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1// SPDX-License-Identifier: GPL-2.0-only
2/* IEEE754 floating point arithmetic
3 * double precision: common utilities
4 */
5/*
6 * MIPS floating point support
7 * Copyright (C) 1994-2000 Algorithmics Ltd.
8 */
9
10#include <linux/compiler.h>
11
12#include "ieee754dp.h"
13
14int ieee754dp_class(union ieee754dp x)
15{
16 COMPXDP;
17 EXPLODEXDP;
18 return xc;
19}
20
21static inline int ieee754dp_isnan(union ieee754dp x)
22{
23 return ieee754_class_nan(ieee754dp_class(x));
24}
25
26static inline int ieee754dp_issnan(union ieee754dp x)
27{
28 int qbit;
29
30 assert(ieee754dp_isnan(x));
31 qbit = (DPMANT(x) & DP_MBIT(DP_FBITS - 1)) == DP_MBIT(DP_FBITS - 1);
32 return ieee754_csr.nan2008 ^ qbit;
33}
34
35
36/*
37 * Raise the Invalid Operation IEEE 754 exception
38 * and convert the signaling NaN supplied to a quiet NaN.
39 */
40union ieee754dp __cold ieee754dp_nanxcpt(union ieee754dp r)
41{
42 assert(ieee754dp_issnan(r));
43
44 ieee754_setcx(IEEE754_INVALID_OPERATION);
45 if (ieee754_csr.nan2008) {
46 DPMANT(r) |= DP_MBIT(DP_FBITS - 1);
47 } else {
48 DPMANT(r) &= ~DP_MBIT(DP_FBITS - 1);
49 if (!ieee754dp_isnan(r))
50 DPMANT(r) |= DP_MBIT(DP_FBITS - 2);
51 }
52
53 return r;
54}
55
56static u64 ieee754dp_get_rounding(int sn, u64 xm)
57{
58 /* inexact must round of 3 bits
59 */
60 if (xm & (DP_MBIT(3) - 1)) {
61 switch (ieee754_csr.rm) {
62 case FPU_CSR_RZ:
63 break;
64 case FPU_CSR_RN:
65 xm += 0x3 + ((xm >> 3) & 1);
66 /* xm += (xm&0x8)?0x4:0x3 */
67 break;
68 case FPU_CSR_RU: /* toward +Infinity */
69 if (!sn) /* ?? */
70 xm += 0x8;
71 break;
72 case FPU_CSR_RD: /* toward -Infinity */
73 if (sn) /* ?? */
74 xm += 0x8;
75 break;
76 }
77 }
78 return xm;
79}
80
81
82/* generate a normal/denormal number with over,under handling
83 * sn is sign
84 * xe is an unbiased exponent
85 * xm is 3bit extended precision value.
86 */
87union ieee754dp ieee754dp_format(int sn, int xe, u64 xm)
88{
89 assert(xm); /* we don't gen exact zeros (probably should) */
90
91 assert((xm >> (DP_FBITS + 1 + 3)) == 0); /* no excess */
92 assert(xm & (DP_HIDDEN_BIT << 3));
93
94 if (xe < DP_EMIN) {
95 /* strip lower bits */
96 int es = DP_EMIN - xe;
97
98 if (ieee754_csr.nod) {
99 ieee754_setcx(IEEE754_UNDERFLOW);
100 ieee754_setcx(IEEE754_INEXACT);
101
102 switch(ieee754_csr.rm) {
103 case FPU_CSR_RN:
104 case FPU_CSR_RZ:
105 return ieee754dp_zero(sn);
106 case FPU_CSR_RU: /* toward +Infinity */
107 if (sn == 0)
108 return ieee754dp_min(0);
109 else
110 return ieee754dp_zero(1);
111 case FPU_CSR_RD: /* toward -Infinity */
112 if (sn == 0)
113 return ieee754dp_zero(0);
114 else
115 return ieee754dp_min(1);
116 }
117 }
118
119 if (xe == DP_EMIN - 1 &&
120 ieee754dp_get_rounding(sn, xm) >> (DP_FBITS + 1 + 3))
121 {
122 /* Not tiny after rounding */
123 ieee754_setcx(IEEE754_INEXACT);
124 xm = ieee754dp_get_rounding(sn, xm);
125 xm >>= 1;
126 /* Clear grs bits */
127 xm &= ~(DP_MBIT(3) - 1);
128 xe++;
129 }
130 else {
131 /* sticky right shift es bits
132 */
133 xm = XDPSRS(xm, es);
134 xe += es;
135 assert((xm & (DP_HIDDEN_BIT << 3)) == 0);
136 assert(xe == DP_EMIN);
137 }
138 }
139 if (xm & (DP_MBIT(3) - 1)) {
140 ieee754_setcx(IEEE754_INEXACT);
141 if ((xm & (DP_HIDDEN_BIT << 3)) == 0) {
