1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
|
/*** UPDATE COMMENTS. ***/
#include "softfloat_types.h"
union ui32_f32 { uint32_t ui; float32_t f; };
union ui64_f64 { uint64_t ui; float64_t f; };
#ifdef LITTLEENDIAN
union ui128_f128 { uint64_t ui0, ui64; float128_t f; };
#else
union ui128_f128 { uint64_t ui64, ui0; float128_t f; };
#endif
enum {
softfloat_mulAdd_subC = 1,
softfloat_mulAdd_subProd = 2
};
uint_fast32_t
softfloat_roundPackToUI32( bool, uint_fast64_t, int_fast8_t, bool );
uint_fast64_t
softfloat_roundPackToUI64(
bool, uint_fast64_t, uint_fast64_t, int_fast8_t, bool );
/*----------------------------------------------------------------------------
| Takes a 64-bit fixed-point value `absZ' with binary point between bits 6
| and 7, and returns the properly rounded 32-bit integer corresponding to the
| input. If `zSign' is 1, the input is negated before being converted to an
| integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input
| is simply rounded to an integer, with the inexact exception raised if the
| input cannot be represented exactly as an integer. However, if the fixed-
| point input is too large, the invalid exception is raised and the largest
| positive or negative integer is returned.
*----------------------------------------------------------------------------*/
int_fast32_t
softfloat_roundPackToI32( bool, uint_fast64_t, int_fast8_t, bool );
/*----------------------------------------------------------------------------
| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
| `absZ1', with binary point between bits 63 and 64 (between the input words),
| and returns the properly rounded 64-bit integer corresponding to the input.
| If `zSign' is 1, the input is negated before being converted to an integer.
| Ordinarily, the fixed-point input is simply rounded to an integer, with
| the inexact exception raised if the input cannot be represented exactly as
| an integer. However, if the fixed-point input is too large, the invalid
| exception is raised and the largest positive or negative integer is
| returned.
*----------------------------------------------------------------------------*/
int_fast64_t
softfloat_roundPackToI64(
bool, uint_fast64_t, uint_fast64_t, int_fast8_t, bool );
/*----------------------------------------------------------------------------
| Returns 1 if the single-precision floating-point value `a' is a NaN;
| otherwise, returns 0.
*----------------------------------------------------------------------------*/
#define isNaNF32UI( ui ) (0xFF000000<(uint32_t)((uint_fast32_t)(ui)<<1))
/*----------------------------------------------------------------------------
| Returns the sign bit of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
#define signF32UI( a ) ((bool)((uint32_t)(a)>>31))
/*----------------------------------------------------------------------------
| Returns the exponent bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
#define expF32UI( a ) ((int_fast16_t)((a)>>23)&0xFF)
/*----------------------------------------------------------------------------
| Returns the fraction bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
#define fracF32UI( a ) ((a)&0x007FFFFF)
/*----------------------------------------------------------------------------
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
| single-precision floating-point value, returning the result. After being
| shifted into the proper positions, the three fields are simply added
| together to form the result. This means that any integer portion of `zSig'
| will be added into the exponent. Since a properly normalized significand
| will have an integer portion equal to 1, the `zExp' input should be 1 less
| than the desired result exponent whenever `zSig' is a complete, normalized
| significand.
*----------------------------------------------------------------------------*/
#define packToF32UI( sign, exp, sig ) (((uint32_t)(sign)<<31)+((uint32_t)(exp)<<23)+(sig))
/*----------------------------------------------------------------------------
| Normalizes the subnormal single-precision floating-point value represented
| by the denormalized significand `aSig'. The normalized exponent and
| significand are stored at the locations pointed to by `zExpPtr' and
| `zSigPtr', respectively.
*----------------------------------------------------------------------------*/
struct exp16_sig32 { int_fast16_t exp; uint_fast32_t sig; };
struct exp16_sig32 softfloat_normSubnormalF32Sig( uint_fast32_t );
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper single-precision floating-
| point value corresponding to the abstract input. Ordinarily, the abstract
| value is simply rounded and packed into the single-precision format, with
| the inexact exception raised if the abstract input cannot be represented
| exactly. However, if the abstract value is too large, the overflow and
| inexact exceptions are raised and an infinity or maximal finite value is
| returned. If the abstract value is too small, the input value is rounded to
| a subnormal number, and the underflow and inexact exceptions are raised if
| the abstract input cannot be represented exactly as a subnormal single-
| precision floating-point number.
| The input significand `zSig' has its binary point between bits 30
| and 29, which is 7 bits to the left of the usual location. This shifted
| significand must be normalized or smaller. If `zSig' is not normalized,
| `zExp' must be 0; in that case, the result returned is a subnormal number,
| and it must not require rounding. In the usual case that `zSig' is
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
| The handling of underflow and overflow follows the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32_t softfloat_roundPackToF32( bool, int_fast16_t, uint_fast32_t );
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper single-precision floating-
| point value corresponding to the abstract input. This routine is just like
| `roundAndPackFloat32' except that `zSig' does not have to be normalized.
| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
| floating-point exponent.
