TLA Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * float.c
4 : * Functions for the built-in floating-point types.
5 : *
6 : * Portions Copyright (c) 1996-2023, PostgreSQL Global Development Group
7 : * Portions Copyright (c) 1994, Regents of the University of California
8 : *
9 : *
10 : * IDENTIFICATION
11 : * src/backend/utils/adt/float.c
12 : *
13 : *-------------------------------------------------------------------------
14 : */
15 : #include "postgres.h"
16 :
17 : #include <ctype.h>
18 : #include <float.h>
19 : #include <math.h>
20 : #include <limits.h>
21 :
22 : #include "catalog/pg_type.h"
23 : #include "common/int.h"
24 : #include "common/pg_prng.h"
25 : #include "common/shortest_dec.h"
26 : #include "libpq/pqformat.h"
27 : #include "miscadmin.h"
28 : #include "utils/array.h"
29 : #include "utils/float.h"
30 : #include "utils/fmgrprotos.h"
31 : #include "utils/sortsupport.h"
32 : #include "utils/timestamp.h"
33 :
34 :
35 : /*
36 : * Configurable GUC parameter
37 : *
38 : * If >0, use shortest-decimal format for output; this is both the default and
39 : * allows for compatibility with clients that explicitly set a value here to
40 : * get round-trip-accurate results. If 0 or less, then use the old, slow,
41 : * decimal rounding method.
42 : */
43 : int extra_float_digits = 1;
44 :
45 : /* Cached constants for degree-based trig functions */
46 : static bool degree_consts_set = false;
47 : static float8 sin_30 = 0;
48 : static float8 one_minus_cos_60 = 0;
49 : static float8 asin_0_5 = 0;
50 : static float8 acos_0_5 = 0;
51 : static float8 atan_1_0 = 0;
52 : static float8 tan_45 = 0;
53 : static float8 cot_45 = 0;
54 :
55 : /*
56 : * These are intentionally not static; don't "fix" them. They will never
57 : * be referenced by other files, much less changed; but we don't want the
58 : * compiler to know that, else it might try to precompute expressions
59 : * involving them. See comments for init_degree_constants().
60 : */
61 : float8 degree_c_thirty = 30.0;
62 : float8 degree_c_forty_five = 45.0;
63 : float8 degree_c_sixty = 60.0;
64 : float8 degree_c_one_half = 0.5;
65 : float8 degree_c_one = 1.0;
66 :
67 : /* State for drandom() and setseed() */
68 : static bool drandom_seed_set = false;
69 : static pg_prng_state drandom_seed;
70 :
71 : /* Local function prototypes */
72 : static double sind_q1(double x);
73 : static double cosd_q1(double x);
74 : static void init_degree_constants(void);
75 :
76 :
77 : /*
78 : * We use these out-of-line ereport() calls to report float overflow,
79 : * underflow, and zero-divide, because following our usual practice of
80 : * repeating them at each call site would lead to a lot of code bloat.
81 : *
82 : * This does mean that you don't get a useful error location indicator.
83 : */
84 : pg_noinline void
85 CBC 18 : float_overflow_error(void)
86 : {
87 18 : ereport(ERROR,
88 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
89 : errmsg("value out of range: overflow")));
90 : }
91 :
92 : pg_noinline void
93 12 : float_underflow_error(void)
94 : {
95 12 : ereport(ERROR,
96 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
97 : errmsg("value out of range: underflow")));
98 : }
99 :
100 : pg_noinline void
101 36 : float_zero_divide_error(void)
102 : {
103 36 : ereport(ERROR,
104 : (errcode(ERRCODE_DIVISION_BY_ZERO),
105 : errmsg("division by zero")));
106 : }
107 :
108 :
109 : /*
110 : * Returns -1 if 'val' represents negative infinity, 1 if 'val'
111 : * represents (positive) infinity, and 0 otherwise. On some platforms,
112 : * this is equivalent to the isinf() macro, but not everywhere: C99
113 : * does not specify that isinf() needs to distinguish between positive
114 : * and negative infinity.
115 : */
116 : int
117 UBC 0 : is_infinite(double val)
118 : {
119 0 : int inf = isinf(val);
120 :
121 0 : if (inf == 0)
122 0 : return 0;
123 0 : else if (val > 0)
124 0 : return 1;
125 : else
126 0 : return -1;
127 : }
128 :
129 :
130 : /* ========== USER I/O ROUTINES ========== */
131 :
132 :
133 : /*
134 : * float4in - converts "num" to float4
135 : *
136 : * Note that this code now uses strtof(), where it used to use strtod().
137 : *
138 : * The motivation for using strtof() is to avoid a double-rounding problem:
139 : * for certain decimal inputs, if you round the input correctly to a double,
140 : * and then round the double to a float, the result is incorrect in that it
141 : * does not match the result of rounding the decimal value to float directly.
142 : *
143 : * One of the best examples is 7.038531e-26:
144 : *
145 : * 0xAE43FDp-107 = 7.03853069185120912085...e-26
146 : * midpoint 7.03853100000000022281...e-26
147 : * 0xAE43FEp-107 = 7.03853130814879132477...e-26
148 : *
149 : * making 0xAE43FDp-107 the correct float result, but if you do the conversion
150 : * via a double, you get
151 : *
152 : * 0xAE43FD.7FFFFFF8p-107 = 7.03853099999999907487...e-26
153 : * midpoint 7.03853099999999964884...e-26
154 : * 0xAE43FD.80000000p-107 = 7.03853100000000022281...e-26
155 : * 0xAE43FD.80000008p-107 = 7.03853100000000137076...e-26
156 : *
157 : * so the value rounds to the double exactly on the midpoint between the two
158 : * nearest floats, and then rounding again to a float gives the incorrect
159 : * result of 0xAE43FEp-107.
160 : *
161 : */
162 : Datum
163 CBC 2012330 : float4in(PG_FUNCTION_ARGS)
164 : {
165 2012330 : char *num = PG_GETARG_CSTRING(0);
166 :
167 GNC 2012330 : PG_RETURN_FLOAT4(float4in_internal(num, NULL, "real", num,
168 : fcinfo->context));
169 : }
170 :
171 : /*
172 : * float4in_internal - guts of float4in()
173 : *
174 : * This is exposed for use by functions that want a reasonably
175 : * platform-independent way of inputting floats. The behavior is
176 : * essentially like strtof + ereturn on error.
177 : *
178 : * Uses the same API as float8in_internal below, so most of its
179 : * comments also apply here, except regarding use in geometric types.
180 : */
181 : float4
182 2017504 : float4in_internal(char *num, char **endptr_p,
183 : const char *type_name, const char *orig_string,
184 : struct Node *escontext)
185 : {
186 ECB : float val;
187 : char *endptr;
188 :
189 : /*
190 : * endptr points to the first character _after_ the sequence we recognized
191 : * as a valid floating point number. orig_string points to the original
192 : * input
193 : * string.
194 : */
195 :
196 : /* skip leading whitespace */
197 GIC 2017609 : while (*num != '\0' && isspace((unsigned char) *num))
198 105 : num++;
199 :
200 : /*
201 ECB : * Check for an empty-string input to begin with, to avoid the vagaries of
202 : * strtod() on different platforms.
203 : */
204 GIC 2017504 : if (*num == '\0')
205 GNC 6 : ereturn(escontext, 0,
206 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
207 : errmsg("invalid input syntax for type %s: \"%s\"",
208 : type_name, orig_string)));
209 :
210 GIC 2017498 : errno = 0;
211 2017498 : val = strtof(num, &endptr);
212 :
213 : /* did we not see anything that looks like a double? */
214 2017498 : if (endptr == num || errno != 0)
215 : {
216 CBC 46 : int save_errno = errno;
217 ECB :
218 : /*
219 : * C99 requires that strtof() accept NaN, [+-]Infinity, and [+-]Inf,
220 : * but not all platforms support all of these (and some accept them
221 : * but set ERANGE anyway...) Therefore, we check for these inputs
222 : * ourselves if strtof() fails.
223 : *
224 : * Note: C99 also requires hexadecimal input as well as some extended
225 : * forms of NaN, but we consider these forms unportable and don't try
226 : * to support them. You can use 'em if your strtof() takes 'em.
227 : */
228 GIC 46 : if (pg_strncasecmp(num, "NaN", 3) == 0)
229 ECB : {
230 LBC 0 : val = get_float4_nan();
231 UIC 0 : endptr = num + 3;
232 : }
233 CBC 46 : else if (pg_strncasecmp(num, "Infinity", 8) == 0)
234 : {
235 LBC 0 : val = get_float4_infinity();
236 UIC 0 : endptr = num + 8;
237 : }
238 GIC 46 : else if (pg_strncasecmp(num, "+Infinity", 9) == 0)
239 : {
240 UIC 0 : val = get_float4_infinity();
241 0 : endptr = num + 9;
242 : }
243 GIC 46 : else if (pg_strncasecmp(num, "-Infinity", 9) == 0)
244 : {
245 UIC 0 : val = -get_float4_infinity();
246 0 : endptr = num + 9;
247 ECB : }
248 GIC 46 : else if (pg_strncasecmp(num, "inf", 3) == 0)
249 EUB : {
250 UBC 0 : val = get_float4_infinity();
251 UIC 0 : endptr = num + 3;
252 ECB : }
253 GIC 46 : else if (pg_strncasecmp(num, "+inf", 4) == 0)
254 EUB : {
255 UBC 0 : val = get_float4_infinity();
256 UIC 0 : endptr = num + 4;
257 ECB : }
258 GIC 46 : else if (pg_strncasecmp(num, "-inf", 4) == 0)
259 EUB : {
260 UBC 0 : val = -get_float4_infinity();
261 UIC 0 : endptr = num + 4;
262 ECB : }
263 GIC 46 : else if (save_errno == ERANGE)
264 EUB : {
265 : /*
266 : * Some platforms return ERANGE for denormalized numbers (those
267 ECB : * that are not zero, but are too close to zero to have full
268 : * precision). We'd prefer not to throw error for that, so try to
269 EUB : * detect whether it's a "real" out-of-range condition by checking
270 : * to see if the result is zero or huge.
271 : */
272 GIC 33 : if (val == 0.0 ||
273 : #if !defined(HUGE_VALF)
274 : isinf(val)
275 EUB : #else
276 GBC 6 : (val >= HUGE_VALF || val <= -HUGE_VALF)
277 : #endif
278 ECB : )
279 : {
280 : /* see comments in float8in_internal for rationale */
281 GNC 33 : char *errnumber = pstrdup(num);
282 :
283 33 : errnumber[endptr - num] = '\0';
284 :
285 33 : ereturn(escontext, 0,
286 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
287 : errmsg("\"%s\" is out of range for type real",
288 : errnumber)));
289 : }
290 : }
291 : else
292 13 : ereturn(escontext, 0,
293 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
294 ECB : errmsg("invalid input syntax for type %s: \"%s\"",
295 : type_name, orig_string)));
296 : }
297 :
298 : /* skip trailing whitespace */
299 GIC 2017551 : while (*endptr != '\0' && isspace((unsigned char) *endptr))
300 99 : endptr++;
301 :
302 : /* report stopping point if wanted, else complain if not end of string */
303 GNC 2017452 : if (endptr_p)
304 UNC 0 : *endptr_p = endptr;
305 GNC 2017452 : else if (*endptr != '\0')
306 18 : ereturn(escontext, 0,
307 ECB : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
308 : errmsg("invalid input syntax for type %s: \"%s\"",
309 : type_name, orig_string)));
310 :
311 GNC 2017434 : return val;
312 : }
313 :
314 : /*
315 : * float4out - converts a float4 number to a string
316 ECB : * using a standard output format
317 : */
318 : Datum
319 GIC 18362 : float4out(PG_FUNCTION_ARGS)
320 : {
321 18362 : float4 num = PG_GETARG_FLOAT4(0);
322 18362 : char *ascii = (char *) palloc(32);
323 CBC 18362 : int ndig = FLT_DIG + extra_float_digits;
324 ECB :
325 GIC 18362 : if (extra_float_digits > 0)
326 : {
327 CBC 11992 : float_to_shortest_decimal_buf(num, ascii);
328 GBC 11992 : PG_RETURN_CSTRING(ascii);
329 ECB : }
330 :
331 GIC 6370 : (void) pg_strfromd(ascii, 32, ndig, num);
332 6370 : PG_RETURN_CSTRING(ascii);
333 : }
334 :
335 ECB : /*
336 : * float4recv - converts external binary format to float4
337 : */
338 : Datum
339 UIC 0 : float4recv(PG_FUNCTION_ARGS)
340 : {
341 0 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
342 :
343 LBC 0 : PG_RETURN_FLOAT4(pq_getmsgfloat4(buf));
344 : }
345 ECB :
346 : /*
347 : * float4send - converts float4 to binary format
348 : */
349 : Datum
350 GIC 3246 : float4send(PG_FUNCTION_ARGS)
351 ECB : {
352 CBC 3246 : float4 num = PG_GETARG_FLOAT4(0);
353 : StringInfoData buf;
354 :
355 3246 : pq_begintypsend(&buf);
356 3246 : pq_sendfloat4(&buf, num);
357 GIC 3246 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
358 : }
359 :
360 : /*
361 : * float8in - converts "num" to float8
362 : */
363 EUB : Datum
364 GIC 338183 : float8in(PG_FUNCTION_ARGS)
365 EUB : {
366 GIC 338183 : char *num = PG_GETARG_CSTRING(0);
367 EUB :
368 GNC 338183 : PG_RETURN_FLOAT8(float8in_internal(num, NULL, "double precision", num,
369 : fcinfo->context));
370 : }
371 :
372 : /*
373 : * float8in_internal - guts of float8in()
374 : *
375 : * This is exposed for use by functions that want a reasonably
376 : * platform-independent way of inputting doubles. The behavior is
377 : * essentially like strtod + ereturn on error, but note the following
378 ECB : * differences:
379 : * 1. Both leading and trailing whitespace are skipped.
380 : * 2. If endptr_p is NULL, we report error if there's trailing junk.
381 : * Otherwise, it's up to the caller to complain about trailing junk.
382 : * 3. In event of a syntax error, the report mentions the given type_name
383 : * and prints orig_string as the input; this is meant to support use of
384 : * this function with types such as "box" and "point", where what we are
385 : * parsing here is just a substring of orig_string.
386 : *
387 : * If escontext points to an ErrorSaveContext node, that is filled instead
388 : * of throwing an error; the caller must check SOFT_ERROR_OCCURRED()
389 : * to detect errors.
390 : *
391 : * "num" could validly be declared "const char *", but that results in an
392 : * unreasonable amount of extra casting both here and in callers, so we don't.
393 : */
394 : float8
395 GNC 464009 : float8in_internal(char *num, char **endptr_p,
396 : const char *type_name, const char *orig_string,
397 : struct Node *escontext)
398 : {
399 : double val;
400 : char *endptr;
401 :
402 : /* skip leading whitespace */
403 GIC 464659 : while (*num != '\0' && isspace((unsigned char) *num))
404 650 : num++;
405 :
406 : /*
407 ECB : * Check for an empty-string input to begin with, to avoid the vagaries of
408 : * strtod() on different platforms.
409 : */
410 GIC 464009 : if (*num == '\0')
411 GNC 9 : ereturn(escontext, 0,
412 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
413 : errmsg("invalid input syntax for type %s: \"%s\"",
414 : type_name, orig_string)));
415 ECB :
416 GIC 464000 : errno = 0;
417 464000 : val = strtod(num, &endptr);
418 :
419 : /* did we not see anything that looks like a double? */
420 464000 : if (endptr == num || errno != 0)
421 ECB : {
422 CBC 132 : int save_errno = errno;
423 :
424 : /*
425 : * C99 requires that strtod() accept NaN, [+-]Infinity, and [+-]Inf,
426 : * but not all platforms support all of these (and some accept them
427 ECB : * but set ERANGE anyway...) Therefore, we check for these inputs
428 : * ourselves if strtod() fails.
429 : *
430 : * Note: C99 also requires hexadecimal input as well as some extended
431 : * forms of NaN, but we consider these forms unportable and don't try
432 : * to support them. You can use 'em if your strtod() takes 'em.
433 : */
434 GIC 132 : if (pg_strncasecmp(num, "NaN", 3) == 0)
435 : {
436 UIC 0 : val = get_float8_nan();
437 0 : endptr = num + 3;
438 : }
439 GIC 132 : else if (pg_strncasecmp(num, "Infinity", 8) == 0)
440 : {
441 UIC 0 : val = get_float8_infinity();
442 0 : endptr = num + 8;
443 : }
444 GIC 132 : else if (pg_strncasecmp(num, "+Infinity", 9) == 0)
445 ECB : {
446 UIC 0 : val = get_float8_infinity();
447 UBC 0 : endptr = num + 9;
448 EUB : }
449 GIC 132 : else if (pg_strncasecmp(num, "-Infinity", 9) == 0)
450 ECB : {
451 UIC 0 : val = -get_float8_infinity();
452 UBC 0 : endptr = num + 9;
453 EUB : }
454 GIC 132 : else if (pg_strncasecmp(num, "inf", 3) == 0)
455 ECB : {
456 UIC 0 : val = get_float8_infinity();
457 UBC 0 : endptr = num + 3;
458 EUB : }
459 GIC 132 : else if (pg_strncasecmp(num, "+inf", 4) == 0)
460 ECB : {
461 UIC 0 : val = get_float8_infinity();
462 UBC 0 : endptr = num + 4;
463 EUB : }
464 GIC 132 : else if (pg_strncasecmp(num, "-inf", 4) == 0)
465 ECB : {
466 UIC 0 : val = -get_float8_infinity();
467 UBC 0 : endptr = num + 4;
468 EUB : }
469 GIC 132 : else if (save_errno == ERANGE)
470 ECB : {
471 : /*
472 EUB : * Some platforms return ERANGE for denormalized numbers (those
473 : * that are not zero, but are too close to zero to have full
474 : * precision). We'd prefer not to throw error for that, so try to
475 ECB : * detect whether it's a "real" out-of-range condition by checking
476 : * to see if the result is zero or huge.
477 EUB : *
478 : * On error, we intentionally complain about double precision not
479 : * the given type name, and we print only the part of the string
480 ECB : * that is the current number.
481 : */
482 GIC 63 : if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
483 : {
484 54 : char *errnumber = pstrdup(num);
485 :
486 54 : errnumber[endptr - num] = '\0';
487 GNC 54 : ereturn(escontext, 0,
488 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
489 : errmsg("\"%s\" is out of range for type double precision",
490 : errnumber)));
491 : }
492 ECB : }
493 : else
494 GNC 69 : ereturn(escontext, 0,
495 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
496 : errmsg("invalid input syntax for type %s: \"%s\"",
497 : type_name, orig_string)));
498 : }
499 :
500 : /* skip trailing whitespace */
501 GIC 464070 : while (*endptr != '\0' && isspace((unsigned char) *endptr))
502 CBC 193 : endptr++;
503 :
504 : /* report stopping point if wanted, else complain if not end of string */
505 GIC 463877 : if (endptr_p)
506 125727 : *endptr_p = endptr;
507 338150 : else if (*endptr != '\0')
508 GNC 21 : ereturn(escontext, 0,
509 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
510 : errmsg("invalid input syntax for type %s: \"%s\"",
511 : type_name, orig_string)));
512 ECB :
513 CBC 463856 : return val;
514 ECB : }
515 :
516 :
517 : /*
518 : * float8out - converts float8 number to a string
519 : * using a standard output format
520 : */
521 : Datum
522 GIC 287938 : float8out(PG_FUNCTION_ARGS)
523 : {
524 287938 : float8 num = PG_GETARG_FLOAT8(0);
525 :
526 287938 : PG_RETURN_CSTRING(float8out_internal(num));
527 : }
528 :
529 : /*
530 : * float8out_internal - guts of float8out()
531 : *
532 ECB : * This is exposed for use by functions that want a reasonably
533 : * platform-independent way of outputting doubles.
534 : * The result is always palloc'd.
