1
2/*============================================================================
3
4This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
5Package, Release 3e, by John R. Hauser.
6
7Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
8All rights reserved.
9
10Redistribution and use in source and binary forms, with or without
11modification, 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
24THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
25EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
26WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
27DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
28DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
29(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
30LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
31ON 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
33SOFTWARE, 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
44float64_t f64_rem( float64_t a, float64_t b )
45{
46    union ui64_f64 uA;
47    uint_fast64_t uiA;
48    bool signA;
49    int_fast16_t expA;
50    uint_fast64_t sigA;
51    union ui64_f64 uB;
52    uint_fast64_t uiB;
53    int_fast16_t expB;
54    uint_fast64_t sigB;
55    struct exp16_sig64 normExpSig;
56    uint64_t rem;
57    int_fast16_t expDiff;
58    uint32_t q, recip32;
59    uint_fast64_t q64;
60    uint64_t altRem, meanRem;
61    bool signRem;
62    uint_fast64_t uiZ;
63    union ui64_f64 uZ;
64
65    /*------------------------------------------------------------------------
66    *------------------------------------------------------------------------*/
67    uA.f = a;
68    uiA = uA.ui;
69    signA = signF64UI( uiA );
70    expA  = expF64UI( uiA );
71    sigA  = fracF64UI( uiA );
72    uB.f = b;
73    uiB = uB.ui;
74    expB = expF64UI( uiB );
75    sigB = fracF64UI( uiB );
76    /*------------------------------------------------------------------------
77    *------------------------------------------------------------------------*/
78    if ( expA == 0x7FF ) {
79        if ( sigA || ((expB == 0x7FF) && sigB) ) goto propagateNaN;
80        goto invalid;
81    }
82    if ( expB == 0x7FF ) {
83        if ( sigB ) goto propagateNaN;
84        return a;
85    }
86    /*------------------------------------------------------------------------
87    *------------------------------------------------------------------------*/
88    if ( expA < expB - 1 ) return a;
89    /*------------------------------------------------------------------------
90    *------------------------------------------------------------------------*/
91    if ( ! expB ) {
92        if ( ! sigB ) goto invalid;
93        normExpSig = softfloat_normSubnormalF64Sig( sigB );
94        expB = normExpSig.exp;
95        sigB = normExpSig.sig;
96    }
97    if ( ! expA ) {
98        if ( ! sigA ) return a;
99        normExpSig = softfloat_normSubnormalF64Sig( sigA );
100        expA = normExpSig.exp;
101        sigA = normExpSig.sig;
102    }
103    /*------------------------------------------------------------------------
104    *------------------------------------------------------------------------*/
105    rem = sigA | UINT64_C( 0x0010000000000000 );
106    sigB |= UINT64_C( 0x0010000000000000 );
107    expDiff = expA - expB;
108    if ( expDiff < 1 ) {
109        if ( expDiff < -1 ) return a;
110        sigB <<= 9;
111        if ( expDiff ) {
112            rem <<= 8;
113            q = 0;
114        } else {
115            rem <<= 9;
116            q = (sigB <= rem);
117            if ( q ) rem -= sigB;
118        }
119    } else {
120        recip32 = softfloat_approxRecip32_1( sigB>>21 );
121        /*--------------------------------------------------------------------
122        | Changing the shift of `rem' here requires also changing the initial
123        | subtraction from `expDiff'.
124        *--------------------------------------------------------------------*/
125        rem <<= 9;
126        expDiff -= 30;
127        /*--------------------------------------------------------------------
128        | The scale of `sigB' affects how many bits are obtained during each
129        | cycle of the loop.  Currently this is 29 bits per loop iteration,
130        | the maximum possible.
131        *--------------------------------------------------------------------*/
132        sigB <<= 9;
133        for (;;) {
134            q64 = (uint32_t) (rem>>32) * (uint_fast64_t) recip32;
135            if ( expDiff < 0 ) break;
136            q = (q64 + 0x80000000)>>32;
137#ifdef SOFTFLOAT_FAST_INT64
138            rem <<= 29;
139#else
140            rem = (uint_fast64_t) (uint32_t) (rem>>3)<<32;
141#endif
142            rem -= q * (uint64_t) sigB;
143            if ( rem & UINT64_C( 0x8000000000000000 ) ) rem += sigB;
144            expDiff -= 29;
145        }
146        /*--------------------------------------------------------------------
147        | (`expDiff' cannot be less than -29 here.)
148        *--------------------------------------------------------------------*/
149        q = (uint32_t) (q64>>32)>>(~expDiff & 31);
150        rem = (rem<<(expDiff + 30)) - q * (uint64_t) sigB;
151        if ( rem & UINT64_C( 0x8000000000000000 ) ) {
152            altRem = rem + sigB;
153            goto selectRem;
154        }
155    }
156    /*------------------------------------------------------------------------
157    *------------------------------------------------------------------------*/
158    do {
159        altRem = rem;
160        ++q;
161        rem -= sigB;
162    } while ( ! (rem & UINT64_C( 0x8000000000000000 )) );
163 selectRem:
164    meanRem = rem + altRem;
165    if (
166        (meanRem & UINT64_C( 0x8000000000000000 )) || (! meanRem && (q & 1))
167    ) {
168        rem = altRem;
169    }
170    signRem = signA;
171    if ( rem & UINT64_C( 0x8000000000000000 ) ) {
172        signRem = ! signRem;
173        rem = -rem;
174    }
175    return softfloat_normRoundPackToF64( signRem, expB, rem );
176    /*------------------------------------------------------------------------
177    *------------------------------------------------------------------------*/
178 propagateNaN:
179    uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
180    goto uiZ;
181 invalid:
182    softfloat_raiseFlags( softfloat_flag_invalid );
183    uiZ = defaultNaNF64UI;
184 uiZ:
185    uZ.ui = uiZ;
186    return uZ.f;
187
188}
189
190