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
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
use alloc::{string::String, vec::Vec};
use core::{
    borrow::BorrowMut,
    cmp::{max, min},
    num::NonZeroUsize,
};

use awint_core::{awint_internals::Digit, Bits};

use crate::{
    awint_internals::{bits_upper_bound, SerdeError, SerdeError::*},
    Awi, FP,
};

// TODO there are variations of algorithms that can eliminate all the cases
// where we take `rhs`s by mutable reference

fn itousize(i: isize) -> Option<usize> {
    usize::try_from(i).ok()
}

/// These functions are associated to avoid name clashes.
///
/// Note: Adding new functions to `FP` is a WIP
// TODO
impl<B: BorrowMut<Bits>> FP<B> {
    /// One-assigns `this`. Returns `None` if a positive one value is not
    /// representable.
    #[must_use]
    pub fn one_(this: &mut Self) -> Option<()> {
        // if fp is negative, one can certainly not be represented
        let fp = itousize(this.fp())?;
        // if `this.signed() && fp == this.bw()`, trying to set the one would set the
        // sign bit
        if fp > this.bw().wrapping_sub(this.signed() as usize) {
            None
        } else {
            this.const_as_mut().zero_();
            this.const_as_mut().digit_or_(1, fp);
            Some(())
        }
    }

    /// Relative significant bit positions, determines the bit positions
    /// (inclusive) of the least and most significant bits relative to the
    /// fixed point
    ///
    /// Note: because the msb position is one less than the bitwidth, the
    /// bitwidth is equal to the difference in the bounds _plus one_
    #[inline]
    #[must_use]
    pub fn rel_sb(this: &Self) -> (isize, isize) {
        // cannot overflow because of the invariants
        let lo = this.fp().wrapping_neg();
        // the msb position is one less than the bitwidth
        (lo, this.ibw().wrapping_sub(1).wrapping_add(lo))
    }

    /// The same as [FP::truncate_] except it always intreprets arguments
    /// as unsigned
    pub fn utruncate_<C: BorrowMut<Bits>>(this: &mut Self, rhs: &FP<C>) {
        this.zero_();
        let lbb = FP::rel_sb(this);
        let rbb = FP::rel_sb(rhs);

        // find overlap
        let lo = max(lbb.0, rbb.0);
        let hi = min(lbb.1, rbb.1);
        if hi < lo {
            // does not overlap
            return
        }
        let width = hi.wrapping_sub(lo).wrapping_add(1) as usize;
        let diff = lbb.0.abs_diff(rbb.0);
        // the fielding will start from 0 in one argument and end at `diff` in the other
        let (to, from) = if lbb.0 < rbb.0 { (diff, 0) } else { (0, diff) };
        this.field(to, rhs, from, width).unwrap();
    }

    /// Truncate-assigns `rhs` to `this`. For the unsigned case, logically what
    /// this does is make `this` and `rhs` into concatenations with infinite
    /// zeros on both ends, aligns the fixed points, and copies from `rhs`
    /// to `this`. For the case of `rhs.signed()`, the absolute value of
    /// `rhs` is used for truncation to `this` followed by
    /// `this.neg_(rhs.msb() && this.signed())`.
    pub fn truncate_<C: BorrowMut<Bits>>(this: &mut Self, rhs: &mut FP<C>) {
        let mut b = rhs.is_negative();
        // reinterpret as unsigned to avoid imin overflow
        rhs.const_as_mut().neg_(b);
        FP::utruncate_(this, rhs);
        rhs.const_as_mut().neg_(b);
        b &= this.signed();
        this.const_as_mut().neg_(b);
    }

    /// The same as [FP::otruncate_] except it always intreprets arguments
    /// as unsigned
    #[must_use = "use `utruncate_` if you do not need the overflow booleans"]
    pub fn outruncate_<C: BorrowMut<Bits>>(this: &mut Self, rhs: &FP<C>) -> (bool, bool) {
        this.zero_();
        if rhs.is_zero() {
            return (false, false)
        }
        let lbb = FP::rel_sb(this);
        let rbb = FP::rel_sb(rhs);

