Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * float.c
4 : * Functions for the built-in floating-point types.
5 : *
6 : * Portions Copyright (c) 1996-2020, 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/shortest_dec.h"
25 : #include "libpq/pqformat.h"
26 : #include "miscadmin.h"
27 : #include "utils/array.h"
28 : #include "utils/float.h"
29 : #include "utils/fmgrprotos.h"
30 : #include "utils/sortsupport.h"
31 : #include "utils/timestamp.h"
32 :
33 :
34 : /*
35 : * Configurable GUC parameter
36 : *
37 : * If >0, use shortest-decimal format for output; this is both the default and
38 : * allows for compatibility with clients that explicitly set a value here to
39 : * get round-trip-accurate results. If 0 or less, then use the old, slow,
40 : * decimal rounding method.
41 : */
42 : int extra_float_digits = 1;
43 :
44 : /* Cached constants for degree-based trig functions */
45 : static bool degree_consts_set = false;
46 : static float8 sin_30 = 0;
47 : static float8 one_minus_cos_60 = 0;
48 : static float8 asin_0_5 = 0;
49 : static float8 acos_0_5 = 0;
50 : static float8 atan_1_0 = 0;
51 : static float8 tan_45 = 0;
52 : static float8 cot_45 = 0;
53 :
54 : /*
55 : * These are intentionally not static; don't "fix" them. They will never
56 : * be referenced by other files, much less changed; but we don't want the
57 : * compiler to know that, else it might try to precompute expressions
58 : * involving them. See comments for init_degree_constants().
59 : */
60 : float8 degree_c_thirty = 30.0;
61 : float8 degree_c_forty_five = 45.0;
62 : float8 degree_c_sixty = 60.0;
63 : float8 degree_c_one_half = 0.5;
64 : float8 degree_c_one = 1.0;
65 :
66 : /* State for drandom() and setseed() */
67 : static bool drandom_seed_set = false;
68 : static unsigned short drandom_seed[3] = {0, 0, 0};
69 :
70 : /* Local function prototypes */
71 : static double sind_q1(double x);
72 : static double cosd_q1(double x);
73 : static void init_degree_constants(void);
74 :
75 :
76 : /*
77 : * We use these out-of-line ereport() calls to report float overflow,
78 : * underflow, and zero-divide, because following our usual practice of
79 : * repeating them at each call site would lead to a lot of code bloat.
80 : *
81 : * This does mean that you don't get a useful error location indicator.
82 : */
83 : pg_noinline void
84 24 : float_overflow_error(void)
85 : {
86 24 : ereport(ERROR,
87 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
88 : errmsg("value out of range: overflow")));
89 : }
90 :
91 : pg_noinline void
92 16 : float_underflow_error(void)
93 : {
94 16 : ereport(ERROR,
95 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
96 : errmsg("value out of range: underflow")));
97 : }
98 :
99 : pg_noinline void
100 44 : float_zero_divide_error(void)
101 : {
102 44 : ereport(ERROR,
103 : (errcode(ERRCODE_DIVISION_BY_ZERO),
104 : errmsg("division by zero")));
105 : }
106 :
107 :
108 : /*
109 : * Returns -1 if 'val' represents negative infinity, 1 if 'val'
110 : * represents (positive) infinity, and 0 otherwise. On some platforms,
111 : * this is equivalent to the isinf() macro, but not everywhere: C99
112 : * does not specify that isinf() needs to distinguish between positive
113 : * and negative infinity.
114 : */
115 : int
116 0 : is_infinite(double val)
117 : {
118 0 : int inf = isinf(val);
119 :
120 0 : if (inf == 0)
121 0 : return 0;
122 0 : else if (val > 0)
123 0 : return 1;
124 : else
125 0 : return -1;
126 : }
127 :
128 :
129 : /* ========== USER I/O ROUTINES ========== */
130 :
131 :
132 : /*
133 : * float4in - converts "num" to float4
134 : *
135 : * Note that this code now uses strtof(), where it used to use strtod().
136 : *
137 : * The motivation for using strtof() is to avoid a double-rounding problem:
138 : * for certain decimal inputs, if you round the input correctly to a double,
139 : * and then round the double to a float, the result is incorrect in that it
140 : * does not match the result of rounding the decimal value to float directly.
141 : *
142 : * One of the best examples is 7.038531e-26:
143 : *
144 : * 0xAE43FDp-107 = 7.03853069185120912085...e-26
145 : * midpoint 7.03853100000000022281...e-26
146 : * 0xAE43FEp-107 = 7.03853130814879132477...e-26
147 : *
148 : * making 0xAE43FDp-107 the correct float result, but if you do the conversion
149 : * via a double, you get
150 : *
151 : * 0xAE43FD.7FFFFFF8p-107 = 7.03853099999999907487...e-26
152 : * midpoint 7.03853099999999964884...e-26
153 : * 0xAE43FD.80000000p-107 = 7.03853100000000022281...e-26
154 : * 0xAE43FD.80000008p-107 = 7.03853100000000137076...e-26
155 : *
156 : * so the value rounds to the double exactly on the midpoint between the two
157 : * nearest floats, and then rounding again to a float gives the incorrect
158 : * result of 0xAE43FEp-107.
159 : *
160 : */
161 : Datum
162 2415192 : float4in(PG_FUNCTION_ARGS)
163 : {
164 2415192 : char *num = PG_GETARG_CSTRING(0);
165 : char *orig_num;
166 : float val;
167 : char *endptr;
168 :
169 : /*
170 : * endptr points to the first character _after_ the sequence we recognized
171 : * as a valid floating point number. orig_num points to the original input
172 : * string.
173 : */
174 2415192 : orig_num = num;
175 :
176 : /* skip leading whitespace */
177 2415332 : while (*num != '\0' && isspace((unsigned char) *num))
178 140 : num++;
179 :
180 : /*
181 : * Check for an empty-string input to begin with, to avoid the vagaries of
182 : * strtod() on different platforms.
183 : */
184 2415192 : if (*num == '\0')
185 8 : ereport(ERROR,
186 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
187 : errmsg("invalid input syntax for type %s: \"%s\"",
188 : "real", orig_num)));
189 :
190 2415184 : errno = 0;
191 2415184 : val = strtof(num, &endptr);
192 :
193 : /* did we not see anything that looks like a double? */
194 2415184 : if (endptr == num || errno != 0)
195 : {
196 48 : int save_errno = errno;
197 :
198 : /*
199 : * C99 requires that strtof() accept NaN, [+-]Infinity, and [+-]Inf,
200 : * but not all platforms support all of these (and some accept them
201 : * but set ERANGE anyway...) Therefore, we check for these inputs
202 : * ourselves if strtof() fails.
203 : *
204 : * Note: C99 also requires hexadecimal input as well as some extended
205 : * forms of NaN, but we consider these forms unportable and don't try
206 : * to support them. You can use 'em if your strtof() takes 'em.
207 : */
208 48 : if (pg_strncasecmp(num, "NaN", 3) == 0)
209 : {
210 0 : val = get_float4_nan();
211 0 : endptr = num + 3;
212 : }
213 48 : else if (pg_strncasecmp(num, "Infinity", 8) == 0)
214 : {
215 0 : val = get_float4_infinity();
216 0 : endptr = num + 8;
217 : }
218 48 : else if (pg_strncasecmp(num, "+Infinity", 9) == 0)
219 : {
220 0 : val = get_float4_infinity();
221 0 : endptr = num + 9;
222 : }
223 48 : else if (pg_strncasecmp(num, "-Infinity", 9) == 0)
224 : {
225 0 : val = -get_float4_infinity();
226 0 : endptr = num + 9;
227 : }
228 48 : else if (pg_strncasecmp(num, "inf", 3) == 0)
229 : {
230 0 : val = get_float4_infinity();
231 0 : endptr = num + 3;
232 : }
233 48 : else if (pg_strncasecmp(num, "+inf", 4) == 0)
234 : {
235 0 : val = get_float4_infinity();
236 0 : endptr = num + 4;
237 : }
238 48 : else if (pg_strncasecmp(num, "-inf", 4) == 0)
239 : {
240 0 : val = -get_float4_infinity();
241 0 : endptr = num + 4;
242 : }
243 48 : else if (save_errno == ERANGE)
244 : {
245 : /*
246 : * Some platforms return ERANGE for denormalized numbers (those
247 : * that are not zero, but are too close to zero to have full
248 : * precision). We'd prefer not to throw error for that, so try to
249 : * detect whether it's a "real" out-of-range condition by checking
250 : * to see if the result is zero or huge.
251 : *
252 : * Use isinf() rather than HUGE_VALF on VS2013 because it
253 : * generates a spurious overflow warning for -HUGE_VALF. Also use
254 : * isinf() if HUGE_VALF is missing.
