summaryrefslogtreecommitdiff
path: root/src/pkg/runtime/softfloat64.go
blob: 4fcf8f269018e90440157f2f7a1dd72dff00e24d (plain)
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
// Copyright 2010 The Go Authors.  All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Software IEEE754 64-bit floating point.
// Only referred to (and thus linked in) by arm port
// and by tests in this directory.

package runtime

const (
	mantbits64 uint = 52
	expbits64  uint = 11
	bias64          = -1<<(expbits64-1) + 1

	nan64 uint64 = (1<<expbits64-1)<<mantbits64 + 1
	inf64 uint64 = (1<<expbits64 - 1) << mantbits64
	neg64 uint64 = 1 << (expbits64 + mantbits64)

	mantbits32 uint = 23
	expbits32  uint = 8
	bias32          = -1<<(expbits32-1) + 1

	nan32 uint32 = (1<<expbits32-1)<<mantbits32 + 1
	inf32 uint32 = (1<<expbits32 - 1) << mantbits32
	neg32 uint32 = 1 << (expbits32 + mantbits32)
)

func funpack64(f uint64) (sign, mant uint64, exp int, inf, nan bool) {
	sign = f & (1 << (mantbits64 + expbits64))
	mant = f & (1<<mantbits64 - 1)
	exp = int(f>>mantbits64) & (1<<expbits64 - 1)

	switch exp {
	case 1<<expbits64 - 1:
		if mant != 0 {
			nan = true
			return
		}
		inf = true
		return

	case 0:
		// denormalized
		if mant != 0 {
			exp += bias64 + 1
			for mant < 1<<mantbits64 {
				mant <<= 1
				exp--
			}
		}

	default:
		// add implicit top bit
		mant |= 1 << mantbits64
		exp += bias64
	}
	return
}

func funpack32(f uint32) (sign, mant uint32, exp int, inf, nan bool) {
	sign = f & (1 << (mantbits32 + expbits32))
	mant = f & (1<<mantbits32 - 1)
	exp = int(f>>mantbits32) & (1<<expbits32 - 1)

	switch exp {
	case 1<<expbits32 - 1:
		if mant != 0 {
			nan = true
			return
		}
		inf = true
		return

	case 0:
		// denormalized
		if mant != 0 {
			exp += bias32 + 1
			for mant < 1<<mantbits32 {
				mant <<= 1
				exp--
			}
		}

	default:
		// add implicit top bit
		mant |= 1 << mantbits32
		exp += bias32
	}
	return
}

func fpack64(sign, mant uint64, exp int, trunc uint64) uint64 {
	mant0, exp0, trunc0 := mant, exp, trunc
	if mant == 0 {
		return sign
	}
	for mant < 1<<mantbits64 {
		mant <<= 1
		exp--
	}
	for mant >= 4<<mantbits64 {
		trunc |= mant & 1
		mant >>= 1
		exp++
	}
	if mant >= 2<<mantbits64 {
		if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
			mant++
			if mant >= 4<<mantbits64 {
				mant >>= 1
				exp++
			}
		}
		mant >>= 1
		exp++
	}
	if exp >= 1<<expbits64-1+bias64 {
		return sign ^ inf64
	}
	if exp < bias64+1 {
		if exp < bias64-int(mantbits64) {
			return sign | 0
		}
		// repeat expecting denormal
		mant, exp, trunc = mant0, exp0, trunc0
		for exp < bias64 {
			trunc |= mant & 1
			mant >>= 1
			exp++
		}
		if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
			mant++
		}
		mant >>= 1
		exp++
		if mant < 1<<mantbits64 {
			return sign | mant
		}
	}
	return sign | uint64(exp-bias64)<<mantbits64 | mant&(1<<mantbits64-1)
}

func fpack32(sign, mant uint32, exp int, trunc uint32) uint32 {
	mant0, exp0, trunc0 := mant, exp, trunc
	if mant == 0 {
		return sign
	}
	for mant < 1<<mantbits32 {
		mant <<= 1
		exp--
	}
	for mant >= 4<<mantbits32 {
		trunc |= mant & 1
		mant >>= 1
		exp++
	}
	if mant >= 2<<mantbits32 {
		if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
			mant++
			if mant >= 4<<mantbits32 {
				mant >>= 1
				exp++
			}
		}
		mant >>= 1
		exp++
	}
	if exp >= 1<<expbits32-1+bias32 {
		return sign ^ inf32
	}
	if exp < bias32+1 {
		if exp < bias32-int(mantbits32) {
			return sign | 0
		}
		// repeat expecting denormal
		mant, exp, trunc = mant0, exp0, trunc0
		for exp < bias32 {
			trunc |= mant & 1
			mant >>= 1
			exp++
		}
		if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
			mant++
		}
		mant >>= 1
		exp++
		if mant < 1<<mantbits32 {
			return sign | mant
		}
	}
	return sign | uint32(exp-bias32)<<mantbits32 | mant&(1<<mantbits32-1)
}

func fadd64(f, g uint64) uint64 {
	fs, fm, fe, fi, fn := funpack64(f)
	gs, gm, ge, gi, gn := funpack64(g)

