1/*
2 * Copyright (c) 2013, Andreas Sandberg
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 *
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above
12 *    copyright notice, this list of conditions and the following
13 *    disclaimer in the documentation and/or other materials provided
14 *    with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
17 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
18 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
19 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
20 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
22 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
23 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
24 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
25 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
27 * OF THE POSSIBILITY OF SUCH DAMAGE.
28 */
29
30#include <fputils/fp80.h>
31#include <fputils/fp64.h>
32#include "fpbits.h"
33
34#include <assert.h>
35#include <stdint.h>
36
37#include <stdio.h>
38
39
40const fp80_t fp80_pinf  = BUILD_FP80(0, 0,               FP80_EXP_SPECIAL);
41const fp80_t fp80_ninf  = BUILD_FP80(1, 0,               FP80_EXP_SPECIAL);
42const fp80_t fp80_qnan  = BUILD_FP80(0, FP80_FRAC_QNAN,  FP80_EXP_SPECIAL);
43const fp80_t fp80_qnani = BUILD_FP80(1, FP80_FRAC_QNANI, FP80_EXP_SPECIAL);
44const fp80_t fp80_snan  = BUILD_FP80(0, FP80_FRAC_SNAN,  FP80_EXP_SPECIAL);
45const fp80_t fp80_nan   = BUILD_FP80(0, FP80_FRAC_QNAN,  FP80_EXP_SPECIAL);
46
47int
48fp80_sgn(fp80_t fp80)
49{
50    return (fp80.repr.se & FP80_SIGN_BIT) ? -1 : 1;
51}
52
53int
54fp80_isspecial(fp80_t fp80)
55{
56    const int exp = FP80_EXP(fp80);
57
58    return exp == FP80_EXP_SPECIAL;
59}
60
61int
62fp80_isinf(fp80_t fp80)
63{
64    const uint64_t frac = FP80_FRAC(fp80);
65
66    return fp80_isspecial(fp80) && frac == 0 ? fp80_sgn(fp80) : 0;
67}
68
69
70int
71fp80_isqnan(fp80_t fp80)
72{
73    const uint64_t frac = FP80_FRAC(fp80);
74
75    return fp80_isspecial(fp80) && (frac & FP80_QNAN_BIT);
76}
77
78int
79fp80_isqnani(fp80_t fp80)
80{
81    const uint64_t frac_low = fp80.repr.fi & (FP80_FRAC_MASK >> 1);
82
83    return fp80_isqnan(fp80) && (fp80.repr.se & FP80_SIGN_BIT) && !frac_low;
84}
85
86int
87fp80_issnan(fp80_t fp80)
88{
89    const uint64_t frac = FP80_FRAC(fp80);
90
91    return fp80_isspecial(fp80) && !(frac & FP80_QNAN_BIT) && frac;
92}
93
94int
95fp80_isfinite(fp80_t fp80)
96{
97    return !fp80_isnan(fp80) && !fp80_isinf(fp80);
98}
99
100int
101fp80_isnan(fp80_t fp80)
102{
103    return fp80_issnan(fp80) || fp80_isqnan(fp80) ? fp80_sgn(fp80) : 0;
104}
105
106int
107fp80_iszero(fp80_t fp80)
108{
109    return fp80.repr.fi == 0 && FP80_EXP(fp80) == 0 ? fp80_sgn(fp80) : 0;
110}
111
112int
113fp80_isnormal(fp80_t fp80)
114{
115    return FP80_EXP(fp80) != 0 && !fp80_isspecial(fp80) ?