255 : */
256 34 : if (val == 0.0 ||
257 : #if !defined(HUGE_VALF) || (defined(_MSC_VER) && (_MSC_VER < 1900))
258 : isinf(val)
259 : #else
260 8 : (val >= HUGE_VALF || val <= -HUGE_VALF)
261 : #endif
262 : )
263 34 : ereport(ERROR,
264 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
265 : errmsg("\"%s\" is out of range for type real",
266 : orig_num)));
267 : }
268 : else
269 14 : ereport(ERROR,
270 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
271 : errmsg("invalid input syntax for type %s: \"%s\"",
272 : "real", orig_num)));
273 : }
274 :
275 : /* skip trailing whitespace */
276 2415268 : while (*endptr != '\0' && isspace((unsigned char) *endptr))
277 132 : endptr++;
278 :
279 : /* if there is any junk left at the end of the string, bail out */
280 2415136 : if (*endptr != '\0')
281 24 : ereport(ERROR,
282 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
283 : errmsg("invalid input syntax for type %s: \"%s\"",
284 : "real", orig_num)));
285 :
286 2415112 : PG_RETURN_FLOAT4(val);
287 : }
288 :
289 : /*
290 : * float4out - converts a float4 number to a string
291 : * using a standard output format
292 : */
293 : Datum
294 24560 : float4out(PG_FUNCTION_ARGS)
295 : {
296 24560 : float4 num = PG_GETARG_FLOAT4(0);
297 24560 : char *ascii = (char *) palloc(32);
298 24560 : int ndig = FLT_DIG + extra_float_digits;
299 :
300 24560 : if (extra_float_digits > 0)
301 : {
302 11884 : float_to_shortest_decimal_buf(num, ascii);
303 11884 : PG_RETURN_CSTRING(ascii);
304 : }
305 :
306 12676 : (void) pg_strfromd(ascii, 32, ndig, num);
307 12676 : PG_RETURN_CSTRING(ascii);
308 : }
309 :
310 : /*
311 : * float4recv - converts external binary format to float4
312 : */
313 : Datum
314 0 : float4recv(PG_FUNCTION_ARGS)
315 : {
316 0 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
317 :
318 0 : PG_RETURN_FLOAT4(pq_getmsgfloat4(buf));
319 : }
320 :
321 : /*
322 : * float4send - converts float4 to binary format
323 : */
324 : Datum
325 4328 : float4send(PG_FUNCTION_ARGS)
326 : {
327 4328 : float4 num = PG_GETARG_FLOAT4(0);
328 : StringInfoData buf;
329 :
330 4328 : pq_begintypsend(&buf);
331 4328 : pq_sendfloat4(&buf, num);
332 4328 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
333 : }
334 :
335 : /*
336 : * float8in - converts "num" to float8
337 : */
338 : Datum
339 441286 : float8in(PG_FUNCTION_ARGS)
340 : {
341 441286 : char *num = PG_GETARG_CSTRING(0);
342 :
343 441286 : PG_RETURN_FLOAT8(float8in_internal(num, NULL, "double precision", num));
344 : }
345 :
346 : /* Convenience macro: set *have_error flag (if provided) or throw error */
347 : #define RETURN_ERROR(throw_error, have_error) \
348 : do { \
349 : if (have_error) { \
350 : *have_error = true; \
351 : return 0.0; \
352 : } else { \
353 : throw_error; \
354 : } \
355 : } while (0)
356 :
357 : /*
358 : * float8in_internal_opt_error - guts of float8in()
359 : *
360 : * This is exposed for use by functions that want a reasonably
361 : * platform-independent way of inputting doubles. The behavior is
362 : * essentially like strtod + ereport on error, but note the following
363 : * differences:
364 : * 1. Both leading and trailing whitespace are skipped.
365 : * 2. If endptr_p is NULL, we throw error if there's trailing junk.
366 : * Otherwise, it's up to the caller to complain about trailing junk.
367 : * 3. In event of a syntax error, the report mentions the given type_name
368 : * and prints orig_string as the input; this is meant to support use of
369 : * this function with types such as "box" and "point", where what we are
370 : * parsing here is just a substring of orig_string.
371 : *
372 : * "num" could validly be declared "const char *", but that results in an
373 : * unreasonable amount of extra casting both here and in callers, so we don't.
374 : *
375 : * When "*have_error" flag is provided, it's set instead of throwing an
376 : * error. This is helpful when caller need to handle errors by itself.
377 : */
378 : double
379 617674 : float8in_internal_opt_error(char *num, char **endptr_p,
380 : const char *type_name, const char *orig_string,
381 : bool *have_error)
382 : {
383 : double val;
384 : char *endptr;
385 :
386 617674 : if (have_error)
387 40 : *have_error = false;
388 :
389 : /* skip leading whitespace */
390 618478 : while (*num != '\0' && isspace((unsigned char) *num))
391 804 : num++;
392 :
393 : /*
394 : * Check for an empty-string input to begin with, to avoid the vagaries of
395 : * strtod() on different platforms.
396 : */
397 617674 : if (*num == '\0')
398 8 : RETURN_ERROR(ereport(ERROR,
399 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
400 : errmsg("invalid input syntax for type %s: \"%s\"",
401 : type_name, orig_string))),
402 : have_error);
403 :
404 617666 : errno = 0;
405 617666 : val = strtod(num, &endptr);
406 :
407 : /* did we not see anything that looks like a double? */
408 617666 : if (endptr == num || errno != 0)
409 : {
410 86 : int save_errno = errno;
411 :
412 : /*
413 : * C99 requires that strtod() accept NaN, [+-]Infinity, and [+-]Inf,
414 : * but not all platforms support all of these (and some accept them
415 : * but set ERANGE anyway...) Therefore, we check for these inputs
416 : * ourselves if strtod() fails.
417 : *
418 : * Note: C99 also requires hexadecimal input as well as some extended
419 : * forms of NaN, but we consider these forms unportable and don't try
420 : * to support them. You can use 'em if your strtod() takes 'em.
421 : */
422 86 : if (pg_strncasecmp(num, "NaN", 3) == 0)
423 : {
424 0 : val = get_float8_nan();
425 0 : endptr = num + 3;
426 : }
427 86 : else if (pg_strncasecmp(num, "Infinity", 8) == 0)
428 : {
429 0 : val = get_float8_infinity();
430 0 : endptr = num + 8;
431 : }
432 86 : else if (pg_strncasecmp(num, "+Infinity", 9) == 0)
433 : {
434 0 : val = get_float8_infinity();
435 0 : endptr = num + 9;
436 : }
437 86 : else if (pg_strncasecmp(num, "-Infinity", 9) == 0)
438 : {
439 0 : val = -get_float8_infinity();
440 0 : endptr = num + 9;
441 : }
442 86 : else if (pg_strncasecmp(num, "inf", 3) == 0)
443 : {
444 0 : val = get_float8_infinity();
445 0 : endptr = num + 3;
446 : }
447 86 : else if (pg_strncasecmp(num, "+inf", 4) == 0)
448 : {
449 0 : val = get_float8_infinity();
450 0 : endptr = num + 4;
451 : }
452 86 : else if (pg_strncasecmp(num, "-inf", 4) == 0)
453 : {
454 0 : val = -get_float8_infinity();
455 0 : endptr = num + 4;
456 : }
457 86 : else if (save_errno == ERANGE)
458 : {
459 : /*
460 : * Some platforms return ERANGE for denormalized numbers (those
461 : * that are not zero, but are too close to zero to have full
462 : * precision). We'd prefer not to throw error for that, so try to
463 : * detect whether it's a "real" out-of-range condition by checking
464 : * to see if the result is zero or huge.
465 : *
466 : * On error, we intentionally complain about double precision not
467 : * the given type name, and we print only the part of the string
468 : * that is the current number.
469 : */
470 42 : if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
471 : {
472 42 : char *errnumber = pstrdup(num);
473 :
474 42 : errnumber[endptr - num] = '\0';
475 42 : RETURN_ERROR(ereport(ERROR,
476 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
477 : errmsg("\"%s\" is out of range for type double precision",
478 : errnumber))),
479 : have_error);
480 : }
481 : }
482 : else
483 44 : RETURN_ERROR(ereport(ERROR,
484 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
485 : errmsg("invalid input syntax for type "
486 : "%s: \"%s\"",
487 : type_name, orig_string))),
488 : have_error);
489 : }
490 :
491 : /* skip trailing whitespace */
492 617856 : while (*endptr != '\0' && isspace((unsigned char) *endptr))
493 276 : endptr++;
494 :
495 : /* report stopping point if wanted, else complain if not end of string */
496 617580 : if (endptr_p)
497 176310 : *endptr_p = endptr;
498 441270 : else if (*endptr != '\0')
499 28 : RETURN_ERROR(ereport(ERROR,
500 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
501 : errmsg("invalid input syntax for type "
502 : "%s: \"%s\"",
503 : type_name, orig_string))),
504 : have_error);
505 :
506 617552 : return val;
507 : }
508 :
509 : /*
510 : * Interface to float8in_internal_opt_error() without "have_error" argument.