	// Special cases.
	switch {
	case fn || gn: // NaN + x or x + NaN = NaN
		return nan64

	case fi && gi && fs != gs: // +Inf + -Inf or -Inf + +Inf = NaN
		return nan64

	case fi: // ±Inf + g = ±Inf
		return f

	case gi: // f + ±Inf = ±Inf
		return g

	case fm == 0 && gm == 0 && fs != 0 && gs != 0: // -0 + -0 = -0
		return f

	case fm == 0: // 0 + g = g but 0 + -0 = +0
		if gm == 0 {
			g ^= gs
		}
		return g

	case gm == 0: // f + 0 = f
		return f

	}

	if fe < ge || fe == ge && fm < gm {
		f, g, fs, fm, fe, gs, gm, ge = g, f, gs, gm, ge, fs, fm, fe
	}

	shift := uint(fe - ge)
	fm <<= 2
	gm <<= 2
	trunc := gm & (1<<shift - 1)
	gm >>= shift
	if fs == gs {
		fm += gm
	} else {
		fm -= gm
		if trunc != 0 {
			fm--
		}
	}
	if fm == 0 {
		fs = 0
	}
	return fpack64(fs, fm, fe-2, trunc)
}

func fsub64(f, g uint64) uint64 {
	return fadd64(f, fneg64(g))
}

func fneg64(f uint64) uint64 {
	return f ^ (1 << (mantbits64 + expbits64))
}

func fmul64(f, g uint64) uint64 {
	fs, fm, fe, fi, fn := funpack64(f)
	gs, gm, ge, gi, gn := funpack64(g)

	// Special cases.
	switch {
	case fn || gn: // NaN * g or f * NaN = NaN
		return nan64

	case fi && gi: // Inf * Inf = Inf (with sign adjusted)
		return f ^ gs

	case fi && gm == 0, fm == 0 && gi: // 0 * Inf = Inf * 0 = NaN
		return nan64

	case fm == 0: // 0 * x = 0 (with sign adjusted)
		return f ^ gs

	case gm == 0: // x * 0 = 0 (with sign adjusted)
		return g ^ fs
	}

	// 53-bit * 53-bit = 107- or 108-bit
	lo, hi := mullu(fm, gm)
	shift := mantbits64 - 1
	trunc := lo & (1<<shift - 1)
	mant := hi<<(64-shift) | lo>>shift
	return fpack64(fs^gs, mant, fe+ge-1, trunc)
}

func fdiv64(f, g uint64) uint64 {
	fs, fm, fe, fi, fn := funpack64(f)
	gs, gm, ge, gi, gn := funpack64(g)

	// Special cases.
	switch {
	case fn || gn: // NaN / g = f / NaN = NaN
		return nan64

	case fi && gi: // ±Inf / ±Inf = NaN
		return nan64

	case !fi && !gi && fm == 0 && gm == 0: // 0 / 0 = NaN
		return nan64

	case fi, !gi && gm == 0: // Inf / g = f / 0 = Inf
		return fs ^ gs ^ inf64

	case gi, fm == 0: // f / Inf = 0 / g = Inf
		return fs ^ gs ^ 0
	}
	_, _, _, _ = fi, fn, gi, gn

	// 53-bit<<54 / 53-bit = 53- or 54-bit.
	shift := mantbits64 + 2
	q, r := divlu(fm>>(64-shift), fm<<shift, gm)
	return fpack64(fs^gs, q, fe-ge-2, r)
}

func f64to32(f uint64) uint32 {
	fs, fm, fe, fi, fn := funpack64(f)
	if fn {
		return nan32
	}
	fs32 := uint32(fs >> 32)
	if fi {
		return fs32 ^ inf32
	}
	const d = mantbits64 - mantbits32 - 1
	return fpack32(fs32, uint32(fm>>d), fe-1, uint32(fm&(1<<d-1)))
}

func f32to64(f uint32) uint64 {
	const d = mantbits64 - mantbits32
	fs, fm, fe, fi, fn := funpack32(f)
	if fn {
		return nan64
	}
	fs64 := uint64(fs) << 32
	if fi {
		return fs64 ^ inf64
	}
	return fpack64(fs64, uint64(fm)<<d, fe, 0)
}

