1 // SPDX-License-Identifier: BSD-3-Clause
2 
3 /*============================================================================
4 
5 This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
6 Package, Release 3a, by John R. Hauser.
7 
8 Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
9 All rights reserved.
10 
11 Redistribution and use in source and binary forms, with or without
12 modification, are permitted provided that the following conditions are met:
13 
14  1. Redistributions of source code must retain the above copyright notice,
15     this list of conditions, and the following disclaimer.
16 
17  2. Redistributions in binary form must reproduce the above copyright notice,
18     this list of conditions, and the following disclaimer in the documentation
19     and/or other materials provided with the distribution.
20 
21  3. Neither the name of the University nor the names of its contributors may
22     be used to endorse or promote products derived from this software without
23     specific prior written permission.
24 
25 THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
26 EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
27 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
28 DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
29 DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
30 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
31 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
32 ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
33 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
34 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35 
36 =============================================================================*/
37 
38 #include <stdbool.h>
39 #include <stdint.h>
40 #include "platform.h"
41 #include "internals.h"
42 #include "specialize.h"
43 #include "softfloat.h"
44 
extF80_rem(extFloat80_t a,extFloat80_t b)45 extFloat80_t extF80_rem( extFloat80_t a, extFloat80_t b )
46 {
47     union { struct extFloat80M s; extFloat80_t f; } uA;
48     uint_fast16_t uiA64;
49     uint_fast64_t uiA0;
50     bool signA;
51     int_fast32_t expA;
52     uint_fast64_t sigA;
53     union { struct extFloat80M s; extFloat80_t f; } uB;
54     uint_fast16_t uiB64;
55     uint_fast64_t uiB0;
56     bool signB;
57     int_fast32_t expB;
58     uint_fast64_t sigB;
59     struct exp32_sig64 normExpSig;
60     int_fast32_t expDiff;
61     struct uint128 rem, shiftedSigB;
62     uint_fast32_t q, recip32;
63     uint_fast64_t q64;
64     struct uint128 term, altRem, meanRem;
65     bool signRem;
66     struct uint128 uiZ;
67     uint_fast16_t uiZ64;
68     uint_fast64_t uiZ0;
69     union { struct extFloat80M s; extFloat80_t f; } uZ;
70 
71     /*------------------------------------------------------------------------
72     *------------------------------------------------------------------------*/
73     uA.f = a;
74     uiA64 = uA.s.signExp;
75     uiA0  = uA.s.signif;
76     signA = signExtF80UI64( uiA64 );
77     expA  = expExtF80UI64( uiA64 );
78     sigA  = uiA0;
79     uB.f = b;
80     uiB64 = uB.s.signExp;
81     uiB0  = uB.s.signif;
82     signB = signExtF80UI64( uiB64 );
83     expB  = expExtF80UI64( uiB64 );
84     sigB  = uiB0;
85     /*------------------------------------------------------------------------
86     *------------------------------------------------------------------------*/
87     if ( expA == 0x7FFF ) {
88         if (
89                (sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF ))
90             || ((expB == 0x7FFF) && (sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF )))
91         ) {
92             goto propagateNaN;
93         }
94         goto invalid;
95     }
96     if ( expB == 0x7FFF ) {
97         if ( sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) goto propagateNaN;
98         /*--------------------------------------------------------------------
99         | Argument b is an infinity.  Doubling `expB' is an easy way to ensure
100         | that `expDiff' later is less than -1, which will result in returning
101         | a canonicalized version of argument a.
