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, 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
44float64_t f64_sqrt( float64_t a )
45{
46    union ui64_f64 uA;
47    uint_fast64_t uiA;
48    bool signA;
49    int_fast16_t expA;
50    uint_fast64_t sigA, uiZ;
51    struct exp16_sig64 normExpSig;
52    int_fast16_t expZ;
53    uint32_t sig32A, recipSqrt32, sig32Z;
54    uint_fast64_t rem;
55    uint32_t q;
56    uint_fast64_t sigZ, shiftedSigZ;
57    union ui64_f64 uZ;
58
59    /*------------------------------------------------------------------------
60    *------------------------------------------------------------------------*/
61    uA.f = a;
62    uiA = uA.ui;
63    signA = signF64UI( uiA );
64    expA  = expF64UI( uiA );
65    sigA  = fracF64UI( uiA );
66    /*------------------------------------------------------------------------
67    *------------------------------------------------------------------------*/
68    if ( expA == 0x7FF ) {
69        if ( sigA ) {
70            uiZ = softfloat_propagateNaNF64UI( uiA, 0 );
71            goto uiZ;
72        }
73        if ( ! signA ) return a;
74        goto invalid;
75    }
76    /*------------------------------------------------------------------------
77    *------------------------------------------------------------------------*/
78    if ( signA ) {
79        if ( ! (expA | sigA) ) return a;
80        goto invalid;
81    }
82    /*------------------------------------------------------------------------
83    *------------------------------------------------------------------------*/
84    if ( ! expA ) {
85        if ( ! sigA ) return a;
86        normExpSig = softfloat_normSubnormalF64Sig( sigA );
87        expA = normExpSig.exp;
88        sigA = normExpSig.sig;
89    }
90    /*------------------------------------------------------------------------
91    | (`sig32Z' is guaranteed to be a lower bound on the square root of
92    | `sig32A', which makes `sig32Z' also a lower bound on the square root of
93    | `sigA'.)
94    *------------------------------------------------------------------------*/
95    expZ = ((expA - 0x3FF)>>1) + 0x3FE;
96    expA &= 1;
97    sigA |= UINT64_C( 0x0010000000000000 );
98    sig32A = sigA>>21;
99    recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
100    sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
101    if ( expA ) {
102        sigA <<= 8;
103        sig32Z >>= 1;
104    } else {
105        sigA <<= 9;
106    }
107    rem = sigA - (uint_fast64_t) sig32Z * sig32Z;
108    q = ((uint32_t) (rem>>2) * (uint_fast64_t) recipSqrt32)>>32;
109    sigZ = ((uint_fast64_t) sig32Z<<32 | 1<<5) + ((uint_fast64_t) q<<3);
110    /*------------------------------------------------------------------------
111    *------------------------------------------------------------------------*/
112    if ( (sigZ & 0x1FF) < 0x22 ) {
113        sigZ &= ~(uint_fast64_t) 0x3F;
114        shiftedSigZ = sigZ>>6;
115        rem = (sigA<<52) - shiftedSigZ * shiftedSigZ;
116        if ( rem & UINT64_C( 0x8000000000000000 ) ) {
117            --sigZ;
118        } else {
119            if ( rem ) sigZ |= 1;
120        }
121    }
122    return softfloat_roundPackToF64( 0, expZ, sigZ );
123    /*------------------------------------------------------------------------
124    *------------------------------------------------------------------------*/
125 invalid:
126    softfloat_raiseFlags( softfloat_flag_invalid );
127    uiZ = defaultNaNF64UI;
128 uiZ:
129    uZ.ui = uiZ;
130    return uZ.f;
131
132}
133
134