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 
f64_rem(float64_t a,float64_t b)45 float64_t f64_rem( float64_t a, float64_t b )
46 {
47     union ui64_f64 uA;
48     uint_fast64_t uiA;
49     bool signA;
50     int_fast16_t expA;
51     uint_fast64_t sigA;
52     union ui64_f64 uB;
53     uint_fast64_t uiB;
54     int_fast16_t expB;
55     uint_fast64_t sigB;
56     struct exp16_sig64 normExpSig;
57     uint64_t rem;
58     int_fast16_t expDiff;
59     uint32_t q, recip32;
60     uint_fast64_t q64;
61     uint64_t altRem, meanRem;
62     bool signRem;
63     uint_fast64_t uiZ;
64     union ui64_f64 uZ;
65 
66     /*------------------------------------------------------------------------
67     *------------------------------------------------------------------------*/
68     uA.f = a;
69     uiA = uA.ui;
70     signA = signF64UI( uiA );
71     expA  = expF64UI( uiA );
72     sigA  = fracF64UI( uiA );
73     uB.f = b;
74     uiB = uB.ui;
75     expB = expF64UI( uiB );
76     sigB = fracF64UI( uiB );
77     /*------------------------------------------------------------------------
78     *------------------------------------------------------------------------*/
79     if ( expA == 0x7FF ) {
80         if ( sigA || ((expB == 0x7FF) && sigB) ) goto propagateNaN;
81         goto invalid;
82     }
83     if ( expB == 0x7FF ) {
84         if ( sigB ) goto propagateNaN;
85         return a;
86     }
87     /*------------------------------------------------------------------------
88     *------------------------------------------------------------------------*/
89     if ( expA < expB - 1 ) return a;
90     /*------------------------------------------------------------------------
91     *------------------------------------------------------------------------*/
92     if ( ! expB ) {
93         if ( ! sigB ) goto invalid;
94         normExpSig = softfloat_normSubnormalF64Sig( sigB );
95         expB = normExpSig.exp;
96         sigB = normExpSig.sig;
97     }
98     if ( ! expA ) {
99         if ( ! sigA ) return a;
100         normExpSig = softfloat_normSubnormalF64Sig( sigA );
101         expA = normExpSig.exp;
102         sigA = normExpSig.sig;
103     }
104     /*------------------------------------------------------------------------
105     *------------------------------------------------------------------------*/
106     rem = sigA | UINT64_C( 0x0010000000000000 );
107     sigB |= UINT64_C( 0x0010000000000000 );
108     expDiff = expA - expB;
109     if ( expDiff < 1 ) {
110         if ( expDiff < -1 ) return a;
111         sigB <<= 9;
112         if ( expDiff ) {
113             rem <<= 8;
114             q = 0;
115         } else {
116             rem <<= 9;
117             q = (sigB <= rem);
118             if ( q ) rem -= sigB;
119         }
120     } else {
121         recip32 = softfloat_approxRecip32_1( sigB>>21 );
122         /*--------------------------------------------------------------------
123         | Changing the shift of `rem' here requires also changing the initial
124         | subtraction from `expDiff'.
125         *--------------------------------------------------------------------*/
126         rem <<= 9;
127         expDiff -= 30;
128         /*--------------------------------------------------------------------
129         | The scale of `sigB' affects how many bits are obtained during each
130         | cycle of the loop.  Currently this is 29 bits per loop iteration,
131         | the maximum possible.
132         *--------------------------------------------------------------------*/
133         sigB <<= 9;
134         for (;;) {
135             q64 = (uint32_t) (rem>>32) * (uint_fast64_t) recip32;
136             if ( expDiff < 0 ) break;
137             q = (q64 + 0x80000000)>>32;
138 #ifdef SOFTFLOAT_FAST_INT64
139             rem <<= 29;
140 #else
141             rem = (uint_fast64_t) (uint32_t) (rem>>3)<<32;
142 #endif
143             rem -= q * (uint64_t) sigB;
144             if ( rem & UINT64_C( 0x8000000000000000 ) ) rem += sigB;
145             expDiff -= 29;
146         }
147         /*--------------------------------------------------------------------
148         | (`expDiff' cannot be less than -29 here.)
149         *--------------------------------------------------------------------*/
150         q = (uint32_t) (q64>>32)>>(~expDiff & 31);
151         rem = (rem<<(expDiff + 30)) - q * (uint64_t) sigB;
152         if ( rem & UINT64_C( 0x8000000000000000 ) ) {
153             altRem = rem + sigB;
154             goto selectRem;
155         }
156     }
157     /*------------------------------------------------------------------------
158     *------------------------------------------------------------------------*/
159     do {
160         altRem = rem;
161         ++q;
162         rem -= sigB;
163     } while ( ! (rem & UINT64_C( 0x8000000000000000 )) );
164  selectRem:
165     meanRem = rem + altRem;
166     if (
167         (meanRem & UINT64_C( 0x8000000000000000 )) || (! meanRem && (q & 1))
168     ) {
169         rem = altRem;
170     }
171     signRem = signA;
172     if ( rem & UINT64_C( 0x8000000000000000 ) ) {
173         signRem = ! signRem;
174         rem = -rem;
175     }
176     return softfloat_normRoundPackToF64( signRem, expB, rem );
177     /*------------------------------------------------------------------------
178     *------------------------------------------------------------------------*/
179  propagateNaN:
180     uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
181     goto uiZ;
182  invalid:
183     softfloat_raiseFlags( softfloat_flag_invalid );
184     uiZ = defaultNaNF64UI;
185  uiZ:
186     uZ.ui = uiZ;
187     return uZ.f;
188 
189 }
190 
191