1 // SPDX-License-Identifier: BSD-3-Clause
2
3 /*============================================================================
4
5 This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
6 Package, Release 3a, by John R. Hauser.
7
8 Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
9 All rights reserved.
10
11 Redistribution and use in source and binary forms, with or without
12 modification, are permitted provided that the following conditions are met:
13
14 1. Redistributions of source code must retain the above copyright notice,
15 this list of conditions, and the following disclaimer.
16
17 2. Redistributions in binary form must reproduce the above copyright notice,
18 this list of conditions, and the following disclaimer in the documentation
19 and/or other materials provided with the distribution.
20
21 3. Neither the name of the University nor the names of its contributors may
22 be used to endorse or promote products derived from this software without
23 specific prior written permission.
24
25 THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
26 EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
27 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
28 DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
29 DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
30 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
31 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
32 ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
33 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
34 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35
36 =============================================================================*/
37
38 #include <stdbool.h>
39 #include <stdint.h>
40 #include "platform.h"
41 #include "internals.h"
42 #include "specialize.h"
43 #include "softfloat.h"
44
f128_rem(float128_t a,float128_t b)45 float128_t f128_rem( float128_t a, float128_t b )
46 {
47 union ui128_f128 uA;
48 uint_fast64_t uiA64, uiA0;
49 bool signA;
50 int_fast32_t expA;
51 struct uint128 sigA;
52 union ui128_f128 uB;
53 uint_fast64_t uiB64, uiB0;
54 bool signB;
55 int_fast32_t expB;
56 struct uint128 sigB;
57 struct exp32_sig128 normExpSig;
58 struct uint128 rem;
59 int_fast32_t expDiff;
60 uint_fast32_t q, recip32;
61 uint_fast64_t q64;
62 struct uint128 term, altRem, meanRem;
63 bool signRem;
64 struct uint128 uiZ;
65 union ui128_f128 uZ;
66
67 /*------------------------------------------------------------------------
68 *------------------------------------------------------------------------*/
69 uA.f = a;
70 uiA64 = uA.ui.v64;
71 uiA0 = uA.ui.v0;
72 signA = signF128UI64( uiA64 );
73 expA = expF128UI64( uiA64 );
74 sigA.v64 = fracF128UI64( uiA64 );
75 sigA.v0 = uiA0;
76 uB.f = b;
77 uiB64 = uB.ui.v64;
78 uiB0 = uB.ui.v0;
79 signB = signF128UI64( uiB64 );
80 expB = expF128UI64( uiB64 );
81 sigB.v64 = fracF128UI64( uiB64 );
82 sigB.v0 = uiB0;
83 /*------------------------------------------------------------------------
84 *------------------------------------------------------------------------*/
85 if ( expA == 0x7FFF ) {
86 if (
87 (sigA.v64 | sigA.v0) || ((expB == 0x7FFF) && (sigB.v64 | sigB.v0))
88 ) {
89 goto propagateNaN;
90 }
91 goto invalid;
92 }
93 if ( expB == 0x7FFF ) {
94 if ( sigB.v64 | sigB.v0 ) goto propagateNaN;
95 return a;
96 }
97 /*------------------------------------------------------------------------
98 *------------------------------------------------------------------------*/
99 if ( ! expB ) {
100 if ( ! (sigB.v64 | sigB.v0) ) goto invalid;
101 normExpSig = softfloat_normSubnormalF128Sig( sigB.v64, sigB.v0 );
102 expB = normExpSig.exp;
103 sigB = normExpSig.sig;
104 }
105 if ( ! expA ) {
106 if ( ! (sigA.v64 | sigA.v0) ) return a;
107 normExpSig = softfloat_normSubnormalF128Sig( sigA.v64, sigA.v0 );
108 expA = normExpSig.exp;
109 sigA = normExpSig.sig;
110 }
111 /*------------------------------------------------------------------------
112 *------------------------------------------------------------------------*/
113 sigA.v64 |= UINT64_C( 0x0001000000000000 );
114 sigB.v64 |= UINT64_C( 0x0001000000000000 );
115 rem = sigA;
116 expDiff = expA - expB;
117 if ( expDiff < 1 ) {
118 if ( expDiff < -1 ) return a;
119 if ( expDiff ) {
120 --expB;
121 sigB = softfloat_add128( sigB.v64, sigB.v0, sigB.v64, sigB.v0 );
122 q = 0;
123 } else {
124 q = softfloat_le128( sigB.v64, sigB.v0, rem.v64, rem.v0 );
125 if ( q ) {
126 rem = softfloat_sub128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
127 }
128 }
129 } else {
130 recip32 = softfloat_approxRecip32_1( sigB.v64>>17 );
131 expDiff -= 30;
132 for (;;) {
133 q64 = (uint_fast64_t) (uint32_t) (rem.v64>>19) * recip32;
134 if ( expDiff < 0 ) break;
135 q = (q64 + 0x80000000)>>32;
136 rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
137 term = softfloat_mul128By32( sigB.v64, sigB.v0, q );
138 rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
139 if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
140 rem = softfloat_add128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
141 }
142 expDiff -= 29;
143 }
144 /*--------------------------------------------------------------------
145 | (`expDiff' cannot be less than -29 here.)
146 *--------------------------------------------------------------------*/
147 q = (uint32_t) (q64>>32)>>(~expDiff & 31);
148 rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, expDiff + 30 );
149 term = softfloat_mul128By32( sigB.v64, sigB.v0, q );
150 rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 );
151 if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
152 altRem = softfloat_add128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
153 goto selectRem;
154 }
155 }
156 /*------------------------------------------------------------------------
157 *------------------------------------------------------------------------*/
158 do {
159 altRem = rem;
160 ++q;
161 rem = softfloat_sub128( rem.v64, rem.v0, sigB.v64, sigB.v0 );
162 } while ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) );
163 selectRem:
164 meanRem = softfloat_add128( rem.v64, rem.v0, altRem.v64, altRem.v0 );
165 if (
166 (meanRem.v64 & UINT64_C( 0x8000000000000000 ))
167 || (! (meanRem.v64 | meanRem.v0) && (q & 1))
168 ) {
169 rem = altRem;
170 }
171 signRem = signA;
172 if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) {
173 signRem = ! signRem;
174 rem = softfloat_sub128( 0, 0, rem.v64, rem.v0 );
175 }
176 return softfloat_normRoundPackToF128( signRem, expB - 1, rem.v64, rem.v0 );
177 /*------------------------------------------------------------------------
178 *------------------------------------------------------------------------*/
179 propagateNaN:
180 uiZ = softfloat_propagateNaNF128UI( uiA64, uiA0, uiB64, uiB0 );
181 goto uiZ;
182 /*------------------------------------------------------------------------
183 *------------------------------------------------------------------------*/
184 invalid:
185 softfloat_raiseFlags( softfloat_flag_invalid );
186 uiZ.v64 = defaultNaNF128UI64;
187 uiZ.v0 = defaultNaNF128UI0;
188 uiZ:
189 uZ.ui = uiZ;
190 return uZ.f;
191
192 }
193
194