535 : */
536 : char *
537 CBC 2088200 : float8out_internal(double num)
538 : {
539 2088200 : char *ascii = (char *) palloc(32);
540 2088200 : int ndig = DBL_DIG + extra_float_digits;
541 :
542 GIC 2088200 : if (extra_float_digits > 0)
543 ECB : {
544 CBC 1979576 : double_to_shortest_decimal_buf(num, ascii);
545 GIC 1979576 : return ascii;
546 : }
547 :
548 108624 : (void) pg_strfromd(ascii, 32, ndig, num);
549 108624 : return ascii;
550 : }
551 ECB :
552 : /*
553 : * float8recv - converts external binary format to float8
554 : */
555 : Datum
556 GIC 13 : float8recv(PG_FUNCTION_ARGS)
557 : {
558 13 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
559 :
560 13 : PG_RETURN_FLOAT8(pq_getmsgfloat8(buf));
561 : }
562 ECB :
563 : /*
564 : * float8send - converts float8 to binary format
565 : */
566 : Datum
567 CBC 2578 : float8send(PG_FUNCTION_ARGS)
568 ECB : {
569 CBC 2578 : float8 num = PG_GETARG_FLOAT8(0);
570 : StringInfoData buf;
571 :
572 GIC 2578 : pq_begintypsend(&buf);
573 2578 : pq_sendfloat8(&buf, num);
574 2578 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
575 : }
576 :
577 :
578 : /* ========== PUBLIC ROUTINES ========== */
579 :
580 :
581 : /*
582 : * ======================
583 : * FLOAT4 BASE OPERATIONS
584 : * ======================
585 : */
586 ECB :
587 : /*
588 : * float4abs - returns |arg1| (absolute value)
589 : */
590 : Datum
591 GIC 15 : float4abs(PG_FUNCTION_ARGS)
592 : {
593 15 : float4 arg1 = PG_GETARG_FLOAT4(0);
594 :
595 GNC 15 : PG_RETURN_FLOAT4(fabsf(arg1));
596 : }
597 ECB :
598 : /*
599 : * float4um - returns -arg1 (unary minus)
600 : */
601 : Datum
602 CBC 8 : float4um(PG_FUNCTION_ARGS)
603 ECB : {
604 GIC 8 : float4 arg1 = PG_GETARG_FLOAT4(0);
605 : float4 result;
606 :
607 GBC 8 : result = -arg1;
608 GIC 8 : PG_RETURN_FLOAT4(result);
609 EUB : }
610 :
611 : Datum
612 UIC 0 : float4up(PG_FUNCTION_ARGS)
613 : {
614 0 : float4 arg = PG_GETARG_FLOAT4(0);
615 ECB :
616 UIC 0 : PG_RETURN_FLOAT4(arg);
617 ECB : }
618 :
619 : Datum
620 GIC 9 : float4larger(PG_FUNCTION_ARGS)
621 ECB : {
622 CBC 9 : float4 arg1 = PG_GETARG_FLOAT4(0);
623 GIC 9 : float4 arg2 = PG_GETARG_FLOAT4(1);
624 ECB : float4 result;
625 :
626 GIC 9 : if (float4_gt(arg1, arg2))
627 3 : result = arg1;
628 : else
629 GBC 6 : result = arg2;
630 GIC 9 : PG_RETURN_FLOAT4(result);
631 EUB : }
632 :
633 : Datum
634 UIC 0 : float4smaller(PG_FUNCTION_ARGS)
635 EUB : {
636 UBC 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
637 UIC 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
638 EUB : float4 result;
639 :
640 UIC 0 : if (float4_lt(arg1, arg2))
641 0 : result = arg1;
642 : else
643 0 : result = arg2;
644 0 : PG_RETURN_FLOAT4(result);
645 : }
646 :
647 : /*
648 : * ======================
649 : * FLOAT8 BASE OPERATIONS
650 : * ======================
651 : */
652 ECB :
653 : /*
654 : * float8abs - returns |arg1| (absolute value)
655 : */
656 : Datum
657 GIC 56216 : float8abs(PG_FUNCTION_ARGS)
658 : {
659 56216 : float8 arg1 = PG_GETARG_FLOAT8(0);
660 :
661 56216 : PG_RETURN_FLOAT8(fabs(arg1));
662 : }
663 :
664 ECB :
665 : /*
666 : * float8um - returns -arg1 (unary minus)
667 : */
668 : Datum
669 CBC 161 : float8um(PG_FUNCTION_ARGS)
670 ECB : {
671 GIC 161 : float8 arg1 = PG_GETARG_FLOAT8(0);
672 : float8 result;
673 :
674 GBC 161 : result = -arg1;
675 GIC 161 : PG_RETURN_FLOAT8(result);
676 EUB : }
677 :
678 : Datum
679 UIC 0 : float8up(PG_FUNCTION_ARGS)
680 : {
681 0 : float8 arg = PG_GETARG_FLOAT8(0);
682 ECB :
683 UIC 0 : PG_RETURN_FLOAT8(arg);
684 ECB : }
685 :
686 : Datum
687 GIC 6438 : float8larger(PG_FUNCTION_ARGS)
688 ECB : {
689 CBC 6438 : float8 arg1 = PG_GETARG_FLOAT8(0);
690 GIC 6438 : float8 arg2 = PG_GETARG_FLOAT8(1);
691 ECB : float8 result;
692 :
693 GIC 6438 : if (float8_gt(arg1, arg2))
694 6100 : result = arg1;
695 : else
696 CBC 338 : result = arg2;
697 GIC 6438 : PG_RETURN_FLOAT8(result);
698 ECB : }
699 :
700 : Datum
701 GIC 576 : float8smaller(PG_FUNCTION_ARGS)
702 ECB : {
703 CBC 576 : float8 arg1 = PG_GETARG_FLOAT8(0);
704 GIC 576 : float8 arg2 = PG_GETARG_FLOAT8(1);
705 ECB : float8 result;
706 :
707 GIC 576 : if (float8_lt(arg1, arg2))
708 444 : result = arg1;
709 : else
710 132 : result = arg2;
711 576 : PG_RETURN_FLOAT8(result);
712 : }
713 :
714 :
715 : /*
716 : * ====================
717 : * ARITHMETIC OPERATORS
718 : * ====================
719 : */
720 :
721 : /*
722 : * float4pl - returns arg1 + arg2
723 ECB : * float4mi - returns arg1 - arg2
724 : * float4mul - returns arg1 * arg2
725 : * float4div - returns arg1 / arg2
726 : */
727 : Datum
728 CBC 27 : float4pl(PG_FUNCTION_ARGS)
729 : {
730 GIC 27 : float4 arg1 = PG_GETARG_FLOAT4(0);
731 27 : float4 arg2 = PG_GETARG_FLOAT4(1);
732 ECB :
733 GIC 27 : PG_RETURN_FLOAT4(float4_pl(arg1, arg2));
734 ECB : }
735 :
736 : Datum
737 CBC 9 : float4mi(PG_FUNCTION_ARGS)
738 : {
739 GIC 9 : float4 arg1 = PG_GETARG_FLOAT4(0);
740 9 : float4 arg2 = PG_GETARG_FLOAT4(1);
741 ECB :
742 GIC 9 : PG_RETURN_FLOAT4(float4_mi(arg1, arg2));
743 ECB : }
744 :
745 : Datum
746 CBC 18 : float4mul(PG_FUNCTION_ARGS)
747 : {
748 GIC 18 : float4 arg1 = PG_GETARG_FLOAT4(0);
749 18 : float4 arg2 = PG_GETARG_FLOAT4(1);
750 ECB :
751 GIC 18 : PG_RETURN_FLOAT4(float4_mul(arg1, arg2));
752 ECB : }
753 :
754 : Datum
755 CBC 24 : float4div(PG_FUNCTION_ARGS)
756 : {
757 GIC 24 : float4 arg1 = PG_GETARG_FLOAT4(0);
758 24 : float4 arg2 = PG_GETARG_FLOAT4(1);
759 :
760 24 : PG_RETURN_FLOAT4(float4_div(arg1, arg2));
761 : }
762 :
763 : /*
764 : * float8pl - returns arg1 + arg2
765 ECB : * float8mi - returns arg1 - arg2
766 : * float8mul - returns arg1 * arg2
767 : * float8div - returns arg1 / arg2
768 : */
769 : Datum
770 CBC 33734 : float8pl(PG_FUNCTION_ARGS)
771 : {
772 GIC 33734 : float8 arg1 = PG_GETARG_FLOAT8(0);
773 33734 : float8 arg2 = PG_GETARG_FLOAT8(1);
774 ECB :
775 GIC 33734 : PG_RETURN_FLOAT8(float8_pl(arg1, arg2));
776 ECB : }
777 :
778 : Datum
779 CBC 6276 : float8mi(PG_FUNCTION_ARGS)
780 : {
781 GIC 6276 : float8 arg1 = PG_GETARG_FLOAT8(0);
782 6276 : float8 arg2 = PG_GETARG_FLOAT8(1);
783 ECB :
784 GIC 6276 : PG_RETURN_FLOAT8(float8_mi(arg1, arg2));
785 ECB : }
786 :
787 : Datum
788 CBC 300409 : float8mul(PG_FUNCTION_ARGS)
789 : {
790 GIC 300409 : float8 arg1 = PG_GETARG_FLOAT8(0);
791 300409 : float8 arg2 = PG_GETARG_FLOAT8(1);
792 ECB :
793 GIC 300409 : PG_RETURN_FLOAT8(float8_mul(arg1, arg2));
794 ECB : }
795 :
796 : Datum
797 CBC 7481 : float8div(PG_FUNCTION_ARGS)
798 : {
799 GIC 7481 : float8 arg1 = PG_GETARG_FLOAT8(0);
800 7481 : float8 arg2 = PG_GETARG_FLOAT8(1);
801 :
802 7481 : PG_RETURN_FLOAT8(float8_div(arg1, arg2));
803 : }
804 :
805 :
806 : /*
807 : * ====================
808 : * COMPARISON OPERATORS
809 : * ====================
810 : */
811 ECB :
812 : /*
813 : * float4{eq,ne,lt,le,gt,ge} - float4/float4 comparison operations
814 : */
815 : int
816 CBC 25266766 : float4_cmp_internal(float4 a, float4 b)
817 ECB : {
818 GIC 25266766 : if (float4_gt(a, b))
819 565349 : return 1;
820 24701417 : if (float4_lt(a, b))
821 CBC 1225781 : return -1;
822 GIC 23475636 : return 0;
823 ECB : }
824 :
825 : Datum
826 CBC 31166 : float4eq(PG_FUNCTION_ARGS)
827 : {
828 GIC 31166 : float4 arg1 = PG_GETARG_FLOAT4(0);
829 31166 : float4 arg2 = PG_GETARG_FLOAT4(1);
830 ECB :
831 GIC 31166 : PG_RETURN_BOOL(float4_eq(arg1, arg2));
832 ECB : }
833 :
834 : Datum
835 CBC 15 : float4ne(PG_FUNCTION_ARGS)
836 : {
837 GIC 15 : float4 arg1 = PG_GETARG_FLOAT4(0);
838 15 : float4 arg2 = PG_GETARG_FLOAT4(1);
839 ECB :
840 GIC 15 : PG_RETURN_BOOL(float4_ne(arg1, arg2));
841 ECB : }
842 :
843 : Datum
844 CBC 37005 : float4lt(PG_FUNCTION_ARGS)
845 : {
846 GIC 37005 : float4 arg1 = PG_GETARG_FLOAT4(0);
847 37005 : float4 arg2 = PG_GETARG_FLOAT4(1);
848 ECB :
849 GIC 37005 : PG_RETURN_BOOL(float4_lt(arg1, arg2));
850 ECB : }
851 :
852 : Datum
853 CBC 1914 : float4le(PG_FUNCTION_ARGS)
854 : {
855 GIC 1914 : float4 arg1 = PG_GETARG_FLOAT4(0);
856 1914 : float4 arg2 = PG_GETARG_FLOAT4(1);
857 ECB :
858 GIC 1914 : PG_RETURN_BOOL(float4_le(arg1, arg2));
859 ECB : }
860 :
861 : Datum
862 CBC 2319 : float4gt(PG_FUNCTION_ARGS)
863 : {
864 GIC 2319 : float4 arg1 = PG_GETARG_FLOAT4(0);
865 2319 : float4 arg2 = PG_GETARG_FLOAT4(1);
866 ECB :
867 GIC 2319 : PG_RETURN_BOOL(float4_gt(arg1, arg2));
868 ECB : }
869 :
870 : Datum
871 CBC 1914 : float4ge(PG_FUNCTION_ARGS)
872 : {
873 GIC 1914 : float4 arg1 = PG_GETARG_FLOAT4(0);
874 1914 : float4 arg2 = PG_GETARG_FLOAT4(1);
875 ECB :
876 GIC 1914 : PG_RETURN_BOOL(float4_ge(arg1, arg2));
877 ECB : }
878 :
879 : Datum
880 CBC 952319 : btfloat4cmp(PG_FUNCTION_ARGS)
881 : {
882 GIC 952319 : float4 arg1 = PG_GETARG_FLOAT4(0);
883 952319 : float4 arg2 = PG_GETARG_FLOAT4(1);
884 ECB :
885 GIC 952319 : PG_RETURN_INT32(float4_cmp_internal(arg1, arg2));
886 ECB : }
887 :
888 : static int
889 CBC 24314447 : btfloat4fastcmp(Datum x, Datum y, SortSupport ssup)
890 : {
891 GIC 24314447 : float4 arg1 = DatumGetFloat4(x);
892 24314447 : float4 arg2 = DatumGetFloat4(y);
893 ECB :
894 GIC 24314447 : return float4_cmp_internal(arg1, arg2);
895 ECB : }
896 :
897 : Datum
898 CBC 1768 : btfloat4sortsupport(PG_FUNCTION_ARGS)
899 : {
900 GIC 1768 : SortSupport ssup = (SortSupport) PG_GETARG_POINTER(0);
901 :
902 1768 : ssup->comparator = btfloat4fastcmp;
903 1768 : PG_RETURN_VOID();
904 : }
905 ECB :
906 : /*
907 : * float8{eq,ne,lt,le,gt,ge} - float8/float8 comparison operations
908 : */
909 : int
910 CBC 12116741 : float8_cmp_internal(float8 a, float8 b)
911 ECB : {
912 GIC 12116741 : if (float8_gt(a, b))
913 4432848 : return 1;
914 7683893 : if (float8_lt(a, b))
915 CBC 7561608 : return -1;
916 GIC 122285 : return 0;
917 ECB : }
918 :
919 : Datum
920 CBC 116340 : float8eq(PG_FUNCTION_ARGS)
921 : {
922 GIC 116340 : float8 arg1 = PG_GETARG_FLOAT8(0);
923 116340 : float8 arg2 = PG_GETARG_FLOAT8(1);
924 ECB :
925 GIC 116340 : PG_RETURN_BOOL(float8_eq(arg1, arg2));
926 ECB : }
927 :
928 : Datum
929 CBC 177 : float8ne(PG_FUNCTION_ARGS)
930 : {
931 GIC 177 : float8 arg1 = PG_GETARG_FLOAT8(0);
932 177 : float8 arg2 = PG_GETARG_FLOAT8(1);
933 ECB :
934 GIC 177 : PG_RETURN_BOOL(float8_ne(arg1, arg2));
935 ECB : }
936 :
937 : Datum
938 CBC 83790 : float8lt(PG_FUNCTION_ARGS)
939 : {
940 GIC 83790 : float8 arg1 = PG_GETARG_FLOAT8(0);
941 83790 : float8 arg2 = PG_GETARG_FLOAT8(1);
942 ECB :
943 GIC 83790 : PG_RETURN_BOOL(float8_lt(arg1, arg2));
944 ECB : }
945 :
946 : Datum
947 CBC 3010 : float8le(PG_FUNCTION_ARGS)
948 : {
949 GIC 3010 : float8 arg1 = PG_GETARG_FLOAT8(0);
950 3010 : float8 arg2 = PG_GETARG_FLOAT8(1);
951 ECB :
952 GIC 3010 : PG_RETURN_BOOL(float8_le(arg1, arg2));
953 ECB : }
954 :
955 : Datum
956 CBC 10033 : float8gt(PG_FUNCTION_ARGS)
957 : {
958 GIC 10033 : float8 arg1 = PG_GETARG_FLOAT8(0);
959 10033 : float8 arg2 = PG_GETARG_FLOAT8(1);
960 ECB :
961 GIC 10033 : PG_RETURN_BOOL(float8_gt(arg1, arg2));
962 ECB : }
963 :
964 : Datum
965 CBC 10652 : float8ge(PG_FUNCTION_ARGS)
966 : {
967 GIC 10652 : float8 arg1 = PG_GETARG_FLOAT8(0);
968 10652 : float8 arg2 = PG_GETARG_FLOAT8(1);
969 ECB :
970 GIC 10652 : PG_RETURN_BOOL(float8_ge(arg1, arg2));
971 ECB : }
972 :
973 : Datum
974 CBC 1646 : btfloat8cmp(PG_FUNCTION_ARGS)
975 : {
976 GIC 1646 : float8 arg1 = PG_GETARG_FLOAT8(0);
977 1646 : float8 arg2 = PG_GETARG_FLOAT8(1);
978 ECB :
979 GIC 1646 : PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
980 ECB : }
981 :
982 : static int
983 CBC 3464685 : btfloat8fastcmp(Datum x, Datum y, SortSupport ssup)
984 : {
985 GIC 3464685 : float8 arg1 = DatumGetFloat8(x);
986 3464685 : float8 arg2 = DatumGetFloat8(y);
987 ECB :
988 GIC 3464685 : return float8_cmp_internal(arg1, arg2);
989 ECB : }
990 :
991 : Datum
992 CBC 467 : btfloat8sortsupport(PG_FUNCTION_ARGS)
993 : {
994 GIC 467 : SortSupport ssup = (SortSupport) PG_GETARG_POINTER(0);
995 :
996 GBC 467 : ssup->comparator = btfloat8fastcmp;
997 GIC 467 : PG_RETURN_VOID();
998 EUB : }
999 :
1000 : Datum
1001 UIC 0 : btfloat48cmp(PG_FUNCTION_ARGS)
1002 EUB : {
1003 UIC 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
1004 0 : float8 arg2 = PG_GETARG_FLOAT8(1);
1005 :
1006 EUB : /* widen float4 to float8 and then compare */
1007 UIC 0 : PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
1008 EUB : }
1009 :
1010 : Datum
1011 UIC 0 : btfloat84cmp(PG_FUNCTION_ARGS)
1012 EUB : {
1013 UIC 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1014 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
1015 :
1016 : /* widen float4 to float8 and then compare */
1017 0 : PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
1018 : }
1019 :
1020 : /*
1021 : * in_range support function for float8.
1022 ECB : *
1023 : * Note: we needn't supply a float8_float4 variant, as implicit coercion
1024 : * of the offset value takes care of that scenario just as well.
1025 : */
1026 : Datum
1027 CBC 576 : in_range_float8_float8(PG_FUNCTION_ARGS)
1028 ECB : {
1029 GIC 576 : float8 val = PG_GETARG_FLOAT8(0);
1030 576 : float8 base = PG_GETARG_FLOAT8(1);
1031 576 : float8 offset = PG_GETARG_FLOAT8(2);
1032 576 : bool sub = PG_GETARG_BOOL(3);
1033 576 : bool less = PG_GETARG_BOOL(4);
1034 : float8 sum;
1035 ECB :
1036 : /*
1037 : * Reject negative or NaN offset. Negative is per spec, and NaN is
1038 : * because appropriate semantics for that seem non-obvious.
1039 : */
1040 GIC 576 : if (isnan(offset) || offset < 0)
1041 3 : ereport(ERROR,
1042 : (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
1043 : errmsg("invalid preceding or following size in window function")));
1044 :
1045 ECB : /*
1046 : * Deal with cases where val and/or base is NaN, following the rule that
1047 : * NaN sorts after non-NaN (cf float8_cmp_internal). The offset cannot
1048 : * affect the conclusion.
1049 : */
1050 CBC 573 : if (isnan(val))
1051 : {
1052 93 : if (isnan(base))
1053 GIC 30 : PG_RETURN_BOOL(true); /* NAN = NAN */
1054 ECB : else
1055 GIC 63 : PG_RETURN_BOOL(!less); /* NAN > non-NAN */
1056 : }
1057 480 : else if (isnan(base))
1058 : {
1059 63 : PG_RETURN_BOOL(less); /* non-NAN < NAN */
1060 : }
1061 :
1062 : /*
1063 : * Deal with cases where both base and offset are infinite, and computing
1064 : * base +/- offset would produce NaN. This corresponds to a window frame
1065 : * whose boundary infinitely precedes +inf or infinitely follows -inf,
1066 : * which is not well-defined. For consistency with other cases involving
1067 : * infinities, such as the fact that +inf infinitely follows +inf, we
1068 : * choose to assume that +inf infinitely precedes +inf and -inf infinitely
1069 : * follows -inf, and therefore that all finite and infinite values are in
1070 ECB : * such a window frame.
1071 : *
1072 : * offset is known positive, so we need only check the sign of base in
1073 : * this test.
1074 : */
1075 GIC 417 : if (isinf(offset) && isinf(base) &&
1076 : (sub ? base > 0 : base < 0))
1077 87 : PG_RETURN_BOOL(true);
1078 :
1079 : /*
1080 ECB : * Otherwise it should be safe to compute base +/- offset. We trust the
1081 : * FPU to cope if an input is +/-inf or the true sum would overflow, and
1082 : * produce a suitably signed infinity, which will compare properly against
1083 : * val whether or not that's infinity.
