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d9579d0f AL |
1 | /*! |
2 | ||
3 | Floating-point number to decimal conversion routines. | |
4 | ||
5 | # Problem statement | |
6 | ||
7 | We are given the floating-point number `v = f * 2^e` with an integer `f`, | |
8 | and its bounds `minus` and `plus` such that any number between `v - minus` and | |
9 | `v + plus` will be rounded to `v`. For the simplicity we assume that | |
10 | this range is exclusive. Then we would like to get the unique decimal | |
11 | representation `V = 0.d[0..n-1] * 10^k` such that: | |
12 | ||
13 | - `d[0]` is non-zero. | |
14 | ||
15 | - It's correctly rounded when parsed back: `v - minus < V < v + plus`. | |
0731742a | 16 | Furthermore it is shortest such one, i.e., there is no representation |
d9579d0f AL |
17 | with less than `n` digits that is correctly rounded. |
18 | ||
19 | - It's closest to the original value: `abs(V - v) <= 10^(k-n) / 2`. Note that | |
20 | there might be two representations satisfying this uniqueness requirement, | |
21 | in which case some tie-breaking mechanism is used. | |
22 | ||
23 | We will call this mode of operation as to the *shortest* mode. This mode is used | |
24 | when there is no additional constraint, and can be thought as a "natural" mode | |
25 | as it matches the ordinary intuition (it at least prints `0.1f32` as "0.1"). | |
26 | ||
27 | We have two more modes of operation closely related to each other. In these modes | |
28 | we are given either the number of significant digits `n` or the last-digit | |
29 | limitation `limit` (which determines the actual `n`), and we would like to get | |
30 | the representation `V = 0.d[0..n-1] * 10^k` such that: | |
31 | ||
32 | - `d[0]` is non-zero, unless `n` was zero in which case only `k` is returned. | |
33 | ||
34 | - It's closest to the original value: `abs(V - v) <= 10^(k-n) / 2`. Again, | |
35 | there might be some tie-breaking mechanism. | |
36 | ||
37 | When `limit` is given but not `n`, we set `n` such that `k - n = limit` | |
38 | so that the last digit `d[n-1]` is scaled by `10^(k-n) = 10^limit`. | |
39 | If such `n` is negative, we clip it to zero so that we will only get `k`. | |
40 | We are also limited by the supplied buffer. This limitation is used to print | |
41 | the number up to given number of fractional digits without knowing | |
42 | the correct `k` beforehand. | |
43 | ||
44 | We will call the mode of operation requiring `n` as to the *exact* mode, | |
45 | and one requiring `limit` as to the *fixed* mode. The exact mode is a subset of | |
46 | the fixed mode: the sufficiently large last-digit limitation will eventually fill | |
47 | the supplied buffer and let the algorithm to return. | |
48 | ||
49 | # Implementation overview | |
50 | ||
51 | It is easy to get the floating point printing correct but slow (Russ Cox has | |
136023e0 | 52 | [demonstrated](https://research.swtch.com/ftoa) how it's easy), or incorrect but |
d9579d0f AL |
53 | fast (naïve division and modulo). But it is surprisingly hard to print |
54 | floating point numbers correctly *and* efficiently. | |
55 | ||
56 | There are two classes of algorithms widely known to be correct. | |
57 | ||
58 | - The "Dragon" family of algorithm is first described by Guy L. Steele Jr. and | |
59 | Jon L. White. They rely on the fixed-size big integer for their correctness. | |
60 | A slight improvement was found later, which is posthumously described by | |
61 | Robert G. Burger and R. Kent Dybvig. David Gay's `dtoa.c` routine is | |
62 | a popular implementation of this strategy. | |
63 | ||
64 | - The "Grisu" family of algorithm is first described by Florian Loitsch. | |
65 | They use very cheap integer-only procedure to determine the close-to-correct | |
66 | representation which is at least guaranteed to be shortest. The variant, | |
67 | Grisu3, actively detects if the resulting representation is incorrect. | |
68 | ||
69 | We implement both algorithms with necessary tweaks to suit our requirements. | |
70 | In particular, published literatures are short of the actual implementation | |
71 | difficulties like how to avoid arithmetic overflows. Each implementation, | |
72 | available in `strategy::dragon` and `strategy::grisu` respectively, | |
