about summary refs log tree commit diff stats
path: root/baremetal/412render-float-decimal.mu
blob: 498781e97194be0a874cb60513611d004d3ee7aa (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
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
# print out floats in decimal
# https://research.swtch.com/ftoa
#
# Basic idea:
#   Ignoring sign, floating point numbers are represented as 1.mantissa * 2^exponent
#   Therefore, to print a float in decimal, we need to:
#     - compute its value without decimal point
#     - convert to an array of decimal digits
#     - print out the array while inserting the decimal point appropriately
#
# Basic complication: the computation generates numbers larger than an int can
# hold. We need a way to represent big ints.
#
# Key insight: use a representation for big ints that's close to what we need
# anyway, an array of decimal digits.
#
# Style note: we aren't creating a big int library here. The only operations
# we need are halving and doubling. Following the link above, it seems more
# comprehensible to keep these operations inlined so that we can track the
# position of the decimal point with dispatch.
#
# This approach turns out to be fast enough for most purposes.
# Optimizations, however, get wildly more complex.

fn test-render-float-decimal-normal {
  var screen-on-stack: screen
  var screen/esi: (addr screen) <- address screen-on-stack
  initialize-screen screen, 0x20, 5  # 32 columns should be more than enough
  # 0.5
  var half/xmm0: float <- rational 1, 2
  var dummy/eax: int <- render-float-decimal screen, half, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "0.5 ", "F - test-render-float-decimal-normal 0.5"
  # 0.25
  clear-screen screen
  var quarter/xmm0: float <- rational 1, 4
  var dummy/eax: int <- render-float-decimal screen, quarter, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "0.25 ", "F - test-render-float-decimal-normal 0.25"
  # 0.75
  clear-screen screen
  var three-quarters/xmm0: float <- rational 3, 4
  var dummy/eax: int <- render-float-decimal screen, three-quarters, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "0.75 ", "F - test-render-float-decimal-normal 0.75"
  # 0.125
  clear-screen screen
  var eighth/xmm0: float <- rational 1, 8
  var dummy/eax: int <- render-float-decimal screen, eighth, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "0.125 ", "F - test-render-float-decimal-normal 0.125"
  # 0.0625; start using scientific notation
  clear-screen screen
  var sixteenth/xmm0: float <- rational 1, 0x10
  var dummy/eax: int <- render-float-decimal screen, sixteenth, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "6.25e-2 ", "F - test-render-float-decimal-normal 0.0625"
  # sqrt(2); truncate floats with lots of digits after the decimal but not too many before
  clear-screen screen
  var two-f/xmm0: float <- rational 2, 1
  var sqrt-2/xmm0: float <- square-root two-f
  var dummy/eax: int <- render-float-decimal screen, sqrt-2, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "1.414 ", "F - test-render-float-decimal-normal √2"
}

# print whole integers without decimals
fn test-render-float-decimal-integer {
  var screen-on-stack: screen
  var screen/esi: (addr screen) <- address screen-on-stack
  initialize-screen screen, 0x20, 5  # 32 columns should be more than enough
  # 1
  var one-f/xmm0: float <- rational 1, 1
  var dummy/eax: int <- render-float-decimal screen, one-f, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "1 ", "F - test-render-float-decimal-integer 1"
  # 2
  clear-screen screen
  var two-f/xmm0: float <- rational 2, 1
  var dummy/eax: int <- render-float-decimal screen, two-f, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "2 ", "F - test-render-float-decimal-integer 2"
  # 10
  clear-screen screen
  var ten-f/xmm0: float <- rational 0xa, 1
  var dummy/eax: int <- render-float-decimal screen, ten-f, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "10 ", "F - test-render-float-decimal-integer 10"
  # -10
  clear-screen screen
  var minus-ten-f/xmm0: float <- rational -0xa, 1
  var dummy/eax: int <- render-float-decimal screen, minus-ten-f, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "-10 ", "F - test-render-float-decimal-integer -10"
  # 999
  clear-screen screen
  var minus-ten-f/xmm0: float <- rational 0x3e7, 1
  var dummy/eax: int <- render-float-decimal screen, minus-ten-f, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "999 ", "F - test-render-float-decimal-integer 1000"
  # 1000 - start using scientific notation
  clear-screen screen
  var minus-ten-f/xmm0: float <- rational 0x3e8, 1
  var dummy/eax: int <- render-float-decimal screen, minus-ten-f, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "1.00e3 ", "F - test-render-float-decimal-integer 1000"
  # 100,000
  clear-screen screen
  var hundred-thousand/eax: int <- copy 0x186a0
  var hundred-thousand-f/xmm0: float <- convert hundred-thousand
  var dummy/eax: int <- render-float-decimal screen, hundred-thousand-f, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "1.00e5 ", "F - test-render-float-decimal-integer 100,000"
}