116        fp80_sgn(fp80) : 0;
117}
118
119int
120fp80_issubnormal(fp80_t fp80)
121{
122    return FP80_FRAC(fp80) && FP80_EXP(fp80) == 0 ? fp80_sgn(fp80) : 0;
123}
124
125int
126fp80_classify(fp80_t fp80)
127{
128    if (fp80_issubnormal(fp80)) {
129        return FP_SUBNORMAL;
130    } else if (fp80_iszero(fp80)) {
131        return FP_ZERO;
132    } else if (fp80_isinf(fp80)) {
133        return FP_INFINITE;
134    } else if (fp80_isnan(fp80)) {
135        return FP_NAN;
136    } else {
137        assert(fp80_isfinite(fp80));
138        return FP_NORMAL;
139    }
140}
141
142double
143fp80_cvtd(fp80_t fp80)
144{
145    return fp80_cvtfp64(fp80).value;
146}
147
148fp64_t
149fp80_cvtfp64(fp80_t fp80)
150{
151    const int sign = fp80.repr.se & FP80_SIGN_BIT;
152
153    if (!fp80_isspecial(fp80)) {
154        const uint64_t frac = fp80.repr.fi;
155        const int unb_exp = FP80_EXP(fp80) - FP80_EXP_BIAS;
156        const int fp64_exp = unb_exp + FP64_EXP_BIAS;
157        const uint64_t fp64_frac = frac >> (FP80_FRAC_BITS - FP64_FRAC_BITS);
158
159        if (fp64_exp > 0 && fp64_exp < FP64_EXP_SPECIAL) {
160            /* These numbers fall in the range of what we can express
161             * as normals */
162            return build_fp64(sign, fp64_frac, fp64_exp);
163        } else if (fp64_exp <= 0) {
164            uint64_t fp64_denormal_frac = fp64_frac >> (-fp64_exp);
165            /* Generate a denormal or zero */
166            return build_fp64(sign, fp64_denormal_frac, 0);
167        } else {
168            /* Infinity */
169            return build_fp64(sign, 0, FP64_EXP_SPECIAL);
170        }
171    } else {
172        if (fp80_isinf(fp80)) {
173            return build_fp64(sign, 0, FP64_EXP_SPECIAL);
174        } else if (fp80_issnan(fp80)) {
175            return fp80_sgn(fp80) > 0 ? fp64_snan : fp64_nsnan;
176        } else if (fp80_isqnani(fp80)) {
177            return fp64_qnani;
178        } else {
179            assert(fp80_isqnan(fp80));
180            return fp80_sgn(fp80) > 0 ? fp64_qnan : fp64_nqnan;
181        }
182    }
183}
184
185fp80_t
186fp80_cvfd(double value)
187{
188    const fp64_t fp64 = { .value = value };
189
190    return fp80_cvffp64(fp64);
191}
192
193fp80_t
194fp80_cvffp64(fp64_t fp64)
195{
196    const uint64_t frac = FP64_FRAC(fp64);
197    const unsigned exp = FP64_EXP(fp64);
198    const int unb_exp = exp - FP64_EXP_BIAS;
199    const uint64_t fp80_frac = frac << (FP80_FRAC_BITS - FP64_FRAC_BITS);
200
201    if (exp != 0) {
202        // Normal, inf, nan
203        const unsigned fp80_exp = exp == FP64_EXP_SPECIAL ?
204            FP80_EXP_SPECIAL : (unb_exp + FP80_EXP_BIAS);
205        const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT,
206                                       fp80_frac, fp80_exp);
207        return fp80;
208    } else if (exp == 0 && frac == 0) {
209        // Zero
210        const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT, 0, 0);
211        return fp80;
212    } else {
213        // Denormal
214        uint64_t fp80_fi = fp80_frac;
215        int shift_amt = 0;
216        while (!(fp80_fi & FP80_INT_BIT)) {
217            fp80_fi <<= 1;
218            ++shift_amt;
219        }
220        const unsigned fp80_exp = (unb_exp - shift_amt) + FP80_EXP_BIAS;
221        const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT,
222                                       fp80_fi, fp80_exp);
223        return fp80;
224    }
225}
226
227void
228fp80_debug_dump(FILE *fout, fp80_t fp80)
229{
230    fprintf(fout, "sgn: %i, int: %i, frac: 0x%llx, exp: 0x%x (%i)\n",
231            fp80_sgn(fp80), !!(fp80.repr.fi & FP80_INT_BIT), FP80_FRAC(fp80),
232            FP80_EXP(fp80), FP80_EXP(fp80) - FP80_EXP_BIAS);
233}
234