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 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
44float16_t f16_rem( float16_t a, float16_t b )
45{
46    union ui16_f16 uA;
47    uint_fast16_t uiA;
48    bool signA;
49    int_fast8_t expA;
50    uint_fast16_t sigA;
51    union ui16_f16 uB;
52    uint_fast16_t uiB;
53    int_fast8_t expB;
54    uint_fast16_t sigB;
55    struct exp8_sig16 normExpSig;
56    uint16_t rem;
57    int_fast8_t expDiff;
58    uint_fast16_t q;
59    uint32_t recip32, q32;
60    uint16_t altRem, meanRem;
61    bool signRem;
62    uint_fast16_t uiZ;
63    union ui16_f16 uZ;
64
65    /*------------------------------------------------------------------------
66    *------------------------------------------------------------------------*/
67    uA.f = a;
68    uiA = uA.ui;
69    signA = signF16UI( uiA );
70    expA  = expF16UI( uiA );
71    sigA  = fracF16UI( uiA );
72    uB.f = b;
73    uiB = uB.ui;
74    expB = expF16UI( uiB );
75    sigB = fracF16UI( uiB );
76    /*------------------------------------------------------------------------
77    *------------------------------------------------------------------------*/
78    if ( expA == 0x1F ) {
79        if ( sigA || ((expB == 0x1F) && sigB) ) goto propagateNaN;
80        goto invalid;
81    }
82    if ( expB == 0x1F ) {
83        if ( sigB ) goto propagateNaN;
84        return a;
85    }
86    /*------------------------------------------------------------------------
87    *------------------------------------------------------------------------*/
88    if ( ! expB ) {
89        if ( ! sigB ) goto invalid;
90        normExpSig = softfloat_normSubnormalF16Sig( sigB );
91        expB = normExpSig.exp;
92        sigB = normExpSig.sig;
93    }
94    if ( ! expA ) {
95        if ( ! sigA ) return a;
96        normExpSig = softfloat_normSubnormalF16Sig( sigA );
97        expA = normExpSig.exp;
98        sigA = normExpSig.sig;
99    }
100    /*------------------------------------------------------------------------
101    *------------------------------------------------------------------------*/
102    rem = sigA | 0x0400;
103    sigB |= 0x0400;
104    expDiff = expA - expB;
105    if ( expDiff < 1 ) {
106        if ( expDiff < -1 ) return a;
107        sigB <<= 3;
108        if ( expDiff ) {
109            rem <<= 2;
110            q = 0;
111        } else {
112            rem <<= 3;
113            q = (sigB <= rem);
114            if ( q ) rem -= sigB;
115        }
116    } else {
117        recip32 = softfloat_approxRecip32_1( (uint_fast32_t) sigB<<21 );
118        /*--------------------------------------------------------------------
119        | Changing the shift of `rem' here requires also changing the initial
120        | subtraction from `expDiff'.
121        *--------------------------------------------------------------------*/
122        rem <<= 4;
123        expDiff -= 31;
124        /*--------------------------------------------------------------------
125        | The scale of `sigB' affects how many bits are obtained during each
126        | cycle of the loop.  Currently this is 29 bits per loop iteration,
127        | which is believed to be the maximum possible.
128        *--------------------------------------------------------------------*/
129        sigB <<= 3;
130        for (;;) {
131            q32 = (rem * (uint_fast64_t) recip32)>>16;
132            if ( expDiff < 0 ) break;
133            rem = -((uint_fast16_t) q32 * sigB);
134            expDiff -= 29;
135        }
136        /*--------------------------------------------------------------------
137        | (`expDiff' cannot be less than -30 here.)
138        *--------------------------------------------------------------------*/
139        q32 >>= ~expDiff & 31;
140        q = q32;
141        rem = (rem<<(expDiff + 30)) - q * sigB;
142    }
143    /*------------------------------------------------------------------------
144    *------------------------------------------------------------------------*/
145    do {
146        altRem = rem;
147        ++q;
148        rem -= sigB;
149    } while ( ! (rem & 0x8000) );
150    meanRem = rem + altRem;
151    if ( (meanRem & 0x8000) || (! meanRem && (q & 1)) ) rem = altRem;
152    signRem = signA;
153    if ( 0x8000 <= rem ) {
154        signRem = ! signRem;
155        rem = -rem;
156    }
157    return softfloat_normRoundPackToF16( signRem, expB, rem );
158    /*------------------------------------------------------------------------
159    *------------------------------------------------------------------------*/
160 propagateNaN:
161    uiZ = softfloat_propagateNaNF16UI( uiA, uiB );
162    goto uiZ;
163 invalid:
164    softfloat_raiseFlags( softfloat_flag_invalid );
165    uiZ = defaultNaNF16UI;
166 uiZ:
167    uZ.ui = uiZ;
168    return uZ.f;
169
170}
171
172