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
|
# 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) {
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-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) {
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
var x/eax: int <- copy 0
{
compare x, width
break-if->=
var real-f/edx: int <- viewport-to-real-f x, width
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: int -> _/edx: int {
# (x - width/2)*4/width
var result-f/eax: int <- int-to-fixed x
var width-f/ecx: int <- copy width
width-f <- shift-left 8/fixed-precision
var half-width-f/edx: 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: int, height: int -> _/ebx: int {
# (y - height/2)*4/width
var result-f/eax: int <- int-to-fixed y
var half-height-f/ecx: int <- copy height
half-height-f <- shift-left 8/fixed-precision
half-height-f <- shift-right-signed 1/log2
result-f <- subtract half-height-f
result-f <- shift-left 2/log4
var width-f/ecx: int <- copy width
width-f <- shift-left 8/fixed-precision
result-f <- divide-fixed result-f, width-f
return result-f
}
|