*----------------------------------------------------------------------------*/
float32_t softfloat_normRoundPackToF32( bool, int_fast16_t, uint_fast32_t );
/*----------------------------------------------------------------------------
| Returns the result of adding the absolute values of the single-precision
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
| before being returned. `zSign' is ignored if the result is a NaN.
| The addition is performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32_t softfloat_addMagsF32( uint_fast32_t, uint_fast32_t, bool );
/*----------------------------------------------------------------------------
| Returns the result of subtracting the absolute values of the single-
| precision floating-point values `a' and `b'. If `zSign' is 1, the
| difference is negated before being returned. `zSign' is ignored if the
| result is a NaN. The subtraction is performed according to the IEC/IEEE
| Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32_t softfloat_subMagsF32( uint_fast32_t, uint_fast32_t, bool );
/*----------------------------------------------------------------------------
*----------------------------------------------------------------------------*/
float32_t
softfloat_mulAddF32( int, uint_fast32_t, uint_fast32_t, uint_fast32_t );
/*----------------------------------------------------------------------------
| Returns 1 if the double-precision floating-point value `a' is a NaN;
| otherwise, returns 0.
*----------------------------------------------------------------------------*/
#define isNaNF64UI( ui ) (UINT64_C(0xFFE0000000000000)<(uint64_t)((uint_fast64_t)(ui)<<1))
/*----------------------------------------------------------------------------
| Returns the sign bit of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
#define signF64UI( a ) ((bool)((uint64_t)(a)>>63))
/*----------------------------------------------------------------------------
| Returns the exponent bits of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
#define expF64UI( a ) ((int_fast16_t)((a)>>52)&0x7FF)
/*----------------------------------------------------------------------------
| Returns the fraction bits of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
#define fracF64UI( a ) ((a)&UINT64_C(0x000FFFFFFFFFFFFF))
/*----------------------------------------------------------------------------
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
| double-precision floating-point value, returning the result. After being
| shifted into the proper positions, the three fields are simply added
| together to form the result. This means that any integer portion of `zSig'
| will be added into the exponent. Since a properly normalized significand
| will have an integer portion equal to 1, the `zExp' input should be 1 less
| than the desired result exponent whenever `zSig' is a complete, normalized
| significand.
*----------------------------------------------------------------------------*/
#define packToF64UI( sign, exp, sig ) (((uint64_t)(sign)<<63)+((uint64_t)(exp)<<52)+(sig))
/*----------------------------------------------------------------------------
| Normalizes the subnormal double-precision floating-point value represented
| by the denormalized significand `aSig'. The normalized exponent and
| significand are stored at the locations pointed to by `zExpPtr' and
| `zSigPtr', respectively.
*----------------------------------------------------------------------------*/
struct exp16_sig64 { int_fast16_t exp; uint_fast64_t sig; };
struct exp16_sig64 softfloat_normSubnormalF64Sig( uint_fast64_t );
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper double-precision floating-
| point value corresponding to the abstract input. Ordinarily, the abstract
| value is simply rounded and packed into the double-precision format, with
| the inexact exception raised if the abstract input cannot be represented
| exactly. However, if the abstract value is too large, the overflow and
| inexact exceptions are raised and an infinity or maximal finite value is
| returned. If the abstract value is too small, the input value is rounded
| to a subnormal number, and the underflow and inexact exceptions are raised
| if the abstract input cannot be represented exactly as a subnormal double-
| precision floating-point number.
| The input significand `zSig' has its binary point between bits 62
| and 61, which is 10 bits to the left of the usual location. This shifted
| significand must be normalized or smaller. If `zSig' is not normalized,
| `zExp' must be 0; in that case, the result returned is a subnormal number,
| and it must not require rounding. In the usual case that `zSig' is
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
| The handling of underflow and overflow follows the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64_t softfloat_roundPackToF64( bool, int_fast16_t, uint_fast64_t );
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper double-precision floating-
| point value corresponding to the abstract input. This routine is just like
| `roundAndPackFloat64' except that `zSig' does not have to be normalized.
| Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
| floating-point exponent.
*----------------------------------------------------------------------------*/
float64_t softfloat_normRoundPackToF64( bool, int_fast16_t, uint_fast64_t );
/*----------------------------------------------------------------------------
| Returns the result of adding the absolute values of the double-precision
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
| before being returned. `zSign' is ignored if the result is a NaN.
| The addition is performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64_t softfloat_addMagsF64( uint_fast64_t, uint_fast64_t, bool );
/*----------------------------------------------------------------------------
| Returns the result of subtracting the absolute values of the double-
| precision floating-point values `a' and `b'. If `zSign' is 1, the
| difference is negated before being returned. `zSign' is ignored if the
| result is a NaN. The subtraction is performed according to the IEC/IEEE
| Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64_t softfloat_subMagsF64( uint_fast64_t, uint_fast64_t, bool );
/*----------------------------------------------------------------------------
*----------------------------------------------------------------------------*/
float64_t
softfloat_mulAddF64( int, uint_fast64_t, uint_fast64_t, uint_fast64_t );
|