511 : */
512 : double
513 617634 : float8in_internal(char *num, char **endptr_p,
514 : const char *type_name, const char *orig_string)
515 : {
516 617634 : return float8in_internal_opt_error(num, endptr_p, type_name,
517 : orig_string, NULL);
518 : }
519 :
520 :
521 : /*
522 : * float8out - converts float8 number to a string
523 : * using a standard output format
524 : */
525 : Datum
526 228336 : float8out(PG_FUNCTION_ARGS)
527 : {
528 228336 : float8 num = PG_GETARG_FLOAT8(0);
529 :
530 228336 : PG_RETURN_CSTRING(float8out_internal(num));
531 : }
532 :
533 : /*
534 : * float8out_internal - guts of float8out()
535 : *
536 : * This is exposed for use by functions that want a reasonably
537 : * platform-independent way of outputting doubles.
538 : * The result is always palloc'd.
539 : */
540 : char *
541 2065320 : float8out_internal(double num)
542 : {
543 2065320 : char *ascii = (char *) palloc(32);
544 2065320 : int ndig = DBL_DIG + extra_float_digits;
545 :
546 2065320 : if (extra_float_digits > 0)
547 : {
548 1923680 : double_to_shortest_decimal_buf(num, ascii);
549 1923680 : return ascii;
550 : }
551 :
552 141640 : (void) pg_strfromd(ascii, 32, ndig, num);
553 141640 : return ascii;
554 : }
555 :
556 : /*
557 : * float8recv - converts external binary format to float8
558 : */
559 : Datum
560 18 : float8recv(PG_FUNCTION_ARGS)
561 : {
562 18 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
563 :
564 18 : PG_RETURN_FLOAT8(pq_getmsgfloat8(buf));
565 : }
566 :
567 : /*
568 : * float8send - converts float8 to binary format
569 : */
570 : Datum
571 3438 : float8send(PG_FUNCTION_ARGS)
572 : {
573 3438 : float8 num = PG_GETARG_FLOAT8(0);
574 : StringInfoData buf;
575 :
576 3438 : pq_begintypsend(&buf);
577 3438 : pq_sendfloat8(&buf, num);
578 3438 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
579 : }
580 :
581 :
582 : /* ========== PUBLIC ROUTINES ========== */
583 :
584 :
585 : /*
586 : * ======================
587 : * FLOAT4 BASE OPERATIONS
588 : * ======================
589 : */
590 :
591 : /*
592 : * float4abs - returns |arg1| (absolute value)
593 : */
594 : Datum
595 20 : float4abs(PG_FUNCTION_ARGS)
596 : {
597 20 : float4 arg1 = PG_GETARG_FLOAT4(0);
598 :
599 20 : PG_RETURN_FLOAT4((float4) fabs(arg1));
600 : }
601 :
602 : /*
603 : * float4um - returns -arg1 (unary minus)
604 : */
605 : Datum
606 10 : float4um(PG_FUNCTION_ARGS)
607 : {
608 10 : float4 arg1 = PG_GETARG_FLOAT4(0);
609 : float4 result;
610 :
611 10 : result = -arg1;
612 10 : PG_RETURN_FLOAT4(result);
613 : }
614 :
615 : Datum
616 0 : float4up(PG_FUNCTION_ARGS)
617 : {
618 0 : float4 arg = PG_GETARG_FLOAT4(0);
619 :
620 0 : PG_RETURN_FLOAT4(arg);
621 : }
622 :
623 : Datum
624 12 : float4larger(PG_FUNCTION_ARGS)
625 : {
626 12 : float4 arg1 = PG_GETARG_FLOAT4(0);
627 12 : float4 arg2 = PG_GETARG_FLOAT4(1);
628 : float4 result;
629 :
630 12 : if (float4_gt(arg1, arg2))
631 4 : result = arg1;
632 : else
633 8 : result = arg2;
634 12 : PG_RETURN_FLOAT4(result);
635 : }
636 :
637 : Datum
638 0 : float4smaller(PG_FUNCTION_ARGS)
639 : {
640 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
641 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
642 : float4 result;
643 :
644 0 : if (float4_lt(arg1, arg2))
645 0 : result = arg1;
646 : else
647 0 : result = arg2;
648 0 : PG_RETURN_FLOAT4(result);
649 : }
650 :
651 : /*
652 : * ======================
653 : * FLOAT8 BASE OPERATIONS
654 : * ======================
655 : */
656 :
657 : /*
658 : * float8abs - returns |arg1| (absolute value)
659 : */
660 : Datum
661 40418 : float8abs(PG_FUNCTION_ARGS)
662 : {
663 40418 : float8 arg1 = PG_GETARG_FLOAT8(0);
664 :
665 40418 : PG_RETURN_FLOAT8(fabs(arg1));
666 : }
667 :
668 :
669 : /*
670 : * float8um - returns -arg1 (unary minus)
671 : */
672 : Datum
673 192 : float8um(PG_FUNCTION_ARGS)
674 : {
675 192 : float8 arg1 = PG_GETARG_FLOAT8(0);
676 : float8 result;
677 :
678 192 : result = -arg1;
679 192 : PG_RETURN_FLOAT8(result);
680 : }
681 :
682 : Datum
683 0 : float8up(PG_FUNCTION_ARGS)
684 : {
685 0 : float8 arg = PG_GETARG_FLOAT8(0);
686 :
687 0 : PG_RETURN_FLOAT8(arg);
688 : }
689 :
690 : Datum
691 592 : float8larger(PG_FUNCTION_ARGS)
692 : {
693 592 : float8 arg1 = PG_GETARG_FLOAT8(0);
694 592 : float8 arg2 = PG_GETARG_FLOAT8(1);
695 : float8 result;
696 :
697 592 : if (float8_gt(arg1, arg2))
698 460 : result = arg1;
699 : else
700 132 : result = arg2;
701 592 : PG_RETURN_FLOAT8(result);
702 : }
703 :
704 : Datum
705 796 : float8smaller(PG_FUNCTION_ARGS)
706 : {
707 796 : float8 arg1 = PG_GETARG_FLOAT8(0);
708 796 : float8 arg2 = PG_GETARG_FLOAT8(1);
709 : float8 result;
710 :
711 796 : if (float8_lt(arg1, arg2))
712 596 : result = arg1;
713 : else
714 200 : result = arg2;
715 796 : PG_RETURN_FLOAT8(result);
716 : }
717 :
718 :
719 : /*
720 : * ====================
721 : * ARITHMETIC OPERATORS
722 : * ====================
723 : */
724 :
725 : /*
726 : * float4pl - returns arg1 + arg2
727 : * float4mi - returns arg1 - arg2
728 : * float4mul - returns arg1 * arg2
729 : * float4div - returns arg1 / arg2
730 : */
731 : Datum
732 36 : float4pl(PG_FUNCTION_ARGS)
733 : {
734 36 : float4 arg1 = PG_GETARG_FLOAT4(0);
735 36 : float4 arg2 = PG_GETARG_FLOAT4(1);
736 :
737 36 : PG_RETURN_FLOAT4(float4_pl(arg1, arg2));
738 : }
739 :
740 : Datum
741 12 : float4mi(PG_FUNCTION_ARGS)
742 : {
743 12 : float4 arg1 = PG_GETARG_FLOAT4(0);
744 12 : float4 arg2 = PG_GETARG_FLOAT4(1);
745 :
746 12 : PG_RETURN_FLOAT4(float4_mi(arg1, arg2));
747 : }
748 :
749 : Datum
750 24 : float4mul(PG_FUNCTION_ARGS)
751 : {
752 24 : float4 arg1 = PG_GETARG_FLOAT4(0);
753 24 : float4 arg2 = PG_GETARG_FLOAT4(1);
754 :
755 24 : PG_RETURN_FLOAT4(float4_mul(arg1, arg2));
756 : }
757 :
758 : Datum
759 32 : float4div(PG_FUNCTION_ARGS)
760 : {
761 32 : float4 arg1 = PG_GETARG_FLOAT4(0);
762 32 : float4 arg2 = PG_GETARG_FLOAT4(1);
763 :
764 32 : PG_RETURN_FLOAT4(float4_div(arg1, arg2));
765 : }
766 :
767 : /*
768 : * float8pl - returns arg1 + arg2
769 : * float8mi - returns arg1 - arg2
770 : * float8mul - returns arg1 * arg2
771 : * float8div - returns arg1 / arg2
772 : */
773 : Datum
774 40016 : float8pl(PG_FUNCTION_ARGS)
775 : {
776 40016 : float8 arg1 = PG_GETARG_FLOAT8(0);
777 40016 : float8 arg2 = PG_GETARG_FLOAT8(1);
778 :
