about summary refs log tree commit diff stats
path: root/mandelbrot-fixed.mu
blob: b633cfe582d3615019e4510a515d8f47a5587a06 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
# Mandelbrot set using fixed-point numbers.
#
# Install:
#   $ git clone https://github.com/akkartik/mu
#   $ cd mu
# Build on Linux:
#   $ ./translate mandelbrot-fixed.mu
# Build on other platforms (slow):
#   $ ./translate_emulated mandelbrot-fixed.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 scene-cx-f: int
  var scene-cy-f: int
  # Initially the viewport shows a section of the scene 4 units wide.
  var scene-width-f: int
  copy-to scene-width-f, 0x400/4
  {
    mandelbrot screen scene-cx-f, scene-cy-f, scene-width-f
    # move at an angle slowly towards the edge
    var adj-f/eax: int <- multiply-fixed scene-width-f, 0x12/0.07
    subtract-from scene-cx-f, adj-f
    add-to scene-cy-f, adj-f
    # slowly shrink the scene width to zoom in
    var tmp-f/eax: int <- multiply-fixed scene-width-f, 0x80/0.5
    copy-to scene-width-f, tmp-f
    loop
  }
}

# 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-f: int, b-f: int -> _/eax: int {
  var result/eax: int <- copy a-f
  result <- multiply b-f
  {
    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), scene-cx-f: int, scene-cy-f: int, scene-width-f: int {
  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-f/ebx: int <- viewport-to-imaginary-f y, width, height, scene-cy-f, scene-width-f
    var x/eax: int <- copy 0
    {
      compare x, width
      break-if->=
      var real-f/edx: int <- viewport-to-real-f x, width, scene-cx-f, scene-width-f
      var iterations/esi: int <- mandelbrot-iterations-for-point real-f, imaginary-f, 0x400/max
      iterations <- shift-right 3
      var color/edx: int <- copy 0
      {
        var dummy/eax: int <- copy 0
        dummy, 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-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: int, scene-cx-f: int, scene-width-f: int -> _/edx: int {
  # 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-f/eax: int <- int-to-fixed x
  result-f <- multiply-fixed result-f, scene-width-f
  var width-f/ecx: int <- copy width
  width-f <- shift-left 8/fixed-precision
  result-f <- divide-fixed result-f, width-f
  result-f <- add scene-cx-f
  var half-scene-width-f/ecx: int <- copy scene-width-f
  half-scene-width-f <- shift-right 1
  result-f <- subtract half-scene-width-f
  return result-f
}

fn viewport-to-imaginary-f y: int, width: int, height: int, scene-cy-f: int, scene-width-f: int -> _/ebx: int {
  # 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-f/eax: int <- int-to-fixed y
  result-f <- multiply-fixed result-f, scene-width-f
  var width-f/ecx: int <- copy width
  width-f <- shift-left 8/fixed-precision
  result-f <- divide-fixed result-f, width-f
  result-f <- add scene-cy-f
  var second-term-f/edx: int <- copy 0
  {
    var _second-term-f/eax: int <- copy scene-width-f
    _second-term-f <- shift-right 1
    var height-f/ebx: int <- copy height
    height-f <- shift-left 8/fixed-precision
    _second-term-f <- multiply-fixed _second-term-f, height-f
    _second-term-f <- divide-fixed _second-term-f, width-f
    second-term-f <- copy _second-term-f
  }
  result-f <- subtract second-term-f
  return result-f
}