softposit 0.3.9

Implementation of Posit numbers
Documentation
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
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
use super::PxE1;
use crate::WithSign;
use core::convert::From;
use core::f64;

impl<const N: u32> From<PxE1<{ N }>> for f32 {
    #[inline]
    fn from(a: PxE1<{ N }>) -> Self {
        f64::from(a) as f32
    }
}

impl<const N: u32> From<PxE1<{ N }>> for f64 {
    #[inline]
    fn from(p_a: PxE1<{ N }>) -> Self {
        let mut ui_a = p_a.to_bits();

        if p_a.is_zero() {
            0.
        } else if p_a.is_nar() {
            f64::NAN
        } else {
            let sign_a = ui_a & 0x_8000_0000;
            if sign_a != 0 {
                ui_a = ui_a.wrapping_neg();
            }
            let (k_a, tmp) = PxE1::<{ N }>::separate_bits_tmp(ui_a);

            let frac_a = ((tmp << 2) as u64) << 20;
            let exp_a = (((k_a as u64) << 1) + ((tmp >> 30) as u64)).wrapping_add(1023) << 52;

            f64::from_bits(exp_a + frac_a + ((sign_a as u64) << 32))
        }
    }
}

impl<const N: u32> From<f64> for PxE1<{ N }> {
    #[allow(clippy::cognitive_complexity)]
    fn from(mut float: f64) -> Self {
        let mut reg: u32;
        let mut frac = 0_u32;
        let mut exp = 0_i32;
        let mut bit_n_plus_one = false;
        let mut bits_more = false;

        if float == 0. {
            return Self::ZERO;
        } else if !float.is_finite() {
            return Self::NAR;
        }

        let sign = float < 0.;

        let u_z: u32 = if float == 1. {
            0x4000_0000
        } else if float == -1. {
            0xC000_0000
        } else if (float > 1.) || (float < -1.) {
            if sign {
                //Make negative numbers positive for easier computation
                float = -float;
            }

            let reg_s = true;
            reg = 1; //because k = m-1; so need to add back 1
                     // minpos
            if (N == 2) && (float <= 8.673_617_379_884_035_e-19) {
                1
            } else {
                //regime
                while float >= 4. {
                    float *= 0.25; // float/=4;
                    reg += 1;
                }
                if float >= 2. {
                    float *= 0.5;
                    exp += 1;
                }
                let frac_length = (N - 3) as isize - (reg as isize);
                if frac_length < 0 {
                    if reg == N - 2 {
                        bit_n_plus_one = exp != 0;
                        exp = 0;
                    }
                    if float > 1. {
                        bits_more = true;
                    }
                } else {
                    frac = crate::convert_fraction_p32(
                        float,
                        frac_length as u16,
                        &mut bit_n_plus_one,
                        &mut bits_more,
                    );
                }

                if (reg == 30) && (frac > 0) {
                    bits_more = true;
                    frac = 0;
                }

                if reg > (N - 2) {
                    if reg_s {
                        0x_7FFF_FFFF & Self::mask()
                    } else {
                        0x1 << (32 - N)
                    }
                } else {
                    //rounding off fraction bits

                    let regime = if reg_s { ((1 << reg) - 1) << 1 } else { 1_u32 };

                    let mut u_z = (regime << (30 - reg))
                        + ((exp as u32) << (29 - reg))
                        + ((frac << (32 - N)) as u32);
                    //minpos
                    if (u_z == 0) && (frac > 0) {
                        u_z = 0x1 << (32 - N);
                    }
                    if bit_n_plus_one {
                        u_z += (((u_z >> (32 - N)) & 0x1) | (bits_more as u32)) << (32 - N);
                    }
                    u_z
                }
                .with_sign(sign)
            }
        } else if (float < 1.) || (float > -1.) {
            if sign {
                //Make negative numbers positive for easier computation
                float = -float;
            }

            let reg_s = false;
            reg = 0;

            //regime
            while float < 1. {
                float *= 4.;
                reg += 1;
            }

            if float >= 2. {
                float *= 0.5;
                exp += 1;
            }

            let frac_length = (N - 3) as isize - (reg as isize);
            if frac_length < 0 {
                if reg == N - 2 {
                    bit_n_plus_one = exp != 0;
                    exp = 0;
                }

                if float > 1. {
                    bits_more = true;
                }
            } else {
                frac = crate::convert_fraction_p32(
                    float,
                    frac_length as u16,
                    &mut bit_n_plus_one,
                    &mut bits_more,
                );
            }

            if (reg == 30) && (frac > 0) {
                bits_more = true;
                frac = 0;
            }

            if reg > (N - 2) {
                if reg_s {
                    0x_7FFF_FFFF & Self::mask()
                } else {
                    0x1 << (32 - N)
                }
            } else {
                //rounding off fraction bits

                let regime = if reg_s { ((1 << reg) - 1) << 1 } else { 1_u32 };