73 | extensively describes all necessary justifications and many proofs for them. | |
74 | (It is still difficult to follow though. You have been warned.) | |
75 | ||
76 | Both implementations expose two public functions: | |
77 | ||
78 | - `format_shortest(decoded, buf)`, which always needs at least | |
79 | `MAX_SIG_DIGITS` digits of buffer. Implements the shortest mode. | |
80 | ||
81 | - `format_exact(decoded, buf, limit)`, which accepts as small as | |
82 | one digit of buffer. Implements exact and fixed modes. | |
83 | ||
84 | They try to fill the `u8` buffer with digits and returns the number of digits | |
85 | written and the exponent `k`. They are total for all finite `f32` and `f64` | |
86 | inputs (Grisu internally falls back to Dragon if necessary). | |
87 | ||
88 | The rendered digits are formatted into the actual string form with | |
89 | four functions: | |
90 | ||
91 | - `to_shortest_str` prints the shortest representation, which can be padded by | |
92 | zeroes to make *at least* given number of fractional digits. | |
93 | ||
94 | - `to_shortest_exp_str` prints the shortest representation, which can be | |
95 | padded by zeroes when its exponent is in the specified ranges, | |
96 | or can be printed in the exponential form such as `1.23e45`. | |
97 | ||
98 | - `to_exact_exp_str` prints the exact representation with given number of | |
99 | digits in the exponential form. | |
100 | ||
101 | - `to_exact_fixed_str` prints the fixed representation with *exactly* | |
102 | given number of fractional digits. | |
103 | ||
104 | They all return a slice of preallocated `Part` array, which corresponds to | |
105 | the individual part of strings: a fixed string, a part of rendered digits, | |
106 | a number of zeroes or a small (`u16`) number. The caller is expected to | |
107 | provide a large enough buffer and `Part` array, and to assemble the final | |
108 | string from resulting `Part`s itself. | |
109 | ||
110 | All algorithms and formatting functions are accompanied by extensive tests | |
cc61c64b | 111 | in `coretests::num::flt2dec` module. It also shows how to use individual |
d9579d0f AL |
112 | functions. |
113 | ||
114 | */ | |
115 | ||
116 | // while this is extensively documented, this is in principle private which is | |
117 | // only made public for testing. do not expose us. | |
118 | #![doc(hidden)] | |
60c5eb7d XL |
119 | #![unstable( |
120 | feature = "flt2dec", | |
121 | reason = "internal routines only exposed for testing", | |
dfeec247 | 122 | issue = "none" |
60c5eb7d | 123 | )] |
d9579d0f | 124 | |
60c5eb7d | 125 | pub use self::decoder::{decode, DecodableFloat, Decoded, FullDecoded}; |
d9579d0f | 126 | |
136023e0 | 127 | use super::fmt::{Formatted, Part}; |
1b1a35ee XL |
128 | use crate::mem::MaybeUninit; |
129 | ||
d9579d0f | 130 | pub mod decoder; |
60c5eb7d | 131 | pub mod estimator; |
d9579d0f AL |
132 | |
133 | /// Digit-generation algorithms. | |
134 | pub mod strategy { | |
135 | pub mod dragon; | |
136 | pub mod grisu; | |
137 | } | |
138 | ||
139 | /// The minimum size of buffer necessary for the shortest mode. | |
140 | /// | |
141 | /// It is a bit non-trivial to derive, but this is one plus the maximal number of | |
142 | /// significant decimal digits from formatting algorithms with the shortest result. | |
143 | /// The exact formula is `ceil(# bits in mantissa * log_10 2 + 1)`. | |
144 | pub const MAX_SIG_DIGITS: usize = 17; | |
145 | ||
1b1a35ee XL |
146 | /// When `d` contains decimal digits, increase the last digit and propagate carry. |
147 | /// Returns a next digit when it causes the length to change. | |
d9579d0f | 148 | #[doc(hidden)] |
1b1a35ee XL |
149 | pub fn round_up(d: &mut [u8]) -> Option<u8> { |
150 | match d.iter().rposition(|&c| c != b'9') { | |
60c5eb7d XL |
151 | Some(i) => { |
152 | // d[i+1..n] is all nines | |
d9579d0f | 153 | d[i] += 1; |
1b1a35ee | 154 | for j in i + 1..d.len() { |
60c5eb7d XL |
155 | d[j] = b'0'; |
156 | } | |
d9579d0f AL |
157 | None |
158 | } | |
1b1a35ee | 159 | None if d.len() > 0 => { |
60c5eb7d | 160 | // 999..999 rounds to 1000..000 with an increased exponent |
d9579d0f | 161 | d[0] = b'1'; |
1b1a35ee | 162 | for j in 1..d.len() { |
60c5eb7d XL |
163 | d[j] = b'0'; |