779 40016 : PG_RETURN_FLOAT8(float8_pl(arg1, arg2));
780 : }
781 :
782 : Datum
783 568 : float8mi(PG_FUNCTION_ARGS)
784 : {
785 568 : float8 arg1 = PG_GETARG_FLOAT8(0);
786 568 : float8 arg2 = PG_GETARG_FLOAT8(1);
787 :
788 568 : PG_RETURN_FLOAT8(float8_mi(arg1, arg2));
789 : }
790 :
791 : Datum
792 578000 : float8mul(PG_FUNCTION_ARGS)
793 : {
794 578000 : float8 arg1 = PG_GETARG_FLOAT8(0);
795 578000 : float8 arg2 = PG_GETARG_FLOAT8(1);
796 :
797 578000 : PG_RETURN_FLOAT8(float8_mul(arg1, arg2));
798 : }
799 :
800 : Datum
801 1328 : float8div(PG_FUNCTION_ARGS)
802 : {
803 1328 : float8 arg1 = PG_GETARG_FLOAT8(0);
804 1328 : float8 arg2 = PG_GETARG_FLOAT8(1);
805 :
806 1328 : PG_RETURN_FLOAT8(float8_div(arg1, arg2));
807 : }
808 :
809 :
810 : /*
811 : * ====================
812 : * COMPARISON OPERATORS
813 : * ====================
814 : */
815 :
816 : /*
817 : * float4{eq,ne,lt,le,gt,ge} - float4/float4 comparison operations
818 : */
819 : int
820 33526580 : float4_cmp_internal(float4 a, float4 b)
821 : {
822 33526580 : if (float4_gt(a, b))
823 713944 : return 1;
824 32812636 : if (float4_lt(a, b))
825 2206512 : return -1;
826 30606124 : return 0;
827 : }
828 :
829 : Datum
830 80432 : float4eq(PG_FUNCTION_ARGS)
831 : {
832 80432 : float4 arg1 = PG_GETARG_FLOAT4(0);
833 80432 : float4 arg2 = PG_GETARG_FLOAT4(1);
834 :
835 80432 : PG_RETURN_BOOL(float4_eq(arg1, arg2));
836 : }
837 :
838 : Datum
839 20 : float4ne(PG_FUNCTION_ARGS)
840 : {
841 20 : float4 arg1 = PG_GETARG_FLOAT4(0);
842 20 : float4 arg2 = PG_GETARG_FLOAT4(1);
843 :
844 20 : PG_RETURN_BOOL(float4_ne(arg1, arg2));
845 : }
846 :
847 : Datum
848 2052 : float4lt(PG_FUNCTION_ARGS)
849 : {
850 2052 : float4 arg1 = PG_GETARG_FLOAT4(0);
851 2052 : float4 arg2 = PG_GETARG_FLOAT4(1);
852 :
853 2052 : PG_RETURN_BOOL(float4_lt(arg1, arg2));
854 : }
855 :
856 : Datum
857 1620 : float4le(PG_FUNCTION_ARGS)
858 : {
859 1620 : float4 arg1 = PG_GETARG_FLOAT4(0);
860 1620 : float4 arg2 = PG_GETARG_FLOAT4(1);
861 :
862 1620 : PG_RETURN_BOOL(float4_le(arg1, arg2));
863 : }
864 :
865 : Datum
866 2168 : float4gt(PG_FUNCTION_ARGS)
867 : {
868 2168 : float4 arg1 = PG_GETARG_FLOAT4(0);
869 2168 : float4 arg2 = PG_GETARG_FLOAT4(1);
870 :
871 2168 : PG_RETURN_BOOL(float4_gt(arg1, arg2));
872 : }
873 :
874 : Datum
875 1620 : float4ge(PG_FUNCTION_ARGS)
876 : {
877 1620 : float4 arg1 = PG_GETARG_FLOAT4(0);
878 1620 : float4 arg2 = PG_GETARG_FLOAT4(1);
879 :
880 1620 : PG_RETURN_BOOL(float4_ge(arg1, arg2));
881 : }
882 :
883 : Datum
884 1875456 : btfloat4cmp(PG_FUNCTION_ARGS)
885 : {
886 1875456 : float4 arg1 = PG_GETARG_FLOAT4(0);
887 1875456 : float4 arg2 = PG_GETARG_FLOAT4(1);
888 :
889 1875456 : PG_RETURN_INT32(float4_cmp_internal(arg1, arg2));
890 : }
891 :
892 : static int
893 31651124 : btfloat4fastcmp(Datum x, Datum y, SortSupport ssup)
894 : {
895 31651124 : float4 arg1 = DatumGetFloat4(x);
896 31651124 : float4 arg2 = DatumGetFloat4(y);
897 :
898 31651124 : return float4_cmp_internal(arg1, arg2);
899 : }
900 :
901 : Datum
902 2446 : btfloat4sortsupport(PG_FUNCTION_ARGS)
903 : {
904 2446 : SortSupport ssup = (SortSupport) PG_GETARG_POINTER(0);
905 :
906 2446 : ssup->comparator = btfloat4fastcmp;
907 2446 : PG_RETURN_VOID();
908 : }
909 :
910 : /*
911 : * float8{eq,ne,lt,le,gt,ge} - float8/float8 comparison operations
912 : */
913 : int
914 12706522 : float8_cmp_internal(float8 a, float8 b)
915 : {
916 12706522 : if (float8_gt(a, b))
917 5116560 : return 1;
918 7589962 : if (float8_lt(a, b))
919 7446774 : return -1;
920 143188 : return 0;
921 : }
922 :
923 : Datum
924 587474 : float8eq(PG_FUNCTION_ARGS)
925 : {
926 587474 : float8 arg1 = PG_GETARG_FLOAT8(0);
927 587474 : float8 arg2 = PG_GETARG_FLOAT8(1);
928 :
929 587474 : PG_RETURN_BOOL(float8_eq(arg1, arg2));
930 : }
931 :
932 : Datum
933 236 : float8ne(PG_FUNCTION_ARGS)
934 : {
935 236 : float8 arg1 = PG_GETARG_FLOAT8(0);
936 236 : float8 arg2 = PG_GETARG_FLOAT8(1);
937 :
938 236 : PG_RETURN_BOOL(float8_ne(arg1, arg2));
939 : }
940 :
941 : Datum
942 24030 : float8lt(PG_FUNCTION_ARGS)
943 : {
944 24030 : float8 arg1 = PG_GETARG_FLOAT8(0);
945 24030 : float8 arg2 = PG_GETARG_FLOAT8(1);
946 :
947 24030 : PG_RETURN_BOOL(float8_lt(arg1, arg2));
948 : }
949 :
950 : Datum
951 3456 : float8le(PG_FUNCTION_ARGS)
952 : {
953 3456 : float8 arg1 = PG_GETARG_FLOAT8(0);
954 3456 : float8 arg2 = PG_GETARG_FLOAT8(1);
955 :
956 3456 : PG_RETURN_BOOL(float8_le(arg1, arg2));
957 : }
958 :
959 : Datum
960 4772 : float8gt(PG_FUNCTION_ARGS)
961 : {
962 4772 : float8 arg1 = PG_GETARG_FLOAT8(0);
963 4772 : float8 arg2 = PG_GETARG_FLOAT8(1);
964 :
965 4772 : PG_RETURN_BOOL(float8_gt(arg1, arg2));
966 : }
967 :
968 : Datum
969 5616 : float8ge(PG_FUNCTION_ARGS)
970 : {
971 5616 : float8 arg1 = PG_GETARG_FLOAT8(0);
972 5616 : float8 arg2 = PG_GETARG_FLOAT8(1);
973 :
974 5616 : PG_RETURN_BOOL(float8_ge(arg1, arg2));
975 : }
976 :
977 : Datum
978 2030 : btfloat8cmp(PG_FUNCTION_ARGS)
979 : {
980 2030 : float8 arg1 = PG_GETARG_FLOAT8(0);
981 2030 : float8 arg2 = PG_GETARG_FLOAT8(1);
982 :
983 2030 : PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
984 : }
985 :
986 : static int
987 3805246 : btfloat8fastcmp(Datum x, Datum y, SortSupport ssup)
988 : {
989 3805246 : float8 arg1 = DatumGetFloat8(x);
990 3805246 : float8 arg2 = DatumGetFloat8(y);
991 :
992 3805246 : return float8_cmp_internal(arg1, arg2);
993 : }
994 :
995 : Datum
996 632 : btfloat8sortsupport(PG_FUNCTION_ARGS)
997 : {
998 632 : SortSupport ssup = (SortSupport) PG_GETARG_POINTER(0);
999 :
1000 632 : ssup->comparator = btfloat8fastcmp;
1001 632 : PG_RETURN_VOID();
1002 : }
1003 :
1004 : Datum
1005 0 : btfloat48cmp(PG_FUNCTION_ARGS)
1006 : {
1007 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
1008 0 : float8 arg2 = PG_GETARG_FLOAT8(1);
1009 :
1010 : /* widen float4 to float8 and then compare */
1011 0 : PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
1012 : }
1013 :
1014 : Datum
1015 0 : btfloat84cmp(PG_FUNCTION_ARGS)
1016 : {
1017 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1018 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
1019 :
1020 : /* widen float4 to float8 and then compare */
1021 0 : PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
1022 : }
1023 :
1024 : /*
1025 : * in_range support function for float8.