                let mut u_z = (regime << (30 - reg))
                    + ((exp as u32) << (29 - reg))
                    + ((frac << (32 - N)) as u32);
                //minpos
                if (u_z == 0) && (frac > 0) {
                    u_z = 0x1 << (32 - N);
                }

                if bit_n_plus_one {
                    u_z += (((u_z >> (32 - N)) & 0x1) | (bits_more as u32)) << (32 - N);
                }
                u_z
            }
            .with_sign(sign)
        } else {
            //NaR - for NaN, INF and all other combinations
            0x8000_0000
        };
        Self::from_bits(u_z)
    }
}

impl<const N: u32> From<PxE1<{ N }>> for i32 {
    #[inline]
    fn from(p_a: PxE1<{ N }>) -> Self {
        //NaR
        if p_a.is_nar() {
            return i32::min_value();
        }

        let mut ui_a = p_a.to_bits();

        let sign = ui_a > 0x_8000_0000; // sign is True if pA > NaR.

        if sign {
            ui_a = ui_a.wrapping_neg(); // A is now |A|.
        }

        let i_z = convert_px1bits_to_u32(ui_a);
        i_z.with_sign(sign) as i32
    }
}

impl<const N: u32> From<PxE1<{ N }>> for u32 {
    #[inline]
    fn from(p_a: PxE1<{ N }>) -> Self {
        let ui_a = p_a.to_bits();
        //NaR
        if ui_a >= 0x_8000_0000 {
            0
        } else {
            convert_px1bits_to_u32(ui_a)
        }
    }
}

fn convert_px1bits_to_u32(mut ui_a: u32) -> u32 {
    if ui_a <= 0x_3000_0000 {
        // 0 <= |pA| <= 1/2 rounds to zero.
        0
    } else if ui_a < 0x_4800_0000 {
        // 1/2 < x < 3/2 rounds to 1.
        1
    } else if ui_a <= 0x_5400_0000 {
        // 3/2 <= x <= 5/2 rounds to 2.
        2
    } else if ui_a > 0x_7FFF_BFFF {
        //4294836223
        4_294_967_295
    } else {
        // Decode the posit, left-justifying as we go.
        let mut scale = 0_u32;

        ui_a -= 0x_4000_0000; // Strip off first regime bit (which is a 1).
        while (0x_2000_0000 & ui_a) != 0 {
            // Increment scale by 2 for each regime sign bit.
            scale += 2; // Regime sign bit is always 1 in this range.
            ui_a = (ui_a - 0x_2000_0000) << 1; // Remove the bit; line up the next regime bit.
        }
        ui_a <<= 1; // Skip over termination bit, which is 0.
        if (0x_2000_0000 & ui_a) != 0 {
            scale += 1;
        } // If exponent is 1, increment the scale.
        let mut i_z64 = ((ui_a | 0x_2000_0000) as u64) << 33; // Left-justify fraction in 64-bit result (one left bit padding)

        let mut mask = 0x4000_0000_0000_0000_u64 >> scale; // Point to the last bit of the integer part.

        let bit_last = i_z64 & mask; // Extract the bit, without shifting it.
        mask >>= 1;
        let mut tmp = i_z64 & mask;
        let bit_n_plus_one = tmp != 0; // "True" if nonzero.
        i_z64 ^= tmp; // Erase the bit, if it was set.
        tmp = i_z64 & (mask - 1); // tmp has any remaining bits. // This is bits_more
        i_z64 ^= tmp; // Erase those bits, if any were set.

        if bit_n_plus_one {
            // logic for round to nearest, tie to even
            if (bit_last | tmp) != 0 {
                i_z64 += mask << 1;
            }
        }

        (i_z64 >> (62 - scale)) as u32 // Right-justify the integer.
    }
}

impl<const N: u32> From<PxE1<{ N }>> for i64 {
    #[inline]
    fn from(p_a: PxE1<{ N }>) -> Self {
        //NaR
        if p_a.is_nar() {
            return i64::min_value();
        }

        let mut ui_a = p_a.to_bits();

        let sign = ui_a > 0x_8000_0000; // sign is True if pA > NaR.

        if sign {
            ui_a = ui_a.wrapping_neg(); // A is now |A|.
        }

        let i_z = convert_px1bits_to_u64(ui_a);

        i_z.with_sign(sign) as i64
    }
}

impl<const N: u32> From<PxE1<{ N }>> for u64 {
    #[inline]
    fn from(p_a: PxE1<{ N }>) -> Self {
        let ui_a = p_a.to_bits();
        //NaR
        if ui_a >= 0x_8000_0000 {
            0
        } else {
            convert_px1bits_to_u64(ui_a)
        }
    }
}