fn test-render-float-decimal-zero {
  var screen-on-stack: screen
  var screen/esi: (addr screen) <- address screen-on-stack
  initialize-screen screen, 0x20, 5  # 32 columns should be more than enough
  var zero: float
  var dummy/eax: int <- render-float-decimal screen, zero, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "0 ", "F - test-render-float-decimal-zero"
}

fn test-render-float-decimal-negative-zero {
  var screen-on-stack: screen
  var screen/esi: (addr screen) <- address screen-on-stack
  initialize-screen screen, 0x20, 5  # 32 columns should be more than enough
  var n: int
  copy-to n, 0x80000000
  var negative-zero/xmm0: float <- reinterpret n
  var dummy/eax: int <- render-float-decimal screen, negative-zero, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "-0 ", "F - test-render-float-decimal-negative-zero"
}

fn test-render-float-decimal-infinity {
  var screen-on-stack: screen
  var screen/esi: (addr screen) <- address screen-on-stack
  initialize-screen screen, 0x20, 5  # 32 columns should be more than enough
  var n: int
  #          0|11111111|00000000000000000000000
  #          0111|1111|1000|0000|0000|0000|0000|0000
  copy-to n, 0x7f800000
  var infinity/xmm0: float <- reinterpret n
  var dummy/eax: int <- render-float-decimal screen, infinity, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "Inf ", "F - test-render-float-decimal-infinity"
}

fn test-render-float-decimal-negative-infinity {
  var screen-on-stack: screen
  var screen/esi: (addr screen) <- address screen-on-stack
  initialize-screen screen, 0x20, 5  # 32 columns should be more than enough
  var n: int
  copy-to n, 0xff800000
  var negative-infinity/xmm0: float <- reinterpret n
  var dummy/eax: int <- render-float-decimal screen, negative-infinity, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "-Inf ", "F - test-render-float-decimal-negative-infinity"
}

fn test-render-float-decimal-not-a-number {
  var screen-on-stack: screen
  var screen/esi: (addr screen) <- address screen-on-stack
  initialize-screen screen, 0x20, 5  # 32 columns should be more than enough
  var n: int
  copy-to n, 0xffffffff  # exponent must be all 1's, and mantissa must be non-zero
  var nan/xmm0: float <- reinterpret n
  var dummy/eax: int <- render-float-decimal screen, nan, 3/precision, 0, 0, 3/fg, 0/bg
  check-screen-row screen, 0/y, "NaN ", "F - test-render-float-decimal-not-a-number"
}

# 'precision' controls the maximum width past which we resort to scientific notation
fn render-float-decimal screen: (addr screen), in: float, precision: int, x: int, y: int, color: int, background-color: int -> _/eax: int {
  # - special names
  var bits/eax: int <- reinterpret in
  compare bits, 0
  {
    break-if-!=
    var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "0", x, y, color, background-color
    return new-x
  }
  compare bits, 0x80000000
  {
    break-if-!=
    var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "-0", x, y, color, background-color
    return new-x
  }
  compare bits, 0x7f800000
  {
    break-if-!=
    var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "Inf", x, y, color, background-color
    return new-x
  }
  compare bits, 0xff800000
  {
    break-if-!=
    var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "-Inf", x, y, color, background-color
    return new-x
  }
  var exponent/ecx: int <- copy bits
  exponent <- shift-right 0x17  # 23 bits of mantissa
  exponent <- and 0xff
  exponent <- subtract 0x7f
  compare exponent, 0x80
  {
    break-if-!=
    var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "NaN", x, y, color, background-color
    return new-x
  }
  # - regular numbers
  var sign/edx: int <- copy bits
  sign <- shift-right 0x1f
  {
    compare sign, 1
    break-if-!=
    draw-code-point screen, 0x2d/minus, x, y, color, background-color
    increment x
  }