        // find overlap
        let lo = max(lbb.0, rbb.0);
        let hi = min(lbb.1, rbb.1);
        if hi < lo {
            // does not overlap
            return (true, true)
        }
        let width = hi.wrapping_sub(lo).wrapping_add(1) as usize;
        let diff = lbb.0.abs_diff(rbb.0);
        let (to, from) = if lbb.0 < rbb.0 { (diff, 0) } else { (0, diff) };
        this.field(to, rhs, from, width).unwrap();
        // when testing if a less significant numerical bit is cut off, we need to be
        // aware that it can be cut off from above even if overlap happens, for
        // example:
        //
        // 1.0
        //  .yyy
        // _____
        //  .000
        //
        // The `1` is the least significant numerical bit, but will get truncated by
        // being above the rel_msb.

        // note overflow cannot happen because of the `rhs.is_zero()` early return and
        // invariants
        let mut lsnb = rhs.tz() as isize;
        lsnb = lsnb.wrapping_add(rbb.0);
        let mut msnb = rhs.bw().wrapping_sub(rhs.lz()).wrapping_sub(1) as isize;
        msnb = msnb.wrapping_add(rbb.0);
        (
            (lsnb < lbb.0) || (lsnb > lbb.1),
            (msnb < lbb.0) || (msnb > lbb.1),
        )
    }

    /// Overflow-truncate-assigns `rhs` to `this`. The same as
    /// [FP::truncate_], except that a tuple of booleans is returned. The
    /// first indicates if the least significant numerical bit was truncated,
    /// and the second indicates if the most significant numerical bit was
    /// truncated. Additionally, if `this.is_negative() != rhs.is_negative()`,
    /// the second overflow is set.
    ///
    /// What this means is that if transitive truncations return no overflow,
    /// then numerical value is preserved. If only `FP::otruncate_(...).0`
    /// is true, then less significant numerical values were changed and only
    /// some kind of truncation rounding has occured to the numerical value. If
    /// `FP::otruncate_(...).1` is true, then the numerical value could be
    /// dramatically changed.
    #[must_use = "use `truncate_` if you do not need the overflow booleans"]
    pub fn otruncate_<C: BorrowMut<Bits>>(this: &mut Self, rhs: &mut FP<C>) -> (bool, bool) {
        let mut b = rhs.is_negative();
        // reinterpret as unsigned to avoid imin overflow
        rhs.const_as_mut().neg_(b);
        let o = FP::outruncate_(this, rhs);
        rhs.const_as_mut().neg_(b);
        // imin works correctly
        b &= this.signed();
        this.const_as_mut().neg_(b);
        (o.0, o.1 || (this.is_negative() != rhs.is_negative()))
    }

    /// Floating-assigns `rhs` to `this`. This modifies the `fp` of `this` to
    /// retain as much significant numerical precision as possible. If
    /// `this.signed()`, the msnb (most significant numerical bit) is moved to
    /// the second msb of `this`. Otherwise, the msnb is moved to the msb of
    /// `this`. If `rhs.is_negative()` and `this` is not signed, the absolute
    /// value of `rhs` is used. If `rhs.is_zero()`, `this` and its `fp` are
    /// zeroed. Returns `None` if the fixed point invariant would be
    /// violated.
    pub fn floating_<C: BorrowMut<Bits>>(this: &mut Self, rhs: &mut FP<C>) -> Option<()> {
        let b = rhs.is_negative();
        rhs.neg_(b);
        let rhs_lz = rhs.lz();
        if rhs_lz == rhs.bw() {
            // efficient zero
            this.zero_();
            // do this since we will also do this in triop situations
            this.set_fp(0).unwrap();
        } else {
            let msnb_add1 = rhs.bw().wrapping_sub(rhs_lz);
            let this_sig_w = this.bw().wrapping_sub(this.signed() as usize);
            let (to, from, width) = if msnb_add1 > this_sig_w {
                (0, msnb_add1.wrapping_sub(this_sig_w), this_sig_w)
            } else {
                (this_sig_w.wrapping_sub(msnb_add1), 0, msnb_add1)
            };
            let rhs_exp = (msnb_add1.wrapping_sub(1) as isize).wrapping_sub(rhs.fp());
            let neg_this = b && this.signed();
            if neg_this && (this.bw() == 1) {
                // corner case: negative powers of two can be represented with one signed bit
                if this.set_fp(rhs_exp.wrapping_neg()).is_none() {
                    rhs.neg_(b);
                    return None
                }
                this.umax_();
            } else {
                if this
                    .set_fp((this_sig_w as isize).wrapping_sub(1).wrapping_sub(rhs_exp))
                    .is_none()
                {
                    rhs.neg_(b);
                    return None
                }
                this.zero_();
                this.field(to, rhs, from, width).unwrap();
                this.neg_(neg_this);
            }
        }
        rhs.neg_(b);
        Some(())
    }

