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# Source file src/strconv/decimal.go

## Documentation: strconv

```     1  // Copyright 2009 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
4
5  // Multiprecision decimal numbers.
6  // For floating-point formatting only; not general purpose.
7  // Only operations are assign and (binary) left/right shift.
8  // Can do binary floating point in multiprecision decimal precisely
9  // because 2 divides 10; cannot do decimal floating point
10  // in multiprecision binary precisely.
11
12  package strconv
13
14  type decimal struct {
15  	d     [800]byte // digits, big-endian representation
16  	nd    int       // number of digits used
17  	dp    int       // decimal point
18  	neg   bool      // negative flag
19  	trunc bool      // discarded nonzero digits beyond d[:nd]
20  }
21
22  func (a *decimal) String() string {
23  	n := 10 + a.nd
24  	if a.dp > 0 {
25  		n += a.dp
26  	}
27  	if a.dp < 0 {
28  		n += -a.dp
29  	}
30
31  	buf := make([]byte, n)
32  	w := 0
33  	switch {
34  	case a.nd == 0:
35  		return "0"
36
37  	case a.dp <= 0:
38  		// zeros fill space between decimal point and digits
39  		buf[w] = '0'
40  		w++
41  		buf[w] = '.'
42  		w++
43  		w += digitZero(buf[w : w+-a.dp])
44  		w += copy(buf[w:], a.d[0:a.nd])
45
46  	case a.dp < a.nd:
47  		// decimal point in middle of digits
48  		w += copy(buf[w:], a.d[0:a.dp])
49  		buf[w] = '.'
50  		w++
51  		w += copy(buf[w:], a.d[a.dp:a.nd])
52
53  	default:
54  		// zeros fill space between digits and decimal point
55  		w += copy(buf[w:], a.d[0:a.nd])
56  		w += digitZero(buf[w : w+a.dp-a.nd])
57  	}
58  	return string(buf[0:w])
59  }
60
61  func digitZero(dst []byte) int {
62  	for i := range dst {
63  		dst[i] = '0'
64  	}
65  	return len(dst)
66  }
67
68  // trim trailing zeros from number.
69  // (They are meaningless; the decimal point is tracked
70  // independent of the number of digits.)
71  func trim(a *decimal) {
72  	for a.nd > 0 && a.d[a.nd-1] == '0' {
73  		a.nd--
74  	}
75  	if a.nd == 0 {
76  		a.dp = 0
77  	}
78  }
79
80  // Assign v to a.
81  func (a *decimal) Assign(v uint64) {
82  	var buf [24]byte
83
84  	// Write reversed decimal in buf.
85  	n := 0
86  	for v > 0 {
87  		v1 := v / 10
88  		v -= 10 * v1
89  		buf[n] = byte(v + '0')
90  		n++
91  		v = v1
92  	}
93
94  	// Reverse again to produce forward decimal in a.d.
95  	a.nd = 0
96  	for n--; n >= 0; n-- {
97  		a.d[a.nd] = buf[n]
98  		a.nd++
99  	}
100  	a.dp = a.nd
101  	trim(a)
102  }
103
104  // Maximum shift that we can do in one pass without overflow.
105  // A uint has 32 or 64 bits, and we have to be able to accommodate 9<<k.
106  const uintSize = 32 << (^uint(0) >> 63)
107  const maxShift = uintSize - 4
108
109  // Binary shift right (/ 2) by k bits.  k <= maxShift to avoid overflow.
110  func rightShift(a *decimal, k uint) {
111  	r := 0 // read pointer
112  	w := 0 // write pointer
113
114  	// Pick up enough leading digits to cover first shift.
115  	var n uint
116  	for ; n>>k == 0; r++ {
117  		if r >= a.nd {
118  			if n == 0 {
119  				// a == 0; shouldn't get here, but handle anyway.
120  				a.nd = 0
121  				return
122  			}
123  			for n>>k == 0 {
124  				n = n * 10
125  				r++
126  			}
127  			break
128  		}
129  		c := uint(a.d[r])
130  		n = n*10 + c - '0'
131  	}
132  	a.dp -= r - 1
133
134  	var mask uint = (1 << k) - 1
135
136  	// Pick up a digit, put down a digit.
137  	for ; r < a.nd; r++ {
138  		c := uint(a.d[r])
139  		dig := n >> k
141  		a.d[w] = byte(dig + '0')
142  		w++
143  		n = n*10 + c - '0'
144  	}
145
146  	// Put down extra digits.
147  	for n > 0 {
148  		dig := n >> k
150  		if w < len(a.d) {
151  			a.d[w] = byte(dig + '0')
152  			w++
153  		} else if dig > 0 {
154  			a.trunc = true
155  		}
156  		n = n * 10
157  	}
158
159  	a.nd = w
160  	trim(a)
161  }
162
163  // Cheat sheet for left shift: table indexed by shift count giving
164  // number of new digits that will be introduced by that shift.