142 ieee754_setcx(IEEE754_UNDERFLOW);
143 }
144
145 /* inexact must round of 3 bits
146 */
147 xm = ieee754dp_get_rounding(sn, xm);
148 /* adjust exponent for rounding add overflowing
149 */
150 if (xm >> (DP_FBITS + 3 + 1)) {
151 /* add causes mantissa overflow */
152 xm >>= 1;
153 xe++;
154 }
155 }
156 /* strip grs bits */
157 xm >>= 3;
158
159 assert((xm >> (DP_FBITS + 1)) == 0); /* no excess */
160 assert(xe >= DP_EMIN);
161
162 if (xe > DP_EMAX) {
163 ieee754_setcx(IEEE754_OVERFLOW);
164 ieee754_setcx(IEEE754_INEXACT);
165 /* -O can be table indexed by (rm,sn) */
166 switch (ieee754_csr.rm) {
167 case FPU_CSR_RN:
168 return ieee754dp_inf(sn);
169 case FPU_CSR_RZ:
170 return ieee754dp_max(sn);
171 case FPU_CSR_RU: /* toward +Infinity */
172 if (sn == 0)
173 return ieee754dp_inf(0);
174 else
175 return ieee754dp_max(1);
176 case FPU_CSR_RD: /* toward -Infinity */
177 if (sn == 0)
178 return ieee754dp_max(0);
179 else
180 return ieee754dp_inf(1);
181 }
182 }
183 /* gen norm/denorm/zero */
184
185 if ((xm & DP_HIDDEN_BIT) == 0) {
186 /* we underflow (tiny/zero) */
187 assert(xe == DP_EMIN);
188 if (ieee754_csr.mx & IEEE754_UNDERFLOW)
189 ieee754_setcx(IEEE754_UNDERFLOW);
190 return builddp(sn, DP_EMIN - 1 + DP_EBIAS, xm);
191 } else {
192 assert((xm >> (DP_FBITS + 1)) == 0); /* no excess */
193 assert(xm & DP_HIDDEN_BIT);
194
195 return builddp(sn, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
196 }
197}
1// SPDX-License-Identifier: GPL-2.0-only
2/* IEEE754 floating point arithmetic
3 * double precision: common utilities
4 */
5/*
6 * MIPS floating point support
7 * Copyright (C) 1994-2000 Algorithmics Ltd.
8 */
9
10#include <linux/compiler.h>
11
12#include "ieee754dp.h"
13
14int ieee754dp_class(union ieee754dp x)
15{
16 COMPXDP;
17 EXPLODEXDP;
18 return xc;
19}
20
21static inline int ieee754dp_isnan(union ieee754dp x)
22{
23 return ieee754_class_nan(ieee754dp_class(x));
24}
25
26static inline int ieee754dp_issnan(union ieee754dp x)
27{
28 int qbit;
29
30 assert(ieee754dp_isnan(x));
31 qbit = (DPMANT(x) & DP_MBIT(DP_FBITS - 1)) == DP_MBIT(DP_FBITS - 1);
32 return ieee754_csr.nan2008 ^ qbit;
33}
34
35
36/*
37 * Raise the Invalid Operation IEEE 754 exception
38 * and convert the signaling NaN supplied to a quiet NaN.
39 */
40union ieee754dp __cold ieee754dp_nanxcpt(union ieee754dp r)
41{
42 assert(ieee754dp_issnan(r));
43
44 ieee754_setcx(IEEE754_INVALID_OPERATION);
45 if (ieee754_csr.nan2008) {
46 DPMANT(r) |= DP_MBIT(DP_FBITS - 1);
47 } else {
48 DPMANT(r) &= ~DP_MBIT(DP_FBITS - 1);
49 if (!ieee754dp_isnan(r))
50 DPMANT(r) |= DP_MBIT(DP_FBITS - 2);
51 }
52
53 return r;
54}
55
56static u64 ieee754dp_get_rounding(int sn, u64 xm)
57{
58 /* inexact must round of 3 bits
59 */
60 if (xm & (DP_MBIT(3) - 1)) {
61 switch (ieee754_csr.rm) {
62 case FPU_CSR_RZ:
63 break;
64 case FPU_CSR_RN:
65 xm += 0x3 + ((xm >> 3) & 1);
66 /* xm += (xm&0x8)?0x4:0x3 */
67 break;
68 case FPU_CSR_RU: /* toward +Infinity */
69 if (!sn) /* ?? */
70 xm += 0x8;
71 break;
72 case FPU_CSR_RD: /* toward -Infinity */
73 if (sn) /* ?? */
74 xm += 0x8;
75 break;
76 }
77 }
78 return xm;
79}
80
81
82/* generate a normal/denormal number with over,under handling
83 * sn is sign
84 * xe is an unbiased exponent
85 * xm is 3bit extended precision value.
