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1// SPDX-License-Identifier: GPL-2.0-only
2/* IEEE754 floating point arithmetic
3 * single precision
4 */
5/*
6 * MIPS floating point support
7 * Copyright (C) 1994-2000 Algorithmics Ltd.
8 */
9
10#include <linux/compiler.h>
11
12#include "ieee754sp.h"
13
14int ieee754sp_class(union ieee754sp x)
15{
16 COMPXSP;
17 EXPLODEXSP;
18 return xc;
19}
20
21static inline int ieee754sp_isnan(union ieee754sp x)
22{
23 return ieee754_class_nan(ieee754sp_class(x));
24}
25
26static inline int ieee754sp_issnan(union ieee754sp x)
27{
28 int qbit;
29
30 assert(ieee754sp_isnan(x));
31 qbit = (SPMANT(x) & SP_MBIT(SP_FBITS - 1)) == SP_MBIT(SP_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 ieee754sp __cold ieee754sp_nanxcpt(union ieee754sp r)
41{
42 assert(ieee754sp_issnan(r));
43
44 ieee754_setcx(IEEE754_INVALID_OPERATION);
45 if (ieee754_csr.nan2008) {
46 SPMANT(r) |= SP_MBIT(SP_FBITS - 1);
47 } else {
48 SPMANT(r) &= ~SP_MBIT(SP_FBITS - 1);
49 if (!ieee754sp_isnan(r))
50 SPMANT(r) |= SP_MBIT(SP_FBITS - 2);
51 }
52
53 return r;
54}
55
56static unsigned int ieee754sp_get_rounding(int sn, unsigned int xm)
57{
58 /* inexact must round of 3 bits
59 */
60 if (xm & (SP_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 ieee754sp ieee754sp_format(int sn, int xe, unsigned int xm)
88{
89 assert(xm); /* we don't gen exact zeros (probably should) */
90
91 assert((xm >> (SP_FBITS + 1 + 3)) == 0); /* no excess */
92 assert(xm & (SP_HIDDEN_BIT << 3));
93
94 if (xe < SP_EMIN) {
95 /* strip lower bits */
96 int es = SP_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 ieee754sp_zero(sn);
106 case FPU_CSR_RU: /* toward +Infinity */
107 if (sn == 0)
108 return ieee754sp_min(0);
109 else
110 return ieee754sp_zero(1);
111 case FPU_CSR_RD: /* toward -Infinity */
112 if (sn == 0)
113 return ieee754sp_zero(0);
114 else
115 return ieee754sp_min(1);
116 }
117 }
118
119 if (xe == SP_EMIN - 1 &&
120 ieee754sp_get_rounding(sn, xm) >> (SP_FBITS + 1 + 3))
121 {
122 /* Not tiny after rounding */
123 ieee754_setcx(IEEE754_INEXACT);
124 xm = ieee754sp_get_rounding(sn, xm);
125 xm >>= 1;
126 /* Clear grs bits */
127 xm &= ~(SP_MBIT(3) - 1);
128 xe++;
129 } else {
130 /* sticky right shift es bits
131 */
132 xm = XSPSRS(xm, es);
133 xe += es;
134 assert((xm & (SP_HIDDEN_BIT << 3)) == 0);
135 assert(xe == SP_EMIN);
136 }
137 }
138 if (xm & (SP_MBIT(3) - 1)) {
139 ieee754_setcx(IEEE754_INEXACT);
140 if ((xm & (SP_HIDDEN_BIT << 3)) == 0) {
141 ieee754_setcx(IEEE754_UNDERFLOW);
142 }
143
144 /* inexact must round of 3 bits
145 */
146 xm = ieee754sp_get_rounding(sn, xm);
147 /* adjust exponent for rounding add overflowing
148 */
149 if (xm >> (SP_FBITS + 1 + 3)) {
150 /* add causes mantissa overflow */
151 xm >>= 1;
152 xe++;
153 }
154 }
155 /* strip grs bits */
156 xm >>= 3;
157
158 assert((xm >> (SP_FBITS + 1)) == 0); /* no excess */
159 assert(xe >= SP_EMIN);
160
161 if (xe > SP_EMAX) {
162 ieee754_setcx(IEEE754_OVERFLOW);
163 ieee754_setcx(IEEE754_INEXACT);
164 /* -O can be table indexed by (rm,sn) */
165 switch (ieee754_csr.rm) {
166 case FPU_CSR_RN:
167 return ieee754sp_inf(sn);
168 case FPU_CSR_RZ:
169 return ieee754sp_max(sn);
170 case FPU_CSR_RU: /* toward +Infinity */
171 if (sn == 0)
172 return ieee754sp_inf(0);
173 else
174 return ieee754sp_max(1);
175 case FPU_CSR_RD: /* toward -Infinity */
176 if (sn == 0)
177 return ieee754sp_max(0);
178 else
179 return ieee754sp_inf(1);
180 }
181 }
182 /* gen norm/denorm/zero */
183
184 if ((xm & SP_HIDDEN_BIT) == 0) {
185 /* we underflow (tiny/zero) */
186 assert(xe == SP_EMIN);
187 if (ieee754_csr.mx & IEEE754_UNDERFLOW)
188 ieee754_setcx(IEEE754_UNDERFLOW);
189 return buildsp(sn, SP_EMIN - 1 + SP_EBIAS, xm);
190 } else {
191 assert((xm >> (SP_FBITS + 1)) == 0); /* no excess */
192 assert(xm & SP_HIDDEN_BIT);
193
194 return buildsp(sn, xe + SP_EBIAS, xm & ~SP_HIDDEN_BIT);
195 }
196}
1// SPDX-License-Identifier: GPL-2.0-only
2/* IEEE754 floating point arithmetic
3 * single precision
4 */
5/*
6 * MIPS floating point support
7 * Copyright (C) 1994-2000 Algorithmics Ltd.
