1 /* Half-float conversion routines.
2
3 Copyright (C) 2008-2023 Free Software Foundation, Inc.
4 Contributed by CodeSourcery.
5
6 This file is free software; you can redistribute it and/or modify it
7 under the terms of the GNU General Public License as published by the
8 Free Software Foundation; either version 3, or (at your option) any
9 later version.
10
11 This file is distributed in the hope that it will be useful, but
12 WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 General Public License for more details.
15
16 Under Section 7 of GPL version 3, you are granted additional
17 permissions described in the GCC Runtime Library Exception, version
18 3.1, as published by the Free Software Foundation.
19
20 You should have received a copy of the GNU General Public License and
21 a copy of the GCC Runtime Library Exception along with this program;
22 see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23 <http://www.gnu.org/licenses/>. */
24
25 struct format
26 {
27 /* Number of bits. */
28 unsigned long long size;
29 /* Exponent bias. */
30 unsigned long long bias;
31 /* Exponent width in bits. */
32 unsigned long long exponent;
33 /* Significand precision in explicitly stored bits. */
34 unsigned long long significand;
35 };
36
37 static const struct format
38 binary32 =
39 {
40 32, /* size. */
41 127, /* bias. */
42 8, /* exponent. */
43 23 /* significand. */
44 };
45
46 static const struct format
47 binary64 =
48 {
49 64, /* size. */
50 1023, /* bias. */
51 11, /* exponent. */
52 52 /* significand. */
53 };
54
55 /* Function prototypes. */
56 unsigned short __gnu_f2h_ieee (unsigned int a);
57 unsigned int __gnu_h2f_ieee (unsigned short a);
58 unsigned short __gnu_f2h_alternative (unsigned int x);
59 unsigned int __gnu_h2f_alternative (unsigned short a);
60 unsigned short __gnu_d2h_ieee (unsigned long long a);
61 unsigned short __gnu_d2h_alternative (unsigned long long x);
62
63 static inline unsigned short
64 __gnu_float2h_internal (const struct format* fmt,
65 unsigned long long a, int ieee)
66 {
67 unsigned long long point = 1ULL << fmt->significand;
68 unsigned short sign = (a >> (fmt->size - 16)) & 0x8000;
69 int aexp;
70 unsigned long long mantissa;
71 unsigned long long mask;
72 unsigned long long increment;
73
74 /* Get the exponent and mantissa encodings. */
75 mantissa = a & (point - 1);
76
77 mask = (1 << fmt->exponent) - 1;
78 aexp = (a >> fmt->significand) & mask;
79
80 /* Infinity, NaN and alternative format special case. */
81 if (((unsigned int) aexp) == mask)
82 {
83 if (!ieee)
84 return sign;
85 if (mantissa == 0)
86 return sign | 0x7c00; /* Infinity. */
87 /* Remaining cases are NaNs. Convert SNaN to QNaN. */
88 return sign | 0x7e00 | (mantissa >> (fmt->significand - 10));
89 }
90
91 /* Zero. */
92 if (aexp == 0 && mantissa == 0)
93 return sign;
94
95 /* Construct the exponent and mantissa. */
96 aexp -= fmt->bias;
97
98 /* Decimal point is immediately after the significand. */
99 mantissa |= point;
100
101 if (aexp < -14)
102 {
103 mask = point | (point - 1);
104 /* Minimum exponent for half-precision is 2^-24. */
105 if (aexp >= -25)
106 mask >>= 25 + aexp;
107 }
108 else
109 mask = (point - 1) >> 10;
110
111 /* Round. */
112 if (mantissa & mask)
113 {
114 increment = (mask + 1) >> 1;
115 if ((mantissa & mask) == increment)
116 increment = mantissa & (increment << 1);
117 mantissa += increment;
118 if (mantissa >= (point << 1))
119 {
120 mantissa >>= 1;
121 aexp++;
122 }
123 }
124
125 if (ieee)
126 {
127 if (aexp > 15)
128 return sign | 0x7c00;
129 }
130 else
131 {
132 if (aexp > 16)
133 return sign | 0x7fff;
134 }
135
136 if (aexp < -24)
137 return sign;
138
139 if (aexp < -14)
140 {
141 mantissa >>= -14 - aexp;
142 aexp = -14;
143 }
144
145 /* Encode the final 16-bit floating-point value.
146
147 This is formed of the sign bit, the bias-adjusted exponent, and the
148 calculated mantissa, with the following caveats:
149
150 1. The mantissa calculated after rounding could have a leading 1.
151 To compensate for this, subtract one from the exponent bias (15)
152 before adding it to the calculated exponent.
153 2. When we were calculating rounding, we left the mantissa with the
154 number of bits of the source operand, it needs reduced to ten
155 bits (+1 for the afforementioned leading 1) by shifting right by
156 the number of bits in the source mantissa - 10.
157 3. To ensure the leading 1 in the mantissa is applied to the exponent
158 we need to add the mantissa rather than apply an arithmetic "or"
159 to it. */
160
161 return sign | (((aexp + 14) << 10) + (mantissa >> (fmt->significand - 10)));
162 }
163
164 static inline unsigned short
165 __gnu_f2h_internal (unsigned int a, int ieee)
166 {
167 return __gnu_float2h_internal (&binary32, (unsigned long long) a, ieee);
168 }
169
170 static inline unsigned short
171 __gnu_d2h_internal (unsigned long long a, int ieee)
172 {
173 return __gnu_float2h_internal (&binary64, a, ieee);
174 }
175
176 static inline unsigned int
177 __gnu_h2f_internal(unsigned short a, int ieee)
178 {
179 unsigned int sign = (unsigned int)(a & 0x8000) << 16;
180 int aexp = (a >> 10) & 0x1f;
181 unsigned int mantissa = a & 0x3ff;
182
183 if (aexp == 0x1f && ieee)
184 return sign | 0x7f800000 | (mantissa << 13);
185
186 if (aexp == 0)
187 {
188 int shift;
189
190 if (mantissa == 0)
191 return sign;
192
193 shift = __builtin_clz(mantissa) - 21;
194 mantissa <<= shift;
195 aexp = -shift;
196 }
197
198 return sign | (((aexp + 0x70) << 23) + (mantissa << 13));
199 }
200
201 unsigned short
202 __gnu_f2h_ieee(unsigned int a)
203 {
204 return __gnu_f2h_internal(a, 1);
205 }
206
207 unsigned int
208 __gnu_h2f_ieee(unsigned short a)
209 {
210 return __gnu_h2f_internal(a, 1);
211 }
212
213 unsigned short
214 __gnu_f2h_alternative(unsigned int x)
215 {
216 return __gnu_f2h_internal(x, 0);
217 }
218
219 unsigned int
220 __gnu_h2f_alternative(unsigned short a)
221 {
222 return __gnu_h2f_internal(a, 0);
223 }
224
225 unsigned short
226 __gnu_d2h_ieee (unsigned long long a)
227 {
228 return __gnu_d2h_internal (a, 1);
229 }
230
231 unsigned short
232 __gnu_d2h_alternative (unsigned long long x)
233 {
234 return __gnu_d2h_internal (x, 0);
235 }