1 /*-------------------------------------------------------------------------
2 *
3 * float.h
4 * Definitions for the built-in floating-point types
5 *
6 * Portions Copyright (c) 1996-2021, PostgreSQL Global Development Group
7 * Portions Copyright (c) 1994, Regents of the University of California
8 *
9 *
10 * IDENTIFICATION
11 * src/include/utils/float.h
12 *
13 *-------------------------------------------------------------------------
14 */
15 #ifndef FLOAT_H
16 #define FLOAT_H
17
18 #include <math.h>
19
20 #ifndef M_PI
21 /* From my RH5.2 gcc math.h file - thomas 2000-04-03 */
22 #define M_PI 3.14159265358979323846
23 #endif
24
25 /* Radians per degree, a.k.a. PI / 180 */
26 #define RADIANS_PER_DEGREE 0.0174532925199432957692
27
28 /* Visual C++ etc lacks NAN, and won't accept 0.0/0.0. */
29 #if defined(WIN32) && !defined(NAN)
30 static const uint32 nan[2] = {0xffffffff, 0x7fffffff};
31
32 #define NAN (*(const float8 *) nan)
33 #endif
34
35 extern PGDLLIMPORT int extra_float_digits;
36
37 /*
38 * Utility functions in float.c
39 */
40 extern void float_overflow_error(void) pg_attribute_noreturn();
41 extern void float_underflow_error(void) pg_attribute_noreturn();
42 extern void float_zero_divide_error(void) pg_attribute_noreturn();
43 extern int is_infinite(float8 val);
44 extern float8 float8in_internal(char *num, char **endptr_p,
45 const char *type_name, const char *orig_string);
46 extern float8 float8in_internal_opt_error(char *num, char **endptr_p,
47 const char *type_name, const char *orig_string,
48 bool *have_error);
49 extern char *float8out_internal(float8 num);
50 extern int float4_cmp_internal(float4 a, float4 b);
51 extern int float8_cmp_internal(float8 a, float8 b);
52
53 /*
54 * Routines to provide reasonably platform-independent handling of
55 * infinity and NaN
56 *
57 * We assume that isinf() and isnan() are available and work per spec.
58 * (On some platforms, we have to supply our own; see src/port.) However,
59 * generating an Infinity or NaN in the first place is less well standardized;
60 * pre-C99 systems tend not to have C99's INFINITY and NaN macros. We
61 * centralize our workarounds for this here.
62 */
63
64 /*
65 * The funny placements of the two #pragmas is necessary because of a
66 * long lived bug in the Microsoft compilers.
67 * See http://support.microsoft.com/kb/120968/en-us for details
68 */
69 #ifdef _MSC_VER
70 #pragma warning(disable:4756)
71 #endif
72 static inline float4
get_float4_infinity(void)73 get_float4_infinity(void)
74 {
75 #ifdef INFINITY
76 /* C99 standard way */
77 return (float4) INFINITY;
78 #else
79 #ifdef _MSC_VER
80 #pragma warning(default:4756)
81 #endif
82
83 /*
84 * On some platforms, HUGE_VAL is an infinity, elsewhere it's just the
85 * largest normal float8. We assume forcing an overflow will get us a
86 * true infinity.
87 */
88 return (float4) (HUGE_VAL * HUGE_VAL);
89 #endif
90 }
91
92 static inline float8
get_float8_infinity(void)93 get_float8_infinity(void)
94 {
95 #ifdef INFINITY
96 /* C99 standard way */
97 return (float8) INFINITY;
98 #else
99
100 /*
101 * On some platforms, HUGE_VAL is an infinity, elsewhere it's just the
102 * largest normal float8. We assume forcing an overflow will get us a
103 * true infinity.
