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
5package strconv
6
7// decimal to binary floating point conversion.
8// Algorithm:
9//   1) Store input in multiprecision decimal.
10//   2) Multiply/divide decimal by powers of two until in range [0.5, 1)
11//   3) Multiply by 2^precision and round to get mantissa.
12
13import "math"
14import "runtime"
15
16var optimize = true // can change for testing
17
18func equalIgnoreCase(s1, s2 string) bool {
19	if len(s1) != len(s2) {
20		return false
21	}
22	for i := 0; i < len(s1); i++ {
23		c1 := s1[i]
24		if 'A' <= c1 && c1 <= 'Z' {
25			c1 += 'a' - 'A'
26		}
27		c2 := s2[i]
28		if 'A' <= c2 && c2 <= 'Z' {
29			c2 += 'a' - 'A'
30		}
31		if c1 != c2 {
32			return false
33		}
34	}
35	return true
36}
37
38func special(s string) (f float64, ok bool) {
39	if len(s) == 0 {
40		return
41	}
42	switch s[0] {
43	default:
44		return
45	case '+':
46		if equalIgnoreCase(s, "+inf") || equalIgnoreCase(s, "+infinity") {
47			return math.Inf(1), true
48		}
49	case '-':
50		if equalIgnoreCase(s, "-inf") || equalIgnoreCase(s, "-infinity") {
51			return math.Inf(-1), true
52		}
53	case 'n', 'N':
54		if equalIgnoreCase(s, "nan") {
55			return math.NaN(), true
56		}
57	case 'i', 'I':
58		if equalIgnoreCase(s, "inf") || equalIgnoreCase(s, "infinity") {
59			return math.Inf(1), true
60		}
61	}
62	return
63}
64
65func (b *decimal) set(s string) (ok bool) {
66	i := 0
67	b.neg = false
68	b.trunc = false
69
70	// optional sign
71	if i >= len(s) {
72		return
73	}
74	switch {
75	case s[i] == '+':
76		i++
77	case s[i] == '-':
78		b.neg = true
79		i++
80	}
81
82	// digits
83	sawdot := false
84	sawdigits := false
85	for ; i < len(s); i++ {
86		switch {
87		case s[i] == '.':
88			if sawdot {
89				return
90			}
91			sawdot = true
92			b.dp = b.nd
93			continue
94
95		case '0' <= s[i] && s[i] <= '9':
96			sawdigits = true
97			if s[i] == '0' && b.nd == 0 { // ignore leading zeros
98				b.dp--
99				continue
100			}
101			if b.nd < len(b.d) {
102				b.d[b.nd] = s[i]
103				b.nd++
104			} else if s[i] != '0' {
105				b.trunc = true
106			}
107			continue
108		}
109		break
110	}
111	if !sawdigits {
112		return
113	}
114	if !sawdot {
115		b.dp = b.nd
116	}
117
118	// optional exponent moves decimal point.
119	// if we read a very large, very long number,
120	// just be sure to move the decimal point by
121	// a lot (say, 100000).  it doesn't matter if it's
122	// not the exact number.
123	if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
124		i++
125		if i >= len(s) {
126			return
127		}
128		esign := 1
129		if s[i] == '+' {
130			i++
131		} else if s[i] == '-' {
132			i++
133			esign = -1
134		}
135		if i >= len(s) || s[i] < '0' || s[i] > '9' {
136			return
137		}
138		e := 0
139		for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
140			if e < 10000 {
141				e = e*10 + int(s[i]) - '0'
142			}
143		}
144		b.dp += e * esign
145	}
146
147	if i != len(s) {
148		return
149	}
150
151	ok = true
152	return
153}
154
155// readFloat reads a decimal mantissa and exponent from a float
156// string representation. It sets ok to false if the number could
157// not fit return types or is invalid.
158func readFloat(s string) (mantissa uint64, exp int, neg, trunc, ok bool) {
159	const uint64digits = 19
160	i := 0
161
162	// optional sign
163	if i >= len(s) {
164		return
165	}
166	switch {
167	case s[i] == '+':
168		i++
169	case s[i] == '-':
170		neg = true
171		i++
172	}
173
174	// digits
175	sawdot := false
176	sawdigits := false
177	nd := 0
178	ndMant := 0
179	dp := 0
180	for ; i < len(s); i++ {
181		switch c := s[i]; true {
182		case c == '.':
183			if sawdot {
184				return
185			}
186			sawdot = true
187			dp = nd
188			continue
189
190		case '0' <= c && c <= '9':
191			sawdigits = true
192			if c == '0' && nd == 0 { // ignore leading zeros
193				dp--
194				continue
195			}
196			nd++
197			if ndMant < uint64digits {
198				mantissa *= 10
199				mantissa += uint64(c - '0')
200				ndMant++
201			} else if s[i] != '0' {
202				trunc = true
203			}
204			continue
205		}
206		break
207	}
208	if !sawdigits {
209		return
210	}
211	if !sawdot {
212		dp = nd
213	}
214
215	// optional exponent moves decimal point.