1084 : */
1085 CBC 330 : if (sub)
1086 180 : sum = base - offset;
1087 : else
1088 150 : sum = base + offset;
1089 :
1090 GIC 330 : if (less)
1091 129 : PG_RETURN_BOOL(val <= sum);
1092 : else
1093 201 : PG_RETURN_BOOL(val >= sum);
1094 : }
1095 :
1096 : /*
1097 : * in_range support function for float4.
1098 ECB : *
1099 : * We would need a float4_float8 variant in any case, so we supply that and
1100 : * let implicit coercion take care of the float4_float4 case.
1101 : */
1102 : Datum
1103 CBC 576 : in_range_float4_float8(PG_FUNCTION_ARGS)
1104 ECB : {
1105 GIC 576 : float4 val = PG_GETARG_FLOAT4(0);
1106 576 : float4 base = PG_GETARG_FLOAT4(1);
1107 576 : float8 offset = PG_GETARG_FLOAT8(2);
1108 576 : bool sub = PG_GETARG_BOOL(3);
1109 576 : bool less = PG_GETARG_BOOL(4);
1110 : float8 sum;
1111 ECB :
1112 : /*
1113 : * Reject negative or NaN offset. Negative is per spec, and NaN is
1114 : * because appropriate semantics for that seem non-obvious.
1115 : */
1116 GIC 576 : if (isnan(offset) || offset < 0)
1117 3 : ereport(ERROR,
1118 : (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
1119 : errmsg("invalid preceding or following size in window function")));
1120 :
1121 ECB : /*
1122 : * Deal with cases where val and/or base is NaN, following the rule that
1123 : * NaN sorts after non-NaN (cf float8_cmp_internal). The offset cannot
1124 : * affect the conclusion.
1125 : */
1126 CBC 573 : if (isnan(val))
1127 : {
1128 93 : if (isnan(base))
1129 GIC 30 : PG_RETURN_BOOL(true); /* NAN = NAN */
1130 ECB : else
1131 GIC 63 : PG_RETURN_BOOL(!less); /* NAN > non-NAN */
1132 : }
1133 480 : else if (isnan(base))
1134 : {
1135 63 : PG_RETURN_BOOL(less); /* non-NAN < NAN */
1136 : }
1137 :
1138 : /*
1139 : * Deal with cases where both base and offset are infinite, and computing
1140 : * base +/- offset would produce NaN. This corresponds to a window frame
1141 : * whose boundary infinitely precedes +inf or infinitely follows -inf,
1142 : * which is not well-defined. For consistency with other cases involving
1143 : * infinities, such as the fact that +inf infinitely follows +inf, we
1144 : * choose to assume that +inf infinitely precedes +inf and -inf infinitely
1145 : * follows -inf, and therefore that all finite and infinite values are in
1146 ECB : * such a window frame.
1147 : *
1148 : * offset is known positive, so we need only check the sign of base in
1149 : * this test.
1150 : */
1151 GIC 417 : if (isinf(offset) && isinf(base) &&
1152 : (sub ? base > 0 : base < 0))
1153 87 : PG_RETURN_BOOL(true);
1154 :
1155 : /*
1156 ECB : * Otherwise it should be safe to compute base +/- offset. We trust the
1157 : * FPU to cope if an input is +/-inf or the true sum would overflow, and
1158 : * produce a suitably signed infinity, which will compare properly against
1159 : * val whether or not that's infinity.
1160 : */
1161 CBC 330 : if (sub)
1162 180 : sum = base - offset;
1163 : else
1164 150 : sum = base + offset;
1165 :
1166 GIC 330 : if (less)
1167 129 : PG_RETURN_BOOL(val <= sum);
1168 : else
1169 201 : PG_RETURN_BOOL(val >= sum);
1170 : }
1171 :
1172 :
1173 : /*
1174 : * ===================
1175 : * CONVERSION ROUTINES
1176 : * ===================
1177 : */
1178 ECB :
1179 : /*
1180 : * ftod - converts a float4 number to a float8 number
1181 : */
1182 : Datum
1183 GIC 147 : ftod(PG_FUNCTION_ARGS)
1184 : {
1185 147 : float4 num = PG_GETARG_FLOAT4(0);
1186 :
1187 147 : PG_RETURN_FLOAT8((float8) num);
1188 : }
1189 :
1190 ECB :
1191 : /*
1192 : * dtof - converts a float8 number to a float4 number
1193 : */
1194 : Datum
1195 CBC 12 : dtof(PG_FUNCTION_ARGS)
1196 ECB : {
1197 CBC 12 : float8 num = PG_GETARG_FLOAT8(0);
1198 ECB : float4 result;
1199 :
1200 GIC 12 : result = (float4) num;
1201 GBC 12 : if (unlikely(isinf(result)) && !isinf(num))
1202 GIC 6 : float_overflow_error();
1203 6 : if (unlikely(result == 0.0f) && num != 0.0)
1204 6 : float_underflow_error();
1205 :
1206 UIC 0 : PG_RETURN_FLOAT4(result);
1207 : }
1208 :
1209 ECB :
1210 : /*
1211 : * dtoi4 - converts a float8 number to an int4 number
1212 : */
1213 : Datum
1214 GIC 298688 : dtoi4(PG_FUNCTION_ARGS)
1215 : {
1216 298688 : float8 num = PG_GETARG_FLOAT8(0);
1217 :
1218 ECB : /*
1219 : * Get rid of any fractional part in the input. This is so we don't fail
1220 : * on just-out-of-range values that would round into range. Note
1221 : * assumption that rint() will pass through a NaN or Inf unchanged.
1222 : */
1223 GIC 298688 : num = rint(num);
1224 :
1225 : /* Range check */
1226 CBC 298688 : if (unlikely(isnan(num) || !FLOAT8_FITS_IN_INT32(num)))
1227 GIC 12 : ereport(ERROR,
1228 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1229 : errmsg("integer out of range")));
1230 :
1231 298676 : PG_RETURN_INT32((int32) num);
1232 : }
1233 :
1234 ECB :
1235 : /*
1236 : * dtoi2 - converts a float8 number to an int2 number
1237 : */
1238 : Datum
1239 GIC 45 : dtoi2(PG_FUNCTION_ARGS)
1240 : {
1241 45 : float8 num = PG_GETARG_FLOAT8(0);
1242 :
1243 ECB : /*
1244 : * Get rid of any fractional part in the input. This is so we don't fail
1245 : * on just-out-of-range values that would round into range. Note
1246 : * assumption that rint() will pass through a NaN or Inf unchanged.
1247 : */
1248 GIC 45 : num = rint(num);
1249 :
1250 : /* Range check */
1251 CBC 45 : if (unlikely(isnan(num) || !FLOAT8_FITS_IN_INT16(num)))
1252 GIC 6 : ereport(ERROR,
1253 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1254 : errmsg("smallint out of range")));
1255 :
1256 39 : PG_RETURN_INT16((int16) num);
1257 : }
1258 :
1259 ECB :
1260 : /*
1261 : * i4tod - converts an int4 number to a float8 number
1262 : */
1263 : Datum
1264 GIC 1159549 : i4tod(PG_FUNCTION_ARGS)
1265 : {
1266 1159549 : int32 num = PG_GETARG_INT32(0);
1267 :
1268 1159549 : PG_RETURN_FLOAT8((float8) num);
1269 : }
1270 :
1271 ECB :
1272 : /*
1273 : * i2tod - converts an int2 number to a float8 number
1274 : */
1275 : Datum
1276 GIC 123 : i2tod(PG_FUNCTION_ARGS)
1277 : {
1278 123 : int16 num = PG_GETARG_INT16(0);
1279 :
1280 123 : PG_RETURN_FLOAT8((float8) num);
1281 : }
1282 :
1283 ECB :
1284 : /*
1285 : * ftoi4 - converts a float4 number to an int4 number
1286 : */
1287 : Datum
1288 GIC 12 : ftoi4(PG_FUNCTION_ARGS)
1289 : {
1290 12 : float4 num = PG_GETARG_FLOAT4(0);
1291 :
1292 ECB : /*
1293 : * Get rid of any fractional part in the input. This is so we don't fail
1294 : * on just-out-of-range values that would round into range. Note
1295 : * assumption that rint() will pass through a NaN or Inf unchanged.
1296 : */
1297 GIC 12 : num = rint(num);
1298 :
1299 : /* Range check */
1300 CBC 12 : if (unlikely(isnan(num) || !FLOAT4_FITS_IN_INT32(num)))
1301 GIC 6 : ereport(ERROR,
1302 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1303 : errmsg("integer out of range")));
1304 :
1305 6 : PG_RETURN_INT32((int32) num);
1306 : }
1307 :
1308 ECB :
1309 : /*
1310 : * ftoi2 - converts a float4 number to an int2 number
1311 : */
1312 : Datum
1313 GIC 12 : ftoi2(PG_FUNCTION_ARGS)
1314 : {
1315 12 : float4 num = PG_GETARG_FLOAT4(0);
1316 :
1317 ECB : /*
1318 : * Get rid of any fractional part in the input. This is so we don't fail
1319 : * on just-out-of-range values that would round into range. Note
1320 : * assumption that rint() will pass through a NaN or Inf unchanged.
1321 : */
1322 GIC 12 : num = rint(num);
1323 :
1324 : /* Range check */
1325 CBC 12 : if (unlikely(isnan(num) || !FLOAT4_FITS_IN_INT16(num)))
1326 GIC 6 : ereport(ERROR,
1327 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1328 : errmsg("smallint out of range")));
1329 :
1330 6 : PG_RETURN_INT16((int16) num);
1331 : }
1332 :
1333 ECB :
1334 : /*
1335 : * i4tof - converts an int4 number to a float4 number
1336 : */
1337 : Datum
1338 GIC 232 : i4tof(PG_FUNCTION_ARGS)
1339 : {
1340 232 : int32 num = PG_GETARG_INT32(0);
1341 :
1342 232 : PG_RETURN_FLOAT4((float4) num);
1343 : }
1344 :
1345 EUB :
1346 : /*
1347 : * i2tof - converts an int2 number to a float4 number
1348 : */
1349 : Datum
1350 UIC 0 : i2tof(PG_FUNCTION_ARGS)
1351 : {
1352 0 : int16 num = PG_GETARG_INT16(0);
1353 :
1354 0 : PG_RETURN_FLOAT4((float4) num);
1355 : }
1356 :
1357 :
1358 : /*
1359 : * =======================
1360 : * RANDOM FLOAT8 OPERATORS
1361 : * =======================
1362 : */
1363 ECB :
1364 : /*
1365 : * dround - returns ROUND(arg1)
1366 : */
1367 : Datum
1368 GIC 9768 : dround(PG_FUNCTION_ARGS)
1369 : {
1370 9768 : float8 arg1 = PG_GETARG_FLOAT8(0);
1371 :
1372 9768 : PG_RETURN_FLOAT8(rint(arg1));
1373 : }
1374 :
1375 ECB : /*
1376 : * dceil - returns the smallest integer greater than or
1377 : * equal to the specified float
1378 : */
1379 : Datum
1380 GIC 30 : dceil(PG_FUNCTION_ARGS)
1381 : {
1382 30 : float8 arg1 = PG_GETARG_FLOAT8(0);
1383 :
1384 30 : PG_RETURN_FLOAT8(ceil(arg1));
1385 : }
1386 :
1387 ECB : /*
1388 : * dfloor - returns the largest integer lesser than or
1389 : * equal to the specified float
1390 : */
1391 : Datum
1392 GIC 30 : dfloor(PG_FUNCTION_ARGS)
1393 : {
1394 30 : float8 arg1 = PG_GETARG_FLOAT8(0);
1395 :
1396 30 : PG_RETURN_FLOAT8(floor(arg1));
1397 : }
1398 :
1399 : /*
1400 ECB : * dsign - returns -1 if the argument is less than 0, 0
1401 : * if the argument is equal to 0, and 1 if the
1402 : * argument is greater than zero.
1403 : */
1404 : Datum
1405 CBC 15 : dsign(PG_FUNCTION_ARGS)
1406 ECB : {
1407 CBC 15 : float8 arg1 = PG_GETARG_FLOAT8(0);
1408 ECB : float8 result;
1409 :
1410 CBC 15 : if (arg1 > 0)
1411 GIC 9 : result = 1.0;
1412 CBC 6 : else if (arg1 < 0)
1413 GIC 3 : result = -1.0;
1414 : else
1415 3 : result = 0.0;
1416 :
1417 15 : PG_RETURN_FLOAT8(result);
1418 : }
1419 :
1420 : /*
1421 : * dtrunc - returns truncation-towards-zero of arg1,
1422 : * arg1 >= 0 ... the greatest integer less
1423 ECB : * than or equal to arg1
1424 : * arg1 < 0 ... the least integer greater
1425 : * than or equal to arg1
1426 : */
1427 : Datum
1428 CBC 15 : dtrunc(PG_FUNCTION_ARGS)
1429 ECB : {
1430 GIC 15 : float8 arg1 = PG_GETARG_FLOAT8(0);
1431 ECB : float8 result;
1432 :
1433 CBC 15 : if (arg1 >= 0)
1434 GIC 12 : result = floor(arg1);
1435 : else
1436 3 : result = -floor(-arg1);
1437 :
1438 15 : PG_RETURN_FLOAT8(result);
1439 : }
1440 :
1441 ECB :
1442 : /*
1443 : * dsqrt - returns square root of arg1
1444 : */
1445 : Datum
1446 CBC 2024 : dsqrt(PG_FUNCTION_ARGS)
1447 EUB : {
1448 GIC 2024 : float8 arg1 = PG_GETARG_FLOAT8(0);
1449 : float8 result;
1450 :
1451 CBC 2024 : if (arg1 < 0)
1452 LBC 0 : ereport(ERROR,
1453 EUB : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
1454 ECB : errmsg("cannot take square root of a negative number")));
1455 EUB :
1456 GIC 2024 : result = sqrt(arg1);
1457 CBC 2024 : if (unlikely(isinf(result)) && !isinf(arg1))
1458 UIC 0 : float_overflow_error();
1459 GIC 2024 : if (unlikely(result == 0.0) && arg1 != 0.0)
1460 UIC 0 : float_underflow_error();
1461 :
1462 GIC 2024 : PG_RETURN_FLOAT8(result);
1463 : }
1464 :
1465 ECB :
1466 : /*
1467 : * dcbrt - returns cube root of arg1
1468 : */
1469 : Datum
1470 CBC 18 : dcbrt(PG_FUNCTION_ARGS)
1471 ECB : {
1472 GBC 18 : float8 arg1 = PG_GETARG_FLOAT8(0);
1473 ECB : float8 result;
1474 EUB :
1475 GIC 18 : result = cbrt(arg1);
1476 CBC 18 : if (unlikely(isinf(result)) && !isinf(arg1))
1477 UIC 0 : float_overflow_error();
1478 GIC 18 : if (unlikely(result == 0.0) && arg1 != 0.0)
1479 UIC 0 : float_underflow_error();
1480 :
1481 GIC 18 : PG_RETURN_FLOAT8(result);
1482 : }
1483 :
1484 ECB :
1485 : /*
1486 : * dpow - returns pow(arg1,arg2)
1487 : */
1488 : Datum
1489 GIC 334 : dpow(PG_FUNCTION_ARGS)
1490 : {
1491 334 : float8 arg1 = PG_GETARG_FLOAT8(0);
1492 334 : float8 arg2 = PG_GETARG_FLOAT8(1);
1493 : float8 result;
1494 :
1495 : /*
1496 ECB : * The POSIX spec says that NaN ^ 0 = 1, and 1 ^ NaN = 1, while all other
1497 : * cases with NaN inputs yield NaN (with no error). Many older platforms
1498 : * get one or more of these cases wrong, so deal with them via explicit
1499 : * logic rather than trusting pow(3).
1500 : */
1501 GIC 334 : if (isnan(arg1))
1502 ECB : {
1503 GIC 9 : if (isnan(arg2) || arg2 != 0.0)
1504 CBC 6 : PG_RETURN_FLOAT8(get_float8_nan());
1505 3 : PG_RETURN_FLOAT8(1.0);
1506 ECB : }
1507 GIC 325 : if (isnan(arg2))
1508 : {
1509 9 : if (arg1 != 1.0)
1510 6 : PG_RETURN_FLOAT8(get_float8_nan());
1511 3 : PG_RETURN_FLOAT8(1.0);
1512 : }
1513 :
1514 ECB : /*
1515 : * The SQL spec requires that we emit a particular SQLSTATE error code for
1516 : * certain error conditions. Specifically, we don't return a
1517 : * divide-by-zero error code for 0 ^ -1.
1518 : */
1519 CBC 316 : if (arg1 == 0 && arg2 < 0)
1520 GIC 3 : ereport(ERROR,
1521 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
1522 : errmsg("zero raised to a negative power is undefined")));
1523 313 : if (arg1 < 0 && floor(arg2) != arg2)
1524 3 : ereport(ERROR,
1525 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
1526 : errmsg("a negative number raised to a non-integer power yields a complex result")));
1527 :
1528 ECB : /*
1529 : * We don't trust the platform's pow() to handle infinity cases per POSIX
1530 : * spec either, so deal with those explicitly too. It's easier to handle
1531 : * infinite y first, so that it doesn't matter if x is also infinite.
1532 : */
1533 CBC 310 : if (isinf(arg2))
1534 ECB : {
1535 GIC 51 : float8 absx = fabs(arg1);
1536 ECB :
1537 CBC 51 : if (absx == 1.0)
1538 GIC 12 : result = 1.0;
1539 CBC 39 : else if (arg2 > 0.0) /* y = +Inf */
1540 : {
1541 GIC 21 : if (absx > 1.0)
1542 12 : result = arg2;
1543 ECB : else
1544 CBC 9 : result = 0.0;
1545 : }
1546 ECB : else /* y = -Inf */
1547 : {
1548 GIC 18 : if (absx > 1.0)
1549 CBC 12 : result = 0.0;
1550 : else
1551 6 : result = -arg2;
1552 ECB : }
1553 : }
1554 GIC 259 : else if (isinf(arg1))
1555 ECB : {
1556 CBC 24 : if (arg2 == 0.0)
1557 GIC 6 : result = 1.0;
1558 CBC 18 : else if (arg1 > 0.0) /* x = +Inf */
1559 : {
1560 GIC 6 : if (arg2 > 0.0)
1561 3 : result = arg1;
1562 : else
1563 3 : result = 0.0;
1564 : }
1565 : else /* x = -Inf */
1566 : {
1567 : /*
1568 ECB : * Per POSIX, the sign of the result depends on whether y is an
1569 : * odd integer. Since x < 0, we already know from the previous
1570 : * domain check that y is an integer. It is odd if y/2 is not
1571 : * also an integer.
1572 : */
1573 GIC 12 : float8 halfy = arg2 / 2; /* should be computed exactly */
1574 CBC 12 : bool yisoddinteger = (floor(halfy) != halfy);
1575 :
1576 GIC 12 : if (arg2 > 0.0)
1577 6 : result = yisoddinteger ? arg1 : -arg1;
1578 : else
1579 6 : result = yisoddinteger ? -0.0 : 0.0;
1580 : }
1581 : }
1582 : else
1583 : {
1584 : /*
1585 : * pow() sets errno on only some platforms, depending on whether it
1586 ECB : * follows _IEEE_, _POSIX_, _XOPEN_, or _SVID_, so we must check both
1587 : * errno and invalid output values. (We can't rely on just the
1588 : * latter, either; some old platforms return a large-but-finite
1589 : * HUGE_VAL when reporting overflow.)
1590 : */
1591 GIC 235 : errno = 0;
1592 235 : result = pow(arg1, arg2);
1593 235 : if (errno == EDOM || isnan(result))
1594 : {
1595 : /*
1596 : * We handled all possible domain errors above, so this should be
1597 : * impossible. However, old glibc versions on x86 have a bug that
1598 : * causes them to fail this way for abs(y) greater than 2^63:
1599 : *
1600 : * https://sourceware.org/bugzilla/show_bug.cgi?id=3866
1601 EUB : *
1602 : * Hence, if we get here, assume y is finite but large (large
1603 : * enough to be certainly even). The result should be 0 if x == 0,
1604 : * 1.0 if abs(x) == 1.0, otherwise an overflow or underflow error.