164 | } | |
d9579d0f AL |
165 | Some(b'0') |
166 | } | |
60c5eb7d XL |
167 | None => { |
168 | // an empty buffer rounds up (a bit strange but reasonable) | |
d9579d0f AL |
169 | Some(b'1') |
170 | } | |
171 | } | |
172 | } | |
173 | ||
d9579d0f AL |
174 | /// Formats given decimal digits `0.<...buf...> * 10^exp` into the decimal form |
175 | /// with at least given number of fractional digits. The result is stored to | |
176 | /// the supplied parts array and a slice of written parts is returned. | |
177 | /// | |
178 | /// `frac_digits` can be less than the number of actual fractional digits in `buf`; | |
179 | /// it will be ignored and full digits will be printed. It is only used to print | |
180 | /// additional zeroes after rendered digits. Thus `frac_digits` of 0 means that | |
181 | /// it will only print given digits and nothing else. | |
60c5eb7d XL |
182 | fn digits_to_dec_str<'a>( |
183 | buf: &'a [u8], | |
184 | exp: i16, | |
185 | frac_digits: usize, | |
1b1a35ee | 186 | parts: &'a mut [MaybeUninit<Part<'a>>], |
60c5eb7d | 187 | ) -> &'a [Part<'a>] { |
d9579d0f AL |
188 | assert!(!buf.is_empty()); |
189 | assert!(buf[0] > b'0'); | |
190 | assert!(parts.len() >= 4); | |
191 | ||
192 | // if there is the restriction on the last digit position, `buf` is assumed to be | |
193 | // left-padded with the virtual zeroes. the number of virtual zeroes, `nzeroes`, | |
194 | // equals to `max(0, exp + frac_digits - buf.len())`, so that the position of | |
195 | // the last digit `exp - buf.len() - nzeroes` is no more than `-frac_digits`: | |
196 | // | |
197 | // |<-virtual->| | |
198 | // |<---- buf ---->| zeroes | exp | |
199 | // 0. 1 2 3 4 5 6 7 8 9 _ _ _ _ _ _ x 10 | |
200 | // | | | | |
201 | // 10^exp 10^(exp-buf.len()) 10^(exp-buf.len()-nzeroes) | |
202 | // | |
203 | // `nzeroes` is individually calculated for each case in order to avoid overflow. | |
204 | ||
205 | if exp <= 0 { | |
206 | // the decimal point is before rendered digits: [0.][000...000][1234][____] | |
207 | let minus_exp = -(exp as i32) as usize; | |
1b1a35ee XL |
208 | parts[0] = MaybeUninit::new(Part::Copy(b"0.")); |
209 | parts[1] = MaybeUninit::new(Part::Zero(minus_exp)); | |
210 | parts[2] = MaybeUninit::new(Part::Copy(buf)); | |
d9579d0f | 211 | if frac_digits > buf.len() && frac_digits - buf.len() > minus_exp { |
1b1a35ee XL |
212 | parts[3] = MaybeUninit::new(Part::Zero((frac_digits - buf.len()) - minus_exp)); |
213 | // SAFETY: we just initialized the elements `..4`. | |
214 | unsafe { MaybeUninit::slice_assume_init_ref(&parts[..4]) } | |
d9579d0f | 215 | } else { |
1b1a35ee XL |
216 | // SAFETY: we just initialized the elements `..3`. |
217 | unsafe { MaybeUninit::slice_assume_init_ref(&parts[..3]) } | |
d9579d0f AL |
218 | } |
219 | } else { | |
220 | let exp = exp as usize; | |
221 | if exp < buf.len() { | |
222 | // the decimal point is inside rendered digits: [12][.][34][____] | |
1b1a35ee XL |
223 | parts[0] = MaybeUninit::new(Part::Copy(&buf[..exp])); |
224 | parts[1] = MaybeUninit::new(Part::Copy(b".")); | |
225 | parts[2] = MaybeUninit::new(Part::Copy(&buf[exp..])); | |
d9579d0f | 226 | if frac_digits > buf.len() - exp { |
1b1a35ee XL |
227 | parts[3] = MaybeUninit::new(Part::Zero(frac_digits - (buf.len() - exp))); |
228 | // SAFETY: we just initialized the elements `..4`. | |
229 | unsafe { MaybeUninit::slice_assume_init_ref(&parts[..4]) } | |
d9579d0f | 230 | } else { |
1b1a35ee XL |
231 | // SAFETY: we just initialized the elements `..3`. |
232 | unsafe { MaybeUninit::slice_assume_init_ref(&parts[..3]) } | |
d9579d0f AL |
233 | } |
234 | } else { | |
235 | // the decimal point is after rendered digits: [1234][____0000] or [1234][__][.][__]. | |
1b1a35ee XL |
236 | parts[0] = MaybeUninit::new(Part::Copy(buf)); |
237 | parts[1] = MaybeUninit::new(Part::Zero(exp - buf.len())); | |
d9579d0f | 238 | if frac_digits > 0 { |
1b1a35ee XL |
239 | parts[2] = MaybeUninit::new(Part::Copy(b".")); |
240 | parts[3] = MaybeUninit::new(Part::Zero(frac_digits)); | |
241 | // SAFETY: we just initialized the elements `..4`. | |
242 | unsafe { MaybeUninit::slice_assume_init_ref(&parts[..4]) } | |
d9579d0f | 243 | } else { |
1b1a35ee XL |
244 | // SAFETY: we just initialized the elements `..2`. |