1026 : *
1027 : * Note: we needn't supply a float8_float4 variant, as implicit coercion
1028 : * of the offset value takes care of that scenario just as well.
1029 : */
1030 : Datum
1031 768 : in_range_float8_float8(PG_FUNCTION_ARGS)
1032 : {
1033 768 : float8 val = PG_GETARG_FLOAT8(0);
1034 768 : float8 base = PG_GETARG_FLOAT8(1);
1035 768 : float8 offset = PG_GETARG_FLOAT8(2);
1036 768 : bool sub = PG_GETARG_BOOL(3);
1037 768 : bool less = PG_GETARG_BOOL(4);
1038 : float8 sum;
1039 :
1040 : /*
1041 : * Reject negative or NaN offset. Negative is per spec, and NaN is
1042 : * because appropriate semantics for that seem non-obvious.
1043 : */
1044 768 : if (isnan(offset) || offset < 0)
1045 4 : ereport(ERROR,
1046 : (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
1047 : errmsg("invalid preceding or following size in window function")));
1048 :
1049 : /*
1050 : * Deal with cases where val and/or base is NaN, following the rule that
1051 : * NaN sorts after non-NaN (cf float8_cmp_internal). The offset cannot
1052 : * affect the conclusion.
1053 : */
1054 764 : if (isnan(val))
1055 : {
1056 124 : if (isnan(base))
1057 40 : PG_RETURN_BOOL(true); /* NAN = NAN */
1058 : else
1059 84 : PG_RETURN_BOOL(!less); /* NAN > non-NAN */
1060 : }
1061 640 : else if (isnan(base))
1062 : {
1063 84 : PG_RETURN_BOOL(less); /* non-NAN < NAN */
1064 : }
1065 :
1066 : /*
1067 : * Deal with cases where both base and offset are infinite, and computing
1068 : * base +/- offset would produce NaN. This corresponds to a window frame
1069 : * whose boundary infinitely precedes +inf or infinitely follows -inf,
1070 : * which is not well-defined. For consistency with other cases involving
1071 : * infinities, such as the fact that +inf infinitely follows +inf, we
1072 : * choose to assume that +inf infinitely precedes +inf and -inf infinitely
1073 : * follows -inf, and therefore that all finite and infinite values are in
1074 : * such a window frame.
1075 : *
1076 : * offset is known positive, so we need only check the sign of base in
1077 : * this test.
1078 : */
1079 556 : if (isinf(offset) && isinf(base) &&
1080 : (sub ? base > 0 : base < 0))
1081 116 : PG_RETURN_BOOL(true);
1082 :
1083 : /*
1084 : * Otherwise it should be safe to compute base +/- offset. We trust the
1085 : * FPU to cope if an input is +/-inf or the true sum would overflow, and
1086 : * produce a suitably signed infinity, which will compare properly against
1087 : * val whether or not that's infinity.
1088 : */
1089 440 : if (sub)
1090 240 : sum = base - offset;
1091 : else
1092 200 : sum = base + offset;
1093 :
1094 440 : if (less)
1095 172 : PG_RETURN_BOOL(val <= sum);
1096 : else
1097 268 : PG_RETURN_BOOL(val >= sum);
1098 : }
1099 :
1100 : /*
1101 : * in_range support function for float4.
1102 : *
1103 : * We would need a float4_float8 variant in any case, so we supply that and
1104 : * let implicit coercion take care of the float4_float4 case.
1105 : */
1106 : Datum
1107 768 : in_range_float4_float8(PG_FUNCTION_ARGS)
1108 : {
1109 768 : float4 val = PG_GETARG_FLOAT4(0);
1110 768 : float4 base = PG_GETARG_FLOAT4(1);
1111 768 : float8 offset = PG_GETARG_FLOAT8(2);
1112 768 : bool sub = PG_GETARG_BOOL(3);
1113 768 : bool less = PG_GETARG_BOOL(4);
1114 : float8 sum;
1115 :
1116 : /*
1117 : * Reject negative or NaN offset. Negative is per spec, and NaN is
1118 : * because appropriate semantics for that seem non-obvious.
1119 : */
1120 768 : if (isnan(offset) || offset < 0)
1121 4 : ereport(ERROR,
1122 : (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
1123 : errmsg("invalid preceding or following size in window function")));
1124 :
1125 : /*
1126 : * Deal with cases where val and/or base is NaN, following the rule that
1127 : * NaN sorts after non-NaN (cf float8_cmp_internal). The offset cannot
1128 : * affect the conclusion.
1129 : */
1130 764 : if (isnan(val))
1131 : {
1132 124 : if (isnan(base))
1133 40 : PG_RETURN_BOOL(true); /* NAN = NAN */
1134 : else
1135 84 : PG_RETURN_BOOL(!less); /* NAN > non-NAN */
1136 : }
1137 640 : else if (isnan(base))
1138 : {
1139 84 : PG_RETURN_BOOL(less); /* non-NAN < NAN */
1140 : }
1141 :
1142 : /*
1143 : * Deal with cases where both base and offset are infinite, and computing
1144 : * base +/- offset would produce NaN. This corresponds to a window frame
1145 : * whose boundary infinitely precedes +inf or infinitely follows -inf,
1146 : * which is not well-defined. For consistency with other cases involving
1147 : * infinities, such as the fact that +inf infinitely follows +inf, we
1148 : * choose to assume that +inf infinitely precedes +inf and -inf infinitely
1149 : * follows -inf, and therefore that all finite and infinite values are in
1150 : * such a window frame.
1151 : *
1152 : * offset is known positive, so we need only check the sign of base in
1153 : * this test.
1154 : */
1155 556 : if (isinf(offset) && isinf(base) &&
1156 : (sub ? base > 0 : base < 0))
1157 116 : PG_RETURN_BOOL(true);
1158 :
1159 : /*
1160 : * Otherwise it should be safe to compute base +/- offset. We trust the
1161 : * FPU to cope if an input is +/-inf or the true sum would overflow, and
1162 : * produce a suitably signed infinity, which will compare properly against
1163 : * val whether or not that's infinity.
1164 : */
1165 440 : if (sub)
1166 240 : sum = base - offset;
1167 : else
1168 200 : sum = base + offset;
1169 :
1170 440 : if (less)
1171 172 : PG_RETURN_BOOL(val <= sum);
1172 : else
1173 268 : PG_RETURN_BOOL(val >= sum);
1174 : }
1175 :
1176 :
1177 : /*
1178 : * ===================
1179 : * CONVERSION ROUTINES
1180 : * ===================
1181 : */
1182 :
1183 : /*
1184 : * ftod - converts a float4 number to a float8 number
1185 : */
1186 : Datum
1187 188 : ftod(PG_FUNCTION_ARGS)
1188 : {
1189 188 : float4 num = PG_GETARG_FLOAT4(0);
1190 :
1191 188 : PG_RETURN_FLOAT8((float8) num);
1192 : }
1193 :
1194 :
1195 : /*
1196 : * dtof - converts a float8 number to a float4 number
1197 : */
1198 : Datum
1199 16 : dtof(PG_FUNCTION_ARGS)
1200 : {
1201 16 : float8 num = PG_GETARG_FLOAT8(0);
1202 : float4 result;
1203 :
1204 16 : result = (float4) num;
1205 16 : if (unlikely(isinf(result)) && !isinf(num))
1206 8 : float_overflow_error();
1207 8 : if (unlikely(result == 0.0f) && num != 0.0)
1208 8 : float_underflow_error();
1209 :
1210 0 : PG_RETURN_FLOAT4(result);
1211 : }
1212 :
1213 :
1214 : /*
1215 : * dtoi4 - converts a float8 number to an int4 number
1216 : */
1217 : Datum
1218 574788 : dtoi4(PG_FUNCTION_ARGS)
1219 : {
1220 574788 : float8 num = PG_GETARG_FLOAT8(0);
1221 :
1222 : /*
1223 : * Get rid of any fractional part in the input. This is so we don't fail
1224 : * on just-out-of-range values that would round into range. Note
1225 : * assumption that rint() will pass through a NaN or Inf unchanged.