86 */
87union ieee754dp ieee754dp_format(int sn, int xe, u64 xm)
88{
89 assert(xm); /* we don't gen exact zeros (probably should) */
90
91 assert((xm >> (DP_FBITS + 1 + 3)) == 0); /* no excess */
92 assert(xm & (DP_HIDDEN_BIT << 3));
93
94 if (xe < DP_EMIN) {
95 /* strip lower bits */
96 int es = DP_EMIN - xe;
97
98 if (ieee754_csr.nod) {
99 ieee754_setcx(IEEE754_UNDERFLOW);
100 ieee754_setcx(IEEE754_INEXACT);
101
102 switch(ieee754_csr.rm) {
103 case FPU_CSR_RN:
104 case FPU_CSR_RZ:
105 return ieee754dp_zero(sn);
106 case FPU_CSR_RU: /* toward +Infinity */
107 if (sn == 0)
108 return ieee754dp_min(0);
109 else
110 return ieee754dp_zero(1);
111 case FPU_CSR_RD: /* toward -Infinity */
112 if (sn == 0)
113 return ieee754dp_zero(0);
114 else
115 return ieee754dp_min(1);
116 }
117 }
118
119 if (xe == DP_EMIN - 1 &&
120 ieee754dp_get_rounding(sn, xm) >> (DP_FBITS + 1 + 3))
121 {
122 /* Not tiny after rounding */
123 ieee754_setcx(IEEE754_INEXACT);
124 xm = ieee754dp_get_rounding(sn, xm);
125 xm >>= 1;
126 /* Clear grs bits */
127 xm &= ~(DP_MBIT(3) - 1);
128 xe++;
129 }
130 else {
131 /* sticky right shift es bits
132 */
133 xm = XDPSRS(xm, es);
134 xe += es;
135 assert((xm & (DP_HIDDEN_BIT << 3)) == 0);
136 assert(xe == DP_EMIN);
137 }
138 }
139 if (xm & (DP_MBIT(3) - 1)) {
140 ieee754_setcx(IEEE754_INEXACT);
141 if ((xm & (DP_HIDDEN_BIT << 3)) == 0) {
142 ieee754_setcx(IEEE754_UNDERFLOW);
143 }
144
145 /* inexact must round of 3 bits
146 */
147 xm = ieee754dp_get_rounding(sn, xm);
148 /* adjust exponent for rounding add overflowing
149 */
150 if (xm >> (DP_FBITS + 3 + 1)) {
151 /* add causes mantissa overflow */
152 xm >>= 1;
153 xe++;
154 }
155 }
156 /* strip grs bits */
157 xm >>= 3;
158
159 assert((xm >> (DP_FBITS + 1)) == 0); /* no excess */
160 assert(xe >= DP_EMIN);
161
162 if (xe > DP_EMAX) {
163 ieee754_setcx(IEEE754_OVERFLOW);
164 ieee754_setcx(IEEE754_INEXACT);
165 /* -O can be table indexed by (rm,sn) */
166 switch (ieee754_csr.rm) {
167 case FPU_CSR_RN:
168 return ieee754dp_inf(sn);
169 case FPU_CSR_RZ:
170 return ieee754dp_max(sn);
171 case FPU_CSR_RU: /* toward +Infinity */
172 if (sn == 0)
173 return ieee754dp_inf(0);
174 else
175 return ieee754dp_max(1);
176 case FPU_CSR_RD: /* toward -Infinity */
177 if (sn == 0)
178 return ieee754dp_max(0);
179 else
180 return ieee754dp_inf(1);
181 }
182 }
183 /* gen norm/denorm/zero */
184
185 if ((xm & DP_HIDDEN_BIT) == 0) {
186 /* we underflow (tiny/zero) */
187 assert(xe == DP_EMIN);
188 if (ieee754_csr.mx & IEEE754_UNDERFLOW)
189 ieee754_setcx(IEEE754_UNDERFLOW);
190 return builddp(sn, DP_EMIN - 1 + DP_EBIAS, xm);
191 } else {
192 assert((xm >> (DP_FBITS + 1)) == 0); /* no excess */
193 assert(xm & DP_HIDDEN_BIT);
194
195 return builddp(sn, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
196 }
197}