  # v = 1.mantissa (in base 2) << 0x17
  var v/ebx: int <- copy bits
  v <- and 0x7fffff
  v <- or 0x00800000  # insert implicit 1
  # e = exponent - 0x17
  var e/ecx: int <- copy exponent
  e <- subtract 0x17  # move decimal place from before mantissa to after

  # initialize buffer with decimal representation of v
  # unlike https://research.swtch.com/ftoa, no ascii here
  var buf-storage: (array byte 0x7f)
  var buf/edi: (addr array byte) <- address buf-storage
  var n/eax: int <- decimal-digits v, buf
  # I suspect we can do without reversing, but we'll follow https://research.swtch.com/ftoa
  # closely for now.
  reverse-digits buf, n

  # loop if e > 0
  {
    compare e, 0
    break-if-<=
    n <- double-array-of-decimal-digits buf, n
    e <- decrement
    loop
  }

  var dp/edx: int <- copy n

  # loop if e < 0
  {
    compare e, 0
    break-if->=
    n, dp <- halve-array-of-decimal-digits buf, n, dp
    e <- increment
    loop
  }

  var new-x/eax: int <- render-float-buffer screen, buf, n, dp, precision, x, y, color, background-color
  return new-x
}

# store the decimal digits of 'n' into 'buf', units first
# n must be positive
fn decimal-digits n: int, _buf: (addr array byte) -> _/eax: int {
  var buf/edi: (addr array byte) <- copy _buf
  var i/ecx: int <- copy 0
  var curr/eax: int <- copy n
  var curr-byte/edx: int <- copy 0
  {
    compare curr, 0
    break-if-=
    curr, curr-byte <- integer-divide curr, 0xa
    var dest/ebx: (addr byte) <- index buf, i
    copy-byte-to *dest, curr-byte
    i <- increment
    loop
  }
  return i
}

fn reverse-digits _buf: (addr array byte), n: int {
  var buf/esi: (addr array byte) <- copy _buf
  var left/ecx: int <- copy 0
  var right/edx: int <- copy n
  right <- decrement
  {
    compare left, right
    break-if->=
    {
      var l-a/ecx: (addr byte) <- index buf, left
      var r-a/edx: (addr byte) <- index buf, right
      var l/ebx: byte <- copy-byte *l-a
      var r/eax: byte <- copy-byte *r-a
      copy-byte-to *l-a, r
      copy-byte-to *r-a, l
    }
    left <- increment
    right <- decrement
    loop
  }
}

fn double-array-of-decimal-digits _buf: (addr array byte), _n: int -> _/eax: int {
  var buf/edi: (addr array byte) <- copy _buf
  # initialize delta
  var delta/edx: int <- copy 0
  {
    var curr/ebx: (addr byte) <- index buf, 0
    var tmp/eax: byte <- copy-byte *curr
    compare tmp, 5
    break-if-<
    delta <- copy 1
  }
  # loop
  var x/eax: int <- copy 0
  var i/ecx: int <- copy _n
  i <- decrement
  {
    compare i, 0
    break-if-<=
    # x += 2*buf[i]
    {
      var tmp/ecx: (addr byte) <- index buf, i
      var tmp2/ecx: byte <- copy-byte *tmp
      x <- add tmp2
      x <- add tmp2
    }
    # x, buf[i+delta] = x/10, x%10
    {
      var dest-index/ecx: int <- copy i
      dest-index <- add delta
      var dest/edi: (addr byte) <- index buf, dest-index
      var next-digit/edx: int <- copy 0
      x, next-digit <- integer-divide x, 0xa
      copy-byte-to *dest, next-digit
    }
    #
    i <- decrement
    loop
  }
  # final patch-up
  var n/eax: int <- copy _n
  compare delta, 1
  {
    break-if-!=
    var curr/ebx: (addr byte) <- index buf, 0
    var one/edx: int <- copy 1
    copy-byte-to *curr, one
    n <- increment
  }
  return n
}

