/
mpfloat.go
336 lines (264 loc) · 6.11 KB
/
mpfloat.go
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
// Copyright 2009 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.
package gc
import (
"fmt"
"math"
"math/big"
)
// implements float arithmetic
const (
// Maximum size in bits for Mpints before signalling
// overflow and also mantissa precision for Mpflts.
Mpprec = 512
// Turn on for constant arithmetic debugging output.
Mpdebug = false
)
// Mpflt represents a floating-point constant.
type Mpflt struct {
Val big.Float
}
// Mpcplx represents a complex constant.
type Mpcplx struct {
Real Mpflt
Imag Mpflt
}
func newMpflt() *Mpflt {
var a Mpflt
a.Val.SetPrec(Mpprec)
return &a
}
func newMpcmplx() *Mpcplx {
var a Mpcplx
a.Real = *newMpflt()
a.Imag = *newMpflt()
return &a
}
func (a *Mpflt) SetInt(b *Mpint) {
if b.checkOverflow(0) {
// sign doesn't really matter but copy anyway
a.Val.SetInf(b.Val.Sign() < 0)
return
}
a.Val.SetInt(&b.Val)
}
func (a *Mpflt) Set(b *Mpflt) {
a.Val.Set(&b.Val)
}
func (a *Mpflt) Add(b *Mpflt) {
if Mpdebug {
fmt.Printf("\n%v + %v", a, b)
}
a.Val.Add(&a.Val, &b.Val)
if Mpdebug {
fmt.Printf(" = %v\n\n", a)
}
}
func (a *Mpflt) AddFloat64(c float64) {
var b Mpflt
b.SetFloat64(c)
a.Add(&b)
}
func (a *Mpflt) Sub(b *Mpflt) {
if Mpdebug {
fmt.Printf("\n%v - %v", a, b)
}
a.Val.Sub(&a.Val, &b.Val)
if Mpdebug {
fmt.Printf(" = %v\n\n", a)
}
}
func (a *Mpflt) Mul(b *Mpflt) {
if Mpdebug {
fmt.Printf("%v\n * %v\n", a, b)
}
a.Val.Mul(&a.Val, &b.Val)
if Mpdebug {
fmt.Printf(" = %v\n\n", a)
}
}
func (a *Mpflt) MulFloat64(c float64) {
var b Mpflt
b.SetFloat64(c)
a.Mul(&b)
}
func (a *Mpflt) Quo(b *Mpflt) {
if Mpdebug {
fmt.Printf("%v\n / %v\n", a, b)
}
a.Val.Quo(&a.Val, &b.Val)
if Mpdebug {
fmt.Printf(" = %v\n\n", a)
}
}
func (a *Mpflt) Cmp(b *Mpflt) int {
return a.Val.Cmp(&b.Val)
}
func (a *Mpflt) CmpFloat64(c float64) int {
if c == 0 {
return a.Val.Sign() // common case shortcut
}
return a.Val.Cmp(big.NewFloat(c))
}
func (a *Mpflt) Float64() float64 {
x, _ := a.Val.Float64()
// check for overflow
if math.IsInf(x, 0) && nsavederrors+nerrors == 0 {
Fatalf("ovf in Mpflt Float64")
}
return x + 0 // avoid -0 (should not be needed, but be conservative)
}
func (a *Mpflt) Float32() float64 {
x32, _ := a.Val.Float32()
x := float64(x32)
// check for overflow
if math.IsInf(x, 0) && nsavederrors+nerrors == 0 {
Fatalf("ovf in Mpflt Float32")
}
return x + 0 // avoid -0 (should not be needed, but be conservative)
}
func (a *Mpflt) SetFloat64(c float64) {
if Mpdebug {
fmt.Printf("\nconst %g", c)
}
// convert -0 to 0
if c == 0 {
c = 0
}
a.Val.SetFloat64(c)
if Mpdebug {
fmt.Printf(" = %v\n", a)
}
}
func (a *Mpflt) Neg() {
// avoid -0
if a.Val.Sign() != 0 {
a.Val.Neg(&a.Val)
}
}
func (a *Mpflt) SetString(as string) {
for len(as) > 0 && (as[0] == ' ' || as[0] == '\t') {
as = as[1:]
}
f, _, err := a.Val.Parse(as, 10)
if err != nil {
yyerror("malformed constant: %s (%v)", as, err)
a.Val.SetFloat64(0)
return
}
if f.IsInf() {
yyerror("constant too large: %s", as)
a.Val.SetFloat64(0)
return
}
// -0 becomes 0
if f.Sign() == 0 && f.Signbit() {
a.Val.SetFloat64(0)
}
}
func (f *Mpflt) String() string {
return fconv(f, 0)
}
func fconv(fvp *Mpflt, flag FmtFlag) string {
if flag&FmtSharp == 0 {
return fvp.Val.Text('b', 0)
}
// use decimal format for error messages
// determine sign
f := &fvp.Val
var sign string
if f.Sign() < 0 {
sign = "-"
f = new(big.Float).Abs(f)
} else if flag&FmtSign != 0 {
sign = "+"
}
// Don't try to convert infinities (will not terminate).