1226 : */
1227 574788 : num = rint(num);
1228 :
1229 : /* Range check */
1230 574788 : if (unlikely(isnan(num) || !FLOAT8_FITS_IN_INT32(num)))
1231 16 : ereport(ERROR,
1232 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1233 : errmsg("integer out of range")));
1234 :
1235 574772 : PG_RETURN_INT32((int32) num);
1236 : }
1237 :
1238 :
1239 : /*
1240 : * dtoi2 - converts a float8 number to an int2 number
1241 : */
1242 : Datum
1243 60 : dtoi2(PG_FUNCTION_ARGS)
1244 : {
1245 60 : float8 num = PG_GETARG_FLOAT8(0);
1246 :
1247 : /*
1248 : * Get rid of any fractional part in the input. This is so we don't fail
1249 : * on just-out-of-range values that would round into range. Note
1250 : * assumption that rint() will pass through a NaN or Inf unchanged.
1251 : */
1252 60 : num = rint(num);
1253 :
1254 : /* Range check */
1255 60 : if (unlikely(isnan(num) || !FLOAT8_FITS_IN_INT16(num)))
1256 8 : ereport(ERROR,
1257 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1258 : errmsg("smallint out of range")));
1259 :
1260 52 : PG_RETURN_INT16((int16) num);
1261 : }
1262 :
1263 :
1264 : /*
1265 : * i4tod - converts an int4 number to a float8 number
1266 : */
1267 : Datum
1268 1591864 : i4tod(PG_FUNCTION_ARGS)
1269 : {
1270 1591864 : int32 num = PG_GETARG_INT32(0);
1271 :
1272 1591864 : PG_RETURN_FLOAT8((float8) num);
1273 : }
1274 :
1275 :
1276 : /*
1277 : * i2tod - converts an int2 number to a float8 number
1278 : */
1279 : Datum
1280 164 : i2tod(PG_FUNCTION_ARGS)
1281 : {
1282 164 : int16 num = PG_GETARG_INT16(0);
1283 :
1284 164 : PG_RETURN_FLOAT8((float8) num);
1285 : }
1286 :
1287 :
1288 : /*
1289 : * ftoi4 - converts a float4 number to an int4 number
1290 : */
1291 : Datum
1292 16 : ftoi4(PG_FUNCTION_ARGS)
1293 : {
1294 16 : float4 num = PG_GETARG_FLOAT4(0);
1295 :
1296 : /*
1297 : * Get rid of any fractional part in the input. This is so we don't fail
1298 : * on just-out-of-range values that would round into range. Note
1299 : * assumption that rint() will pass through a NaN or Inf unchanged.
1300 : */
1301 16 : num = rint(num);
1302 :
1303 : /* Range check */
1304 16 : if (unlikely(isnan(num) || !FLOAT4_FITS_IN_INT32(num)))
1305 8 : ereport(ERROR,
1306 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1307 : errmsg("integer out of range")));
1308 :
1309 8 : PG_RETURN_INT32((int32) num);
1310 : }
1311 :
1312 :
1313 : /*
1314 : * ftoi2 - converts a float4 number to an int2 number
1315 : */
1316 : Datum
1317 16 : ftoi2(PG_FUNCTION_ARGS)
1318 : {
1319 16 : float4 num = PG_GETARG_FLOAT4(0);
1320 :
1321 : /*
1322 : * Get rid of any fractional part in the input. This is so we don't fail
1323 : * on just-out-of-range values that would round into range. Note
1324 : * assumption that rint() will pass through a NaN or Inf unchanged.
1325 : */
1326 16 : num = rint(num);
1327 :
1328 : /* Range check */
1329 16 : if (unlikely(isnan(num) || !FLOAT4_FITS_IN_INT16(num)))
1330 8 : ereport(ERROR,
1331 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1332 : errmsg("smallint out of range")));
1333 :
1334 8 : PG_RETURN_INT16((int16) num);
1335 : }
1336 :
1337 :
1338 : /*
1339 : * i4tof - converts an int4 number to a float4 number
1340 : */
1341 : Datum
1342 306 : i4tof(PG_FUNCTION_ARGS)
1343 : {
1344 306 : int32 num = PG_GETARG_INT32(0);
1345 :
1346 306 : PG_RETURN_FLOAT4((float4) num);
1347 : }
1348 :
1349 :
1350 : /*
1351 : * i2tof - converts an int2 number to a float4 number
1352 : */
1353 : Datum
1354 0 : i2tof(PG_FUNCTION_ARGS)
1355 : {
1356 0 : int16 num = PG_GETARG_INT16(0);
1357 :
1358 0 : PG_RETURN_FLOAT4((float4) num);
1359 : }
1360 :
1361 :
1362 : /*
1363 : * =======================
1364 : * RANDOM FLOAT8 OPERATORS
1365 : * =======================
1366 : */
1367 :
1368 : /*
1369 : * dround - returns ROUND(arg1)
1370 : */
1371 : Datum
1372 12984 : dround(PG_FUNCTION_ARGS)
1373 : {
1374 12984 : float8 arg1 = PG_GETARG_FLOAT8(0);
1375 :
1376 12984 : PG_RETURN_FLOAT8(rint(arg1));
1377 : }
1378 :
1379 : /*
1380 : * dceil - returns the smallest integer greater than or
1381 : * equal to the specified float
1382 : */
1383 : Datum
1384 40 : dceil(PG_FUNCTION_ARGS)
1385 : {
1386 40 : float8 arg1 = PG_GETARG_FLOAT8(0);
1387 :
1388 40 : PG_RETURN_FLOAT8(ceil(arg1));
1389 : }
1390 :
1391 : /*
1392 : * dfloor - returns the largest integer lesser than or
1393 : * equal to the specified float
1394 : */
1395 : Datum
1396 40 : dfloor(PG_FUNCTION_ARGS)
1397 : {
1398 40 : float8 arg1 = PG_GETARG_FLOAT8(0);
1399 :
1400 40 : PG_RETURN_FLOAT8(floor(arg1));
1401 : }
1402 :
1403 : /*
1404 : * dsign - returns -1 if the argument is less than 0, 0
1405 : * if the argument is equal to 0, and 1 if the
1406 : * argument is greater than zero.
1407 : */
1408 : Datum
1409 20 : dsign(PG_FUNCTION_ARGS)
1410 : {
1411 20 : float8 arg1 = PG_GETARG_FLOAT8(0);
1412 : float8 result;
1413 :
1414 20 : if (arg1 > 0)
1415 12 : result = 1.0;
1416 8 : else if (arg1 < 0)
1417 4 : result = -1.0;
1418 : else
1419 4 : result = 0.0;
1420 :
1421 20 : PG_RETURN_FLOAT8(result);
1422 : }
1423 :
1424 : /*
1425 : * dtrunc - returns truncation-towards-zero of arg1,
1426 : * arg1 >= 0 ... the greatest integer less
1427 : * than or equal to arg1
1428 : * arg1 < 0 ... the least integer greater
1429 : * than or equal to arg1
1430 : */
1431 : Datum
1432 20 : dtrunc(PG_FUNCTION_ARGS)
1433 : {
1434 20 : float8 arg1 = PG_GETARG_FLOAT8(0);
1435 : float8 result;
1436 :
1437 20 : if (arg1 >= 0)
1438 16 : result = floor(arg1);
1439 : else
1440 4 : result = -floor(-arg1);
1441 :
1442 20 : PG_RETURN_FLOAT8(result);
1443 : }
1444 :
1445 :
1446 : /*
1447 : * dsqrt - returns square root of arg1
1448 : */
1449 : Datum
1450 4020 : dsqrt(PG_FUNCTION_ARGS)
1451 : {
1452 4020 : float8 arg1 = PG_GETARG_FLOAT8(0);
1453 : float8 result;
1454 :
1455 4020 : if (arg1 < 0)
1456 0 : ereport(ERROR,
1457 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
1458 : errmsg("cannot take square root of a negative number")));
1459 :
1460 4020 : result = sqrt(arg1);
1461 4020 : if (unlikely(isinf(result)) && !isinf(arg1))
1462 0 : float_overflow_error();
1463 4020 : if (unlikely(result == 0.0) && arg1 != 0.0)
1464 0 : float_underflow_error();
1465 :
1466 4020 : PG_RETURN_FLOAT8(result);
1467 : }
1468 :
1469 :
1470 : /*
1471 : * dcbrt - returns cube root of arg1
1472 : */
1473 : Datum
1474 24 : dcbrt(PG_FUNCTION_ARGS)
1475 : {
1476 24 : float8 arg1 = PG_GETARG_FLOAT8(0);
1477 : float8 result;
1478 :
1479 24 : result = cbrt(arg1);
1480 24 : if (unlikely(isinf(result)) && !isinf(arg1))
1481 0 : float_overflow_error();
1482 24 : if (unlikely(result == 0.0) && arg1 != 0.0)
1483 0 : float_underflow_error();
1484 :
1485 24 : PG_RETURN_FLOAT8(result);
1486 : }
1487 :
1488 :
1489 : /*
1490 : * dpow - returns pow(arg1,arg2)
1491 : */
1492 : Datum
1493 446 : dpow(PG_FUNCTION_ARGS)
1494 : {
1495 446 : float8 arg1 = PG_GETARG_FLOAT8(0);
1496 446 : float8 arg2 = PG_GETARG_FLOAT8(1);
1497 : float8 result;
1498 :
1499 : /*
1500 : * The POSIX spec says that NaN ^ 0 = 1, and 1 ^ NaN = 1, while all other
1501 : * cases with NaN inputs yield NaN (with no error). Many older platforms
1502 : * get one or more of these cases wrong, so deal with them via explicit
1503 : * logic rather than trusting pow(3).