1605 : */
1606 UIC 0 : if (arg1 == 0.0)
1607 UBC 0 : result = 0.0; /* we already verified y is positive */
1608 EUB : else
1609 : {
1610 UBC 0 : float8 absx = fabs(arg1);
1611 :
1612 0 : if (absx == 1.0)
1613 UIC 0 : result = 1.0;
1614 0 : else if (arg2 >= 0.0 ? (absx > 1.0) : (absx < 1.0))
1615 LBC 0 : float_overflow_error();
1616 : else
1617 0 : float_underflow_error();
1618 ECB : }
1619 : }
1620 GBC 235 : else if (errno == ERANGE)
1621 : {
1622 GIC 3 : if (result != 0.0)
1623 3 : float_overflow_error();
1624 ECB : else
1625 UBC 0 : float_underflow_error();
1626 ECB : }
1627 EUB : else
1628 : {
1629 GIC 232 : if (unlikely(isinf(result)))
1630 UIC 0 : float_overflow_error();
1631 CBC 232 : if (unlikely(result == 0.0) && arg1 != 0.0)
1632 UIC 0 : float_underflow_error();
1633 : }
1634 : }
1635 :
1636 GIC 307 : PG_RETURN_FLOAT8(result);
1637 : }
1638 :
1639 ECB :
1640 : /*
1641 : * dexp - returns the exponential function of arg1
1642 : */
1643 : Datum
1644 GIC 27 : dexp(PG_FUNCTION_ARGS)
1645 : {
1646 27 : float8 arg1 = PG_GETARG_FLOAT8(0);
1647 : float8 result;
1648 :
1649 ECB : /*
1650 : * Handle NaN and Inf cases explicitly. This avoids needing to assume
1651 : * that the platform's exp() conforms to POSIX for these cases, and it
1652 : * removes some edge cases for the overflow checks below.
1653 : */
1654 CBC 27 : if (isnan(arg1))
1655 GIC 3 : result = arg1;
1656 24 : else if (isinf(arg1))
1657 : {
1658 : /* Per POSIX, exp(-Inf) is 0 */
1659 6 : result = (arg1 > 0.0) ? arg1 : 0;
1660 : }
1661 : else
1662 ECB : {
1663 : /*
1664 : * On some platforms, exp() will not set errno but just return Inf or
1665 : * zero to report overflow/underflow; therefore, test both cases.
1666 : */
1667 GBC 18 : errno = 0;
1668 GIC 18 : result = exp(arg1);
1669 CBC 18 : if (unlikely(errno == ERANGE))
1670 : {
1671 3 : if (result != 0.0)
1672 UBC 0 : float_overflow_error();
1673 ECB : else
1674 GBC 3 : float_underflow_error();
1675 : }
1676 GIC 15 : else if (unlikely(isinf(result)))
1677 LBC 0 : float_overflow_error();
1678 GIC 15 : else if (unlikely(result == 0.0))
1679 UIC 0 : float_underflow_error();
1680 : }
1681 :
1682 GIC 24 : PG_RETURN_FLOAT8(result);
1683 : }
1684 :
1685 ECB :
1686 : /*
1687 : * dlog1 - returns the natural logarithm of arg1
1688 : */
1689 : Datum
1690 GIC 15 : dlog1(PG_FUNCTION_ARGS)
1691 : {
1692 15 : float8 arg1 = PG_GETARG_FLOAT8(0);
1693 : float8 result;
1694 ECB :
1695 : /*
1696 : * Emit particular SQLSTATE error codes for ln(). This is required by the
1697 : * SQL standard.
1698 : */
1699 CBC 15 : if (arg1 == 0.0)
1700 GIC 3 : ereport(ERROR,
1701 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1702 : errmsg("cannot take logarithm of zero")));
1703 CBC 12 : if (arg1 < 0)
1704 3 : ereport(ERROR,
1705 EUB : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1706 ECB : errmsg("cannot take logarithm of a negative number")));
1707 EUB :
1708 GIC 9 : result = log(arg1);
1709 CBC 9 : if (unlikely(isinf(result)) && !isinf(arg1))
1710 UIC 0 : float_overflow_error();
1711 GIC 9 : if (unlikely(result == 0.0) && arg1 != 1.0)
1712 UIC 0 : float_underflow_error();
1713 :
1714 GIC 9 : PG_RETURN_FLOAT8(result);
1715 : }
1716 :
1717 EUB :
1718 : /*
1719 : * dlog10 - returns the base 10 logarithm of arg1
1720 : */
1721 : Datum
1722 UIC 0 : dlog10(PG_FUNCTION_ARGS)
1723 : {
1724 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1725 : float8 result;
1726 :
1727 EUB : /*
1728 : * Emit particular SQLSTATE error codes for log(). The SQL spec doesn't
1729 : * define log(), but it does define ln(), so it makes sense to emit the
1730 : * same error code for an analogous error condition.
1731 : */
1732 UBC 0 : if (arg1 == 0.0)
1733 UIC 0 : ereport(ERROR,
1734 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1735 : errmsg("cannot take logarithm of zero")));
1736 UBC 0 : if (arg1 < 0)
1737 0 : ereport(ERROR,
1738 EUB : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1739 : errmsg("cannot take logarithm of a negative number")));
1740 :
1741 UIC 0 : result = log10(arg1);
1742 UBC 0 : if (unlikely(isinf(result)) && !isinf(arg1))
1743 UIC 0 : float_overflow_error();
1744 0 : if (unlikely(result == 0.0) && arg1 != 1.0)
1745 0 : float_underflow_error();
1746 :
1747 0 : PG_RETURN_FLOAT8(result);
1748 : }
1749 :
1750 EUB :
1751 : /*
1752 : * dacos - returns the arccos of arg1 (radians)
1753 : */
1754 : Datum
1755 UIC 0 : dacos(PG_FUNCTION_ARGS)
1756 EUB : {
1757 UBC 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1758 : float8 result;
1759 :
1760 : /* Per the POSIX spec, return NaN if the input is NaN */
1761 UIC 0 : if (isnan(arg1))
1762 0 : PG_RETURN_FLOAT8(get_float8_nan());
1763 :
1764 EUB : /*
1765 : * The principal branch of the inverse cosine function maps values in the
1766 : * range [-1, 1] to values in the range [0, Pi], so we should reject any
1767 : * inputs outside that range and the result will always be finite.
1768 : */
1769 UBC 0 : if (arg1 < -1.0 || arg1 > 1.0)
1770 0 : ereport(ERROR,
1771 EUB : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1772 : errmsg("input is out of range")));
1773 :
1774 UIC 0 : result = acos(arg1);
1775 0 : if (unlikely(isinf(result)))
1776 0 : float_overflow_error();
1777 :
1778 0 : PG_RETURN_FLOAT8(result);
1779 : }
1780 :
1781 ECB :
1782 : /*
1783 : * dasin - returns the arcsin of arg1 (radians)
1784 : */
1785 : Datum
1786 GIC 55 : dasin(PG_FUNCTION_ARGS)
1787 ECB : {
1788 GBC 55 : float8 arg1 = PG_GETARG_FLOAT8(0);
1789 : float8 result;
1790 :
1791 : /* Per the POSIX spec, return NaN if the input is NaN */
1792 GIC 55 : if (isnan(arg1))
1793 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
1794 :
1795 ECB : /*
1796 EUB : * The principal branch of the inverse sine function maps values in the
1797 : * range [-1, 1] to values in the range [-Pi/2, Pi/2], so we should reject
1798 : * any inputs outside that range and the result will always be finite.
1799 : */
1800 CBC 55 : if (arg1 < -1.0 || arg1 > 1.0)
1801 LBC 0 : ereport(ERROR,
1802 EUB : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1803 : errmsg("input is out of range")));
1804 ECB :
1805 GIC 55 : result = asin(arg1);
1806 55 : if (unlikely(isinf(result)))
1807 UIC 0 : float_overflow_error();
1808 :
1809 GIC 55 : PG_RETURN_FLOAT8(result);
1810 : }
1811 :
1812 EUB :
1813 : /*
1814 : * datan - returns the arctan of arg1 (radians)
1815 : */
1816 : Datum
1817 UIC 0 : datan(PG_FUNCTION_ARGS)
1818 EUB : {
1819 UBC 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1820 : float8 result;
1821 :
1822 : /* Per the POSIX spec, return NaN if the input is NaN */
1823 UIC 0 : if (isnan(arg1))
1824 0 : PG_RETURN_FLOAT8(get_float8_nan());
1825 :
1826 EUB : /*
1827 : * The principal branch of the inverse tangent function maps all inputs to
1828 : * values in the range [-Pi/2, Pi/2], so the result should always be
1829 : * finite, even if the input is infinite.
1830 : */
1831 UIC 0 : result = atan(arg1);
1832 0 : if (unlikely(isinf(result)))
1833 0 : float_overflow_error();
1834 :
1835 0 : PG_RETURN_FLOAT8(result);
1836 : }
1837 :
1838 ECB :
1839 : /*
1840 : * atan2 - returns the arctan of arg1/arg2 (radians)
1841 : */
1842 : Datum
1843 GIC 20 : datan2(PG_FUNCTION_ARGS)
1844 : {
1845 CBC 20 : float8 arg1 = PG_GETARG_FLOAT8(0);
1846 GBC 20 : float8 arg2 = PG_GETARG_FLOAT8(1);
1847 : float8 result;
1848 :
1849 : /* Per the POSIX spec, return NaN if either input is NaN */
1850 GIC 20 : if (isnan(arg1) || isnan(arg2))
1851 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
1852 ECB :
1853 : /*
1854 EUB : * atan2 maps all inputs to values in the range [-Pi, Pi], so the result
1855 : * should always be finite, even if the inputs are infinite.
1856 ECB : */
1857 GIC 20 : result = atan2(arg1, arg2);
1858 20 : if (unlikely(isinf(result)))
1859 UIC 0 : float_overflow_error();
1860 :
1861 GIC 20 : PG_RETURN_FLOAT8(result);
1862 : }
1863 :
1864 ECB :
1865 : /*
1866 : * dcos - returns the cosine of arg1 (radians)
1867 : */
1868 : Datum
1869 GIC 585 : dcos(PG_FUNCTION_ARGS)
1870 ECB : {
1871 GBC 585 : float8 arg1 = PG_GETARG_FLOAT8(0);
1872 : float8 result;
1873 :
1874 : /* Per the POSIX spec, return NaN if the input is NaN */
1875 GIC 585 : if (isnan(arg1))
1876 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
1877 :
1878 : /*
1879 : * cos() is periodic and so theoretically can work for all finite inputs,
1880 : * but some implementations may choose to throw error if the input is so
1881 : * large that there are no significant digits in the result. So we should
1882 : * check for errors. POSIX allows an error to be reported either via
1883 : * errno or via fetestexcept(), but currently we only support checking
1884 : * errno. (fetestexcept() is rumored to report underflow unreasonably
1885 : * early on some platforms, so it's not clear that believing it would be a
1886 : * net improvement anyway.)
1887 : *
1888 ECB : * For infinite inputs, POSIX specifies that the trigonometric functions
1889 : * should return a domain error; but we won't notice that unless the
1890 : * platform reports via errno, so also explicitly test for infinite
1891 EUB : * inputs.
1892 : */
1893 GIC 585 : errno = 0;
1894 CBC 585 : result = cos(arg1);
1895 GBC 585 : if (errno != 0 || isinf(arg1))
1896 UIC 0 : ereport(ERROR,
1897 ECB : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1898 : errmsg("input is out of range")));
1899 GIC 585 : if (unlikely(isinf(result)))
1900 UIC 0 : float_overflow_error();
1901 :
1902 GIC 585 : PG_RETURN_FLOAT8(result);
1903 : }
1904 :
1905 EUB :
1906 : /*
1907 : * dcot - returns the cotangent of arg1 (radians)
1908 : */
1909 : Datum
1910 UIC 0 : dcot(PG_FUNCTION_ARGS)
1911 EUB : {
1912 UBC 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1913 : float8 result;
1914 :
1915 EUB : /* Per the POSIX spec, return NaN if the input is NaN */
1916 UBC 0 : if (isnan(arg1))
1917 0 : PG_RETURN_FLOAT8(get_float8_nan());
1918 EUB :
1919 : /* Be sure to throw an error if the input is infinite --- see dcos() */
1920 UIC 0 : errno = 0;
1921 0 : result = tan(arg1);
1922 UBC 0 : if (errno != 0 || isinf(arg1))
1923 UIC 0 : ereport(ERROR,
1924 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1925 EUB : errmsg("input is out of range")));
1926 :
1927 UIC 0 : result = 1.0 / result;
1928 : /* Not checking for overflow because cot(0) == Inf */
1929 :
1930 0 : PG_RETURN_FLOAT8(result);
1931 : }
1932 :
1933 ECB :
1934 : /*
1935 : * dsin - returns the sine of arg1 (radians)
1936 : */
1937 : Datum
1938 GIC 469 : dsin(PG_FUNCTION_ARGS)
1939 ECB : {
1940 GBC 469 : float8 arg1 = PG_GETARG_FLOAT8(0);
1941 : float8 result;
1942 :
1943 ECB : /* Per the POSIX spec, return NaN if the input is NaN */
1944 CBC 469 : if (isnan(arg1))
1945 LBC 0 : PG_RETURN_FLOAT8(get_float8_nan());
1946 EUB :
1947 : /* Be sure to throw an error if the input is infinite --- see dcos() */
1948 GIC 469 : errno = 0;
1949 CBC 469 : result = sin(arg1);
1950 GBC 469 : if (errno != 0 || isinf(arg1))
1951 UIC 0 : ereport(ERROR,
1952 ECB : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1953 : errmsg("input is out of range")));
1954 GIC 469 : if (unlikely(isinf(result)))
1955 UIC 0 : float_overflow_error();
1956 :
1957 GIC 469 : PG_RETURN_FLOAT8(result);
1958 : }
1959 :
1960 EUB :
1961 : /*
1962 : * dtan - returns the tangent of arg1 (radians)
1963 : */
1964 : Datum
1965 UIC 0 : dtan(PG_FUNCTION_ARGS)
1966 EUB : {
1967 UBC 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1968 : float8 result;
1969 :
1970 EUB : /* Per the POSIX spec, return NaN if the input is NaN */
1971 UBC 0 : if (isnan(arg1))
1972 0 : PG_RETURN_FLOAT8(get_float8_nan());
1973 EUB :
1974 : /* Be sure to throw an error if the input is infinite --- see dcos() */
1975 UIC 0 : errno = 0;
1976 0 : result = tan(arg1);
1977 0 : if (errno != 0 || isinf(arg1))
1978 UBC 0 : ereport(ERROR,
1979 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1980 : errmsg("input is out of range")));
1981 : /* Not checking for overflow because tan(pi/2) == Inf */
1982 :
1983 UIC 0 : PG_RETURN_FLOAT8(result);
1984 : }
1985 :
1986 :
1987 : /* ========== DEGREE-BASED TRIGONOMETRIC FUNCTIONS ========== */
1988 :
1989 :
1990 : /*
1991 : * Initialize the cached constants declared at the head of this file
1992 : * (sin_30 etc). The fact that we need those at all, let alone need this
1993 : * Rube-Goldberg-worthy method of initializing them, is because there are
1994 : * compilers out there that will precompute expressions such as sin(constant)
1995 : * using a sin() function different from what will be used at runtime. If we
1996 : * want exact results, we must ensure that none of the scaling constants used
1997 : * in the degree-based trig functions are computed that way. To do so, we
1998 : * compute them from the variables degree_c_thirty etc, which are also really
1999 : * constants, but the compiler cannot assume that.
2000 : *
2001 : * Other hazards we are trying to forestall with this kluge include the
2002 : * possibility that compilers will rearrange the expressions, or compute
2003 : * some intermediate results in registers wider than a standard double.
2004 : *
2005 : * In the places where we use these constants, the typical pattern is like
2006 : * volatile float8 sin_x = sin(x * RADIANS_PER_DEGREE);
2007 : * return (sin_x / sin_30);
2008 : * where we hope to get a value of exactly 1.0 from the division when x = 30.
2009 : * The volatile temporary variable is needed on machines with wide float
2010 : * registers, to ensure that the result of sin(x) is rounded to double width
2011 : * the same as the value of sin_30 has been. Experimentation with gcc shows
2012 : * that marking the temp variable volatile is necessary to make the store and
2013 : * reload actually happen; hopefully the same trick works for other compilers.
2014 ECB : * (gcc's documentation suggests using the -ffloat-store compiler switch to
2015 : * ensure this, but that is compiler-specific and it also pessimizes code in
2016 : * many places where we don't care about this.)
2017 : */
2018 : static void
2019 CBC 3 : init_degree_constants(void)
2020 ECB : {
2021 CBC 3 : sin_30 = sin(degree_c_thirty * RADIANS_PER_DEGREE);
2022 3 : one_minus_cos_60 = 1.0 - cos(degree_c_sixty * RADIANS_PER_DEGREE);
2023 3 : asin_0_5 = asin(degree_c_one_half);
2024 3 : acos_0_5 = acos(degree_c_one_half);
2025 GIC 3 : atan_1_0 = atan(degree_c_one);
2026 3 : tan_45 = sind_q1(degree_c_forty_five) / cosd_q1(degree_c_forty_five);
2027 3 : cot_45 = cosd_q1(degree_c_forty_five) / sind_q1(degree_c_forty_five);
2028 3 : degree_consts_set = true;
2029 3 : }
2030 :
2031 : #define INIT_DEGREE_CONSTANTS() \
2032 : do { \
2033 : if (!degree_consts_set) \
2034 : init_degree_constants(); \
2035 : } while(0)
2036 :
2037 :
2038 : /*
2039 : * asind_q1 - returns the inverse sine of x in degrees, for x in
2040 : * the range [0, 1]. The result is an angle in the
2041 : * first quadrant --- [0, 90] degrees.
2042 : *
2043 ECB : * For the 3 special case inputs (0, 0.5 and 1), this
2044 : * function will return exact values (0, 30 and 90
2045 : * degrees respectively).
2046 : */
2047 : static double
2048 GIC 42 : asind_q1(double x)
2049 : {
2050 : /*
2051 ECB : * Stitch together inverse sine and cosine functions for the ranges [0,
2052 : * 0.5] and (0.5, 1]. Each expression below is guaranteed to return
2053 : * exactly 30 for x=0.5, so the result is a continuous monotonic function
2054 : * over the full range.
2055 : */
2056 GIC 42 : if (x <= 0.5)
2057 : {
2058 24 : volatile float8 asin_x = asin(x);
2059 ECB :
2060 GIC 24 : return (asin_x / asin_0_5) * 30.0;
2061 ECB : }
2062 : else
2063 : {
2064 GIC 18 : volatile float8 acos_x = acos(x);
2065 :
2066 18 : return 90.0 - (acos_x / acos_0_5) * 60.0;
2067 : }
2068 : }
2069 :
2070 :
2071 : /*
2072 : * acosd_q1 - returns the inverse cosine of x in degrees, for x in
2073 : * the range [0, 1]. The result is an angle in the
2074 : * first quadrant --- [0, 90] degrees.
2075 : *
2076 ECB : * For the 3 special case inputs (0, 0.5 and 1), this
2077 : * function will return exact values (0, 60 and 90
2078 : * degrees respectively).
2079 : */
2080 : static double
2081 GIC 18 : acosd_q1(double x)
2082 : {
2083 : /*
2084 ECB : * Stitch together inverse sine and cosine functions for the ranges [0,
2085 : * 0.5] and (0.5, 1]. Each expression below is guaranteed to return
2086 : * exactly 60 for x=0.5, so the result is a continuous monotonic function
2087 : * over the full range.
2088 : */
2089 GIC 18 : if (x <= 0.5)
2090 : {
2091 12 : volatile float8 asin_x = asin(x);
2092 ECB :
2093 GIC 12 : return 90.0 - (asin_x / asin_0_5) * 30.0;
2094 ECB : }
2095 : else
2096 : {
2097 GIC 6 : volatile float8 acos_x = acos(x);
2098 :
2099 6 : return (acos_x / acos_0_5) * 60.0;
2100 : }
2101 : }
2102 :
2103 ECB :
2104 : /*
2105 : * dacosd - returns the arccos of arg1 (degrees)
2106 : */
2107 : Datum
2108 GIC 30 : dacosd(PG_FUNCTION_ARGS)
2109 ECB : {
2110 GBC 30 : float8 arg1 = PG_GETARG_FLOAT8(0);
2111 : float8 result;
2112 ECB :
2113 : /* Per the POSIX spec, return NaN if the input is NaN */
2114 GIC 30 : if (isnan(arg1))
2115 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
2116 :
2117 GIC 30 : INIT_DEGREE_CONSTANTS();
2118 :
2119 ECB : /*
2120 EUB : * The principal branch of the inverse cosine function maps values in the
2121 : * range [-1, 1] to values in the range [0, 180], so we should reject any
2122 : * inputs outside that range and the result will always be finite.