165  //
166  // For example, leftcheats[4] = {2, "625"}.  That means that
167  // if we are shifting by 4 (multiplying by 16), it will add 2 digits
168  // when the string prefix is "625" through "999", and one fewer digit
169  // if the string prefix is "000" through "624".
170  //
171  // Credit for this trick goes to Ken.
172
173  type leftCheat struct {
174  	delta  int    // number of new digits
175  	cutoff string // minus one digit if original < a.
176  }
177
178  var leftcheats = []leftCheat{
179  	// Leading digits of 1/2^i = 5^i.
180  	// 5^23 is not an exact 64-bit floating point number,
181  	// so have to use bc for the math.
182  	// Go up to 60 to be large enough for 32bit and 64bit platforms.
183  	/*
184  		seq 60 | sed 's/^/5^/' | bc |
185  		awk 'BEGIN{ print "\t{ 0, \"\" }," }
186  		{
187  			log2 = log(2)/log(10)
188  			printf("\t{ %d, \"%s\" },\t// * %d\n",
189  				int(log2*NR+1), \$0, 2**NR)
190  		}'
191  	*/
192  	{0, ""},
193  	{1, "5"},                                           // * 2
194  	{1, "25"},                                          // * 4
195  	{1, "125"},                                         // * 8
196  	{2, "625"},                                         // * 16
197  	{2, "3125"},                                        // * 32
198  	{2, "15625"},                                       // * 64
199  	{3, "78125"},                                       // * 128
200  	{3, "390625"},                                      // * 256
201  	{3, "1953125"},                                     // * 512
202  	{4, "9765625"},                                     // * 1024
203  	{4, "48828125"},                                    // * 2048
204  	{4, "244140625"},                                   // * 4096
205  	{4, "1220703125"},                                  // * 8192
206  	{5, "6103515625"},                                  // * 16384
207  	{5, "30517578125"},                                 // * 32768
208  	{5, "152587890625"},                                // * 65536
209  	{6, "762939453125"},                                // * 131072
210  	{6, "3814697265625"},                               // * 262144
211  	{6, "19073486328125"},                              // * 524288
212  	{7, "95367431640625"},                              // * 1048576
213  	{7, "476837158203125"},                             // * 2097152
214  	{7, "2384185791015625"},                            // * 4194304
215  	{7, "11920928955078125"},                           // * 8388608
216  	{8, "59604644775390625"},                           // * 16777216
217  	{8, "298023223876953125"},                          // * 33554432
218  	{8, "1490116119384765625"},                         // * 67108864
219  	{9, "7450580596923828125"},                         // * 134217728
220  	{9, "37252902984619140625"},                        // * 268435456
221  	{9, "186264514923095703125"},                       // * 536870912
222  	{10, "931322574615478515625"},                      // * 1073741824
223  	{10, "4656612873077392578125"},                     // * 2147483648
224  	{10, "23283064365386962890625"},                    // * 4294967296
225  	{10, "116415321826934814453125"},                   // * 8589934592
226  	{11, "582076609134674072265625"},                   // * 17179869184
227  	{11, "2910383045673370361328125"},                  // * 34359738368
228  	{11, "14551915228366851806640625"},                 // * 68719476736
229  	{12, "72759576141834259033203125"},                 // * 137438953472
230  	{12, "363797880709171295166015625"},                // * 274877906944
231  	{12, "1818989403545856475830078125"},               // * 549755813888
232  	{13, "9094947017729282379150390625"},               // * 1099511627776
233  	{13, "45474735088646411895751953125"},              // * 2199023255552
234  	{13, "227373675443232059478759765625"},             // * 4398046511104
235  	{13, "1136868377216160297393798828125"},            // * 8796093022208
236  	{14, "5684341886080801486968994140625"},            // * 17592186044416
237  	{14, "28421709430404007434844970703125"},           // * 35184372088832
238  	{14, "142108547152020037174224853515625"},          // * 70368744177664
239  	{15, "710542735760100185871124267578125"},          // * 140737488355328
240  	{15, "3552713678800500929355621337890625"},         // * 281474976710656
241  	{15, "17763568394002504646778106689453125"},        // * 562949953421312
242  	{16, "88817841970012523233890533447265625"},        // * 1125899906842624
243  	{16, "444089209850062616169452667236328125"},       // * 2251799813685248
244  	{16, "2220446049250313080847263336181640625"},      // * 4503599627370496
245  	{16, "11102230246251565404236316680908203125"},     // * 9007199254740992
246  	{17, "55511151231257827021181583404541015625"},     // * 18014398509481984
247  	{17, "277555756156289135105907917022705078125"},    // * 36028797018963968
248  	{17, "1387778780781445675529539585113525390625"},   // * 72057594037927936
249  	{18, "6938893903907228377647697925567626953125"},   // * 144115188075855872
250  	{18, "34694469519536141888238489627838134765625"},  // * 288230376151711744
251  	{18, "173472347597680709441192448139190673828125"}, // * 576460752303423488
252  	{19, "867361737988403547205962240695953369140625"}, // * 1152921504606846976
253  }
254
255  // Is the leading prefix of b lexicographically less than s?
