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, 2016, 2017 The Regents of the
8University of California.  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
44extFloat80_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