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, 2015, 2017 The Regents of the University of
8California.  All 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
44#ifdef SOFTFLOAT_FAST_INT64
45
46void extF80M_sqrt( const extFloat80_t *aPtr, extFloat80_t *zPtr )
47{
48
49    *zPtr = extF80_sqrt( *aPtr );
50
51}
52
53#else
54
55void extF80M_sqrt( const extFloat80_t *aPtr, extFloat80_t *zPtr )
56{
57    const struct extFloat80M *aSPtr;
58    struct extFloat80M *zSPtr;
59    uint_fast16_t uiA64, signUI64;
60    int32_t expA;
61    uint64_t rem64;
62    int32_t expZ;
63    uint32_t rem96[3], sig32A, recipSqrt32, sig32Z, q;
64    uint64_t sig64Z, x64;
65    uint32_t rem32, term[4], rem[4], extSigZ[3];
66
67    /*------------------------------------------------------------------------
68    *------------------------------------------------------------------------*/
69    aSPtr = (const struct extFloat80M *) aPtr;
70    zSPtr = (struct extFloat80M *) zPtr;
71    /*------------------------------------------------------------------------
72    *------------------------------------------------------------------------*/
73    uiA64 = aSPtr->signExp;
74    signUI64 = uiA64 & packToExtF80UI64( 1, 0 );
75    expA = expExtF80UI64( uiA64 );
76    rem64 = aSPtr->signif;
77    /*------------------------------------------------------------------------
78    *------------------------------------------------------------------------*/
79    if ( expA == 0x7FFF ) {
80        if ( rem64 & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) {
81            softfloat_propagateNaNExtF80M( aSPtr, 0, zSPtr );
82            return;
83        }
84        if ( signUI64 ) goto invalid;
85        rem64 = UINT64_C( 0x8000000000000000 );
86        goto copyA;
87    }
88    /*------------------------------------------------------------------------
89    *------------------------------------------------------------------------*/
90    if ( ! expA ) expA = 1;
91    if ( ! (rem64 & UINT64_C( 0x8000000000000000 )) ) {
92        if ( ! rem64 ) {
93            uiA64 = signUI64;
94            goto copyA;
95        }
96        expA += softfloat_normExtF80SigM( &rem64 );
97    }
98    if ( signUI64 ) goto invalid;
99    /*------------------------------------------------------------------------
100    *------------------------------------------------------------------------*/
101    expZ = ((expA - 0x3FFF)>>1) + 0x3FFF;
102    expA &= 1;
103    softfloat_shortShiftLeft64To96M( rem64, 30 - expA, rem96 );
104    sig32A = rem64>>32;
105    recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
106    sig32Z = ((uint64_t) sig32A * recipSqrt32)>>32;
107    if ( expA ) sig32Z >>= 1;
108    rem64 =
109        ((uint64_t) rem96[indexWord( 3, 2 )]<<32 | rem96[indexWord( 3, 1 )])
110            - (uint64_t) sig32Z * sig32Z;
111    rem96[indexWord( 3, 2 )] = rem64>>32;
112    rem96[indexWord( 3, 1 )] = rem64;
113    /*------------------------------------------------------------------------
114    *------------------------------------------------------------------------*/
115    q = ((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32;
116    sig64Z = ((uint64_t) sig32Z<<32) + ((uint64_t) q<<3);
117    term[indexWord( 3, 2 )] = 0;
118    /*------------------------------------------------------------------------
119    | (Repeating this loop is a rare occurrence.)
120    *------------------------------------------------------------------------*/
121    for (;;) {
122        x64 = ((uint64_t) sig32Z<<32) + sig64Z;
123        term[indexWord( 3, 1 )] = x64>>32;
124        term[indexWord( 3, 0 )] = x64;
125        softfloat_remStep96MBy32(
126            rem96, 29, term, q, &rem[indexMultiwordHi( 4, 3 )] );
127        rem32 = rem[indexWord( 4, 3 )];
128        if ( ! (rem32 & 0x80000000) ) break;
129        --q;
130        sig64Z -= 1<<3;
131    }
132    rem64 = (uint64_t) rem32<<32 | rem[indexWord( 4, 2 )];
133    /*------------------------------------------------------------------------
134    *------------------------------------------------------------------------*/
135    q = (((uint32_t) (rem64>>2) * (uint64_t) recipSqrt32)>>32) + 2;
136    if ( rem64>>34 ) q += recipSqrt32;
137    x64 = (uint64_t) q<<7;
138    extSigZ[indexWord( 3, 0 )] = x64;
139    x64 = (sig64Z<<1) + (x64>>32);
140    extSigZ[indexWord( 3, 2 )] = x64>>32;
141    extSigZ[indexWord( 3, 1 )] = x64;
142    /*------------------------------------------------------------------------
143    *------------------------------------------------------------------------*/
144    if ( (q & 0xFFFFFF) <= 2 ) {
145        q &= ~(uint32_t) 0xFFFF;
146        extSigZ[indexWordLo( 3 )] = q<<7;
147        x64 = sig64Z + (q>>27);
148        term[indexWord( 4, 3 )] = 0;
149        term[indexWord( 4, 2 )] = x64>>32;
150        term[indexWord( 4, 1 )] = x64;
151        term[indexWord( 4, 0 )] = q<<5;
152        rem[indexWord( 4, 0 )] = 0;
153        softfloat_remStep128MBy32( rem, 28, term, q, rem );
154        q = rem[indexWordHi( 4 )];
155        if ( q & 0x80000000 ) {
156            softfloat_sub1X96M( extSigZ );
157        } else {
158            if ( q || rem[indexWord( 4, 1 )] || rem[indexWord( 4, 2 )] ) {
159                extSigZ[indexWordLo( 3 )] |= 1;
160            }
161        }
162    }
163    softfloat_roundPackMToExtF80M(
164        0, expZ, extSigZ, extF80_roundingPrecision, zSPtr );
165    return;
166    /*------------------------------------------------------------------------
167    *------------------------------------------------------------------------*/
168 invalid:
169    softfloat_invalidExtF80M( zSPtr );
170    return;
171    /*------------------------------------------------------------------------
172    *------------------------------------------------------------------------*/
173 copyA:
174    zSPtr->signExp = uiA64;
175    zSPtr->signif  = rem64;
176
177}
178
179#endif
180
181