func fcmp64(f, g uint64) (cmp int, isnan bool) {
	fs, fm, _, fi, fn := funpack64(f)
	gs, gm, _, gi, gn := funpack64(g)

	switch {
	case fn, gn: // flag NaN
		return 0, true

	case !fi && !gi && fm == 0 && gm == 0: // ±0 == ±0
		return 0, false

	case fs > gs: // f < 0, g > 0
		return -1, false

	case fs < gs: // f > 0, g < 0
		return +1, false

	// Same sign, not NaN.
	// Can compare encodings directly now.
	// Reverse for sign.
	case fs == 0 && f < g, fs != 0 && f > g:
		return -1, false

	case fs == 0 && f > g, fs != 0 && f < g:
		return +1, false
	}

	// f == g
	return 0, false
}

func f64toint(f uint64) (val int64, ok bool) {
	fs, fm, fe, fi, fn := funpack64(f)

	switch {
	case fi, fn: // NaN
		return 0, false

	case fe < -1: // f < 0.5
		return 0, false

	case fe > 63: // f >= 2^63
		if fs != 0 && fm == 0 { // f == -2^63
			return -1 << 63, true
		}
		if fs != 0 {
			return 0, false
		}
		return 0, false
	}

	for fe > int(mantbits64) {
		fe--
		fm <<= 1
	}
	for fe < int(mantbits64) {
		fe++
		fm >>= 1
	}
	val = int64(fm)
	if fs != 0 {
		val = -val
	}
	return val, true
}

func fintto64(val int64) (f uint64) {
	fs := uint64(val) & (1 << 63)
	mant := uint64(val)
	if fs != 0 {
		mant = -mant
	}
	return fpack64(fs, mant, int(mantbits64), 0)
}

// 64x64 -> 128 multiply.
// adapted from hacker's delight.
func mullu(u, v uint64) (lo, hi uint64) {
	const (
		s    = 32
		mask = 1<<s - 1
	)
	u0 := u & mask
	u1 := u >> s
	v0 := v & mask
	v1 := v >> s
	w0 := u0 * v0
	t := u1*v0 + w0>>s
	w1 := t & mask
	w2 := t >> s
	w1 += u0 * v1
	return u * v, u1*v1 + w2 + w1>>s
}

// 128/64 -> 64 quotient, 64 remainder.
// adapted from hacker's delight
func divlu(u1, u0, v uint64) (q, r uint64) {
	const b = 1 << 32

	if u1 >= v {
		return 1<<64 - 1, 1<<64 - 1
	}

	// s = nlz(v); v <<= s
	s := uint(0)
	for v&(1<<63) == 0 {
		s++
		v <<= 1
	}

	vn1 := v >> 32
	vn0 := v & (1<<32 - 1)
	un32 := u1<<s | u0>>(64-s)
	un10 := u0 << s
	un1 := un10 >> 32
	un0 := un10 & (1<<32 - 1)
	q1 := un32 / vn1
	rhat := un32 - q1*vn1

again1:
	if q1 >= b || q1*vn0 > b*rhat+un1 {
		q1--
		rhat += vn1
		if rhat < b {
			goto again1
		}
	}

	un21 := un32*b + un1 - q1*v
	q0 := un21 / vn1
	rhat = un21 - q0*vn1

again2:
	if q0 >= b || q0*vn0 > b*rhat+un0 {
		q0--
		rhat += vn1
		if rhat < b {
			goto again2
		}
	}

	return q1*b + q0, (un21*b + un0 - q0*v) >> s
}

// callable from C

func fadd64c(f, g uint64, ret *uint64)            { *ret = fadd64(f, g) }
func fsub64c(f, g uint64, ret *uint64)            { *ret = fsub64(f, g) }
func fmul64c(f, g uint64, ret *uint64)            { *ret = fmul64(f, g) }
func fdiv64c(f, g uint64, ret *uint64)            { *ret = fdiv64(f, g) }
func fneg64c(f uint64, ret *uint64)               { *ret = fneg64(f) }
func f32to64c(f uint32, ret *uint64)              { *ret = f32to64(f) }
func f64to32c(f uint64, ret *uint32)              { *ret = f64to32(f) }
func fcmp64c(f, g uint64, ret *int, retnan *bool) { *ret, *retnan = fcmp64(f, g) }
func fintto64c(val int64, ret *uint64)            { *ret = fintto64(val) }
func f64tointc(f uint64, ret *int64, retok *bool) { *ret, *retok = f64toint(f) }