245 | unsafe { MaybeUninit::slice_assume_init_ref(&parts[..2]) } | |
d9579d0f AL |
246 | } |
247 | } | |
248 | } | |
249 | } | |
250 | ||
532ac7d7 XL |
251 | /// Formats the given decimal digits `0.<...buf...> * 10^exp` into the exponential |
252 | /// form with at least the given number of significant digits. When `upper` is `true`, | |
d9579d0f AL |
253 | /// the exponent will be prefixed by `E`; otherwise that's `e`. The result is |
254 | /// stored to the supplied parts array and a slice of written parts is returned. | |
255 | /// | |
256 | /// `min_digits` can be less than the number of actual significant digits in `buf`; | |
257 | /// it will be ignored and full digits will be printed. It is only used to print | |
532ac7d7 XL |
258 | /// additional zeroes after rendered digits. Thus, `min_digits == 0` means that |
259 | /// it will only print the given digits and nothing else. | |
60c5eb7d XL |
260 | fn digits_to_exp_str<'a>( |
261 | buf: &'a [u8], | |
262 | exp: i16, | |
263 | min_ndigits: usize, | |
264 | upper: bool, | |
1b1a35ee | 265 | parts: &'a mut [MaybeUninit<Part<'a>>], |
60c5eb7d | 266 | ) -> &'a [Part<'a>] { |
d9579d0f AL |
267 | assert!(!buf.is_empty()); |
268 | assert!(buf[0] > b'0'); | |
269 | assert!(parts.len() >= 6); | |
270 | ||
271 | let mut n = 0; | |
272 | ||
1b1a35ee | 273 | parts[n] = MaybeUninit::new(Part::Copy(&buf[..1])); |
d9579d0f AL |
274 | n += 1; |
275 | ||
276 | if buf.len() > 1 || min_ndigits > 1 { | |
1b1a35ee XL |
277 | parts[n] = MaybeUninit::new(Part::Copy(b".")); |
278 | parts[n + 1] = MaybeUninit::new(Part::Copy(&buf[1..])); | |
d9579d0f AL |
279 | n += 2; |
280 | if min_ndigits > buf.len() { | |
1b1a35ee | 281 | parts[n] = MaybeUninit::new(Part::Zero(min_ndigits - buf.len())); |
d9579d0f AL |
282 | n += 1; |
283 | } | |
284 | } | |
285 | ||
286 | // 0.1234 x 10^exp = 1.234 x 10^(exp-1) | |
287 | let exp = exp as i32 - 1; // avoid underflow when exp is i16::MIN | |
288 | if exp < 0 { | |
1b1a35ee XL |
289 | parts[n] = MaybeUninit::new(Part::Copy(if upper { b"E-" } else { b"e-" })); |
290 | parts[n + 1] = MaybeUninit::new(Part::Num(-exp as u16)); | |
d9579d0f | 291 | } else { |
1b1a35ee XL |
292 | parts[n] = MaybeUninit::new(Part::Copy(if upper { b"E" } else { b"e" })); |
293 | parts[n + 1] = MaybeUninit::new(Part::Num(exp as u16)); | |
d9579d0f | 294 | } |
1b1a35ee XL |
295 | // SAFETY: we just initialized the elements `..n + 2`. |
296 | unsafe { MaybeUninit::slice_assume_init_ref(&parts[..n + 2]) } | |
d9579d0f AL |
297 | } |
298 | ||
299 | /// Sign formatting options. | |
300 | #[derive(Copy, Clone, PartialEq, Eq, Debug)] | |
301 | pub enum Sign { | |
cdc7bbd5 XL |
302 | /// Prints `-` for any negative value. |
303 | Minus, // -inf -1 -0 0 1 inf nan | |
304 | /// Prints `-` for any negative value, or `+` otherwise. | |
305 | MinusPlus, // -inf -1 -0 +0 +1 +inf nan | |
d9579d0f AL |
306 | } |
307 | ||
308 | /// Returns the static byte string corresponding to the sign to be formatted. | |
74b04a01 XL |
309 | /// It can be either `""`, `"+"` or `"-"`. |
310 | fn determine_sign(sign: Sign, decoded: &FullDecoded, negative: bool) -> &'static str { | |
d9579d0f | 311 | match (*decoded, sign) { |
74b04a01 | 312 | (FullDecoded::Nan, _) => "", |
cdc7bbd5 | 313 | (_, Sign::Minus) => { |
60c5eb7d | 314 | if negative { |
74b04a01 | 315 | "-" |
60c5eb7d | 316 | } else { |
74b04a01 | 317 | "" |
60c5eb7d XL |
318 | } |
319 | } | |
cdc7bbd5 | 320 | (_, Sign::MinusPlus) => { |
60c5eb7d | 321 | if negative { |
74b04a01 | 322 | "-" |
60c5eb7d | 323 | } else { |
74b04a01 | 324 | "+" |
60c5eb7d XL |
325 | } |
326 | } | |
d9579d0f AL |
327 | } |
328 | } | |
329 | ||
532ac7d7 | 330 | /// Formats the given floating point number into the decimal form with at least |
d9579d0f AL |
331 | /// given number of fractional digits. The result is stored to the supplied parts |
332 | /// array while utilizing given byte buffer as a scratch. `upper` is currently | |
333 | /// unused but left for the future decision to change the case of non-finite values, | |
0731742a | 334 | /// i.e., `inf` and `nan`. The first part to be rendered is always a `Part::Sign` |
d9579d0f AL |
335 | /// (which can be an empty string if no sign is rendered). |
336 | /// | |
