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