102         *--------------------------------------------------------------------*/
103         expB += expB;
104     }
105     /*------------------------------------------------------------------------
106     *------------------------------------------------------------------------*/
107     if ( ! expB ) expB = 1;
108     if ( ! (sigB & UINT64_C( 0x8000000000000000 )) ) {
109         if ( ! sigB ) goto invalid;
110         normExpSig = softfloat_normSubnormalExtF80Sig( sigB );
111         expB += normExpSig.exp;
112         sigB = normExpSig.sig;
113     }
114     if ( ! expA ) expA = 1;
115     if ( ! (sigA & UINT64_C( 0x8000000000000000 )) ) {
116         if ( ! sigA ) {
117             expA = 0;
118             goto copyA;
119         }
120         normExpSig = softfloat_normSubnormalExtF80Sig( sigA );
121         expA += normExpSig.exp;
122         sigA = normExpSig.sig;
123     }
124     /*------------------------------------------------------------------------
125     *------------------------------------------------------------------------*/
126     expDiff = expA - expB;
127     if ( expDiff < -1 ) goto copyA;
128     rem = softfloat_shortShiftLeft128( 0, sigA, 32 );
129     shiftedSigB = softfloat_shortShiftLeft128( 0, sigB, 32 );
130     if ( expDiff < 1 ) {
131         if ( expDiff ) {
132             --expB;
133             shiftedSigB = softfloat_shortShiftLeft128( 0, sigB, 33 );
134             q = 0;
135         } else {
136             q = (sigB <= sigA);
137             if ( q ) {
138                 rem =
139                     softfloat_sub128(
140                         rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 );
141             }
142         }
143     } else {
144         recip32 = softfloat_approxRecip32_1( sigB>>32 );
145         expDiff -= 30;
146         for (;;) {
147             q64 = (uint_fast64_t) (uint32_t) (rem.v64>>2) * recip32;
148             if ( expDiff < 0 ) break;
149             q = (q64 + 0x80000000)>>32;
150             rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
151             term = softfloat_mul64ByShifted32To128( sigB, q );
152             rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
153             if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
154                 rem =
155                     softfloat_add128(
156                         rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 );
157             }
158             expDiff -= 29;
159         }
160         /*--------------------------------------------------------------------
161         | (`expDiff' cannot be less than -29 here.)
162         *--------------------------------------------------------------------*/
163         q = (uint32_t) (q64>>32)>>(~expDiff & 31);
164         rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, expDiff + 30 );
165         term = softfloat_mul64ByShifted32To128( sigB, q );
166         rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
167         if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
168             altRem =
169                 softfloat_add128(
170                     rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 );
171             goto selectRem;
172         }
173     }
174     /*------------------------------------------------------------------------
175     *------------------------------------------------------------------------*/
176     do {
177         altRem = rem;
178         ++q;
179         rem =
180             softfloat_sub128(
181                 rem.v64, rem.v0, shiftedSigB.v64, shiftedSigB.v0 );
182     } while ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) );
183  selectRem:
184     meanRem = softfloat_add128( rem.v64, rem.v0, altRem.v64, altRem.v0 );
185     if (
186         (meanRem.v64 & UINT64_C( 0x8000000000000000 ))
187             || (! (meanRem.v64 | meanRem.v0) && (q & 1))
188     ) {
189         rem = altRem;
190     }
191     signRem = signA;
192     if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
193         signRem = ! signRem;
194         rem = softfloat_sub128( 0, 0, rem.v64, rem.v0 );
195     }
196     return
197         softfloat_normRoundPackToExtF80(
198             signRem, expB + 32, rem.v64, rem.v0, 80 );
199     /*------------------------------------------------------------------------
200     *------------------------------------------------------------------------*/
201  propagateNaN:
202     uiZ = softfloat_propagateNaNExtF80UI( uiA64, uiA0, uiB64, uiB0 );
203     uiZ64 = uiZ.v64;
204     uiZ0  = uiZ.v0;
205     goto uiZ;
206     /*------------------------------------------------------------------------
207     *------------------------------------------------------------------------*/
208  invalid:
209     softfloat_raiseFlags( softfloat_flag_invalid );
210     uiZ64 = defaultNaNExtF80UI64;
211     uiZ0  = defaultNaNExtF80UI0;
212     goto uiZ;
213     /*------------------------------------------------------------------------
214     *------------------------------------------------------------------------*/
215  copyA:
216     if ( expA < 1 ) {
217         sigA >>= 1 - expA;
218         expA = 0;
219     }
220     uiZ64 = packToExtF80UI64( signA, expA );
221     uiZ0  = sigA;
222  uiZ:
223     uZ.s.signExp = uiZ64;
224     uZ.s.signif  = uiZ0;
225     return uZ.f;
226 
227 }
228 
229