337 | /// `format_shortest` should be the underlying digit-generation function. | |
1b1a35ee | 338 | /// It should return the part of the buffer that it initialized. |
d9579d0f AL |
339 | /// You probably would want `strategy::grisu::format_shortest` for this. |
340 | /// | |
341 | /// `frac_digits` can be less than the number of actual fractional digits in `v`; | |
342 | /// it will be ignored and full digits will be printed. It is only used to print | |
343 | /// additional zeroes after rendered digits. Thus `frac_digits` of 0 means that | |
344 | /// it will only print given digits and nothing else. | |
345 | /// | |
346 | /// The byte buffer should be at least `MAX_SIG_DIGITS` bytes long. | |
7cac9316 XL |
347 | /// There should be at least 4 parts available, due to the worst case like |
348 | /// `[+][0.][0000][2][0000]` with `frac_digits = 10`. | |
60c5eb7d XL |
349 | pub fn to_shortest_str<'a, T, F>( |
350 | mut format_shortest: F, | |
351 | v: T, | |
352 | sign: Sign, | |
353 | frac_digits: usize, | |
1b1a35ee XL |
354 | buf: &'a mut [MaybeUninit<u8>], |
355 | parts: &'a mut [MaybeUninit<Part<'a>>], | |
60c5eb7d XL |
356 | ) -> Formatted<'a> |
357 | where | |
358 | T: DecodableFloat, | |
1b1a35ee | 359 | F: FnMut(&Decoded, &'a mut [MaybeUninit<u8>]) -> (&'a [u8], i16), |
60c5eb7d | 360 | { |
d9579d0f AL |
361 | assert!(parts.len() >= 4); |
362 | assert!(buf.len() >= MAX_SIG_DIGITS); | |
363 | ||
364 | let (negative, full_decoded) = decode(v); | |
365 | let sign = determine_sign(sign, &full_decoded, negative); | |
366 | match full_decoded { | |
367 | FullDecoded::Nan => { | |
1b1a35ee XL |
368 | parts[0] = MaybeUninit::new(Part::Copy(b"NaN")); |
369 | // SAFETY: we just initialized the elements `..1`. | |
370 | Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } } | |
d9579d0f AL |
371 | } |
372 | FullDecoded::Infinite => { | |
1b1a35ee XL |
373 | parts[0] = MaybeUninit::new(Part::Copy(b"inf")); |
374 | // SAFETY: we just initialized the elements `..1`. | |
375 | Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } } | |
d9579d0f AL |
376 | } |
377 | FullDecoded::Zero => { | |
60c5eb7d XL |
378 | if frac_digits > 0 { |
379 | // [0.][0000] | |
1b1a35ee XL |
380 | parts[0] = MaybeUninit::new(Part::Copy(b"0.")); |
381 | parts[1] = MaybeUninit::new(Part::Zero(frac_digits)); | |
382 | Formatted { | |
383 | sign, | |
384 | // SAFETY: we just initialized the elements `..2`. | |
385 | parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..2]) }, | |
386 | } | |
d9579d0f | 387 | } else { |
1b1a35ee XL |
388 | parts[0] = MaybeUninit::new(Part::Copy(b"0")); |
389 | Formatted { | |
390 | sign, | |
391 | // SAFETY: we just initialized the elements `..1`. | |
392 | parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) }, | |
393 | } | |
d9579d0f AL |
394 | } |
395 | } | |
396 | FullDecoded::Finite(ref decoded) => { | |
1b1a35ee XL |
397 | let (buf, exp) = format_shortest(decoded, buf); |
398 | Formatted { sign, parts: digits_to_dec_str(buf, exp, frac_digits, parts) } | |
d9579d0f AL |
399 | } |
400 | } | |
401 | } | |
402 | ||
532ac7d7 | 403 | /// Formats the given floating point number into the decimal form or |
d9579d0f AL |
404 | /// the exponential form, depending on the resulting exponent. The result is |
405 | /// stored to the supplied parts array while utilizing given byte buffer | |
406 | /// as a scratch. `upper` is used to determine the case of non-finite values | |
407 | /// (`inf` and `nan`) or the case of the exponent prefix (`e` or `E`). | |
408 | /// The first part to be rendered is always a `Part::Sign` (which can be | |
409 | /// an empty string if no sign is rendered). | |
410 | /// | |
411 | /// `format_shortest` should be the underlying digit-generation function. | |
1b1a35ee | 412 | /// It should return the part of the buffer that it initialized. |
d9579d0f AL |
413 | /// You probably would want `strategy::grisu::format_shortest` for this. |
414 | /// | |
415 | /// The `dec_bounds` is a tuple `(lo, hi)` such that the number is formatted | |
b039eaaf | 416 | /// as decimal only when `10^lo <= V < 10^hi`. Note that this is the *apparent* `V` |
d9579d0f AL |
417 | /// instead of the actual `v`! Thus any printed exponent in the exponential form |