216	// if we read a very large, very long number,
217	// just be sure to move the decimal point by
218	// a lot (say, 100000).  it doesn't matter if it's
219	// not the exact number.
220	if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
221		i++
222		if i >= len(s) {
223			return
224		}
225		esign := 1
226		if s[i] == '+' {
227			i++
228		} else if s[i] == '-' {
229			i++
230			esign = -1
231		}
232		if i >= len(s) || s[i] < '0' || s[i] > '9' {
233			return
234		}
235		e := 0
236		for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
237			if e < 10000 {
238				e = e*10 + int(s[i]) - '0'
239			}
240		}
241		dp += e * esign
242	}
243
244	if i != len(s) {
245		return
246	}
247
248	exp = dp - ndMant
249	ok = true
250	return
251
252}
253
254// decimal power of ten to binary power of two.
255var powtab = []int{1, 3, 6, 9, 13, 16, 19, 23, 26}
256
257func (d *decimal) floatBits(flt *floatInfo) (b uint64, overflow bool) {
258	var exp int
259	var mant uint64
260
261	// Zero is always a special case.
262	if d.nd == 0 {
263		mant = 0
264		exp = flt.bias
265		goto out
266	}
267
268	// Obvious overflow/underflow.
269	// These bounds are for 64-bit floats.
270	// Will have to change if we want to support 80-bit floats in the future.
271	if d.dp > 310 {
272		goto overflow
273	}
274	if d.dp < -330 {
275		// zero
276		mant = 0
277		exp = flt.bias
278		goto out
279	}
280
281	// Scale by powers of two until in range [0.5, 1.0)
282	exp = 0
283	for d.dp > 0 {
284		var n int
285		if d.dp >= len(powtab) {
286			n = 27
287		} else {
288			n = powtab[d.dp]
289		}
290		d.Shift(-n)
291		exp += n
292	}
293	for d.dp < 0 || d.dp == 0 && d.d[0] < '5' {
294		var n int
295		if -d.dp >= len(powtab) {
296			n = 27
297		} else {
298			n = powtab[-d.dp]
299		}
300		d.Shift(n)
301		exp -= n
302	}
303
304	// Our range is [0.5,1) but floating point range is [1,2).
305	exp--
306
307	// Minimum representable exponent is flt.bias+1.
308	// If the exponent is smaller, move it up and
309	// adjust d accordingly.
310	if exp < flt.bias+1 {
311		n := flt.bias + 1 - exp
312		d.Shift(-n)
313		exp += n
314	}
315
316	if exp-flt.bias >= 1<<flt.expbits-1 {
317		goto overflow
318	}
319
320	// Extract 1+flt.mantbits bits.
321	d.Shift(int(1 + flt.mantbits))
322	mant = d.RoundedInteger()
323
324	// Rounding might have added a bit; shift down.
325	if mant == 2<<flt.mantbits {
326		mant >>= 1
327		exp++
328		if exp-flt.bias >= 1<<flt.expbits-1 {
329			goto overflow
330		}
331	}
332
333	// Denormalized?
334	if mant&(1<<flt.mantbits) == 0 {
335		exp = flt.bias
336	}
337	goto out
338
339overflow:
340	// ±Inf
341	mant = 0
342	exp = 1<<flt.expbits - 1 + flt.bias
343	overflow = true
344
345out:
346	// Assemble bits.
347	bits := mant & (uint64(1)<<flt.mantbits - 1)
348	bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
349	if d.neg {
350		bits |= 1 << flt.mantbits << flt.expbits
351	}
352	return bits, overflow
353}
354
355// Exact powers of 10.
356var float64pow10 = []float64{
357	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
358	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
359	1e20, 1e21, 1e22,
360}
361var float32pow10 = []float32{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10}
362
363// If possible to convert decimal representation to 64-bit float f exactly,
364// entirely in floating-point math, do so, avoiding the expense of decimalToFloatBits.
365// Three common cases:
366//	value is exact integer
367//	value is exact integer * exact power of ten
368//	value is exact integer / exact power of ten
369// These all produce potentially inexact but correctly rounded answers.
370func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
371	if mantissa>>float64info.mantbits != 0 {
372		return
373	}
374	// gccgo gets this wrong on 32-bit i386 when not using -msse.
375	// See TestRoundTrip in atof_test.go for a test case.
376	if runtime.GOARCH == "386" {
377		return
378	}
379	f = float64(mantissa)
380	if neg {
381		f = -f
382	}
383	switch {
384	case exp == 0:
385		// an integer.
386		return f, true
387	// Exact integers are <= 10^15.
388	// Exact powers of ten are <= 10^22.
