decimal.mx raw
1 // Copyright 2009 The Go Authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style
3 // license that can be found in the LICENSE file.
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 := []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
140 n &= mask
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
149 n &= mask
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 []byte // 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 []byte) 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