418 | /// cannot be in this range, avoiding any confusion. | |
419 | /// | |
420 | /// The byte buffer should be at least `MAX_SIG_DIGITS` bytes long. | |
7cac9316 XL |
421 | /// There should be at least 6 parts available, due to the worst case like |
422 | /// `[+][1][.][2345][e][-][6]`. | |
60c5eb7d XL |
423 | pub fn to_shortest_exp_str<'a, T, F>( |
424 | mut format_shortest: F, | |
425 | v: T, | |
426 | sign: Sign, | |
427 | dec_bounds: (i16, i16), | |
428 | upper: bool, | |
1b1a35ee XL |
429 | buf: &'a mut [MaybeUninit<u8>], |
430 | parts: &'a mut [MaybeUninit<Part<'a>>], | |
60c5eb7d XL |
431 | ) -> Formatted<'a> |
432 | where | |
433 | T: DecodableFloat, | |
1b1a35ee | 434 | F: FnMut(&Decoded, &'a mut [MaybeUninit<u8>]) -> (&'a [u8], i16), |
60c5eb7d | 435 | { |
d9579d0f AL |
436 | assert!(parts.len() >= 6); |
437 | assert!(buf.len() >= MAX_SIG_DIGITS); | |
438 | assert!(dec_bounds.0 <= dec_bounds.1); | |
439 | ||
440 | let (negative, full_decoded) = decode(v); | |
441 | let sign = determine_sign(sign, &full_decoded, negative); | |
442 | match full_decoded { | |
443 | FullDecoded::Nan => { | |
1b1a35ee XL |
444 | parts[0] = MaybeUninit::new(Part::Copy(b"NaN")); |
445 | // SAFETY: we just initialized the elements `..1`. | |
446 | Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } } | |
d9579d0f AL |
447 | } |
448 | FullDecoded::Infinite => { | |
1b1a35ee XL |
449 | parts[0] = MaybeUninit::new(Part::Copy(b"inf")); |
450 | // SAFETY: we just initialized the elements `..1`. | |
451 | Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } } | |
d9579d0f AL |
452 | } |
453 | FullDecoded::Zero => { | |
454 | parts[0] = if dec_bounds.0 <= 0 && 0 < dec_bounds.1 { | |
1b1a35ee | 455 | MaybeUninit::new(Part::Copy(b"0")) |
d9579d0f | 456 | } else { |
1b1a35ee | 457 | MaybeUninit::new(Part::Copy(if upper { b"0E0" } else { b"0e0" })) |
d9579d0f | 458 | }; |
1b1a35ee XL |
459 | // SAFETY: we just initialized the elements `..1`. |
460 | Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } } | |
d9579d0f AL |
461 | } |
462 | FullDecoded::Finite(ref decoded) => { | |
1b1a35ee | 463 | let (buf, exp) = format_shortest(decoded, buf); |
d9579d0f AL |
464 | let vis_exp = exp as i32 - 1; |
465 | let parts = if dec_bounds.0 as i32 <= vis_exp && vis_exp < dec_bounds.1 as i32 { | |
1b1a35ee | 466 | digits_to_dec_str(buf, exp, 0, parts) |
d9579d0f | 467 | } else { |
1b1a35ee | 468 | digits_to_exp_str(buf, exp, 0, upper, parts) |
d9579d0f | 469 | }; |
b7449926 | 470 | Formatted { sign, parts } |
d9579d0f AL |
471 | } |
472 | } | |
473 | } | |
474 | ||
532ac7d7 | 475 | /// Returns a rather crude approximation (upper bound) for the maximum buffer size |
d9579d0f AL |
476 | /// calculated from the given decoded exponent. |
477 | /// | |
478 | /// The exact limit is: | |
479 | /// | |
480 | /// - when `exp < 0`, the maximum length is `ceil(log_10 (5^-exp * (2^64 - 1)))`. | |
481 | /// - when `exp >= 0`, the maximum length is `ceil(log_10 (2^exp * (2^64 - 1)))`. | |
482 | /// | |
483 | /// `ceil(log_10 (x^exp * (2^64 - 1)))` is less than `ceil(log_10 (2^64 - 1)) + | |
484 | /// ceil(exp * log_10 x)`, which is in turn less than `20 + (1 + exp * log_10 x)`. | |
485 | /// We use the facts that `log_10 2 < 5/16` and `log_10 5 < 12/16`, which is | |
486 | /// enough for our purposes. | |
487 | /// | |
488 | /// Why do we need this? `format_exact` functions will fill the entire buffer | |
489 | /// unless limited by the last digit restriction, but it is possible that | |
490 | /// the number of digits requested is ridiculously large (say, 30,000 digits). | |
491 | /// The vast majority of buffer will be filled with zeroes, so we don't want to | |
492 | /// allocate all the buffer beforehand. Consequently, for any given arguments, | |
493 | /// 826 bytes of buffer should be sufficient for `f64`. Compare this with | |
494 | /// the actual number for the worst case: 770 bytes (when `exp = -1074`). | |
495 | fn estimate_max_buf_len(exp: i16) -> usize { | |
496 | 21 + ((if exp < 0 { -12 } else { 5 } * exp as i32) as usize >> 4) | |
497 | } | |
498 | ||
499 | /// Formats given floating point number into the exponential form with | |
500 | /// exactly given number of significant digits. The result is stored to | |