104 */
105 return (float8) (HUGE_VAL * HUGE_VAL);
106 #endif
107 }
108
109 static inline float4
get_float4_nan(void)110 get_float4_nan(void)
111 {
112 #ifdef NAN
113 /* C99 standard way */
114 return (float4) NAN;
115 #else
116 /* Assume we can get a NAN via zero divide */
117 return (float4) (0.0 / 0.0);
118 #endif
119 }
120
121 static inline float8
get_float8_nan(void)122 get_float8_nan(void)
123 {
124 /* (float8) NAN doesn't work on some NetBSD/MIPS releases */
125 #if defined(NAN) && !(defined(__NetBSD__) && defined(__mips__))
126 /* C99 standard way */
127 return (float8) NAN;
128 #else
129 /* Assume we can get a NaN via zero divide */
130 return (float8) (0.0 / 0.0);
131 #endif
132 }
133
134 /*
135 * Floating-point arithmetic with overflow/underflow reported as errors
136 *
137 * There isn't any way to check for underflow of addition/subtraction
138 * because numbers near the underflow value have already been rounded to
139 * the point where we can't detect that the two values were originally
140 * different, e.g. on x86, '1e-45'::float4 == '2e-45'::float4 ==
141 * 1.4013e-45.
142 */
143
144 static inline float4
float4_pl(const float4 val1,const float4 val2)145 float4_pl(const float4 val1, const float4 val2)
146 {
147 float4 result;
148
149 result = val1 + val2;
150 if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
151 float_overflow_error();
152
153 return result;
154 }
155
156 static inline float8
float8_pl(const float8 val1,const float8 val2)157 float8_pl(const float8 val1, const float8 val2)
158 {
159 float8 result;
160
161 result = val1 + val2;
162 if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
163 float_overflow_error();
164
165 return result;
166 }
167
168 static inline float4
float4_mi(const float4 val1,const float4 val2)169 float4_mi(const float4 val1, const float4 val2)
170 {
171 float4 result;
172
173 result = val1 - val2;
174 if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
175 float_overflow_error();
176
177 return result;
178 }
179
180 static inline float8
float8_mi(const float8 val1,const float8 val2)181 float8_mi(const float8 val1, const float8 val2)
182 {
183 float8 result;
184
185 result = val1 - val2;
186 if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
187 float_overflow_error();
188
189 return result;
190 }
191
192 static inline float4
float4_mul(const float4 val1,const float4 val2)193 float4_mul(const float4 val1, const float4 val2)
194 {
195 float4 result;
196
197 result = val1 * val2;
198 if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
199 float_overflow_error();
200 if (unlikely(result == 0.0f) && val1 != 0.0f && val2 != 0.0f)
201 float_underflow_error();
202
203 return result;
204 }
205
206 static inline float8
float8_mul(const float8 val1,const float8 val2)207 float8_mul(const float8 val1, const float8 val2)
208 {
209 float8 result;
210
211 result = val1 * val2;
212 if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
213 float_overflow_error();
214 if (unlikely(result == 0.0) && val1 != 0.0 && val2 != 0.0)
215 float_underflow_error();
216
217 return result;
218 }
219
220 static inline float4
float4_div(const float4 val1,const float4 val2)221 float4_div(const float4 val1, const float4 val2)
222 {
223 float4 result;
224
225 if (unlikely(val2 == 0.0f) && !isnan(val1))
226 float_zero_divide_error();
227 result = val1 / val2;
228 if (unlikely(isinf(result)) && !isinf(val1))
229 float_overflow_error();
230 if (unlikely(result == 0.0f) && val1 != 0.0f && !isinf(val2))
231 float_underflow_error();
232
233 return result;
234 }
235
236 static inline float8
float8_div(const float8 val1,const float8 val2)237 float8_div(const float8 val1, const float8 val2)
238 {
239 float8 result;
240
241 if (unlikely(val2 == 0.0) && !isnan(val1))
242 float_zero_divide_error();
243 result = val1 / val2;
244 if (unlikely(isinf(result)) && !isinf(val1))
245 float_overflow_error();
246 if (unlikely(result == 0.0) && val1 != 0.0 && !isinf(val2))
247 float_underflow_error();
248
249 return result;
250 }
251
252 /*
253 * Routines for NaN-aware comparisons
254 *
255 * We consider all NaNs to be equal and larger than any non-NaN. This is
256 * somewhat arbitrary; the important thing is to have a consistent sort
257 * order.