    /// Creates a tuple of `Vec<u8>`s representing the integer and fraction
    /// parts `this` (sign indicators, prefixes, points, and postfixes not
    /// included). This function performs allocation. This is the inverse of
    /// [Awi::from_bytes_general] and extends the abilities of
    /// [Awi::bits_to_vec_radix]. Signedness and fixed point position
    /// information is taken from `this`. `min_integer_chars` specifies the
    /// minimum number of chars in the integer part, inserting leading '0's if
    /// there are not enough chars. `min_fraction_chars` works likewise for the
    /// fraction part, inserting trailing '0's. For `max_ufp` see the errors
    /// section.
    ///
    /// ```
    /// use awint::awi::*;
    /// // note: a user may want to define their own helper functions to do
    /// // this in one step and combine the output into one string using
    /// // the notation they prefer.
    ///
    /// // This creates a fixed point value of -42.1234_i32f16 (see `Awi::from_str`)
    /// let val = Awi::from_str_general(Some(true), "42", "1234", 0, 10, bw(32), 16).unwrap();
    /// let fp_awi = FP::new(true, val, 16).unwrap();
    /// assert_eq!(
    ///     // note: in many situations users will want at least 1 zero for
    ///     // both parts so that zero parts result in "0" strings and not "",
    ///     // so `min_..._chars` will be 1. See also
    ///     // `FPType::unique_min_fraction_digits`.
    ///     FP::to_str_general(&fp_awi, 10, false, 1, 1, 4096),
    ///     Ok(("42".to_owned(), "1234".to_owned()))
    /// );
    /// ```
    ///
    /// # Errors
    ///
    /// Because it would be trivial to cause resource exhaustion with extremely
    /// large fixed points (the bitwidth is limited roughly by what it takes to
    /// allocate `this.b()` in the first place, but the fixed point can easily
    /// be set to huge positive or negative values to result in extremely
    /// long `Vec<u8>`s and internal calculations), for practical reasons we
    /// need a built in failsafe that triggers if
    /// `this.fp().unsigned_abs() > max_ufp`. If so, `Overflow` is returned.
    ///
    /// This can only return an error if `radix` is not in the range 2..=36 or
    /// if resource exhaustion occurs.
    pub fn to_vec_general(
        this: &Self,
        radix: u8,
        upper: bool,
        min_integer_chars: usize,
        min_fraction_chars: usize,
        max_ufp: usize,
    ) -> Result<(Vec<u8>, Vec<u8>), SerdeError> {
        if radix < 2 || radix > 36 {
            return Err(InvalidRadix)
        }
        if this.fp().unsigned_abs() > max_ufp {
            return Err(Overflow)
        }
        // I was originally going to include b'-', but it causes insertion performance
        // problems here, and users have to remove it anyway in the usage cases where a
        // prefix is added (we want "-0x123" and not "0x-123")

        let is_zero = this.is_zero();
        let is_negative = this.is_negative();
        let mut unsigned = Awi::zero(this.nzbw());
        unsigned.copy_(this).unwrap();
        // reinterpret as unsigned for `imin`
        unsigned.neg_(is_negative);
        // safe because of invariants
        let tot_lz = unsigned.lz() as isize;

