, b <- screen-size screen
var width/esi: int <- copy a
width <- shift-left 3/log2-font-width
var height/edi: int <- copy b
height <- shift-left 4/log2-font-height
var y/ecx: int <- copy 0
{
compare y, height
break-if->=
var imaginary/xmm1: float <- viewport-to-imaginary y, width, height, scene-cy, scene-width
var x/ebx: int <- copy 0
{
compare x, width
break-if->=
var real/xmm0: float <- viewport-to-real x, width, scene-cx, scene-width
var iterations/eax: int <- mandelbrot-iterations-for-point real, imaginary, 0x400/max
iterations <- shift-right 3
var color/edx: int <- copy 0
iterations, color <- integer-divide iterations, 0x18/24/size-of-cycle-0
color <- add 0x20/cycle-0
pixel screen, x, y, color
x <- increment
loop
}
y <- increment
loop
}
}
fn mandelbrot-iterations-for-point real: float, imaginary: float, max: int -> _/eax: int {
var zero: float
var x/xmm0: float <- copy zero
var y/xmm1: float <- copy zero
var iterations/ecx: int <- copy 0
{
var done?/eax: boolean <- mandelbrot-done? x, y
compare done?, 0/false
break-if-!=
compare iterations, max
break-if->=
var newx/xmm2: float <- mandelbrot-x x, y, real
var newy/xmm3: float <- mandelbrot-y x, y, imaginary
x <- copy newx
y <- copy newy
iterations <- increment
loop
}
return iterations
}
fn mandelbrot-done? x: float, y: float -> _/eax: boolean {
# x*x + y*y > 4
var x2/xmm0: float <- copy x
x2 <- multiply x
var y2/xmm1: float <- copy y
y2 <- multiply y
var sum/xmm0: float <- copy x2
sum <- add y2
var four/eax: int <- copy 4
var four-f/xmm1: float <- convert four
compare sum, four-f
{
break-if-float>
return 0/false
}
return 1/true
}
fn mandelbrot-x x: float, y: float, real: float -> _/xmm2: float {
# x*x - y*y + real
var x2/xmm0: float <- copy x
x2 <- multiply x
var y2/xmm1: float <- copy y
y2 <- multiply y
var result/xmm0: float <- copy x2
result <- subtract y2
result <- add real
return result
}
fn mandelbrot-y x: float, y: float, imaginary: float -> _/xmm3: float {
# 2*x*y + imaginary
var two/eax: int <- copy 2
var result/xmm0: float <- convert two
result <- multiply x
result <- multiply y
result <- add imaginary
return result
}
# 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 x: int, width: int, scene-cx: float, scene-width: float -> _/xmm0: float {
# 0 in the viewport goes to scene-cx - scene-width/2
# width in the viewport goes to scene-cx + scene-width/2
# Therefore:
# x in the viewport goes to (scene-cx - scene-width/2) + x*scene-width/width
# At most two numbers being multiplied before a divide, so no risk of overflow.
var result/xmm0: float <- convert x
result <- multiply scene-width
var width-f/xmm1: float <- convert width
result <- divide width-f
result <- add scene-cx
var two/eax: int <- copy 2
var two-f/xmm2: float <- convert two
var half-scene-width/xmm1: float <- copy scene-width
half-scene-width <- divide two-f
result <- subtract half-scene-width
return result
}
fn viewport-to-imaginary y: int, width: int, height: int, scene-cy: float, scene-width: float -> _/xmm1: float {
# 0 in the viewport goes to scene-cy - scene-width/2*height/width
# height in the viewport goes to scene-cy + scene-width/2*height/width
# Therefore:
# y in the viewport goes to (scene-cy - scene-width/2*height/width) + y*scene-width/width
# scene-cy - scene-width/width * (height/2 + y)
# At most two numbers being multiplied before a divide, so no risk of overflow.
var result/xmm0: float <- convert y
result <- multiply scene-width
var width-f/xmm1: float <- convert width
result <- divide width-f
result <- add scene-cy
var two/eax: int <- copy 2
var two-f/xmm2: float <- convert two
var second-term/xmm1: float <- copy scene-width
second-term <- divide two-f
var height-f/xmm2: float <- convert height
second-term <- multiply height-f
var width-f/xmm2: float <- convert width
second-term <- divide width-f
result <- subtract second-term
return result
}
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