389	case exp > 0 && exp <= 15+22: // int * 10^k
390		// If exponent is big but number of digits is not,
391		// can move a few zeros into the integer part.
392		if exp > 22 {
393			f *= float64pow10[exp-22]
394			exp = 22
395		}
396		if f > 1e15 || f < -1e15 {
397			// the exponent was really too large.
398			return
399		}
400		return f * float64pow10[exp], true
401	case exp < 0 && exp >= -22: // int / 10^k
402		return f / float64pow10[-exp], true
403	}
404	return
405}
406
407// If possible to compute mantissa*10^exp to 32-bit float f exactly,
408// entirely in floating-point math, do so, avoiding the machinery above.
409func atof32exact(mantissa uint64, exp int, neg bool) (f float32, ok bool) {
410	if mantissa>>float32info.mantbits != 0 {
411		return
412	}
413	f = float32(mantissa)
414	if neg {
415		f = -f
416	}
417	switch {
418	case exp == 0:
419		return f, true
420	// Exact integers are <= 10^7.
421	// Exact powers of ten are <= 10^10.
422	case exp > 0 && exp <= 7+10: // int * 10^k
423		// If exponent is big but number of digits is not,
424		// can move a few zeros into the integer part.
425		if exp > 10 {
426			f *= float32pow10[exp-10]
427			exp = 10
428		}
429		if f > 1e7 || f < -1e7 {
430			// the exponent was really too large.
431			return
432		}
433		return f * float32pow10[exp], true
434	case exp < 0 && exp >= -10: // int / 10^k
435		return f / float32pow10[-exp], true
436	}
437	return
438}
439
440const fnParseFloat = "ParseFloat"
441
442func atof32(s string) (f float32, err error) {
443	if val, ok := special(s); ok {
444		return float32(val), nil
445	}
446
447	if optimize {
448		// Parse mantissa and exponent.
449		mantissa, exp, neg, trunc, ok := readFloat(s)
450		if ok {
451			// Try pure floating-point arithmetic conversion.
452			if !trunc {
453				if f, ok := atof32exact(mantissa, exp, neg); ok {
454					return f, nil
455				}
456			}
457			// Try another fast path.
458			ext := new(extFloat)
459			if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float32info); ok {
460				b, ovf := ext.floatBits(&float32info)
461				f = math.Float32frombits(uint32(b))
462				if ovf {
463					err = rangeError(fnParseFloat, s)
464				}
465				return f, err
466			}
467		}
468	}
469	var d decimal
470	if !d.set(s) {
471		return 0, syntaxError(fnParseFloat, s)
472	}
473	b, ovf := d.floatBits(&float32info)
474	f = math.Float32frombits(uint32(b))
475	if ovf {
476		err = rangeError(fnParseFloat, s)
477	}
478	return f, err
479}
480
481func atof64(s string) (f float64, err error) {
482	if val, ok := special(s); ok {
483		return val, nil
484	}
485
486	if optimize {
487		// Parse mantissa and exponent.
488		mantissa, exp, neg, trunc, ok := readFloat(s)
489		if ok {
490			// Try pure floating-point arithmetic conversion.
491			if !trunc {
492				if f, ok := atof64exact(mantissa, exp, neg); ok {
493					return f, nil
494				}
495			}
496			// Try another fast path.
497			ext := new(extFloat)
498			if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float64info); ok {
499				b, ovf := ext.floatBits(&float64info)
500				f = math.Float64frombits(b)
501				if ovf {
502					err = rangeError(fnParseFloat, s)
503				}
504				return f, err
505			}
506		}
507	}
508	var d decimal
509	if !d.set(s) {
510		return 0, syntaxError(fnParseFloat, s)
511	}
512	b, ovf := d.floatBits(&float64info)
513	f = math.Float64frombits(b)
514	if ovf {
515		err = rangeError(fnParseFloat, s)
516	}
517	return f, err
518}
519
520// ParseFloat converts the string s to a floating-point number
521// with the precision specified by bitSize: 32 for float32, or 64 for float64.
522// When bitSize=32, the result still has type float64, but it will be
523// convertible to float32 without changing its value.
524//
525// If s is well-formed and near a valid floating point number,
526// ParseFloat returns the nearest floating point number rounded
527// using IEEE754 unbiased rounding.
528//
529// The errors that ParseFloat returns have concrete type *NumError
530// and include err.Num = s.
531//
532// If s is not syntactically well-formed, ParseFloat returns err.Err = ErrSyntax.
533//
534// If s is syntactically well-formed but is more than 1/2 ULP
535// away from the largest floating point number of the given size,
536// ParseFloat returns f = ±Inf, err.Err = ErrRange.
537func ParseFloat(s string, bitSize int) (f float64, err error) {
538	if bitSize == 32 {
539		f1, err1 := atof32(s)
540		return float64(f1), err1
541	}
542	f1, err1 := atof64(s)
543	return f1, err1
544}
545