fn halve-array-of-decimal-digits _buf: (addr array byte), _n: int, _dp: int -> _/eax: int, _/edx: int {
  var buf/edi: (addr array byte) <- copy _buf
  var n/eax: int <- copy _n
  var dp/edx: int <- copy _dp
  # initialize one side
  {
    # if buf[n-1]%2 == 0, break
    var right-index/ecx: int <- copy n
    right-index <- decrement
    var right-a/ecx: (addr byte) <- index buf, right-index
    var right/ecx: byte <- copy-byte *right-a
    var right-int/ecx: int <- copy right
    var remainder/edx: int <- copy 0
    {
      var dummy/eax: int <- copy 0
      dummy, remainder <- integer-divide right-int, 2
    }
    compare remainder, 0
    break-if-=
    # buf[n] = 0
    var next-a/ecx: (addr byte) <- index buf, n
    var zero/edx: byte <- copy 0
    copy-byte-to *next-a, zero
    # n++
    n <- increment
  }
  # initialize the other
  var delta/ebx: int <- copy 0
  var x/esi: int <- copy 0
  {
    # if buf[0] >= 2, break
    var left/ecx: (addr byte) <- index buf, 0
    var src/ecx: byte <- copy-byte *left
    compare src, 2
    break-if->=
    # delta, x = 1, buf[0]
    delta <- copy 1
    x <- copy src
    # n--
    n <- decrement
    # dp--
    dp <- decrement
  }
  # loop
  var i/ecx: int <- copy 0
  {
    compare i, n
    break-if->=
    # x = x*10 + buf[i+delta]
    {
      var ten/edx: int <- copy 0xa
      x <- multiply ten
      var src-index/edx: int <- copy i
      src-index <- add delta
      var src-a/edx: (addr byte) <- index buf, src-index
      var src/edx: byte <- copy-byte *src-a
      x <- add src
    }
    # buf[i], x = x/2, x%2
    {
      var quotient/eax: int <- copy 0
      var remainder/edx: int <- copy 0
      quotient, remainder <- integer-divide x, 2
      x <- copy remainder
      var dest/edx: (addr byte) <- index buf, i
      copy-byte-to *dest, quotient
    }
    #
    i <- increment
    loop
  }
  return n, dp
}

fn render-float-buffer screen: (addr screen), _buf: (addr array byte), n: int, dp: int, precision: int, x: int, y: int, color: int, background-color: int -> _/eax: int {
  var buf/edi: (addr array byte) <- copy _buf
  {
    compare dp, 0
    break-if->=
    var new-x/eax: int <- render-float-buffer-in-scientific-notation screen, buf, n, dp, precision, x, y, color, background-color
    return new-x
  }
  {
    var dp2/eax: int <- copy dp
    compare dp2, precision
    break-if-<=
    var new-x/eax: int <- render-float-buffer-in-scientific-notation screen, buf, n, dp, precision, x, y, color, background-color
    return new-x
  }
  {
    compare dp, 0
    break-if-!=
    draw-code-point screen, 0x30/0, x, y, color, background-color
    increment x
  }
  var i/eax: int <- copy 0
  # bounds = min(n, dp+3)
  var limit/edx: int <- copy dp
  limit <- add 3
  {
    compare limit, n
    break-if-<=
    limit <- copy n
  }
  {
    compare i, limit
    break-if->=
    # print '.' if necessary
    compare i, dp
    {
      break-if-!=
      draw-code-point screen, 0x2e/decimal-point, x, y, color, background-color
      increment x
    }
    var curr-a/ecx: (addr byte) <- index buf, i
    var curr/ecx: byte <- copy-byte *curr-a
    curr <- add 0x30/0
    var curr-grapheme/ecx: grapheme <- copy curr
    draw-grapheme screen, curr-grapheme, x, y, color, background-color
    increment x
    i <- increment
    loop
  }
  return x
}