2123 : */
2124 CBC 30 : if (arg1 < -1.0 || arg1 > 1.0)
2125 LBC 0 : ereport(ERROR,
2126 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2127 ECB : errmsg("input is out of range")));
2128 :
2129 CBC 30 : if (arg1 >= 0.0)
2130 GBC 18 : result = acosd_q1(arg1);
2131 : else
2132 CBC 12 : result = 90.0 + asind_q1(-arg1);
2133 :
2134 GIC 30 : if (unlikely(isinf(result)))
2135 UIC 0 : float_overflow_error();
2136 :
2137 GIC 30 : PG_RETURN_FLOAT8(result);
2138 : }
2139 :
2140 ECB :
2141 : /*
2142 : * dasind - returns the arcsin of arg1 (degrees)
2143 : */
2144 : Datum
2145 GIC 30 : dasind(PG_FUNCTION_ARGS)
2146 ECB : {
2147 GBC 30 : float8 arg1 = PG_GETARG_FLOAT8(0);
2148 : float8 result;
2149 ECB :
2150 : /* Per the POSIX spec, return NaN if the input is NaN */
2151 GIC 30 : if (isnan(arg1))
2152 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
2153 :
2154 GIC 30 : INIT_DEGREE_CONSTANTS();
2155 :
2156 ECB : /*
2157 EUB : * The principal branch of the inverse sine function maps values in the
2158 : * range [-1, 1] to values in the range [-90, 90], so we should reject any
2159 : * inputs outside that range and the result will always be finite.
2160 : */
2161 CBC 30 : if (arg1 < -1.0 || arg1 > 1.0)
2162 LBC 0 : ereport(ERROR,
2163 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2164 ECB : errmsg("input is out of range")));
2165 :
2166 CBC 30 : if (arg1 >= 0.0)
2167 GBC 18 : result = asind_q1(arg1);
2168 : else
2169 CBC 12 : result = -asind_q1(-arg1);
2170 :
2171 GIC 30 : if (unlikely(isinf(result)))
2172 UIC 0 : float_overflow_error();
2173 :
2174 GIC 30 : PG_RETURN_FLOAT8(result);
2175 : }
2176 :
2177 ECB :
2178 : /*
2179 : * datand - returns the arctan of arg1 (degrees)
2180 : */
2181 : Datum
2182 GIC 30 : datand(PG_FUNCTION_ARGS)
2183 : {
2184 CBC 30 : float8 arg1 = PG_GETARG_FLOAT8(0);
2185 EUB : float8 result;
2186 : volatile float8 atan_arg1;
2187 ECB :
2188 : /* Per the POSIX spec, return NaN if the input is NaN */
2189 GIC 30 : if (isnan(arg1))
2190 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
2191 :
2192 GIC 30 : INIT_DEGREE_CONSTANTS();
2193 :
2194 : /*
2195 ECB : * The principal branch of the inverse tangent function maps all inputs to
2196 : * values in the range [-90, 90], so the result should always be finite,
2197 : * even if the input is infinite. Additionally, we take care to ensure
2198 : * than when arg1 is 1, the result is exactly 45.
2199 EUB : */
2200 GIC 30 : atan_arg1 = atan(arg1);
2201 CBC 30 : result = (atan_arg1 / atan_1_0) * 45.0;
2202 :
2203 GIC 30 : if (unlikely(isinf(result)))
2204 UIC 0 : float_overflow_error();
2205 :
2206 GIC 30 : PG_RETURN_FLOAT8(result);
2207 : }
2208 :
2209 ECB :
2210 : /*
2211 : * atan2d - returns the arctan of arg1/arg2 (degrees)
2212 : */
2213 : Datum
2214 GIC 30 : datan2d(PG_FUNCTION_ARGS)
2215 : {
2216 30 : float8 arg1 = PG_GETARG_FLOAT8(0);
2217 CBC 30 : float8 arg2 = PG_GETARG_FLOAT8(1);
2218 EUB : float8 result;
2219 : volatile float8 atan2_arg1_arg2;
2220 ECB :
2221 : /* Per the POSIX spec, return NaN if either input is NaN */
2222 GIC 30 : if (isnan(arg1) || isnan(arg2))
2223 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
2224 :
2225 GIC 30 : INIT_DEGREE_CONSTANTS();
2226 :
2227 : /*
2228 : * atan2d maps all inputs to values in the range [-180, 180], so the
2229 : * result should always be finite, even if the inputs are infinite.
2230 : *
2231 ECB : * Note: this coding assumes that atan(1.0) is a suitable scaling constant
2232 : * to get an exact result from atan2(). This might well fail on us at
2233 : * some point, requiring us to decide exactly what inputs we think we're
2234 : * going to guarantee an exact result for.
2235 EUB : */
2236 GIC 30 : atan2_arg1_arg2 = atan2(arg1, arg2);
2237 CBC 30 : result = (atan2_arg1_arg2 / atan_1_0) * 45.0;
2238 :
2239 GIC 30 : if (unlikely(isinf(result)))
2240 UIC 0 : float_overflow_error();
2241 :
2242 GIC 30 : PG_RETURN_FLOAT8(result);
2243 : }
2244 :
2245 :
2246 : /*
2247 ECB : * sind_0_to_30 - returns the sine of an angle that lies between 0 and
2248 : * 30 degrees. This will return exactly 0 when x is 0,
2249 : * and exactly 0.5 when x is 30 degrees.
2250 : */
2251 : static double
2252 GIC 159 : sind_0_to_30(double x)
2253 : {
2254 159 : volatile float8 sin_x = sin(x * RADIANS_PER_DEGREE);
2255 :
2256 159 : return (sin_x / sin_30) / 2.0;
2257 : }
2258 :
2259 :
2260 : /*
2261 ECB : * cosd_0_to_60 - returns the cosine of an angle that lies between 0
2262 : * and 60 degrees. This will return exactly 1 when x
2263 : * is 0, and exactly 0.5 when x is 60 degrees.
2264 : */
2265 : static double
2266 GIC 267 : cosd_0_to_60(double x)
2267 : {
2268 267 : volatile float8 one_minus_cos_x = 1.0 - cos(x * RADIANS_PER_DEGREE);
2269 :
2270 267 : return 1.0 - (one_minus_cos_x / one_minus_cos_60) / 2.0;
2271 : }
2272 :
2273 :
2274 ECB : /*
2275 : * sind_q1 - returns the sine of an angle in the first quadrant
2276 : * (0 to 90 degrees).
2277 : */
2278 : static double
2279 GIC 213 : sind_q1(double x)
2280 : {
2281 : /*
2282 ECB : * Stitch together the sine and cosine functions for the ranges [0, 30]
2283 : * and (30, 90]. These guarantee to return exact answers at their
2284 : * endpoints, so the overall result is a continuous monotonic function
2285 : * that gives exact results when x = 0, 30 and 90 degrees.
2286 : */
2287 GIC 213 : if (x <= 30.0)
2288 105 : return sind_0_to_30(x);
2289 : else
2290 108 : return cosd_0_to_60(90.0 - x);
2291 : }
2292 :
2293 :
2294 ECB : /*
2295 : * cosd_q1 - returns the cosine of an angle in the first quadrant
2296 : * (0 to 90 degrees).
2297 : */
2298 : static double
2299 GIC 213 : cosd_q1(double x)
2300 : {
2301 : /*
2302 ECB : * Stitch together the sine and cosine functions for the ranges [0, 60]
2303 : * and (60, 90]. These guarantee to return exact answers at their
2304 : * endpoints, so the overall result is a continuous monotonic function
2305 : * that gives exact results when x = 0, 60 and 90 degrees.
2306 : */
2307 GIC 213 : if (x <= 60.0)
2308 159 : return cosd_0_to_60(x);
2309 : else
2310 54 : return sind_0_to_30(90.0 - x);
2311 : }
2312 :
2313 ECB :
2314 : /*
2315 : * dcosd - returns the cosine of arg1 (degrees)
2316 : */
2317 : Datum
2318 GIC 99 : dcosd(PG_FUNCTION_ARGS)
2319 : {
2320 99 : float8 arg1 = PG_GETARG_FLOAT8(0);
2321 : float8 result;
2322 99 : int sign = 1;
2323 ECB :
2324 EUB : /*
2325 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2326 ECB : * if the input is infinite.
2327 EUB : */
2328 GIC 99 : if (isnan(arg1))
2329 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
2330 :
2331 CBC 99 : if (isinf(arg1))
2332 UIC 0 : ereport(ERROR,
2333 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2334 ECB : errmsg("input is out of range")));
2335 :
2336 CBC 99 : INIT_DEGREE_CONSTANTS();
2337 :
2338 : /* Reduce the range of the input to [0,90] degrees */
2339 GBC 99 : arg1 = fmod(arg1, 360.0);
2340 :
2341 GIC 99 : if (arg1 < 0.0)
2342 ECB : {
2343 : /* cosd(-x) = cosd(x) */
2344 UIC 0 : arg1 = -arg1;
2345 ECB : }
2346 :
2347 GIC 99 : if (arg1 > 180.0)
2348 ECB : {
2349 : /* cosd(360-x) = cosd(x) */
2350 GIC 27 : arg1 = 360.0 - arg1;
2351 ECB : }
2352 :
2353 GIC 99 : if (arg1 > 90.0)
2354 : {
2355 ECB : /* cosd(180-x) = -cosd(x) */
2356 GIC 27 : arg1 = 180.0 - arg1;
2357 CBC 27 : sign = -sign;
2358 EUB : }
2359 :
2360 CBC 99 : result = sign * cosd_q1(arg1);
2361 :
2362 GIC 99 : if (unlikely(isinf(result)))
2363 UIC 0 : float_overflow_error();
2364 :
2365 GIC 99 : PG_RETURN_FLOAT8(result);
2366 : }
2367 :
2368 ECB :
2369 : /*
2370 : * dcotd - returns the cotangent of arg1 (degrees)
2371 : */
2372 : Datum
2373 CBC 54 : dcotd(PG_FUNCTION_ARGS)
2374 : {
2375 GIC 54 : float8 arg1 = PG_GETARG_FLOAT8(0);
2376 : float8 result;
2377 : volatile float8 cot_arg1;
2378 54 : int sign = 1;
2379 ECB :
2380 EUB : /*
2381 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2382 ECB : * if the input is infinite.
2383 EUB : */
2384 GIC 54 : if (isnan(arg1))
2385 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
2386 :
2387 CBC 54 : if (isinf(arg1))
2388 UIC 0 : ereport(ERROR,
2389 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2390 ECB : errmsg("input is out of range")));
2391 :
2392 CBC 54 : INIT_DEGREE_CONSTANTS();
2393 :
2394 : /* Reduce the range of the input to [0,90] degrees */
2395 GBC 54 : arg1 = fmod(arg1, 360.0);
2396 EUB :
2397 GIC 54 : if (arg1 < 0.0)
2398 : {
2399 ECB : /* cotd(-x) = -cotd(x) */
2400 UIC 0 : arg1 = -arg1;
2401 0 : sign = -sign;
2402 ECB : }
2403 :
2404 GIC 54 : if (arg1 > 180.0)
2405 : {
2406 ECB : /* cotd(360-x) = -cotd(x) */
2407 GIC 18 : arg1 = 360.0 - arg1;
2408 18 : sign = -sign;
2409 ECB : }
2410 :
2411 GIC 54 : if (arg1 > 90.0)
2412 : {
2413 ECB : /* cotd(180-x) = -cotd(x) */
2414 CBC 18 : arg1 = 180.0 - arg1;
2415 GIC 18 : sign = -sign;
2416 : }
2417 :
2418 54 : cot_arg1 = cosd_q1(arg1) / sind_q1(arg1);
2419 54 : result = sign * (cot_arg1 / cot_45);
2420 :
2421 ECB : /*
2422 : * On some machines we get cotd(270) = minus zero, but this isn't always
2423 : * true. For portability, and because the user constituency for this
2424 : * function probably doesn't want minus zero, force it to plain zero.
2425 : */
2426 CBC 54 : if (result == 0.0)
2427 GIC 12 : result = 0.0;
2428 :
2429 : /* Not checking for overflow because cotd(0) == Inf */
2430 :
2431 54 : PG_RETURN_FLOAT8(result);
2432 : }
2433 :
2434 ECB :
2435 : /*
2436 : * dsind - returns the sine of arg1 (degrees)
2437 : */
2438 : Datum
2439 GIC 99 : dsind(PG_FUNCTION_ARGS)
2440 : {
2441 99 : float8 arg1 = PG_GETARG_FLOAT8(0);
2442 : float8 result;
2443 99 : int sign = 1;
2444 ECB :
2445 EUB : /*
2446 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2447 ECB : * if the input is infinite.
2448 EUB : */
2449 GIC 99 : if (isnan(arg1))
2450 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
2451 :
2452 CBC 99 : if (isinf(arg1))
2453 UIC 0 : ereport(ERROR,
2454 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2455 ECB : errmsg("input is out of range")));
2456 :
2457 CBC 99 : INIT_DEGREE_CONSTANTS();
2458 :
2459 : /* Reduce the range of the input to [0,90] degrees */
2460 GBC 99 : arg1 = fmod(arg1, 360.0);
2461 EUB :
2462 GIC 99 : if (arg1 < 0.0)
2463 : {
2464 ECB : /* sind(-x) = -sind(x) */
2465 UIC 0 : arg1 = -arg1;
2466 0 : sign = -sign;
2467 ECB : }
2468 :
2469 GIC 99 : if (arg1 > 180.0)
2470 : {
2471 ECB : /* sind(360-x) = -sind(x) */
2472 GIC 27 : arg1 = 360.0 - arg1;
2473 27 : sign = -sign;
2474 ECB : }
2475 :
2476 GIC 99 : if (arg1 > 90.0)
2477 ECB : {
2478 : /* sind(180-x) = sind(x) */
2479 CBC 27 : arg1 = 180.0 - arg1;
2480 EUB : }
2481 :
2482 CBC 99 : result = sign * sind_q1(arg1);
2483 :
2484 GIC 99 : if (unlikely(isinf(result)))
2485 UIC 0 : float_overflow_error();
2486 :
2487 GIC 99 : PG_RETURN_FLOAT8(result);
2488 : }
2489 :
2490 ECB :
2491 : /*
2492 : * dtand - returns the tangent of arg1 (degrees)
2493 : */
2494 : Datum
2495 CBC 54 : dtand(PG_FUNCTION_ARGS)
2496 : {
2497 GIC 54 : float8 arg1 = PG_GETARG_FLOAT8(0);
2498 : float8 result;
2499 : volatile float8 tan_arg1;
2500 54 : int sign = 1;
2501 ECB :
2502 EUB : /*
2503 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2504 ECB : * if the input is infinite.
2505 EUB : */
2506 GIC 54 : if (isnan(arg1))
2507 UIC 0 : PG_RETURN_FLOAT8(get_float8_nan());
2508 :
2509 CBC 54 : if (isinf(arg1))
2510 UIC 0 : ereport(ERROR,
2511 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2512 ECB : errmsg("input is out of range")));
2513 :
2514 CBC 54 : INIT_DEGREE_CONSTANTS();
2515 :
2516 : /* Reduce the range of the input to [0,90] degrees */
2517 GBC 54 : arg1 = fmod(arg1, 360.0);
2518 EUB :
2519 GIC 54 : if (arg1 < 0.0)
2520 : {
2521 ECB : /* tand(-x) = -tand(x) */
2522 UIC 0 : arg1 = -arg1;
2523 0 : sign = -sign;
2524 ECB : }
2525 :
2526 GIC 54 : if (arg1 > 180.0)
2527 : {
2528 ECB : /* tand(360-x) = -tand(x) */
2529 GIC 18 : arg1 = 360.0 - arg1;
2530 18 : sign = -sign;
2531 ECB : }
2532 :
2533 GIC 54 : if (arg1 > 90.0)
2534 : {
2535 ECB : /* tand(180-x) = -tand(x) */
2536 CBC 18 : arg1 = 180.0 - arg1;
2537 GIC 18 : sign = -sign;
2538 : }
2539 :
2540 54 : tan_arg1 = sind_q1(arg1) / cosd_q1(arg1);
2541 54 : result = sign * (tan_arg1 / tan_45);
2542 :
2543 ECB : /*
2544 : * On some machines we get tand(180) = minus zero, but this isn't always
2545 : * true. For portability, and because the user constituency for this
2546 : * function probably doesn't want minus zero, force it to plain zero.
2547 : */
2548 CBC 54 : if (result == 0.0)
2549 GIC 18 : result = 0.0;
2550 :
2551 : /* Not checking for overflow because tand(90) == Inf */
2552 :
2553 54 : PG_RETURN_FLOAT8(result);
2554 : }
2555 :
2556 ECB :
2557 : /*
2558 : * degrees - returns degrees converted from radians
2559 : */
2560 : Datum
2561 GIC 40 : degrees(PG_FUNCTION_ARGS)
2562 : {
2563 40 : float8 arg1 = PG_GETARG_FLOAT8(0);
2564 :
2565 40 : PG_RETURN_FLOAT8(float8_div(arg1, RADIANS_PER_DEGREE));
2566 : }
2567 :
2568 ECB :
2569 : /*
2570 : * dpi - returns the constant PI
2571 : */
2572 : Datum
2573 GIC 95 : dpi(PG_FUNCTION_ARGS)
2574 : {
2575 95 : PG_RETURN_FLOAT8(M_PI);
2576 : }
2577 :
2578 ECB :
2579 : /*
2580 : * radians - returns radians converted from degrees
2581 : */
2582 : Datum
2583 GIC 955 : radians(PG_FUNCTION_ARGS)
2584 : {
2585 955 : float8 arg1 = PG_GETARG_FLOAT8(0);
2586 :
2587 955 : PG_RETURN_FLOAT8(float8_mul(arg1, RADIANS_PER_DEGREE));
2588 : }
2589 :
2590 :
2591 : /* ========== HYPERBOLIC FUNCTIONS ========== */
2592 :
2593 ECB :
2594 : /*
2595 : * dsinh - returns the hyperbolic sine of arg1
2596 : */
2597 : Datum
2598 CBC 12 : dsinh(PG_FUNCTION_ARGS)
2599 ECB : {
2600 GIC 12 : float8 arg1 = PG_GETARG_FLOAT8(0);
2601 : float8 result;
2602 :
2603 12 : errno = 0;
2604 12 : result = sinh(arg1);
2605 :
2606 ECB : /*
2607 : * if an ERANGE error occurs, it means there is an overflow. For sinh,
2608 EUB : * the result should be either -infinity or infinity, depending on the
2609 : * sign of arg1.
2610 : */
2611 GBC 12 : if (errno == ERANGE)
2612 : {
2613 UIC 0 : if (arg1 < 0)
2614 LBC 0 : result = -get_float8_infinity();
2615 : else
2616 UIC 0 : result = get_float8_infinity();
2617 : }
2618 :
2619 GIC 12 : PG_RETURN_FLOAT8(result);
2620 : }
2621 :
2622 ECB :
2623 : /*
2624 : * dcosh - returns the hyperbolic cosine of arg1
2625 : */
2626 : Datum
2627 CBC 12 : dcosh(PG_FUNCTION_ARGS)
2628 ECB : {
2629 GIC 12 : float8 arg1 = PG_GETARG_FLOAT8(0);
2630 : float8 result;
2631 :
2632 12 : errno = 0;
2633 12 : result = cosh(arg1);
2634 ECB :
2635 EUB : /*
2636 : * if an ERANGE error occurs, it means there is an overflow. As cosh is
2637 ECB : * always positive, it always means the result is positive infinity.
2638 EUB : */
2639 GIC 12 : if (errno == ERANGE)
2640 LBC 0 : result = get_float8_infinity();
2641 :
2642 GIC 12 : if (unlikely(result == 0.0))
2643 UIC 0 : float_underflow_error();
2644 :
2645 GIC 12 : PG_RETURN_FLOAT8(result);
2646 : }
2647 ECB :
2648 : /*
2649 : * dtanh - returns the hyperbolic tangent of arg1
2650 : */
2651 : Datum
2652 GIC 12 : dtanh(PG_FUNCTION_ARGS)
2653 : {
2654 12 : float8 arg1 = PG_GETARG_FLOAT8(0);
2655 ECB : float8 result;
2656 :
2657 : /*
2658 EUB : * For tanh, we don't need an errno check because it never overflows.
2659 : */
2660 CBC 12 : result = tanh(arg1);
2661 :
2662 GIC 12 : if (unlikely(isinf(result)))
2663 UIC 0 : float_overflow_error();
2664 :
2665 GIC 12 : PG_RETURN_FLOAT8(result);
2666 : }
2667 ECB :
2668 : /*
2669 : * dasinh - returns the inverse hyperbolic sine of arg1
2670 : */
2671 : Datum
2672 GIC 12 : dasinh(PG_FUNCTION_ARGS)
2673 : {
2674 12 : float8 arg1 = PG_GETARG_FLOAT8(0);
2675 ECB : float8 result;
2676 :
2677 : /*
2678 : * For asinh, we don't need an errno check because it never overflows.