if f.IsInf() {
return sign + "Inf"
}
// Use exact fmt formatting if in float64 range (common case):
// proceed if f doesn't underflow to 0 or overflow to inf.
if x, _ := f.Float64(); f.Sign() == 0 == (x == 0) && !math.IsInf(x, 0) {
return fmt.Sprintf("%s%.6g", sign, x)
}
// Out of float64 range. Do approximate manual to decimal
// conversion to avoid precise but possibly slow Float
// formatting.
// f = mant * 2**exp
var mant big.Float
exp := f.MantExp(&mant) // 0.5 <= mant < 1.0
// approximate float64 mantissa m and decimal exponent d
// f ~ m * 10**d
m, _ := mant.Float64() // 0.5 <= m < 1.0
d := float64(exp) * (math.Ln2 / math.Ln10) // log_10(2)
// adjust m for truncated (integer) decimal exponent e
e := int64(d)
m *= math.Pow(10, d-float64(e))
// ensure 1 <= m < 10
switch {
case m < 1-0.5e-6:
// The %.6g format below rounds m to 5 digits after the
// decimal point. Make sure that m*10 < 10 even after
// rounding up: m*10 + 0.5e-5 < 10 => m < 1 - 0.5e6.
m *= 10
e--
case m >= 10:
m /= 10
e++
}
return fmt.Sprintf("%s%.6ge%+d", sign, m, e)
}
// complex multiply v *= rv
// (a, b) * (c, d) = (a*c - b*d, b*c + a*d)
func (v *Mpcplx) Mul(rv *Mpcplx) {
var ac, ad, bc, bd Mpflt
ac.Set(&v.Real)
ac.Mul(&rv.Real) // ac
bd.Set(&v.Imag)
bd.Mul(&rv.Imag) // bd
bc.Set(&v.Imag)
bc.Mul(&rv.Real) // bc
ad.Set(&v.Real)
ad.Mul(&rv.Imag) // ad
v.Real.Set(&ac)
v.Real.Sub(&bd) // ac-bd
v.Imag.Set(&bc)
v.Imag.Add(&ad) // bc+ad
}
// complex divide v /= rv
// (a, b) / (c, d) = ((a*c + b*d), (b*c - a*d))/(c*c + d*d)
func (v *Mpcplx) Div(rv *Mpcplx) bool {
if rv.Real.CmpFloat64(0) == 0 && rv.Imag.CmpFloat64(0) == 0 {
return false
}
var ac, ad, bc, bd, cc_plus_dd Mpflt
cc_plus_dd.Set(&rv.Real)
cc_plus_dd.Mul(&rv.Real) // cc
ac.Set(&rv.Imag)
ac.Mul(&rv.Imag) // dd
cc_plus_dd.Add(&ac) // cc+dd
// We already checked that c and d are not both zero, but we can't
// assume that c²+d² != 0 follows, because for tiny values of c
// and/or d c²+d² can underflow to zero. Check that c²+d² is
// nonzero, return if it's not.
if cc_plus_dd.CmpFloat64(0) == 0 {
return false
}
ac.Set(&v.Real)
ac.Mul(&rv.Real) // ac
bd.Set(&v.Imag)
bd.Mul(&rv.Imag) // bd
bc.Set(&v.Imag)
bc.Mul(&rv.Real) // bc
ad.Set(&v.Real)
ad.Mul(&rv.Imag) // ad
v.Real.Set(&ac)
v.Real.Add(&bd) // ac+bd
v.Real.Quo(&cc_plus_dd) // (ac+bd)/(cc+dd)
v.Imag.Set(&bc)
v.Imag.Sub(&ad) // bc-ad
v.Imag.Quo(&cc_plus_dd) // (bc+ad)/(cc+dd)
return true
}