256  func prefixIsLessThan(b []byte, s string) bool {
257  	for i := 0; i < len(s); i++ {
258  		if i >= len(b) {
259  			return true
260  		}
261  		if b[i] != s[i] {
262  			return b[i] < s[i]
263  		}
264  	}
265  	return false
266  }
267
268  // Binary shift left (* 2) by k bits.  k <= maxShift to avoid overflow.
269  func leftShift(a *decimal, k uint) {
270  	delta := leftcheats[k].delta
271  	if prefixIsLessThan(a.d[0:a.nd], leftcheats[k].cutoff) {
272  		delta--
273  	}
274
275  	r := a.nd         // read index
276  	w := a.nd + delta // write index
277
278  	// Pick up a digit, put down a digit.
279  	var n uint
280  	for r--; r >= 0; r-- {
281  		n += (uint(a.d[r]) - '0') << k
282  		quo := n / 10
283  		rem := n - 10*quo
284  		w--
285  		if w < len(a.d) {
286  			a.d[w] = byte(rem + '0')
287  		} else if rem != 0 {
288  			a.trunc = true
289  		}
290  		n = quo
291  	}
292
293  	// Put down extra digits.
294  	for n > 0 {
295  		quo := n / 10
296  		rem := n - 10*quo
297  		w--
298  		if w < len(a.d) {
299  			a.d[w] = byte(rem + '0')
300  		} else if rem != 0 {
301  			a.trunc = true
302  		}
303  		n = quo
304  	}
305
306  	a.nd += delta
307  	if a.nd >= len(a.d) {
308  		a.nd = len(a.d)
309  	}
310  	a.dp += delta
311  	trim(a)
312  }
313
314  // Binary shift left (k > 0) or right (k < 0).
315  func (a *decimal) Shift(k int) {
316  	switch {
317  	case a.nd == 0:
318  		// nothing to do: a == 0
319  	case k > 0:
320  		for k > maxShift {
321  			leftShift(a, maxShift)
322  			k -= maxShift
323  		}
324  		leftShift(a, uint(k))
325  	case k < 0:
326  		for k < -maxShift {
327  			rightShift(a, maxShift)
328  			k += maxShift
329  		}
330  		rightShift(a, uint(-k))
331  	}
332  }
333
334  // If we chop a at nd digits, should we round up?
335  func shouldRoundUp(a *decimal, nd int) bool {
336  	if nd < 0 || nd >= a.nd {
337  		return false
338  	}
339  	if a.d[nd] == '5' && nd+1 == a.nd { // exactly halfway - round to even
340  		// if we truncated, a little higher than what's recorded - always round up
341  		if a.trunc {
342  			return true
343  		}
344  		return nd > 0 && (a.d[nd-1]-'0')%2 != 0
345  	}
346  	// not halfway - digit tells all
347  	return a.d[nd] >= '5'
348  }
349
350  // Round a to nd digits (or fewer).
351  // If nd is zero, it means we're rounding
352  // just to the left of the digits, as in
353  // 0.09 -> 0.1.
354  func (a *decimal) Round(nd int) {
355  	if nd < 0 || nd >= a.nd {
356  		return
357  	}
358  	if shouldRoundUp(a, nd) {
359  		a.RoundUp(nd)
360  	} else {
361  		a.RoundDown(nd)
362  	}
363  }
364
365  // Round a down to nd digits (or fewer).
366  func (a *decimal) RoundDown(nd int) {
367  	if nd < 0 || nd >= a.nd {
368  		return
369  	}
370  	a.nd = nd
371  	trim(a)
372  }
373
374  // Round a up to nd digits (or fewer).
375  func (a *decimal) RoundUp(nd int) {
376  	if nd < 0 || nd >= a.nd {
377  		return
378  	}
379
380  	// round up
381  	for i := nd - 1; i >= 0; i-- {
382  		c := a.d[i]
383  		if c < '9' { // can stop after this digit
384  			a.d[i]++
385  			a.nd = i + 1
386  			return
387  		}
388  	}
389
390  	// Number is all 9s.
391  	// Change to single 1 with adjusted decimal point.
392  	a.d[0] = '1'
393  	a.nd = 1
394  	a.dp++
395  }
396
397  // Extract integer part, rounded appropriately.
398  // No guarantees about overflow.
399  func (a *decimal) RoundedInteger() uint64 {
400  	if a.dp > 20 {
401  		return 0xFFFFFFFFFFFFFFFF
402  	}
403  	var i int
404  	n := uint64(0)
405  	for i = 0; i < a.dp && i < a.nd; i++ {
406  		n = n*10 + uint64(a.d[i]-'0')
407  	}
408  	for ; i < a.dp; i++ {
409  		n *= 10
410  	}
411  	if shouldRoundUp(a, a.dp) {
412  		n++
413  	}
414  	return n
415  }
416
```

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