fn convert_px1bits_to_u64(mut ui_a: u32) -> u64 {
    if ui_a <= 0x_3000_0000 {
        // 0 <= |pA| <= 1/2 rounds to zero.
        0
    } else if ui_a < 0x_4800_0000 {
        // 1/2 < x < 3/2 rounds to 1.
        1
    } else if ui_a <= 0x_5400_0000 {
        // 3/2 <= x <= 5/2 rounds to 2.
        2
    } else {
        // Decode the posit, left-justifying as we go.
        let mut scale = 0_u32;

        ui_a -= 0x_4000_0000; // Strip off first regime bit (which is a 1).
        while (0x_2000_0000 & ui_a) != 0 {
            // Increment scale by 2 for each regime sign bit.
            scale += 2; // Regime sign bit is always 1 in this range.
            ui_a = (ui_a - 0x_2000_0000) << 1; // Remove the bit; line up the next regime bit.
        }
        ui_a <<= 1; // Skip over termination bit, which is 0.
        if (0x_2000_0000 & ui_a) != 0 {
            scale += 1;
        } // If exponent is 1, increment the scale.
        let mut i_z = ((ui_a | 0x_2000_0000) as u64) << 33; // Left-justify fraction in 64-bit result (one left bit padding)
        let mut mask = 0x_4000_0000_0000_0000 >> scale; // Point to the last bit of the integer part.

        let bit_last = i_z & mask; // Extract the bit, without shifting it.
        mask >>= 1;
        let mut tmp = i_z & mask;
        let bit_n_plus_one = tmp != 0; // "True" if nonzero.
        i_z ^= tmp; // Erase the bit, if it was set.
        tmp = i_z & (mask - 1); // tmp has any remaining bits. // This is bits_more
        i_z ^= tmp; // Erase those bits, if any were set.

        if bit_n_plus_one {
            // logic for round to nearest, tie to even
            if (bit_last | tmp) != 0 {
                i_z += mask << 1;
            }
        }

        i_z >> (62 - scale) // Right-justify the integer.
    }
}

fn convert_u64_to_px1bits<const N: u32>(a: u64) -> u32 {
    let mut log2 = 63_i8; //60;//length of bit (e.g. 576460752303423488 = 2^59) in int (64 but because we have only 64 bits, so one bit off to accommodate that fact)
    let mut mask = 0x_8000_0000_0000_0000_u64;
    if a < 0x2 {
        (a as u32) << 30
    } else {
        let mut frac64_a = a;
        while (frac64_a & mask) == 0 {
            log2 -= 1;
            frac64_a <<= 1;
        }

        let k = (log2 >> 1) as u32;

        let exp_a = (log2 & 0x1) as u32;
        frac64_a ^= mask;

        let mut ui_a: u32;
        if k >= (N - 2) {
            //maxpos
            ui_a = 0x_7FFF_FFFF & PxE1::<{ N }>::mask();
        } else if k == (N - 3) {
            //bitNPlusOne-> exp bit //bitLast is zero
            ui_a = 0x_7FFF_FFFF ^ (0x_3FFF_FFFF >> k);
            if ((exp_a & 0x1) != 0) && (frac64_a != 0) {
                //bitNPlusOne //bitsMore
                ui_a |= 0x_8000_0000_u32 >> (N - 1);
            }
        } else if k == (N - 4) {
            //bitLast = regime terminating bit
            ui_a = (0x_7FFF_FFFF ^ (0x_3FFF_FFFF >> k)) | (exp_a << (28 - k));
            mask = 0x_0008_0000_0000_u64 << (k + 32 - N);
            if (mask & frac64_a) != 0 {
                //bitNPlusOne
                if (((mask - 1) & frac64_a) | ((exp_a & 0x1) as u64)) != 0 {
                    ui_a += 0x_8000_0000_u32 >> (N - 1);
                }
            }
        } else {
            ui_a = (0x_7FFF_FFFF ^ (0x_3FFF_FFFF >> k))
                | (exp_a << (28 - k))
                | (((frac64_a >> (k + 36)) as u32) & PxE1::<{ N }>::mask());
            mask = 0x_0008_0000_0000_u64 << (k + 32 - N); //bitNPlusOne position
            if ((mask & frac64_a) != 0)
                && ((((mask - 1) & frac64_a) | ((mask << 1) & frac64_a)) != 0)
            {
                ui_a += 0x_8000_0000_u32 >> (N - 1);
            }
        }
        ui_a
    }
}

impl<const N: u32> From<u64> for PxE1<{ N }> {
    #[inline]
    fn from(a: u64) -> Self {
        let ui_a = if a == 0x_8000_0000_0000_0000 {
            0x_8000_0000
        } else if (N == 2) && (a > 0) {
            0x_4000_0000
        } else if a > 0x_8000_0000_0000_0000 {
            //576460752303423488 -> wrong number need to change
            0x_7FFF_FFFF & ((0x_8000_0000_u64 >> (N - 1)) as u32) // 1152921504606847000
        } else {
            convert_u64_to_px1bits::<{ N }>(a)
        };
        Self::from_bits(ui_a)
    }
}