501 | /// the supplied parts array while utilizing given byte buffer as a scratch. | |
502 | /// `upper` is used to determine the case of the exponent prefix (`e` or `E`). | |
503 | /// The first part to be rendered is always a `Part::Sign` (which can be | |
504 | /// an empty string if no sign is rendered). | |
505 | /// | |
506 | /// `format_exact` should be the underlying digit-generation function. | |
1b1a35ee | 507 | /// It should return the part of the buffer that it initialized. |
d9579d0f AL |
508 | /// You probably would want `strategy::grisu::format_exact` for this. |
509 | /// | |
510 | /// The byte buffer should be at least `ndigits` bytes long unless `ndigits` is | |
511 | /// so large that only the fixed number of digits will be ever written. | |
512 | /// (The tipping point for `f64` is about 800, so 1000 bytes should be enough.) | |
7cac9316 XL |
513 | /// There should be at least 6 parts available, due to the worst case like |
514 | /// `[+][1][.][2345][e][-][6]`. | |
60c5eb7d XL |
515 | pub fn to_exact_exp_str<'a, T, F>( |
516 | mut format_exact: F, | |
517 | v: T, | |
518 | sign: Sign, | |
519 | ndigits: usize, | |
520 | upper: bool, | |
1b1a35ee XL |
521 | buf: &'a mut [MaybeUninit<u8>], |
522 | parts: &'a mut [MaybeUninit<Part<'a>>], | |
60c5eb7d XL |
523 | ) -> Formatted<'a> |
524 | where | |
525 | T: DecodableFloat, | |
1b1a35ee | 526 | F: FnMut(&Decoded, &'a mut [MaybeUninit<u8>], i16) -> (&'a [u8], i16), |
60c5eb7d | 527 | { |
d9579d0f AL |
528 | assert!(parts.len() >= 6); |
529 | assert!(ndigits > 0); | |
530 | ||
531 | let (negative, full_decoded) = decode(v); | |
532 | let sign = determine_sign(sign, &full_decoded, negative); | |
533 | match full_decoded { | |
534 | FullDecoded::Nan => { | |
1b1a35ee XL |
535 | parts[0] = MaybeUninit::new(Part::Copy(b"NaN")); |
536 | // SAFETY: we just initialized the elements `..1`. | |
537 | Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } } | |
d9579d0f AL |
538 | } |
539 | FullDecoded::Infinite => { | |
1b1a35ee XL |
540 | parts[0] = MaybeUninit::new(Part::Copy(b"inf")); |
541 | // SAFETY: we just initialized the elements `..1`. | |
542 | Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } } | |
d9579d0f AL |
543 | } |
544 | FullDecoded::Zero => { | |
60c5eb7d XL |
545 | if ndigits > 1 { |
546 | // [0.][0000][e0] | |
1b1a35ee XL |
547 | parts[0] = MaybeUninit::new(Part::Copy(b"0.")); |
548 | parts[1] = MaybeUninit::new(Part::Zero(ndigits - 1)); | |
549 | parts[2] = MaybeUninit::new(Part::Copy(if upper { b"E0" } else { b"e0" })); | |
550 | Formatted { | |
551 | sign, | |
552 | // SAFETY: we just initialized the elements `..3`. | |
553 | parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..3]) }, | |
554 | } | |
d9579d0f | 555 | } else { |
1b1a35ee XL |
556 | parts[0] = MaybeUninit::new(Part::Copy(if upper { b"0E0" } else { b"0e0" })); |
557 | Formatted { | |
558 | sign, | |
559 | // SAFETY: we just initialized the elements `..1`. | |
560 | parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) }, | |
561 | } | |
d9579d0f AL |
562 | } |
563 | } | |
564 | FullDecoded::Finite(ref decoded) => { | |
565 | let maxlen = estimate_max_buf_len(decoded.exp); | |
566 | assert!(buf.len() >= ndigits || buf.len() >= maxlen); | |
567 | ||
568 | let trunc = if ndigits < maxlen { ndigits } else { maxlen }; | |
1b1a35ee XL |
569 | let (buf, exp) = format_exact(decoded, &mut buf[..trunc], i16::MIN); |
570 | Formatted { sign, parts: digits_to_exp_str(buf, exp, ndigits, upper, parts) } | |
d9579d0f AL |
571 | } |
572 | } | |
573 | } | |
574 | ||
575 | /// Formats given floating point number into the decimal form with exactly | |
576 | /// given number of fractional digits. The result is stored to the supplied parts | |
577 | /// array while utilizing given byte buffer as a scratch. `upper` is currently | |
578 | /// unused but left for the future decision to change the case of non-finite values, | |
0731742a | 579 | /// i.e., `inf` and `nan`. The first part to be rendered is always a `Part::Sign` |
d9579d0f AL |
580 | /// (which can be an empty string if no sign is rendered). |
581 | /// | |
582 | /// `format_exact` should be the underlying digit-generation function. | |
1b1a35ee | 583 | /// It should return the part of the buffer that it initialized. |