2679 : */
2680 GIC 12 : result = asinh(arg1);
2681 :
2682 12 : PG_RETURN_FLOAT8(result);
2683 : }
2684 ECB :
2685 : /*
2686 : * dacosh - returns the inverse hyperbolic cosine of arg1
2687 : */
2688 : Datum
2689 GIC 9 : dacosh(PG_FUNCTION_ARGS)
2690 : {
2691 9 : float8 arg1 = PG_GETARG_FLOAT8(0);
2692 : float8 result;
2693 :
2694 : /*
2695 ECB : * acosh is only defined for inputs >= 1.0. By checking this ourselves,
2696 : * we need not worry about checking for an EDOM error, which is a good
2697 : * thing because some implementations will report that for NaN. Otherwise,
2698 : * no error is possible.
2699 : */
2700 CBC 9 : if (arg1 < 1.0)
2701 GIC 3 : ereport(ERROR,
2702 ECB : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2703 : errmsg("input is out of range")));
2704 :
2705 GIC 6 : result = acosh(arg1);
2706 :
2707 6 : PG_RETURN_FLOAT8(result);
2708 : }
2709 ECB :
2710 : /*
2711 : * datanh - returns the inverse hyperbolic tangent of arg1
2712 : */
2713 : Datum
2714 GIC 12 : datanh(PG_FUNCTION_ARGS)
2715 : {
2716 12 : float8 arg1 = PG_GETARG_FLOAT8(0);
2717 : float8 result;
2718 :
2719 ECB : /*
2720 : * atanh is only defined for inputs between -1 and 1. By checking this
2721 : * ourselves, we need not worry about checking for an EDOM error, which is
2722 : * a good thing because some implementations will report that for NaN.
2723 : */
2724 GIC 12 : if (arg1 < -1.0 || arg1 > 1.0)
2725 6 : ereport(ERROR,
2726 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2727 : errmsg("input is out of range")));
2728 :
2729 ECB : /*
2730 EUB : * Also handle the infinity cases ourselves; this is helpful because old
2731 ECB : * glibc versions may produce the wrong errno for this. All other inputs
2732 EUB : * cannot produce an error.
2733 : */
2734 CBC 6 : if (arg1 == -1.0)
2735 UIC 0 : result = -get_float8_infinity();
2736 CBC 6 : else if (arg1 == 1.0)
2737 UIC 0 : result = get_float8_infinity();
2738 : else
2739 GIC 6 : result = atanh(arg1);
2740 :
2741 6 : PG_RETURN_FLOAT8(result);
2742 : }
2743 :
2744 :
2745 : /* ========== ERROR FUNCTIONS ========== */
2746 :
2747 :
2748 : /*
2749 : * derf - returns the error function: erf(arg1)
2750 ECB : */
2751 : Datum
2752 GNC 3066 : derf(PG_FUNCTION_ARGS)
2753 : {
2754 3066 : float8 arg1 = PG_GETARG_FLOAT8(0);
2755 : float8 result;
2756 :
2757 : /*
2758 : * For erf, we don't need an errno check because it never overflows.
2759 : */
2760 3066 : result = erf(arg1);
2761 :
2762 3066 : if (unlikely(isinf(result)))
2763 UNC 0 : float_overflow_error();
2764 :
2765 GNC 3066 : PG_RETURN_FLOAT8(result);
2766 : }
2767 :
2768 : /*
2769 : * derfc - returns the complementary error function: 1 - erf(arg1)
2770 : */
2771 : Datum
2772 66 : derfc(PG_FUNCTION_ARGS)
2773 : {
2774 66 : float8 arg1 = PG_GETARG_FLOAT8(0);
2775 : float8 result;
2776 :
2777 : /*
2778 : * For erfc, we don't need an errno check because it never overflows.
2779 : */
2780 66 : result = erfc(arg1);
2781 :
2782 66 : if (unlikely(isinf(result)))
2783 UNC 0 : float_overflow_error();
2784 :
2785 GNC 66 : PG_RETURN_FLOAT8(result);
2786 : }
2787 :
2788 :
2789 : /* ========== RANDOM FUNCTIONS ========== */
2790 :
2791 :
2792 : /*
2793 : * initialize_drandom_seed - initialize drandom_seed if not yet done
2794 : */
2795 : static void
2796 445537 : initialize_drandom_seed(void)
2797 : {
2798 : /* Initialize random seed, if not done yet in this process */
2799 GIC 445537 : if (unlikely(!drandom_seed_set))
2800 ECB : {
2801 : /*
2802 : * If possible, initialize the seed using high-quality random bits.
2803 EUB : * Should that fail for some reason, we fall back on a lower-quality
2804 : * seed based on current time and PID.
2805 ECB : */
2806 GIC 52 : if (unlikely(!pg_prng_strong_seed(&drandom_seed)))
2807 : {
2808 UIC 0 : TimestampTz now = GetCurrentTimestamp();
2809 : uint64 iseed;
2810 :
2811 : /* Mix the PID with the most predictable bits of the timestamp */
2812 LBC 0 : iseed = (uint64) now ^ ((uint64) MyProcPid << 32);
2813 UIC 0 : pg_prng_seed(&drandom_seed, iseed);
2814 ECB : }
2815 GIC 52 : drandom_seed_set = true;
2816 : }
2817 GNC 445537 : }
2818 :
2819 : /*
2820 : * drandom - returns a random number
2821 : */
2822 : Datum
2823 438877 : drandom(PG_FUNCTION_ARGS)
2824 : {
2825 : float8 result;
2826 :
2827 438877 : initialize_drandom_seed();
2828 :
2829 : /* pg_prng_double produces desired result range [0.0 - 1.0) */
2830 GIC 438877 : result = pg_prng_double(&drandom_seed);
2831 ECB :
2832 GIC 438877 : PG_RETURN_FLOAT8(result);
2833 ECB : }
2834 EUB :
2835 : /*
2836 : * drandom_normal - returns a random number from a normal distribution
2837 : */
2838 : Datum
2839 GNC 6660 : drandom_normal(PG_FUNCTION_ARGS)
2840 : {
2841 6660 : float8 mean = PG_GETARG_FLOAT8(0);
2842 6660 : float8 stddev = PG_GETARG_FLOAT8(1);
2843 : float8 result,
2844 : z;
2845 :
2846 6660 : initialize_drandom_seed();
2847 :
2848 : /* Get random value from standard normal(mean = 0.0, stddev = 1.0) */
2849 6660 : z = pg_prng_double_normal(&drandom_seed);
2850 : /* Transform the normal standard variable (z) */
2851 : /* using the target normal distribution parameters */
2852 6660 : result = (stddev * z) + mean;
2853 :
2854 6660 : PG_RETURN_FLOAT8(result);
2855 : }
2856 :
2857 ECB : /*
2858 : * setseed - set seed for the random number generator
2859 : */
2860 : Datum
2861 GIC 4 : setseed(PG_FUNCTION_ARGS)
2862 : {
2863 4 : float8 seed = PG_GETARG_FLOAT8(0);
2864 :
2865 4 : if (seed < -1 || seed > 1 || isnan(seed))
2866 UIC 0 : ereport(ERROR,
2867 : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
2868 ECB : errmsg("setseed parameter %g is out of allowed range [-1,1]",
2869 : seed)));
2870 :
2871 CBC 4 : pg_prng_fseed(&drandom_seed, seed);
2872 GIC 4 : drandom_seed_set = true;
2873 :
2874 4 : PG_RETURN_VOID();
2875 : }
2876 :
2877 :
2878 ECB :
2879 : /*
2880 EUB : * =========================
2881 : * FLOAT AGGREGATE OPERATORS
2882 : * =========================
2883 : *
2884 : * float8_accum - accumulate for AVG(), variance aggregates, etc.
2885 : * float4_accum - same, but input data is float4
2886 : * float8_avg - produce final result for float AVG()
2887 ECB : * float8_var_samp - produce final result for float VAR_SAMP()
2888 : * float8_var_pop - produce final result for float VAR_POP()
2889 : * float8_stddev_samp - produce final result for float STDDEV_SAMP()
2890 : * float8_stddev_pop - produce final result for float STDDEV_POP()
2891 : *
2892 : * The naive schoolbook implementation of these aggregates works by
2893 : * accumulating sum(X) and sum(X^2). However, this approach suffers from
2894 : * large rounding errors in the final computation of quantities like the
2895 : * population variance (N*sum(X^2) - sum(X)^2) / N^2, since each of the
2896 : * intermediate terms is potentially very large, while the difference is often
2897 : * quite small.
2898 : *
2899 : * Instead we use the Youngs-Cramer algorithm [1] which works by accumulating
2900 : * Sx=sum(X) and Sxx=sum((X-Sx/N)^2), using a numerically stable algorithm to
2901 : * incrementally update those quantities. The final computations of each of
2902 : * the aggregate values is then trivial and gives more accurate results (for
2903 : * example, the population variance is just Sxx/N). This algorithm is also
2904 : * fairly easy to generalize to allow parallel execution without loss of
2905 : * precision (see, for example, [2]). For more details, and a comparison of
2906 : * this with other algorithms, see [3].
2907 : *
2908 : * The transition datatype for all these aggregates is a 3-element array
2909 : * of float8, holding the values N, Sx, Sxx in that order.
2910 : *
2911 : * Note that we represent N as a float to avoid having to build a special
2912 : * datatype. Given a reasonable floating-point implementation, there should
2913 : * be no accuracy loss unless N exceeds 2 ^ 52 or so (by which time the
2914 : * user will have doubtless lost interest anyway...)
2915 : *
2916 : * [1] Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms,
2917 : * E. A. Youngs and E. M. Cramer, Technometrics Vol 13, No 3, August 1971.
2918 : *
2919 : * [2] Updating Formulae and a Pairwise Algorithm for Computing Sample
2920 : * Variances, T. F. Chan, G. H. Golub & R. J. LeVeque, COMPSTAT 1982.
2921 : *
2922 : * [3] Numerically Stable Parallel Computation of (Co-)Variance, Erich
2923 : * Schubert and Michael Gertz, Proceedings of the 30th International
2924 : * Conference on Scientific and Statistical Database Management, 2018.
2925 : */
2926 :
2927 : static float8 *
2928 GIC 746 : check_float8_array(ArrayType *transarray, const char *caller, int n)
2929 : {
2930 : /*
2931 : * We expect the input to be an N-element float array; verify that. We
2932 : * don't need to use deconstruct_array() since the array data is just
2933 ECB : * going to look like a C array of N float8 values.
2934 : */
2935 CBC 746 : if (ARR_NDIM(transarray) != 1 ||
2936 GIC 746 : ARR_DIMS(transarray)[0] != n ||
2937 CBC 746 : ARR_HASNULL(transarray) ||
2938 GBC 746 : ARR_ELEMTYPE(transarray) != FLOAT8OID)
2939 UIC 0 : elog(ERROR, "%s: expected %d-element float8 array", caller, n);
2940 GIC 746 : return (float8 *) ARR_DATA_PTR(transarray);
2941 : }
2942 :
2943 ECB : /*
2944 : * float8_combine
2945 : *
2946 : * An aggregate combine function used to combine two 3 fields
2947 : * aggregate transition data into a single transition data.
2948 : * This function is used only in two stage aggregation and
2949 : * shouldn't be called outside aggregate context.
2950 : */
2951 : Datum
2952 GIC 9 : float8_combine(PG_FUNCTION_ARGS)
2953 : {
2954 9 : ArrayType *transarray1 = PG_GETARG_ARRAYTYPE_P(0);
2955 9 : ArrayType *transarray2 = PG_GETARG_ARRAYTYPE_P(1);
2956 : float8 *transvalues1;
2957 : float8 *transvalues2;
2958 : float8 N1,
2959 : Sx1,
2960 : Sxx1,
2961 : N2,
2962 : Sx2,
2963 : Sxx2,
2964 : tmp,
2965 : N,
2966 : Sx,
2967 : Sxx;
2968 :
2969 9 : transvalues1 = check_float8_array(transarray1, "float8_combine", 3);
2970 9 : transvalues2 = check_float8_array(transarray2, "float8_combine", 3);
2971 :
2972 9 : N1 = transvalues1[0];
2973 9 : Sx1 = transvalues1[1];
2974 9 : Sxx1 = transvalues1[2];
2975 :
2976 9 : N2 = transvalues2[0];
2977 9 : Sx2 = transvalues2[1];
2978 9 : Sxx2 = transvalues2[2];
2979 :
2980 : /*--------------------
2981 : * The transition values combine using a generalization of the
2982 : * Youngs-Cramer algorithm as follows:
2983 : *
2984 : * N = N1 + N2
2985 : * Sx = Sx1 + Sx2
2986 : * Sxx = Sxx1 + Sxx2 + N1 * N2 * (Sx1/N1 - Sx2/N2)^2 / N;
2987 : *
2988 : * It's worth handling the special cases N1 = 0 and N2 = 0 separately
2989 : * since those cases are trivial, and we then don't need to worry about
2990 : * division-by-zero errors in the general case.
2991 : *--------------------
2992 : */
2993 9 : if (N1 == 0.0)
2994 : {
2995 3 : N = N2;
2996 3 : Sx = Sx2;
2997 3 : Sxx = Sxx2;
2998 : }
2999 6 : else if (N2 == 0.0)
3000 ECB : {
3001 GIC 3 : N = N1;
3002 3 : Sx = Sx1;
3003 3 : Sxx = Sxx1;
3004 : }
3005 : else
3006 : {
3007 CBC 3 : N = N1 + N2;
3008 3 : Sx = float8_pl(Sx1, Sx2);
3009 3 : tmp = Sx1 / N1 - Sx2 / N2;
3010 3 : Sxx = Sxx1 + Sxx2 + N1 * N2 * tmp * tmp / N;
3011 GBC 3 : if (unlikely(isinf(Sxx)) && !isinf(Sxx1) && !isinf(Sxx2))
3012 LBC 0 : float_overflow_error();
3013 : }
3014 :
3015 : /*
3016 : * If we're invoked as an aggregate, we can cheat and modify our first
3017 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3018 : * new array with the updated transition data and return it.
3019 : */
3020 GIC 9 : if (AggCheckCallContext(fcinfo, NULL))
3021 : {
3022 UIC 0 : transvalues1[0] = N;
3023 0 : transvalues1[1] = Sx;
3024 LBC 0 : transvalues1[2] = Sxx;
3025 :
3026 0 : PG_RETURN_ARRAYTYPE_P(transarray1);
3027 ECB : }
3028 : else
3029 : {
3030 : Datum transdatums[3];
3031 : ArrayType *result;
3032 :
3033 GIC 9 : transdatums[0] = Float8GetDatumFast(N);
3034 9 : transdatums[1] = Float8GetDatumFast(Sx);
3035 9 : transdatums[2] = Float8GetDatumFast(Sxx);
3036 :
3037 9 : result = construct_array(transdatums, 3,
3038 : FLOAT8OID,
3039 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
3040 :
3041 CBC 9 : PG_RETURN_ARRAYTYPE_P(result);
3042 ECB : }
3043 : }
3044 :
3045 : Datum
3046 CBC 181 : float8_accum(PG_FUNCTION_ARGS)
3047 : {
3048 181 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3049 181 : float8 newval = PG_GETARG_FLOAT8(1);
3050 ECB : float8 *transvalues;
3051 : float8 N,
3052 : Sx,
3053 : Sxx,
3054 : tmp;
3055 :
3056 GIC 181 : transvalues = check_float8_array(transarray, "float8_accum", 3);
3057 181 : N = transvalues[0];
3058 181 : Sx = transvalues[1];
3059 181 : Sxx = transvalues[2];
3060 :
3061 : /*
3062 : * Use the Youngs-Cramer algorithm to incorporate the new value into the
3063 : * transition values.
3064 : */
3065 CBC 181 : N += 1.0;
3066 GIC 181 : Sx += newval;
3067 CBC 181 : if (transvalues[0] > 0.0)
3068 ECB : {
3069 CBC 132 : tmp = newval * N - Sx;
3070 GIC 132 : Sxx += tmp * tmp / (N * transvalues[0]);
3071 ECB :
3072 : /*
3073 : * Overflow check. We only report an overflow error when finite
3074 : * inputs lead to infinite results. Note also that Sxx should be NaN
3075 : * if any of the inputs are infinite, so we intentionally prevent Sxx
3076 : * from becoming infinite.
3077 : */
3078 GIC 132 : if (isinf(Sx) || isinf(Sxx))
3079 ECB : {
3080 CBC 12 : if (!isinf(transvalues[1]) && !isinf(newval))
3081 LBC 0 : float_overflow_error();
3082 ECB :
3083 CBC 12 : Sxx = get_float8_nan();
3084 EUB : }
3085 : }
3086 : else
3087 : {
3088 : /*
3089 : * At the first input, we normally can leave Sxx as 0. However, if
3090 : * the first input is Inf or NaN, we'd better force Sxx to NaN;
3091 : * otherwise we will falsely report variance zero when there are no
3092 ECB : * more inputs.
3093 : */
3094 GBC 49 : if (isnan(newval) || isinf(newval))
3095 24 : Sxx = get_float8_nan();
3096 EUB : }
3097 :
3098 : /*
3099 : * If we're invoked as an aggregate, we can cheat and modify our first
3100 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3101 : * new array with the updated transition data and return it.
3102 : */
3103 GIC 181 : if (AggCheckCallContext(fcinfo, NULL))
3104 : {
3105 CBC 178 : transvalues[0] = N;
3106 178 : transvalues[1] = Sx;
3107 178 : transvalues[2] = Sxx;
3108 :
3109 178 : PG_RETURN_ARRAYTYPE_P(transarray);
3110 : }
3111 : else
3112 : {
3113 ECB : Datum transdatums[3];
3114 : ArrayType *result;
3115 :
3116 GIC 3 : transdatums[0] = Float8GetDatumFast(N);
3117 3 : transdatums[1] = Float8GetDatumFast(Sx);
3118 CBC 3 : transdatums[2] = Float8GetDatumFast(Sxx);
3119 :
3120 3 : result = construct_array(transdatums, 3,
3121 ECB : FLOAT8OID,
3122 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
3123 :
3124 GIC 3 : PG_RETURN_ARRAYTYPE_P(result);
3125 : }
3126 : }
3127 :
3128 ECB : Datum
3129 CBC 144 : float4_accum(PG_FUNCTION_ARGS)
3130 ECB : {
3131 CBC 144 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3132 :
3133 : /* do computations as float8 */
3134 GIC 144 : float8 newval = PG_GETARG_FLOAT4(1);
3135 : float8 *transvalues;
3136 : float8 N,
3137 ECB : Sx,
3138 : Sxx,
3139 : tmp;
3140 :
3141 CBC 144 : transvalues = check_float8_array(transarray, "float4_accum", 3);
3142 144 : N = transvalues[0];
3143 GIC 144 : Sx = transvalues[1];
3144 144 : Sxx = transvalues[2];
3145 :
3146 : /*
3147 : * Use the Youngs-Cramer algorithm to incorporate the new value into the
3148 : * transition values.
3149 : */
3150 CBC 144 : N += 1.0;
3151 GIC 144 : Sx += newval;
3152 CBC 144 : if (transvalues[0] > 0.0)
3153 EUB : {
3154 GIC 102 : tmp = newval * N - Sx;
3155 CBC 102 : Sxx += tmp * tmp / (N * transvalues[0]);
3156 :
3157 : /*
3158 : * Overflow check. We only report an overflow error when finite
3159 : * inputs lead to infinite results. Note also that Sxx should be NaN
3160 : * if any of the inputs are infinite, so we intentionally prevent Sxx
3161 : * from becoming infinite.
3162 : */
3163 GIC 102 : if (isinf(Sx) || isinf(Sxx))
3164 : {
3165 UIC 0 : if (!isinf(transvalues[1]) && !isinf(newval))
3166 LBC 0 : float_overflow_error();
3167 ECB :
3168 UIC 0 : Sxx = get_float8_nan();
3169 : }
3170 : }
3171 : else
3172 : {
3173 : /*
3174 : * At the first input, we normally can leave Sxx as 0. However, if
3175 ECB : * the first input is Inf or NaN, we'd better force Sxx to NaN;
3176 : * otherwise we will falsely report variance zero when there are no
3177 : * more inputs.
3178 : */
3179 CBC 42 : if (isnan(newval) || isinf(newval))
3180 GIC 12 : Sxx = get_float8_nan();
3181 ECB : }
3182 :
3183 : /*
3184 : * If we're invoked as an aggregate, we can cheat and modify our first
3185 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3186 : * new array with the updated transition data and return it.