fn render-float-buffer-in-scientific-notation screen: (addr screen), _buf: (addr array byte), n: int, dp: int, precision: int, x: int, y: int, color: int, background-color: int -> _/eax: int {
  var buf/edi: (addr array byte) <- copy _buf
  var i/eax: int <- copy 0
  {
    compare i, n
    break-if->=
    compare i, precision
    break-if->=
    compare i, 1
    {
      break-if-!=
      draw-code-point screen, 0x2e/decimal-point, x, y, color, background-color
      increment x
    }
    var curr-a/ecx: (addr byte) <- index buf, i
    var curr/ecx: byte <- copy-byte *curr-a
    curr <- add 0x30/0
    var curr-grapheme/ecx: grapheme <- copy curr
    draw-grapheme screen, curr-grapheme, x, y, color, background-color
    increment x
    #
    i <- increment
    loop
  }
  draw-code-point screen, 0x65/e, x, y, color, background-color
  increment x
  decrement dp
  var new-x/eax: int <- copy 0
  var new-y/ecx: int <- copy 0
  new-x, new-y <- draw-int32-decimal-wrapping-right-then-down-over-full-screen screen, dp, x, y, color, background-color
  return new-x
}

# follows the structure of render-float-decimal
# 'precision' controls the maximum width past which we resort to scientific notation
fn float-size in: float, precision: int -> _/eax: int {
  # - special names
  var bits/eax: int <- reinterpret in
  compare bits, 0
  {
    break-if-!=
    return 1  # for "0"
  }
  compare bits, 0x80000000
  {
    break-if-!=
    return 2  # for "-0"
  }
  compare bits, 0x7f800000
  {
    break-if-!=
    return 3  # for "Inf"
  }
  compare bits, 0xff800000
  {
    break-if-!=
    return 4  # for "-Inf"
  }
  var exponent/ecx: int <- copy bits
  exponent <- shift-right 0x17  # 23 bits of mantissa
  exponent <- and 0xff
  exponent <- subtract 0x7f
  compare exponent, 0x80
  {
    break-if-!=
    return 3  # for "NaN"
  }
  # - regular numbers
  # v = 1.mantissa (in base 2) << 0x17
  var v/ebx: int <- copy bits
  v <- and 0x7fffff
  v <- or 0x00800000  # insert implicit 1
  # e = exponent - 0x17
  var e/ecx: int <- copy exponent
  e <- subtract 0x17  # move decimal place from before mantissa to after

  # initialize buffer with decimal representation of v
  var buf-storage: (array byte 0x7f)
  var buf/edi: (addr array byte) <- address buf-storage
  var n/eax: int <- decimal-digits v, buf
  reverse-digits buf, n

  # loop if e > 0
  {
    compare e, 0
    break-if-<=
    n <- double-array-of-decimal-digits buf, n
    e <- decrement
    loop
  }

  var dp/edx: int <- copy n

  # loop if e < 0
  {
    compare e, 0
    break-if->=
    n, dp <- halve-array-of-decimal-digits buf, n, dp
    e <- increment
    loop
  }

  compare dp, 0
  {
    break-if->=
    return 8  # hacky for scientific notation
  }
  {
    var dp2/eax: int <- copy dp
    compare dp2, precision
    break-if-<=
    return 8  # hacky for scientific notation
  }

  # result = min(n, dp+3)
  var result/ecx: int <- copy dp
  result <- add 3
  {
    compare result, n
    break-if-<=
    result <- copy n
  }

  # account for decimal point
  compare dp, n
  {
    break-if->=
    result <- increment
  }

  # account for sign
  var sign/edx: int <- reinterpret in
  sign <- shift-right 0x1f
  {
    compare sign, 1
    break-if-!=
    result <- increment
  }
  return result
}