8 */
9
10#include <linux/compiler.h>
11
12#include "ieee754sp.h"
13
14int ieee754sp_class(union ieee754sp x)
15{
16 COMPXSP;
17 EXPLODEXSP;
18 return xc;
19}
20
21static inline int ieee754sp_isnan(union ieee754sp x)
22{
23 return ieee754_class_nan(ieee754sp_class(x));
24}
25
26static inline int ieee754sp_issnan(union ieee754sp x)
27{
28 int qbit;
29
30 assert(ieee754sp_isnan(x));
31 qbit = (SPMANT(x) & SP_MBIT(SP_FBITS - 1)) == SP_MBIT(SP_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 ieee754sp __cold ieee754sp_nanxcpt(union ieee754sp r)
41{
42 assert(ieee754sp_issnan(r));
43
44 ieee754_setcx(IEEE754_INVALID_OPERATION);
45 if (ieee754_csr.nan2008) {
46 SPMANT(r) |= SP_MBIT(SP_FBITS - 1);
47 } else {
48 SPMANT(r) &= ~SP_MBIT(SP_FBITS - 1);
49 if (!ieee754sp_isnan(r))
50 SPMANT(r) |= SP_MBIT(SP_FBITS - 2);
51 }
52
53 return r;
54}
55
56static unsigned int ieee754sp_get_rounding(int sn, unsigned int xm)
57{
58 /* inexact must round of 3 bits
59 */
60 if (xm & (SP_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 ieee754sp ieee754sp_format(int sn, int xe, unsigned int xm)
88{
89 assert(xm); /* we don't gen exact zeros (probably should) */
90
91 assert((xm >> (SP_FBITS + 1 + 3)) == 0); /* no excess */
92 assert(xm & (SP_HIDDEN_BIT << 3));
93
94 if (xe < SP_EMIN) {
95 /* strip lower bits */
96 int es = SP_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 ieee754sp_zero(sn);
106 case FPU_CSR_RU: /* toward +Infinity */
107 if (sn == 0)
108 return ieee754sp_min(0);
109 else
110 return ieee754sp_zero(1);
111 case FPU_CSR_RD: /* toward -Infinity */
112 if (sn == 0)
113 return ieee754sp_zero(0);
114 else
115 return ieee754sp_min(1);
116 }
117 }
118
119 if (xe == SP_EMIN - 1 &&
120 ieee754sp_get_rounding(sn, xm) >> (SP_FBITS + 1 + 3))
121 {
122 /* Not tiny after rounding */
123 ieee754_setcx(IEEE754_INEXACT);
124 xm = ieee754sp_get_rounding(sn, xm);
125 xm >>= 1;
126 /* Clear grs bits */
127 xm &= ~(SP_MBIT(3) - 1);
128 xe++;
129 } else {
130 /* sticky right shift es bits
131 */
132 xm = XSPSRS(xm, es);
133 xe += es;
134 assert((xm & (SP_HIDDEN_BIT << 3)) == 0);
135 assert(xe == SP_EMIN);
136 }
137 }
138 if (xm & (SP_MBIT(3) - 1)) {
139 ieee754_setcx(IEEE754_INEXACT);
140 if ((xm & (SP_HIDDEN_BIT << 3)) == 0) {
141 ieee754_setcx(IEEE754_UNDERFLOW);
142 }
143
144 /* inexact must round of 3 bits
145 */
146 xm = ieee754sp_get_rounding(sn, xm);
147 /* adjust exponent for rounding add overflowing
148 */
149 if (xm >> (SP_FBITS + 1 + 3)) {
150 /* add causes mantissa overflow */
151 xm >>= 1;
152 xe++;
153 }
154 }
155 /* strip grs bits */
156 xm >>= 3;
157
158 assert((xm >> (SP_FBITS + 1)) == 0); /* no excess */
159 assert(xe >= SP_EMIN);
160
161 if (xe > SP_EMAX) {
162 ieee754_setcx(IEEE754_OVERFLOW);
163 ieee754_setcx(IEEE754_INEXACT);
164 /* -O can be table indexed by (rm,sn) */
165 switch (ieee754_csr.rm) {
166 case FPU_CSR_RN:
167 return ieee754sp_inf(sn);
168 case FPU_CSR_RZ:
169 return ieee754sp_max(sn);
170 case FPU_CSR_RU: /* toward +Infinity */
171 if (sn == 0)
172 return ieee754sp_inf(0);
173 else
174 return ieee754sp_max(1);
175 case FPU_CSR_RD: /* toward -Infinity */
176 if (sn == 0)
177 return ieee754sp_max(0);
178 else
179 return ieee754sp_inf(1);
180 }
181 }
182 /* gen norm/denorm/zero */
183
184 if ((xm & SP_HIDDEN_BIT) == 0) {
185 /* we underflow (tiny/zero) */
186 assert(xe == SP_EMIN);
187 if (ieee754_csr.mx & IEEE754_UNDERFLOW)
188 ieee754_setcx(IEEE754_UNDERFLOW);
189 return buildsp(sn, SP_EMIN - 1 + SP_EBIAS, xm);
190 } else {
191 assert((xm >> (SP_FBITS + 1)) == 0); /* no excess */
192 assert(xm & SP_HIDDEN_BIT);
193
194 return buildsp(sn, xe + SP_EBIAS, xm & ~SP_HIDDEN_BIT);
195 }
196}