1504 : */
1505 446 : if (isnan(arg1))
1506 : {
1507 12 : if (isnan(arg2) || arg2 != 0.0)
1508 8 : PG_RETURN_FLOAT8(get_float8_nan());
1509 4 : PG_RETURN_FLOAT8(1.0);
1510 : }
1511 434 : if (isnan(arg2))
1512 : {
1513 12 : if (arg1 != 1.0)
1514 8 : PG_RETURN_FLOAT8(get_float8_nan());
1515 4 : PG_RETURN_FLOAT8(1.0);
1516 : }
1517 :
1518 : /*
1519 : * The SQL spec requires that we emit a particular SQLSTATE error code for
1520 : * certain error conditions. Specifically, we don't return a
1521 : * divide-by-zero error code for 0 ^ -1.
1522 : */
1523 422 : if (arg1 == 0 && arg2 < 0)
1524 4 : ereport(ERROR,
1525 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
1526 : errmsg("zero raised to a negative power is undefined")));
1527 418 : if (arg1 < 0 && floor(arg2) != arg2)
1528 4 : ereport(ERROR,
1529 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
1530 : errmsg("a negative number raised to a non-integer power yields a complex result")));
1531 :
1532 : /*
1533 : * We don't trust the platform's pow() to handle infinity cases per POSIX
1534 : * spec either, so deal with those explicitly too. It's easier to handle
1535 : * infinite y first, so that it doesn't matter if x is also infinite.
1536 : */
1537 414 : if (isinf(arg2))
1538 : {
1539 68 : float8 absx = fabs(arg1);
1540 :
1541 68 : if (absx == 1.0)
1542 16 : result = 1.0;
1543 52 : else if (arg2 > 0.0) /* y = +Inf */
1544 : {
1545 28 : if (absx > 1.0)
1546 16 : result = arg2;
1547 : else
1548 12 : result = 0.0;
1549 : }
1550 : else /* y = -Inf */
1551 : {
1552 24 : if (absx > 1.0)
1553 16 : result = 0.0;
1554 : else
1555 8 : result = -arg2;
1556 : }
1557 : }
1558 346 : else if (isinf(arg1))
1559 : {
1560 32 : if (arg2 == 0.0)
1561 8 : result = 1.0;
1562 24 : else if (arg1 > 0.0) /* x = +Inf */
1563 : {
1564 8 : if (arg2 > 0.0)
1565 4 : result = arg1;
1566 : else
1567 4 : result = 0.0;
1568 : }
1569 : else /* x = -Inf */
1570 : {
1571 : /*
1572 : * Per POSIX, the sign of the result depends on whether y is an
1573 : * odd integer. Since x < 0, we already know from the previous
1574 : * domain check that y is an integer. It is odd if y/2 is not
1575 : * also an integer.
1576 : */
1577 16 : float8 halfy = arg2 / 2; /* should be computed exactly */
1578 16 : bool yisoddinteger = (floor(halfy) != halfy);
1579 :
1580 16 : if (arg2 > 0.0)
1581 8 : result = yisoddinteger ? arg1 : -arg1;
1582 : else
1583 8 : result = yisoddinteger ? -0.0 : 0.0;
1584 : }
1585 : }
1586 : else
1587 : {
1588 : /*
1589 : * pow() sets errno on only some platforms, depending on whether it
1590 : * follows _IEEE_, _POSIX_, _XOPEN_, or _SVID_, so we must check both
1591 : * errno and invalid output values. (We can't rely on just the
1592 : * latter, either; some old platforms return a large-but-finite
1593 : * HUGE_VAL when reporting overflow.)
1594 : */
1595 314 : errno = 0;
1596 314 : result = pow(arg1, arg2);
1597 314 : if (errno == EDOM || isnan(result))
1598 : {
1599 : /*
1600 : * We handled all possible domain errors above, so this should be
1601 : * impossible. However, old glibc versions on x86 have a bug that
1602 : * causes them to fail this way for abs(y) greater than 2^63:
1603 : *
1604 : * https://sourceware.org/bugzilla/show_bug.cgi?id=3866
1605 : *
1606 : * Hence, if we get here, assume y is finite but large (large
1607 : * enough to be certainly even). The result should be 0 if x == 0,
1608 : * 1.0 if abs(x) == 1.0, otherwise an overflow or underflow error.
1609 : */
1610 0 : if (arg1 == 0.0)
1611 0 : result = 0.0; /* we already verified y is positive */
1612 : else
1613 : {
1614 0 : float8 absx = fabs(arg1);
1615 :
1616 0 : if (absx == 1.0)
1617 0 : result = 1.0;
1618 0 : else if (arg2 >= 0.0 ? (absx > 1.0) : (absx < 1.0))
1619 0 : float_overflow_error();
1620 : else
1621 0 : float_underflow_error();
1622 : }
1623 : }
1624 314 : else if (errno == ERANGE)
1625 : {
1626 4 : if (result != 0.0)
1627 4 : float_overflow_error();
1628 : else
1629 0 : float_underflow_error();
1630 : }
1631 : else
1632 : {
1633 310 : if (unlikely(isinf(result)))
1634 0 : float_overflow_error();
1635 310 : if (unlikely(result == 0.0) && arg1 != 0.0)
1636 0 : float_underflow_error();
1637 : }
1638 : }
1639 :
1640 410 : PG_RETURN_FLOAT8(result);
1641 : }
1642 :
1643 :
1644 : /*
1645 : * dexp - returns the exponential function of arg1
1646 : */
1647 : Datum
1648 36 : dexp(PG_FUNCTION_ARGS)
1649 : {
1650 36 : float8 arg1 = PG_GETARG_FLOAT8(0);
1651 : float8 result;
1652 :
1653 : /*
1654 : * Handle NaN and Inf cases explicitly. This avoids needing to assume
1655 : * that the platform's exp() conforms to POSIX for these cases, and it
1656 : * removes some edge cases for the overflow checks below.
1657 : */
1658 36 : if (isnan(arg1))
1659 4 : result = arg1;
1660 32 : else if (isinf(arg1))
1661 : {
1662 : /* Per POSIX, exp(-Inf) is 0 */
1663 8 : result = (arg1 > 0.0) ? arg1 : 0;
1664 : }
1665 : else
1666 : {
1667 : /*
1668 : * On some platforms, exp() will not set errno but just return Inf or
1669 : * zero to report overflow/underflow; therefore, test both cases.
1670 : */
1671 24 : errno = 0;
1672 24 : result = exp(arg1);
1673 24 : if (unlikely(errno == ERANGE))
1674 : {
1675 4 : if (result != 0.0)
1676 0 : float_overflow_error();
1677 : else
1678 4 : float_underflow_error();
1679 : }
1680 20 : else if (unlikely(isinf(result)))
1681 0 : float_overflow_error();
1682 20 : else if (unlikely(result == 0.0))
1683 0 : float_underflow_error();
1684 : }
1685 :
1686 32 : PG_RETURN_FLOAT8(result);
1687 : }
1688 :
1689 :
1690 : /*
1691 : * dlog1 - returns the natural logarithm of arg1
1692 : */
1693 : Datum
1694 20 : dlog1(PG_FUNCTION_ARGS)
1695 : {
1696 20 : float8 arg1 = PG_GETARG_FLOAT8(0);
1697 : float8 result;
1698 :
1699 : /*
1700 : * Emit particular SQLSTATE error codes for ln(). This is required by the
1701 : * SQL standard.