258 */
259
260 static inline bool
float4_eq(const float4 val1,const float4 val2)261 float4_eq(const float4 val1, const float4 val2)
262 {
263 return isnan(val1) ? isnan(val2) : !isnan(val2) && val1 == val2;
264 }
265
266 static inline bool
float8_eq(const float8 val1,const float8 val2)267 float8_eq(const float8 val1, const float8 val2)
268 {
269 return isnan(val1) ? isnan(val2) : !isnan(val2) && val1 == val2;
270 }
271
272 static inline bool
float4_ne(const float4 val1,const float4 val2)273 float4_ne(const float4 val1, const float4 val2)
274 {
275 return isnan(val1) ? !isnan(val2) : isnan(val2) || val1 != val2;
276 }
277
278 static inline bool
float8_ne(const float8 val1,const float8 val2)279 float8_ne(const float8 val1, const float8 val2)
280 {
281 return isnan(val1) ? !isnan(val2) : isnan(val2) || val1 != val2;
282 }
283
284 static inline bool
float4_lt(const float4 val1,const float4 val2)285 float4_lt(const float4 val1, const float4 val2)
286 {
287 return !isnan(val1) && (isnan(val2) || val1 < val2);
288 }
289
290 static inline bool
float8_lt(const float8 val1,const float8 val2)291 float8_lt(const float8 val1, const float8 val2)
292 {
293 return !isnan(val1) && (isnan(val2) || val1 < val2);
294 }
295
296 static inline bool
float4_le(const float4 val1,const float4 val2)297 float4_le(const float4 val1, const float4 val2)
298 {
299 return isnan(val2) || (!isnan(val1) && val1 <= val2);
300 }
301
302 static inline bool
float8_le(const float8 val1,const float8 val2)303 float8_le(const float8 val1, const float8 val2)
304 {
305 return isnan(val2) || (!isnan(val1) && val1 <= val2);
306 }
307
308 static inline bool
float4_gt(const float4 val1,const float4 val2)309 float4_gt(const float4 val1, const float4 val2)
310 {
311 return !isnan(val2) && (isnan(val1) || val1 > val2);
312 }
313
314 static inline bool
float8_gt(const float8 val1,const float8 val2)315 float8_gt(const float8 val1, const float8 val2)
316 {
317 return !isnan(val2) && (isnan(val1) || val1 > val2);
318 }
319
320 static inline bool
float4_ge(const float4 val1,const float4 val2)321 float4_ge(const float4 val1, const float4 val2)
322 {
323 return isnan(val1) || (!isnan(val2) && val1 >= val2);
324 }
325
326 static inline bool
float8_ge(const float8 val1,const float8 val2)327 float8_ge(const float8 val1, const float8 val2)
328 {
329 return isnan(val1) || (!isnan(val2) && val1 >= val2);
330 }
331
332 static inline float4
float4_min(const float4 val1,const float4 val2)333 float4_min(const float4 val1, const float4 val2)
334 {
335 return float4_lt(val1, val2) ? val1 : val2;
336 }
337
338 static inline float8
float8_min(const float8 val1,const float8 val2)339 float8_min(const float8 val1, const float8 val2)
340 {
341 return float8_lt(val1, val2) ? val1 : val2;
342 }
343
344 static inline float4
float4_max(const float4 val1,const float4 val2)345 float4_max(const float4 val1, const float4 val2)
346 {
347 return float4_gt(val1, val2) ? val1 : val2;
348 }
349
350 static inline float8
float8_max(const float8 val1,const float8 val2)351 float8_max(const float8 val1, const float8 val2)
352 {
353 return float8_gt(val1, val2) ? val1 : val2;
354 }
355
356 #endif /* FLOAT_H */
357