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 
ieee754sp_class(union ieee754sp x)14 int ieee754sp_class(union ieee754sp x)
15 {
16 	COMPXSP;
17 	EXPLODEXSP;
18 	return xc;
19 }
20 
ieee754sp_isnan(union ieee754sp x)21 static inline int ieee754sp_isnan(union ieee754sp x)
22 {
23 	return ieee754_class_nan(ieee754sp_class(x));
24 }
25 
ieee754sp_issnan(union ieee754sp x)26 static 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  */
ieee754sp_nanxcpt(union ieee754sp r)40 union 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 
ieee754sp_get_rounding(int sn,unsigned int xm)56 static 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  */
ieee754sp_format(int sn,int xe,unsigned int xm)87 union 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 }
197