d9579d0f AL |
584 | /// You probably would want `strategy::grisu::format_exact` for this. |
585 | /// | |
586 | /// The byte buffer should be enough for the output unless `frac_digits` is | |
587 | /// so large that only the fixed number of digits will be ever written. | |
588 | /// (The tipping point for `f64` is about 800, and 1000 bytes should be enough.) | |
7cac9316 XL |
589 | /// There should be at least 4 parts available, due to the worst case like |
590 | /// `[+][0.][0000][2][0000]` with `frac_digits = 10`. | |
60c5eb7d XL |
591 | pub fn to_exact_fixed_str<'a, T, F>( |
592 | mut format_exact: F, | |
593 | v: T, | |
594 | sign: Sign, | |
595 | frac_digits: usize, | |
1b1a35ee XL |
596 | buf: &'a mut [MaybeUninit<u8>], |
597 | parts: &'a mut [MaybeUninit<Part<'a>>], | |
60c5eb7d XL |
598 | ) -> Formatted<'a> |
599 | where | |
600 | T: DecodableFloat, | |
1b1a35ee | 601 | F: FnMut(&Decoded, &'a mut [MaybeUninit<u8>], i16) -> (&'a [u8], i16), |
60c5eb7d | 602 | { |
d9579d0f AL |
603 | assert!(parts.len() >= 4); |
604 | ||
605 | let (negative, full_decoded) = decode(v); | |
606 | let sign = determine_sign(sign, &full_decoded, negative); | |
607 | match full_decoded { | |
608 | FullDecoded::Nan => { | |
1b1a35ee XL |
609 | parts[0] = MaybeUninit::new(Part::Copy(b"NaN")); |
610 | // SAFETY: we just initialized the elements `..1`. | |
611 | Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } } | |
d9579d0f AL |
612 | } |
613 | FullDecoded::Infinite => { | |
1b1a35ee XL |
614 | parts[0] = MaybeUninit::new(Part::Copy(b"inf")); |
615 | // SAFETY: we just initialized the elements `..1`. | |
616 | Formatted { sign, parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) } } | |
d9579d0f AL |
617 | } |
618 | FullDecoded::Zero => { | |
60c5eb7d XL |
619 | if frac_digits > 0 { |
620 | // [0.][0000] | |
1b1a35ee XL |
621 | parts[0] = MaybeUninit::new(Part::Copy(b"0.")); |
622 | parts[1] = MaybeUninit::new(Part::Zero(frac_digits)); | |
623 | Formatted { | |
624 | sign, | |
625 | // SAFETY: we just initialized the elements `..2`. | |
626 | parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..2]) }, | |
627 | } | |
d9579d0f | 628 | } else { |
1b1a35ee XL |
629 | parts[0] = MaybeUninit::new(Part::Copy(b"0")); |
630 | Formatted { | |
631 | sign, | |
632 | // SAFETY: we just initialized the elements `..1`. | |
633 | parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) }, | |
634 | } | |
d9579d0f AL |
635 | } |
636 | } | |
637 | FullDecoded::Finite(ref decoded) => { | |
638 | let maxlen = estimate_max_buf_len(decoded.exp); | |
639 | assert!(buf.len() >= maxlen); | |
640 | ||
641 | // it *is* possible that `frac_digits` is ridiculously large. | |
642 | // `format_exact` will end rendering digits much earlier in this case, | |
643 | // because we are strictly limited by `maxlen`. | |
644 | let limit = if frac_digits < 0x8000 { -(frac_digits as i16) } else { i16::MIN }; | |
1b1a35ee | 645 | let (buf, exp) = format_exact(decoded, &mut buf[..maxlen], limit); |
d9579d0f AL |
646 | if exp <= limit { |
647 | // the restriction couldn't been met, so this should render like zero no matter | |
648 | // `exp` was. this does not include the case that the restriction has been met | |
649 | // only after the final rounding-up; it's a regular case with `exp = limit + 1`. | |
1b1a35ee | 650 | debug_assert_eq!(buf.len(), 0); |
60c5eb7d XL |
651 | if frac_digits > 0 { |
652 | // [0.][0000] | |
1b1a35ee XL |
653 | parts[0] = MaybeUninit::new(Part::Copy(b"0.")); |
654 | parts[1] = MaybeUninit::new(Part::Zero(frac_digits)); | |
655 | Formatted { | |
656 | sign, | |
657 | // SAFETY: we just initialized the elements `..2`. | |
658 | parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..2]) }, | |
659 | } | |
d9579d0f | 660 | } else { |
1b1a35ee XL |
661 | parts[0] = MaybeUninit::new(Part::Copy(b"0")); |
662 | Formatted { | |
663 | sign, | |
664 | // SAFETY: we just initialized the elements `..1`. | |
665 | parts: unsafe { MaybeUninit::slice_assume_init_ref(&parts[..1]) }, | |
666 | } | |
d9579d0f AL |
667 | } |
668 | } else { | |
1b1a35ee | 669 | Formatted { sign, parts: digits_to_dec_str(buf, exp, frac_digits, parts) } |
d9579d0f AL |
670 | } |
671 | } | |
672 | } | |
673 | } |