3187 : */
3188 CBC 144 : if (AggCheckCallContext(fcinfo, NULL))
3189 ECB : {
3190 CBC 144 : transvalues[0] = N;
3191 GIC 144 : transvalues[1] = Sx;
3192 CBC 144 : transvalues[2] = Sxx;
3193 :
3194 GIC 144 : PG_RETURN_ARRAYTYPE_P(transarray);
3195 : }
3196 ECB : else
3197 : {
3198 : Datum transdatums[3];
3199 : ArrayType *result;
3200 :
3201 LBC 0 : transdatums[0] = Float8GetDatumFast(N);
3202 UIC 0 : transdatums[1] = Float8GetDatumFast(Sx);
3203 LBC 0 : transdatums[2] = Float8GetDatumFast(Sxx);
3204 :
3205 UIC 0 : result = construct_array(transdatums, 3,
3206 ECB : FLOAT8OID,
3207 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
3208 :
3209 UIC 0 : PG_RETURN_ARRAYTYPE_P(result);
3210 : }
3211 : }
3212 :
3213 ECB : Datum
3214 CBC 31 : float8_avg(PG_FUNCTION_ARGS)
3215 ECB : {
3216 CBC 31 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3217 : float8 *transvalues;
3218 : float8 N,
3219 : Sx;
3220 :
3221 GIC 31 : transvalues = check_float8_array(transarray, "float8_avg", 3);
3222 CBC 31 : N = transvalues[0];
3223 31 : Sx = transvalues[1];
3224 ECB : /* ignore Sxx */
3225 :
3226 : /* SQL defines AVG of no values to be NULL */
3227 CBC 31 : if (N == 0.0)
3228 GIC 3 : PG_RETURN_NULL();
3229 :
3230 28 : PG_RETURN_FLOAT8(Sx / N);
3231 : }
3232 :
3233 : Datum
3234 42 : float8_var_pop(PG_FUNCTION_ARGS)
3235 ECB : {
3236 GIC 42 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3237 EUB : float8 *transvalues;
3238 : float8 N,
3239 : Sxx;
3240 :
3241 GIC 42 : transvalues = check_float8_array(transarray, "float8_var_pop", 3);
3242 42 : N = transvalues[0];
3243 : /* ignore Sx */
3244 42 : Sxx = transvalues[2];
3245 :
3246 : /* Population variance is undefined when N is 0, so return NULL */
3247 42 : if (N == 0.0)
3248 UIC 0 : PG_RETURN_NULL();
3249 :
3250 : /* Note that Sxx is guaranteed to be non-negative */
3251 ECB :
3252 CBC 42 : PG_RETURN_FLOAT8(Sxx / N);
3253 : }
3254 :
3255 : Datum
3256 GIC 21 : float8_var_samp(PG_FUNCTION_ARGS)
3257 : {
3258 21 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3259 : float8 *transvalues;
3260 ECB : float8 N,
3261 : Sxx;
3262 :
3263 CBC 21 : transvalues = check_float8_array(transarray, "float8_var_samp", 3);
3264 21 : N = transvalues[0];
3265 : /* ignore Sx */
3266 21 : Sxx = transvalues[2];
3267 :
3268 : /* Sample variance is undefined when N is 0 or 1, so return NULL */
3269 GIC 21 : if (N <= 1.0)
3270 18 : PG_RETURN_NULL();
3271 :
3272 : /* Note that Sxx is guaranteed to be non-negative */
3273 EUB :
3274 GBC 3 : PG_RETURN_FLOAT8(Sxx / (N - 1.0));
3275 EUB : }
3276 :
3277 : Datum
3278 GIC 21 : float8_stddev_pop(PG_FUNCTION_ARGS)
3279 : {
3280 21 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3281 EUB : float8 *transvalues;
3282 : float8 N,
3283 : Sxx;
3284 :
3285 GIC 21 : transvalues = check_float8_array(transarray, "float8_stddev_pop", 3);
3286 CBC 21 : N = transvalues[0];
3287 : /* ignore Sx */
3288 21 : Sxx = transvalues[2];
3289 :
3290 : /* Population stddev is undefined when N is 0, so return NULL */
3291 GIC 21 : if (N == 0.0)
3292 UIC 0 : PG_RETURN_NULL();
3293 ECB :
3294 : /* Note that Sxx is guaranteed to be non-negative */
3295 :
3296 GIC 21 : PG_RETURN_FLOAT8(sqrt(Sxx / N));
3297 : }
3298 :
3299 ECB : Datum
3300 CBC 24 : float8_stddev_samp(PG_FUNCTION_ARGS)
3301 : {
3302 24 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3303 : float8 *transvalues;
3304 : float8 N,
3305 : Sxx;
3306 ECB :
3307 GIC 24 : transvalues = check_float8_array(transarray, "float8_stddev_samp", 3);
3308 CBC 24 : N = transvalues[0];
3309 : /* ignore Sx */
3310 GIC 24 : Sxx = transvalues[2];
3311 :
3312 : /* Sample stddev is undefined when N is 0 or 1, so return NULL */
3313 CBC 24 : if (N <= 1.0)
3314 18 : PG_RETURN_NULL();
3315 :
3316 ECB : /* Note that Sxx is guaranteed to be non-negative */
3317 :
3318 GIC 6 : PG_RETURN_FLOAT8(sqrt(Sxx / (N - 1.0)));
3319 ECB : }
3320 EUB :
3321 : /*
3322 : * =========================
3323 : * SQL2003 BINARY AGGREGATES
3324 ECB : * =========================
3325 : *
3326 : * As with the preceding aggregates, we use the Youngs-Cramer algorithm to
3327 : * reduce rounding errors in the aggregate final functions.
3328 : *
3329 : * The transition datatype for all these aggregates is a 6-element array of
3330 : * float8, holding the values N, Sx=sum(X), Sxx=sum((X-Sx/N)^2), Sy=sum(Y),
3331 : * Syy=sum((Y-Sy/N)^2), Sxy=sum((X-Sx/N)*(Y-Sy/N)) in that order.
3332 : *
3333 : * Note that Y is the first argument to all these aggregates!
3334 : *
3335 : * It might seem attractive to optimize this by having multiple accumulator
3336 : * functions that only calculate the sums actually needed. But on most
3337 : * modern machines, a couple of extra floating-point multiplies will be
3338 : * insignificant compared to the other per-tuple overhead, so I've chosen
3339 : * to minimize code space instead.
3340 : */
3341 :
3342 : Datum
3343 GIC 159 : float8_regr_accum(PG_FUNCTION_ARGS)
3344 : {
3345 159 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3346 CBC 159 : float8 newvalY = PG_GETARG_FLOAT8(1);
3347 GIC 159 : float8 newvalX = PG_GETARG_FLOAT8(2);
3348 : float8 *transvalues;
3349 : float8 N,
3350 ECB : Sx,
3351 : Sxx,
3352 : Sy,
3353 : Syy,
3354 : Sxy,
3355 : tmpX,
3356 : tmpY,
3357 : scale;
3358 :
3359 GIC 159 : transvalues = check_float8_array(transarray, "float8_regr_accum", 6);
3360 CBC 159 : N = transvalues[0];
3361 GIC 159 : Sx = transvalues[1];
3362 159 : Sxx = transvalues[2];
3363 CBC 159 : Sy = transvalues[3];
3364 GBC 159 : Syy = transvalues[4];
3365 GIC 159 : Sxy = transvalues[5];
3366 :
3367 : /*
3368 ECB : * Use the Youngs-Cramer algorithm to incorporate the new values into the
3369 : * transition values.
3370 : */
3371 GIC 159 : N += 1.0;
3372 CBC 159 : Sx += newvalX;
3373 GIC 159 : Sy += newvalY;
3374 CBC 159 : if (transvalues[0] > 0.0)
3375 : {
3376 GIC 105 : tmpX = newvalX * N - Sx;
3377 105 : tmpY = newvalY * N - Sy;
3378 105 : scale = 1.0 / (N * transvalues[0]);
3379 CBC 105 : Sxx += tmpX * tmpX * scale;
3380 105 : Syy += tmpY * tmpY * scale;
3381 GIC 105 : Sxy += tmpX * tmpY * scale;
3382 ECB :
3383 : /*
3384 : * Overflow check. We only report an overflow error when finite
3385 : * inputs lead to infinite results. Note also that Sxx, Syy and Sxy
3386 : * should be NaN if any of the relevant inputs are infinite, so we
3387 : * intentionally prevent them from becoming infinite.
3388 : */
3389 GIC 105 : if (isinf(Sx) || isinf(Sxx) || isinf(Sy) || isinf(Syy) || isinf(Sxy))
3390 ECB : {
3391 UIC 0 : if (((isinf(Sx) || isinf(Sxx)) &&
3392 0 : !isinf(transvalues[1]) && !isinf(newvalX)) ||
3393 0 : ((isinf(Sy) || isinf(Syy)) &&
3394 0 : !isinf(transvalues[3]) && !isinf(newvalY)) ||
3395 0 : (isinf(Sxy) &&
3396 0 : !isinf(transvalues[1]) && !isinf(newvalX) &&
3397 0 : !isinf(transvalues[3]) && !isinf(newvalY)))
3398 0 : float_overflow_error();
3399 :
3400 0 : if (isinf(Sxx))
3401 0 : Sxx = get_float8_nan();
3402 0 : if (isinf(Syy))
3403 0 : Syy = get_float8_nan();
3404 0 : if (isinf(Sxy))
3405 0 : Sxy = get_float8_nan();
3406 : }
3407 : }
3408 : else
3409 : {
3410 : /*
3411 : * At the first input, we normally can leave Sxx et al as 0. However,
3412 : * if the first input is Inf or NaN, we'd better force the dependent
3413 : * sums to NaN; otherwise we will falsely report variance zero when
3414 : * there are no more inputs.
3415 ECB : */
3416 GIC 54 : if (isnan(newvalX) || isinf(newvalX))
3417 CBC 12 : Sxx = Sxy = get_float8_nan();
3418 54 : if (isnan(newvalY) || isinf(newvalY))
3419 LBC 0 : Syy = Sxy = get_float8_nan();
3420 : }
3421 :
3422 : /*
3423 : * If we're invoked as an aggregate, we can cheat and modify our first
3424 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3425 : * new array with the updated transition data and return it.
3426 : */
3427 GIC 159 : if (AggCheckCallContext(fcinfo, NULL))
3428 : {
3429 156 : transvalues[0] = N;
3430 156 : transvalues[1] = Sx;
3431 CBC 156 : transvalues[2] = Sxx;
3432 156 : transvalues[3] = Sy;
3433 156 : transvalues[4] = Syy;
3434 156 : transvalues[5] = Sxy;
3435 ECB :
3436 CBC 156 : PG_RETURN_ARRAYTYPE_P(transarray);
3437 ECB : }
3438 : else
3439 : {
3440 : Datum transdatums[6];
3441 : ArrayType *result;
3442 :
3443 CBC 3 : transdatums[0] = Float8GetDatumFast(N);
3444 3 : transdatums[1] = Float8GetDatumFast(Sx);
3445 3 : transdatums[2] = Float8GetDatumFast(Sxx);
3446 3 : transdatums[3] = Float8GetDatumFast(Sy);
3447 GIC 3 : transdatums[4] = Float8GetDatumFast(Syy);
3448 CBC 3 : transdatums[5] = Float8GetDatumFast(Sxy);
3449 ECB :
3450 CBC 3 : result = construct_array(transdatums, 6,
3451 ECB : FLOAT8OID,
3452 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
3453 :
3454 GIC 3 : PG_RETURN_ARRAYTYPE_P(result);
3455 : }
3456 : }
3457 :
3458 : /*
3459 : * float8_regr_combine
3460 : *
3461 ECB : * An aggregate combine function used to combine two 6 fields
3462 : * aggregate transition data into a single transition data.
3463 EUB : * This function is used only in two stage aggregation and
3464 : * shouldn't be called outside aggregate context.
3465 : */
3466 : Datum
3467 GBC 9 : float8_regr_combine(PG_FUNCTION_ARGS)
3468 EUB : {
3469 GBC 9 : ArrayType *transarray1 = PG_GETARG_ARRAYTYPE_P(0);
3470 9 : ArrayType *transarray2 = PG_GETARG_ARRAYTYPE_P(1);
3471 : float8 *transvalues1;
3472 EUB : float8 *transvalues2;
3473 : float8 N1,
3474 : Sx1,
3475 : Sxx1,
3476 : Sy1,
3477 : Syy1,
3478 : Sxy1,
3479 : N2,
3480 : Sx2,
3481 : Sxx2,
3482 : Sy2,
3483 : Syy2,
3484 : Sxy2,
3485 : tmp1,
3486 : tmp2,
3487 : N,
3488 ECB : Sx,
3489 : Sxx,
3490 : Sy,
3491 EUB : Syy,
3492 : Sxy;
3493 :
3494 GIC 9 : transvalues1 = check_float8_array(transarray1, "float8_regr_combine", 6);
3495 9 : transvalues2 = check_float8_array(transarray2, "float8_regr_combine", 6);
3496 :
3497 9 : N1 = transvalues1[0];
3498 9 : Sx1 = transvalues1[1];
3499 CBC 9 : Sxx1 = transvalues1[2];
3500 GIC 9 : Sy1 = transvalues1[3];
3501 CBC 9 : Syy1 = transvalues1[4];
3502 9 : Sxy1 = transvalues1[5];
3503 ECB :
3504 CBC 9 : N2 = transvalues2[0];
3505 9 : Sx2 = transvalues2[1];
3506 9 : Sxx2 = transvalues2[2];
3507 GIC 9 : Sy2 = transvalues2[3];
3508 CBC 9 : Syy2 = transvalues2[4];
3509 GIC 9 : Sxy2 = transvalues2[5];
3510 :
3511 : /*--------------------
3512 : * The transition values combine using a generalization of the
3513 : * Youngs-Cramer algorithm as follows:
3514 : *
3515 ECB : * N = N1 + N2
3516 : * Sx = Sx1 + Sx2
3517 : * Sxx = Sxx1 + Sxx2 + N1 * N2 * (Sx1/N1 - Sx2/N2)^2 / N
3518 : * Sy = Sy1 + Sy2
3519 : * Syy = Syy1 + Syy2 + N1 * N2 * (Sy1/N1 - Sy2/N2)^2 / N
3520 : * Sxy = Sxy1 + Sxy2 + N1 * N2 * (Sx1/N1 - Sx2/N2) * (Sy1/N1 - Sy2/N2) / N
3521 : *
3522 : * It's worth handling the special cases N1 = 0 and N2 = 0 separately
3523 : * since those cases are trivial, and we then don't need to worry about
3524 : * division-by-zero errors in the general case.
3525 : *--------------------
3526 : */
3527 GIC 9 : if (N1 == 0.0)
3528 : {
3529 3 : N = N2;
3530 3 : Sx = Sx2;
3531 3 : Sxx = Sxx2;
3532 3 : Sy = Sy2;
3533 3 : Syy = Syy2;
3534 3 : Sxy = Sxy2;
3535 : }
3536 6 : else if (N2 == 0.0)
3537 : {
3538 3 : N = N1;
3539 CBC 3 : Sx = Sx1;
3540 GIC 3 : Sxx = Sxx1;
3541 CBC 3 : Sy = Sy1;
3542 3 : Syy = Syy1;
3543 GIC 3 : Sxy = Sxy1;
3544 : }
3545 : else
3546 : {
3547 3 : N = N1 + N2;
3548 3 : Sx = float8_pl(Sx1, Sx2);
3549 3 : tmp1 = Sx1 / N1 - Sx2 / N2;
3550 3 : Sxx = Sxx1 + Sxx2 + N1 * N2 * tmp1 * tmp1 / N;
3551 3 : if (unlikely(isinf(Sxx)) && !isinf(Sxx1) && !isinf(Sxx2))
3552 UIC 0 : float_overflow_error();
3553 GIC 3 : Sy = float8_pl(Sy1, Sy2);
3554 3 : tmp2 = Sy1 / N1 - Sy2 / N2;
3555 3 : Syy = Syy1 + Syy2 + N1 * N2 * tmp2 * tmp2 / N;
3556 3 : if (unlikely(isinf(Syy)) && !isinf(Syy1) && !isinf(Syy2))
3557 UIC 0 : float_overflow_error();
3558 GIC 3 : Sxy = Sxy1 + Sxy2 + N1 * N2 * tmp1 * tmp2 / N;
3559 3 : if (unlikely(isinf(Sxy)) && !isinf(Sxy1) && !isinf(Sxy2))
3560 UIC 0 : float_overflow_error();
3561 : }
3562 :
3563 : /*
3564 : * If we're invoked as an aggregate, we can cheat and modify our first
3565 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3566 ECB : * new array with the updated transition data and return it.
