1 
2 /*============================================================================
3 
4 This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
5 Package, Release 3e, by John R. Hauser.
6 
7 Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 The Regents of the
8 University of California.  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_sqrt(extFloat80_t a)44 extFloat80_t extF80_sqrt( extFloat80_t a )
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     struct uint128 uiZ;
53     uint_fast16_t uiZ64;
54     uint_fast64_t uiZ0;
55     struct exp32_sig64 normExpSig;
56     int_fast32_t expZ;
57     uint_fast32_t sig32A, recipSqrt32, sig32Z;
58     struct uint128 rem;
59     uint_fast64_t q, x64, sigZ;
60     struct uint128 y, term;
61     uint_fast64_t sigZExtra;
62     union { struct extFloat80M s; extFloat80_t f; } uZ;
63 
64     /*------------------------------------------------------------------------
65     *------------------------------------------------------------------------*/
66     uA.f = a;
67     uiA64 = uA.s.signExp;
68     uiA0  = uA.s.signif;
69     signA = signExtF80UI64( uiA64 );
70     expA  = expExtF80UI64( uiA64 );
71     sigA  = uiA0;
72     /*------------------------------------------------------------------------
73     *------------------------------------------------------------------------*/
74     if ( expA == 0x7FFF ) {
75         if ( sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) {
76             uiZ = softfloat_propagateNaNExtF80UI( uiA64, uiA0, 0, 0 );
77             uiZ64 = uiZ.v64;
78             uiZ0  = uiZ.v0;
79             goto uiZ;
80         }
81         if ( ! signA ) return a;
82         goto invalid;
83     }
84     /*------------------------------------------------------------------------
85     *------------------------------------------------------------------------*/
86     if ( signA ) {
87         if ( ! sigA ) goto zero;
88         goto invalid;
89     }
90     /*------------------------------------------------------------------------
91     *------------------------------------------------------------------------*/
92     if ( ! expA ) expA = 1;
93     if ( ! (sigA & UINT64_C( 0x8000000000000000 )) ) {
94         if ( ! sigA ) goto zero;
95         normExpSig = softfloat_normSubnormalExtF80Sig( sigA );
96         expA += normExpSig.exp;
97         sigA = normExpSig.sig;
98     }
99     /*------------------------------------------------------------------------
100     | (`sig32Z' is guaranteed to be a lower bound on the square root of
101     | `sig32A', which makes `sig32Z' also a lower bound on the square root of
102     | `sigA'.)
103     *------------------------------------------------------------------------*/
104     expZ = ((expA - 0x3FFF)>>1) + 0x3FFF;
105     expA &= 1;
106     sig32A = sigA>>32;
107     recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
108     sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
109     if ( expA ) {
110         sig32Z >>= 1;
111         rem = softfloat_shortShiftLeft128( 0, sigA, 61 );
112     } else {
113         rem = softfloat_shortShiftLeft128( 0, sigA, 62 );
114     }
115     rem.v64 -= (uint_fast64_t) sig32Z * sig32Z;
116     /*------------------------------------------------------------------------
117     *------------------------------------------------------------------------*/
118     q = ((uint32_t) (rem.v64>>2) * (uint_fast64_t) recipSqrt32)>>32;
119     x64 = (uint_fast64_t) sig32Z<<32;
120     sigZ = x64 + (q<<3);
121     y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
122     /*------------------------------------------------------------------------
123     | (Repeating this loop is a rare occurrence.)
124     *------------------------------------------------------------------------*/
125     for (;;) {
126         term = softfloat_mul64ByShifted32To128( x64 + sigZ, q );
127         rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 );
128         if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break;
129         --q;
130         sigZ -= 1<<3;
131     }
132     /*------------------------------------------------------------------------
133     *------------------------------------------------------------------------*/
134     q = (((rem.v64>>2) * recipSqrt32)>>32) + 2;
135     x64 = sigZ;
136     sigZ = (sigZ<<1) + (q>>25);
137     sigZExtra = (uint64_t) (q<<39);
138     /*------------------------------------------------------------------------
139     *------------------------------------------------------------------------*/
140     if ( (q & 0xFFFFFF) <= 2 ) {
141         q &= ~(uint_fast64_t) 0xFFFF;
142         sigZExtra = (uint64_t) (q<<39);
143         term = softfloat_mul64ByShifted32To128( x64 + (q>>27), q );
144         x64 = (uint32_t) (q<<5) * (uint_fast64_t) (uint32_t) q;
145         term = softfloat_add128( term.v64, term.v0, 0, x64 );
146         rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 28 );
147         rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
148         if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
149             if ( ! sigZExtra ) --sigZ;
150             --sigZExtra;
151         } else {
152             if ( rem.v64 | rem.v0 ) sigZExtra |= 1;
153         }
154     }
155     return
156         softfloat_roundPackToExtF80(
157             0, expZ, sigZ, sigZExtra, extF80_roundingPrecision );
158     /*------------------------------------------------------------------------
159     *------------------------------------------------------------------------*/
160  invalid:
161     softfloat_raiseFlags( softfloat_flag_invalid );
162     uiZ64 = defaultNaNExtF80UI64;
163     uiZ0  = defaultNaNExtF80UI0;
164     goto uiZ;
165     /*------------------------------------------------------------------------
166     *------------------------------------------------------------------------*/
167  zero:
168     uiZ64 = packToExtF80UI64( signA, 0 );
169     uiZ0  = 0;
170  uiZ:
171     uZ.s.signExp = uiZ64;
172     uZ.s.signif  = uiZ0;
173     return uZ.f;
174 
175 }
176 
177