        // the order of these `||` is important to avoid overflow
        let integer_part_zero =
            is_zero || (this.fp() > this.ibw()) || (tot_lz > (this.ibw() - this.fp()));
        let mut integer_part = if integer_part_zero {
            alloc::vec![b'0'; min_integer_chars]
        } else {
            let from = max(this.fp(), 0) as usize;
            // no overflow because of `integer_part_zero` checks
            let bits = this.ibw().wrapping_sub(tot_lz);
            let integer_bits = bits.wrapping_sub(this.fp()) as usize;
            let field_bits = bits.wrapping_sub(from as isize) as usize;
            // if the fixed point mandates more trailing zeroes in the integer part
            let extra_zeros = if this.fp() < 0 {
                this.fp().unsigned_abs()
            } else {
                0
            };
            match NonZeroUsize::new(integer_bits) {
                Some(integer_bits) => {
                    let mut tmp = Awi::zero(integer_bits);
                    tmp.field(extra_zeros, &unsigned, from, field_bits).unwrap();
                    // note: we do not unwrap here in case of resource exhaustion
                    Awi::bits_to_vec_radix(&tmp, false, radix, upper, min_integer_chars)?
                }
                None => alloc::vec![b'0'; min_integer_chars],
            }
        };

        let tot_tz = unsigned.tz() as isize;
        // order is important again
        let fraction_part_zero = is_zero || (this.fp() <= 0) || (tot_tz >= this.fp());
        let mut fraction_part = if fraction_part_zero {
            alloc::vec![b'0'; min_fraction_chars]
        } else {
            let unique_digits = this.fp_ty().unique_min_fraction_digits(radix).unwrap();
            let calc_digits = max(unique_digits, min_fraction_chars);
            let multiplier_bits = bits_upper_bound(calc_digits, radix)?;
            // avoid needing some calculation by dropping zero bits that have no impact
            let calc_fp = this.fp().wrapping_sub(tot_tz) as usize;
            let field_bits = min(this.fp(), this.ibw()).wrapping_sub(tot_tz) as usize;
            let mut tmp = Awi::zero(
                NonZeroUsize::new(multiplier_bits.checked_add(calc_fp).ok_or(Overflow)?).unwrap(),
            );
            tmp.field_from(&unsigned, tot_tz as usize, field_bits)
                .unwrap();
            for _ in 0..calc_digits {
                tmp.digit_cin_mul_(0, Digit::from(radix));
            }
            let inc = if (tmp.get_digit(calc_fp.checked_sub(1).ok_or(Overflow)?) & 1) == 0 {
                // round down
                false
            } else if tmp.tz().checked_add(1).ok_or(Overflow)? == calc_fp {
                // round to even
                (tmp.get_digit(calc_fp) & 1) == 0
            } else {
                // round up
                true
            };
            tmp.lshr_(calc_fp).unwrap();
            tmp.inc_(inc);
            // note: we do not unwrap here in case of resource exhaustion
            let mut s = Awi::bits_to_vec_radix(&tmp, false, radix, upper, calc_digits)?;
            // trim off zeroes
            while s.len() > min_fraction_chars {
                // s.len() > 0 so this cannot overflow
                if s[s.len().wrapping_sub(1)] == b'0' {
                    let _ = s.pop();
                } else {
                    break
                }
            }
            s
        };
        integer_part.shrink_to_fit();
        fraction_part.shrink_to_fit();
        Ok((integer_part, fraction_part))
    }

    /// Creates a tuple of `String`s representing the integer and fraction
    /// parts of `this`. This does the same thing as [FP::to_vec_general]
    /// but with `String`s.
    pub fn to_str_general(
        this: &Self,
        radix: u8,
        upper: bool,
        min_integer_chars: usize,
        min_fraction_chars: usize,
        max_ufp: usize,
    ) -> Result<(String, String), SerdeError> {
        let (i, f) = FP::to_vec_general(
            this,
            radix,
            upper,
            min_integer_chars,
            min_fraction_chars,
            max_ufp,
        )?;
        Ok((String::from_utf8(i).unwrap(), String::from_utf8(f).unwrap()))
    }
}