3567 : */
3568 GIC 9 : if (AggCheckCallContext(fcinfo, NULL))
3569 ECB : {
3570 LBC 0 : transvalues1[0] = N;
3571 0 : transvalues1[1] = Sx;
3572 0 : transvalues1[2] = Sxx;
3573 0 : transvalues1[3] = Sy;
3574 0 : transvalues1[4] = Syy;
3575 UIC 0 : transvalues1[5] = Sxy;
3576 ECB :
3577 LBC 0 : PG_RETURN_ARRAYTYPE_P(transarray1);
3578 ECB : }
3579 : else
3580 : {
3581 : Datum transdatums[6];
3582 : ArrayType *result;
3583 :
3584 GIC 9 : transdatums[0] = Float8GetDatumFast(N);
3585 9 : transdatums[1] = Float8GetDatumFast(Sx);
3586 9 : transdatums[2] = Float8GetDatumFast(Sxx);
3587 9 : transdatums[3] = Float8GetDatumFast(Sy);
3588 9 : transdatums[4] = Float8GetDatumFast(Syy);
3589 9 : transdatums[5] = Float8GetDatumFast(Sxy);
3590 :
3591 9 : result = construct_array(transdatums, 6,
3592 : FLOAT8OID,
3593 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
3594 :
3595 9 : PG_RETURN_ARRAYTYPE_P(result);
3596 : }
3597 : }
3598 :
3599 ECB :
3600 : Datum
3601 CBC 15 : float8_regr_sxx(PG_FUNCTION_ARGS)
3602 ECB : {
3603 CBC 15 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3604 ECB : float8 *transvalues;
3605 : float8 N,
3606 : Sxx;
3607 :
3608 CBC 15 : transvalues = check_float8_array(transarray, "float8_regr_sxx", 6);
3609 GIC 15 : N = transvalues[0];
3610 CBC 15 : Sxx = transvalues[2];
3611 ECB :
3612 : /* if N is 0 we should return NULL */
3613 CBC 15 : if (N < 1.0)
3614 LBC 0 : PG_RETURN_NULL();
3615 ECB :
3616 : /* Note that Sxx is guaranteed to be non-negative */
3617 :
3618 GIC 15 : PG_RETURN_FLOAT8(Sxx);
3619 ECB : }
3620 :
3621 : Datum
3622 CBC 15 : float8_regr_syy(PG_FUNCTION_ARGS)
3623 ECB : {
3624 GBC 15 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3625 ECB : float8 *transvalues;
3626 : float8 N,
3627 : Syy;
3628 :
3629 GBC 15 : transvalues = check_float8_array(transarray, "float8_regr_syy", 6);
3630 CBC 15 : N = transvalues[0];
3631 15 : Syy = transvalues[4];
3632 EUB :
3633 : /* if N is 0 we should return NULL */
3634 GIC 15 : if (N < 1.0)
3635 UIC 0 : PG_RETURN_NULL();
3636 :
3637 : /* Note that Syy is guaranteed to be non-negative */
3638 :
3639 GIC 15 : PG_RETURN_FLOAT8(Syy);
3640 ECB : }
3641 :
3642 EUB : Datum
3643 GBC 15 : float8_regr_sxy(PG_FUNCTION_ARGS)
3644 EUB : {
3645 GBC 15 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3646 EUB : float8 *transvalues;
3647 : float8 N,
3648 : Sxy;
3649 :
3650 GIC 15 : transvalues = check_float8_array(transarray, "float8_regr_sxy", 6);
3651 15 : N = transvalues[0];
3652 15 : Sxy = transvalues[5];
3653 :
3654 : /* if N is 0 we should return NULL */
3655 15 : if (N < 1.0)
3656 LBC 0 : PG_RETURN_NULL();
3657 ECB :
3658 : /* A negative result is valid here */
3659 :
3660 CBC 15 : PG_RETURN_FLOAT8(Sxy);
3661 ECB : }
3662 :
3663 : Datum
3664 GIC 3 : float8_regr_avgx(PG_FUNCTION_ARGS)
3665 : {
3666 3 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3667 ECB : float8 *transvalues;
3668 : float8 N,
3669 : Sx;
3670 :
3671 GIC 3 : transvalues = check_float8_array(transarray, "float8_regr_avgx", 6);
3672 3 : N = transvalues[0];
3673 CBC 3 : Sx = transvalues[1];
3674 :
3675 ECB : /* if N is 0 we should return NULL */
3676 GIC 3 : if (N < 1.0)
3677 UIC 0 : PG_RETURN_NULL();
3678 :
3679 GIC 3 : PG_RETURN_FLOAT8(Sx / N);
3680 ECB : }
3681 :
3682 : Datum
3683 GIC 3 : float8_regr_avgy(PG_FUNCTION_ARGS)
3684 : {
3685 CBC 3 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3686 EUB : float8 *transvalues;
3687 : float8 N,
3688 : Sy;
3689 :
3690 CBC 3 : transvalues = check_float8_array(transarray, "float8_regr_avgy", 6);
3691 GIC 3 : N = transvalues[0];
3692 3 : Sy = transvalues[3];
3693 :
3694 ECB : /* if N is 0 we should return NULL */
3695 GIC 3 : if (N < 1.0)
3696 LBC 0 : PG_RETURN_NULL();
3697 :
3698 GIC 3 : PG_RETURN_FLOAT8(Sy / N);
3699 : }
3700 :
3701 ECB : Datum
3702 CBC 12 : float8_covar_pop(PG_FUNCTION_ARGS)
3703 ECB : {
3704 GIC 12 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3705 : float8 *transvalues;
3706 ECB : float8 N,
3707 EUB : Sxy;
3708 :
3709 GIC 12 : transvalues = check_float8_array(transarray, "float8_covar_pop", 6);
3710 12 : N = transvalues[0];
3711 CBC 12 : Sxy = transvalues[5];
3712 :
3713 : /* if N is 0 we should return NULL */
3714 GIC 12 : if (N < 1.0)
3715 LBC 0 : PG_RETURN_NULL();
3716 :
3717 CBC 12 : PG_RETURN_FLOAT8(Sxy / N);
3718 : }
3719 :
3720 : Datum
3721 GIC 12 : float8_covar_samp(PG_FUNCTION_ARGS)
3722 ECB : {
3723 CBC 12 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3724 ECB : float8 *transvalues;
3725 : float8 N,
3726 : Sxy;
3727 :
3728 GBC 12 : transvalues = check_float8_array(transarray, "float8_covar_samp", 6);
3729 GIC 12 : N = transvalues[0];
3730 12 : Sxy = transvalues[5];
3731 :
3732 ECB : /* if N is <= 1 we should return NULL */
3733 GIC 12 : if (N < 2.0)
3734 9 : PG_RETURN_NULL();
3735 :
3736 CBC 3 : PG_RETURN_FLOAT8(Sxy / (N - 1.0));
3737 : }
3738 ECB :
3739 : Datum
3740 GIC 3 : float8_corr(PG_FUNCTION_ARGS)
3741 : {
3742 3 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3743 ECB : float8 *transvalues;
3744 : float8 N,
3745 : Sxx,
3746 : Syy,
3747 : Sxy;
3748 :
3749 GBC 3 : transvalues = check_float8_array(transarray, "float8_corr", 6);
3750 GIC 3 : N = transvalues[0];
3751 CBC 3 : Sxx = transvalues[2];
3752 GIC 3 : Syy = transvalues[4];
3753 3 : Sxy = transvalues[5];
3754 :
3755 ECB : /* if N is 0 we should return NULL */
3756 GIC 3 : if (N < 1.0)
3757 LBC 0 : PG_RETURN_NULL();
3758 :
3759 : /* Note that Sxx and Syy are guaranteed to be non-negative */
3760 :
3761 : /* per spec, return NULL for horizontal and vertical lines */
3762 CBC 3 : if (Sxx == 0 || Syy == 0)
3763 LBC 0 : PG_RETURN_NULL();
3764 ECB :
3765 GIC 3 : PG_RETURN_FLOAT8(Sxy / sqrt(Sxx * Syy));
3766 : }
3767 ECB :
3768 EUB : Datum
3769 GIC 3 : float8_regr_r2(PG_FUNCTION_ARGS)
3770 ECB : {
3771 GIC 3 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3772 : float8 *transvalues;
3773 : float8 N,
3774 ECB : Sxx,
3775 : Syy,
3776 : Sxy;
3777 :
3778 GIC 3 : transvalues = check_float8_array(transarray, "float8_regr_r2", 6);
3779 3 : N = transvalues[0];
3780 3 : Sxx = transvalues[2];
3781 CBC 3 : Syy = transvalues[4];
3782 3 : Sxy = transvalues[5];
3783 ECB :
3784 : /* if N is 0 we should return NULL */
3785 GIC 3 : if (N < 1.0)
3786 LBC 0 : PG_RETURN_NULL();
3787 EUB :
3788 : /* Note that Sxx and Syy are guaranteed to be non-negative */
3789 ECB :
3790 : /* per spec, return NULL for a vertical line */
3791 GIC 3 : if (Sxx == 0)
3792 UIC 0 : PG_RETURN_NULL();
3793 ECB :
3794 : /* per spec, return 1.0 for a horizontal line */
3795 CBC 3 : if (Syy == 0)
3796 UIC 0 : PG_RETURN_FLOAT8(1.0);
3797 :
3798 GIC 3 : PG_RETURN_FLOAT8((Sxy * Sxy) / (Sxx * Syy));
3799 : }
3800 ECB :
3801 : Datum
3802 CBC 3 : float8_regr_slope(PG_FUNCTION_ARGS)
3803 : {
3804 GIC 3 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3805 ECB : float8 *transvalues;
3806 : float8 N,
3807 : Sxx,
3808 : Sxy;
3809 :
3810 GIC 3 : transvalues = check_float8_array(transarray, "float8_regr_slope", 6);
3811 3 : N = transvalues[0];
3812 CBC 3 : Sxx = transvalues[2];
3813 GIC 3 : Sxy = transvalues[5];
3814 ECB :
3815 : /* if N is 0 we should return NULL */
3816 GIC 3 : if (N < 1.0)
3817 UIC 0 : PG_RETURN_NULL();
3818 :
3819 : /* Note that Sxx is guaranteed to be non-negative */
3820 :
3821 ECB : /* per spec, return NULL for a vertical line */
3822 CBC 3 : if (Sxx == 0)
3823 LBC 0 : PG_RETURN_NULL();
3824 ECB :
3825 CBC 3 : PG_RETURN_FLOAT8(Sxy / Sxx);
3826 : }
3827 :
3828 ECB : Datum
3829 GBC 3 : float8_regr_intercept(PG_FUNCTION_ARGS)
3830 : {
3831 GIC 3 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3832 : float8 *transvalues;
3833 : float8 N,
3834 ECB : Sx,
3835 EUB : Sxx,
3836 : Sy,
3837 ECB : Sxy;
3838 :
3839 GIC 3 : transvalues = check_float8_array(transarray, "float8_regr_intercept", 6);
3840 3 : N = transvalues[0];
3841 CBC 3 : Sx = transvalues[1];
3842 GIC 3 : Sxx = transvalues[2];
3843 CBC 3 : Sy = transvalues[3];
3844 GIC 3 : Sxy = transvalues[5];
3845 :
3846 : /* if N is 0 we should return NULL */
3847 3 : if (N < 1.0)
3848 UIC 0 : PG_RETURN_NULL();
3849 :
3850 ECB : /* Note that Sxx is guaranteed to be non-negative */
3851 :
3852 : /* per spec, return NULL for a vertical line */
3853 CBC 3 : if (Sxx == 0)
3854 LBC 0 : PG_RETURN_NULL();
3855 :
3856 GIC 3 : PG_RETURN_FLOAT8((Sy - Sx * Sxy / Sxx) / N);
3857 ECB : }
3858 EUB :
3859 :
3860 : /*
3861 : * ====================================
3862 : * MIXED-PRECISION ARITHMETIC OPERATORS
3863 ECB : * ====================================
3864 EUB : */
3865 :
3866 : /*
3867 ECB : * float48pl - returns arg1 + arg2
3868 EUB : * float48mi - returns arg1 - arg2
3869 : * float48mul - returns arg1 * arg2
3870 ECB : * float48div - returns arg1 / arg2
3871 : */
3872 : Datum
3873 GIC 3 : float48pl(PG_FUNCTION_ARGS)
3874 ECB : {
3875 GIC 3 : float4 arg1 = PG_GETARG_FLOAT4(0);
3876 CBC 3 : float8 arg2 = PG_GETARG_FLOAT8(1);
3877 :
3878 GIC 3 : PG_RETURN_FLOAT8(float8_pl((float8) arg1, arg2));
3879 : }
3880 :
3881 : Datum
3882 LBC 0 : float48mi(PG_FUNCTION_ARGS)
3883 ECB : {
3884 LBC 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
3885 0 : float8 arg2 = PG_GETARG_FLOAT8(1);
3886 :
3887 UIC 0 : PG_RETURN_FLOAT8(float8_mi((float8) arg1, arg2));
3888 ECB : }
3889 EUB :
3890 : Datum
3891 UIC 0 : float48mul(PG_FUNCTION_ARGS)
3892 : {
3893 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
3894 LBC 0 : float8 arg2 = PG_GETARG_FLOAT8(1);
3895 EUB :
3896 UIC 0 : PG_RETURN_FLOAT8(float8_mul((float8) arg1, arg2));
3897 ECB : }
3898 :
3899 : Datum
3900 GIC 3 : float48div(PG_FUNCTION_ARGS)
3901 ECB : {
3902 GIC 3 : float4 arg1 = PG_GETARG_FLOAT4(0);
3903 CBC 3 : float8 arg2 = PG_GETARG_FLOAT8(1);
3904 :
3905 GIC 3 : PG_RETURN_FLOAT8(float8_div((float8) arg1, arg2));
3906 : }
3907 :
3908 : /*
3909 : * float84pl - returns arg1 + arg2
3910 : * float84mi - returns arg1 - arg2
3911 ECB : * float84mul - returns arg1 * arg2
3912 : * float84div - returns arg1 / arg2
3913 : */
3914 : Datum
3915 CBC 6 : float84pl(PG_FUNCTION_ARGS)
3916 ECB : {
3917 GIC 6 : float8 arg1 = PG_GETARG_FLOAT8(0);
3918 6 : float4 arg2 = PG_GETARG_FLOAT4(1);
3919 ECB :
3920 GBC 6 : PG_RETURN_FLOAT8(float8_pl(arg1, (float8) arg2));
3921 : }
3922 :
3923 : Datum
3924 UIC 0 : float84mi(PG_FUNCTION_ARGS)
3925 ECB : {
3926 UBC 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
3927 UIC 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
3928 ECB :
3929 UIC 0 : PG_RETURN_FLOAT8(float8_mi(arg1, (float8) arg2));
3930 : }
3931 :
3932 : Datum
3933 0 : float84mul(PG_FUNCTION_ARGS)
3934 : {
3935 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
3936 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
3937 :
3938 0 : PG_RETURN_FLOAT8(float8_mul(arg1, (float8) arg2));
3939 : }
3940 :
3941 : Datum
3942 GIC 3 : float84div(PG_FUNCTION_ARGS)
3943 : {
3944 3 : float8 arg1 = PG_GETARG_FLOAT8(0);
3945 CBC 3 : float4 arg2 = PG_GETARG_FLOAT4(1);
3946 :
3947 3 : PG_RETURN_FLOAT8(float8_div(arg1, (float8) arg2));
3948 ECB : }
3949 :
3950 : /*
3951 : * ====================
3952 : * COMPARISON OPERATORS
3953 : * ====================
3954 EUB : */
3955 :
3956 : /*
3957 : * float48{eq,ne,lt,le,gt,ge} - float4/float8 comparison operations
3958 : */
3959 : Datum
3960 GIC 1491 : float48eq(PG_FUNCTION_ARGS)
3961 : {
3962 1491 : float4 arg1 = PG_GETARG_FLOAT4(0);
3963 GBC 1491 : float8 arg2 = PG_GETARG_FLOAT8(1);
3964 :
3965 1491 : PG_RETURN_BOOL(float8_eq((float8) arg1, arg2));
3966 EUB : }
3967 :
3968 : Datum
3969 GIC 9735 : float48ne(PG_FUNCTION_ARGS)
3970 : {
3971 9735 : float4 arg1 = PG_GETARG_FLOAT4(0);
3972 CBC 9735 : float8 arg2 = PG_GETARG_FLOAT8(1);
3973 :
3974 9735 : PG_RETURN_BOOL(float8_ne((float8) arg1, arg2));
3975 ECB : }
3976 :
3977 : Datum
3978 GIC 2134 : float48lt(PG_FUNCTION_ARGS)
3979 : {
3980 2134 : float4 arg1 = PG_GETARG_FLOAT4(0);
3981 2134 : float8 arg2 = PG_GETARG_FLOAT8(1);
3982 :
3983 2134 : PG_RETURN_BOOL(float8_lt((float8) arg1, arg2));
3984 : }
3985 :
3986 : Datum
3987 CBC 12811 : float48le(PG_FUNCTION_ARGS)
3988 : {
3989 12811 : float4 arg1 = PG_GETARG_FLOAT4(0);
3990 12811 : float8 arg2 = PG_GETARG_FLOAT8(1);
3991 :
3992 12811 : PG_RETURN_BOOL(float8_le((float8) arg1, arg2));
3993 : }
3994 :
3995 : Datum
3996 GBC 2246 : float48gt(PG_FUNCTION_ARGS)
3997 : {
3998 2246 : float4 arg1 = PG_GETARG_FLOAT4(0);
3999 2246 : float8 arg2 = PG_GETARG_FLOAT8(1);
4000 :
4001 2246 : PG_RETURN_BOOL(float8_gt((float8) arg1, arg2));
4002 : }
4003 :
4004 : Datum
4005 2446 : float48ge(PG_FUNCTION_ARGS)
4006 : {
4007 2446 : float4 arg1 = PG_GETARG_FLOAT4(0);
4008 2446 : float8 arg2 = PG_GETARG_FLOAT8(1);
4009 :
4010 2446 : PG_RETURN_BOOL(float8_ge((float8) arg1, arg2));
4011 : }
4012 :
4013 : /*
4014 ECB : * float84{eq,ne,lt,le,gt,ge} - float8/float4 comparison operations
4015 : */
4016 : Datum
4017 CBC 906 : float84eq(PG_FUNCTION_ARGS)
4018 : {
4019 906 : float8 arg1 = PG_GETARG_FLOAT8(0);
4020 GIC 906 : float4 arg2 = PG_GETARG_FLOAT4(1);
4021 :
4022 906 : PG_RETURN_BOOL(float8_eq(arg1, (float8) arg2));
4023 : }
4024 :
4025 : Datum
4026 UIC 0 : float84ne(PG_FUNCTION_ARGS)
4027 : {
4028 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
4029 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
4030 :
4031 0 : PG_RETURN_BOOL(float8_ne(arg1, (float8) arg2));
4032 ECB : }
4033 :
4034 : Datum
4035 CBC 1599 : float84lt(PG_FUNCTION_ARGS)
4036 : {
4037 1599 : float8 arg1 = PG_GETARG_FLOAT8(0);
4038 GIC 1599 : float4 arg2 = PG_GETARG_FLOAT4(1);
4039 :
4040 1599 : PG_RETURN_BOOL(float8_lt(arg1, (float8) arg2));
4041 ECB : }
4042 :
4043 : Datum
4044 CBC 1899 : float84le(PG_FUNCTION_ARGS)
4045 : {
4046 1899 : float8 arg1 = PG_GETARG_FLOAT8(0);
4047 GIC 1899 : float4 arg2 = PG_GETARG_FLOAT4(1);
4048 :
4049 1899 : PG_RETURN_BOOL(float8_le(arg1, (float8) arg2));
4050 ECB : }
4051 :
4052 : Datum
4053 CBC 1599 : float84gt(PG_FUNCTION_ARGS)
4054 : {
4055 1599 : float8 arg1 = PG_GETARG_FLOAT8(0);
4056 GIC 1599 : float4 arg2 = PG_GETARG_FLOAT4(1);
4057 :
4058 1599 : PG_RETURN_BOOL(float8_gt(arg1, (float8) arg2));
4059 ECB : }
4060 :
4061 : Datum
4062 CBC 1602 : float84ge(PG_FUNCTION_ARGS)
4063 : {
4064 1602 : float8 arg1 = PG_GETARG_FLOAT8(0);
4065 GIC 1602 : float4 arg2 = PG_GETARG_FLOAT4(1);
4066 :
4067 1602 : PG_RETURN_BOOL(float8_ge(arg1, (float8) arg2));
4068 ECB : }
4069 :
4070 : /*
4071 : * Implements the float8 version of the width_bucket() function
4072 : * defined by SQL2003. See also width_bucket_numeric().
4073 : *
4074 : * 'bound1' and 'bound2' are the lower and upper bounds of the
4075 : * histogram's range, respectively. 'count' is the number of buckets
4076 : * in the histogram. width_bucket() returns an integer indicating the
4077 : * bucket number that 'operand' belongs to in an equiwidth histogram
4078 : * with the specified characteristics. An operand smaller than the
4079 : * lower bound is assigned to bucket 0. An operand greater than the
4080 : * upper bound is assigned to an additional bucket (with number
4081 : * count+1). We don't allow "NaN" for any of the float8 inputs, and we
4082 : * don't allow either of the histogram bounds to be +/- infinity.
4083 : */
4084 : Datum
4085 GIC 432 : width_bucket_float8(PG_FUNCTION_ARGS)
4086 : {
4087 432 : float8 operand = PG_GETARG_FLOAT8(0);
4088 432 : float8 bound1 = PG_GETARG_FLOAT8(1);
4089 CBC 432 : float8 bound2 = PG_GETARG_FLOAT8(2);
4090 GIC 432 : int32 count = PG_GETARG_INT32(3);
4091 ECB : int32 result;
4092 :
4093 GNC 432 : if (count <= 0)
4094 CBC 6 : ereport(ERROR,
4095 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4096 : errmsg("count must be greater than zero")));
4097 :
4098 GBC 426 : if (isnan(operand) || isnan(bound1) || isnan(bound2))
4099 GIC 3 : ereport(ERROR,
4100 EUB : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4101 : errmsg("operand, lower bound, and upper bound cannot be NaN")));
4102 :
4103 : /* Note that we allow "operand" to be infinite */
4104 GIC 423 : if (isinf(bound1) || isinf(bound2))
4105 9 : ereport(ERROR,
4106 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4107 ECB : errmsg("lower and upper bounds must be finite")));
4108 :
4109 CBC 414 : if (bound1 < bound2)
4110 ECB : {
4111 GIC 297 : if (operand < bound1)
4112 CBC 57 : result = 0;
4113 GIC 240 : else if (operand >= bound2)
4114 : {
4115 60 : if (pg_add_s32_overflow(count, 1, &result))
4116 CBC 3 : ereport(ERROR,
4117 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
4118 ECB : errmsg("integer out of range")));
4119 : }
4120 : else
4121 : {
4122 GNC 180 : if (!isinf(bound2 - bound1))
4123 : {
4124 : /* The quotient is surely in [0,1], so this can't overflow */
4125 171 : result = count * ((operand - bound1) / (bound2 - bound1));
4126 : }
4127 : else
4128 : {
4129 : /*
4130 : * We get here if bound2 - bound1 overflows DBL_MAX. Since
4131 : * both bounds are finite, their difference can't exceed twice
4132 : * DBL_MAX; so we can perform the computation without overflow
4133 : * by dividing all the inputs by 2. That should be exact too,
4134 : * except in the case where a very small operand underflows to
4135 : * zero, which would have negligible impact on the result
4136 : * given such large bounds.
4137 : */
4138 9 : result = count * ((operand / 2 - bound1 / 2) / (bound2 / 2 - bound1 / 2));
4139 : }
4140 : /* The quotient could round to 1.0, which would be a lie */
4141 180 : if (result >= count)
4142 3 : result = count - 1;
4143 : /* Having done that, we can add 1 without fear of overflow */
4144 180 : result++;
4145 : }
4146 : }
4147 GIC 117 : else if (bound1 > bound2)
4148 : {
4149 CBC 114 : if (operand > bound1)
4150 GIC 6 : result = 0;
4151 CBC 108 : else if (operand <= bound2)
4152 ECB : {
4153 GIC 15 : if (pg_add_s32_overflow(count, 1, &result))
4154 CBC 3 : ereport(ERROR,
4155 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
4156 : errmsg("integer out of range")));
4157 : }
4158 ECB : else
4159 : {
4160 GNC 93 : if (!isinf(bound1 - bound2))
4161 84 : result = count * ((bound1 - operand) / (bound1 - bound2));
4162 : else
4163 9 : result = count * ((bound1 / 2 - operand / 2) / (bound1 / 2 - bound2 / 2));
4164 93 : if (result >= count)
4165 3 : result = count - 1;
4166 93 : result++;
4167 : }
4168 ECB : }
4169 : else
4170 : {
4171 CBC 3 : ereport(ERROR,
4172 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4173 : errmsg("lower bound cannot equal upper bound")));
4174 : result = 0; /* keep the compiler quiet */
4175 : }
4176 :
4177 GIC 405 : PG_RETURN_INT32(result);
4178 : }
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