1702 : */
1703 20 : if (arg1 == 0.0)
1704 4 : ereport(ERROR,
1705 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1706 : errmsg("cannot take logarithm of zero")));
1707 16 : if (arg1 < 0)
1708 4 : ereport(ERROR,
1709 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1710 : errmsg("cannot take logarithm of a negative number")));
1711 :
1712 12 : result = log(arg1);
1713 12 : if (unlikely(isinf(result)) && !isinf(arg1))
1714 0 : float_overflow_error();
1715 12 : if (unlikely(result == 0.0) && arg1 != 1.0)
1716 0 : float_underflow_error();
1717 :
1718 12 : PG_RETURN_FLOAT8(result);
1719 : }
1720 :
1721 :
1722 : /*
1723 : * dlog10 - returns the base 10 logarithm of arg1
1724 : */
1725 : Datum
1726 0 : dlog10(PG_FUNCTION_ARGS)
1727 : {
1728 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1729 : float8 result;
1730 :
1731 : /*
1732 : * Emit particular SQLSTATE error codes for log(). The SQL spec doesn't
1733 : * define log(), but it does define ln(), so it makes sense to emit the
1734 : * same error code for an analogous error condition.
1735 : */
1736 0 : if (arg1 == 0.0)
1737 0 : ereport(ERROR,
1738 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1739 : errmsg("cannot take logarithm of zero")));
1740 0 : if (arg1 < 0)
1741 0 : ereport(ERROR,
1742 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1743 : errmsg("cannot take logarithm of a negative number")));
1744 :
1745 0 : result = log10(arg1);
1746 0 : if (unlikely(isinf(result)) && !isinf(arg1))
1747 0 : float_overflow_error();
1748 0 : if (unlikely(result == 0.0) && arg1 != 1.0)
1749 0 : float_underflow_error();
1750 :
1751 0 : PG_RETURN_FLOAT8(result);
1752 : }
1753 :
1754 :
1755 : /*
1756 : * dacos - returns the arccos of arg1 (radians)
1757 : */
1758 : Datum
1759 0 : dacos(PG_FUNCTION_ARGS)
1760 : {
1761 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1762 : float8 result;
1763 :
1764 : /* Per the POSIX spec, return NaN if the input is NaN */
1765 0 : if (isnan(arg1))
1766 0 : PG_RETURN_FLOAT8(get_float8_nan());
1767 :
1768 : /*
1769 : * The principal branch of the inverse cosine function maps values in the
1770 : * range [-1, 1] to values in the range [0, Pi], so we should reject any
1771 : * inputs outside that range and the result will always be finite.
1772 : */
1773 0 : if (arg1 < -1.0 || arg1 > 1.0)
1774 0 : ereport(ERROR,
1775 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1776 : errmsg("input is out of range")));
1777 :
1778 0 : result = acos(arg1);
1779 0 : if (unlikely(isinf(result)))
1780 0 : float_overflow_error();
1781 :
1782 0 : PG_RETURN_FLOAT8(result);
1783 : }
1784 :
1785 :
1786 : /*
1787 : * dasin - returns the arcsin of arg1 (radians)
1788 : */
1789 : Datum
1790 110 : dasin(PG_FUNCTION_ARGS)
1791 : {
1792 110 : float8 arg1 = PG_GETARG_FLOAT8(0);
1793 : float8 result;
1794 :
1795 : /* Per the POSIX spec, return NaN if the input is NaN */
1796 110 : if (isnan(arg1))
1797 0 : PG_RETURN_FLOAT8(get_float8_nan());
1798 :
1799 : /*
1800 : * The principal branch of the inverse sine function maps values in the
1801 : * range [-1, 1] to values in the range [-Pi/2, Pi/2], so we should reject
1802 : * any inputs outside that range and the result will always be finite.
1803 : */
1804 110 : if (arg1 < -1.0 || arg1 > 1.0)
1805 0 : ereport(ERROR,
1806 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1807 : errmsg("input is out of range")));
1808 :
1809 110 : result = asin(arg1);
1810 110 : if (unlikely(isinf(result)))
1811 0 : float_overflow_error();
1812 :
1813 110 : PG_RETURN_FLOAT8(result);
1814 : }
1815 :
1816 :
1817 : /*
1818 : * datan - returns the arctan of arg1 (radians)
1819 : */
1820 : Datum
1821 0 : datan(PG_FUNCTION_ARGS)
1822 : {
1823 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1824 : float8 result;
1825 :
1826 : /* Per the POSIX spec, return NaN if the input is NaN */
1827 0 : if (isnan(arg1))
1828 0 : PG_RETURN_FLOAT8(get_float8_nan());
1829 :
1830 : /*
1831 : * The principal branch of the inverse tangent function maps all inputs to
1832 : * values in the range [-Pi/2, Pi/2], so the result should always be
1833 : * finite, even if the input is infinite.
1834 : */
1835 0 : result = atan(arg1);
1836 0 : if (unlikely(isinf(result)))
1837 0 : float_overflow_error();
1838 :
1839 0 : PG_RETURN_FLOAT8(result);
1840 : }
1841 :
1842 :
1843 : /*
1844 : * atan2 - returns the arctan of arg1/arg2 (radians)
1845 : */
1846 : Datum
1847 40 : datan2(PG_FUNCTION_ARGS)
1848 : {
1849 40 : float8 arg1 = PG_GETARG_FLOAT8(0);
1850 40 : float8 arg2 = PG_GETARG_FLOAT8(1);
1851 : float8 result;
1852 :
1853 : /* Per the POSIX spec, return NaN if either input is NaN */
1854 40 : if (isnan(arg1) || isnan(arg2))
1855 0 : PG_RETURN_FLOAT8(get_float8_nan());
1856 :
1857 : /*
1858 : * atan2 maps all inputs to values in the range [-Pi, Pi], so the result
1859 : * should always be finite, even if the inputs are infinite.
1860 : */
1861 40 : result = atan2(arg1, arg2);
1862 40 : if (unlikely(isinf(result)))
1863 0 : float_overflow_error();
1864 :
1865 40 : PG_RETURN_FLOAT8(result);
1866 : }
1867 :
1868 :
1869 : /*
1870 : * dcos - returns the cosine of arg1 (radians)
1871 : */
1872 : Datum
1873 1162 : dcos(PG_FUNCTION_ARGS)
1874 : {
1875 1162 : float8 arg1 = PG_GETARG_FLOAT8(0);
1876 : float8 result;
1877 :
1878 : /* Per the POSIX spec, return NaN if the input is NaN */
1879 1162 : if (isnan(arg1))
1880 0 : PG_RETURN_FLOAT8(get_float8_nan());
1881 :
1882 : /*
1883 : * cos() is periodic and so theoretically can work for all finite inputs,
1884 : * but some implementations may choose to throw error if the input is so
1885 : * large that there are no significant digits in the result. So we should
1886 : * check for errors. POSIX allows an error to be reported either via
1887 : * errno or via fetestexcept(), but currently we only support checking
1888 : * errno. (fetestexcept() is rumored to report underflow unreasonably
1889 : * early on some platforms, so it's not clear that believing it would be a
1890 : * net improvement anyway.)
1891 : *
1892 : * For infinite inputs, POSIX specifies that the trigonometric functions
1893 : * should return a domain error; but we won't notice that unless the
1894 : * platform reports via errno, so also explicitly test for infinite
1895 : * inputs.
1896 : */
1897 1162 : errno = 0;
1898 1162 : result = cos(arg1);
1899 1162 : if (errno != 0 || isinf(arg1))
1900 0 : ereport(ERROR,
1901 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1902 : errmsg("input is out of range")));
1903 1162 : if (unlikely(isinf(result)))
1904 0 : float_overflow_error();
1905 :
1906 1162 : PG_RETURN_FLOAT8(result);
1907 : }
1908 :
1909 :
1910 : /*
1911 : * dcot - returns the cotangent of arg1 (radians)
1912 : */
1913 : Datum
1914 0 : dcot(PG_FUNCTION_ARGS)
1915 : {
1916 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1917 : float8 result;
1918 :
1919 : /* Per the POSIX spec, return NaN if the input is NaN */
1920 0 : if (isnan(arg1))
1921 0 : PG_RETURN_FLOAT8(get_float8_nan());
1922 :
1923 : /* Be sure to throw an error if the input is infinite --- see dcos() */
1924 0 : errno = 0;
1925 0 : result = tan(arg1);
1926 0 : if (errno != 0 || isinf(arg1))
1927 0 : ereport(ERROR,
1928 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1929 : errmsg("input is out of range")));
1930 :
1931 0 : result = 1.0 / result;
1932 : /* Not checking for overflow because cot(0) == Inf */
1933 :
1934 0 : PG_RETURN_FLOAT8(result);
1935 : }
1936 :
1937 :
1938 : /*
1939 : * dsin - returns the sine of arg1 (radians)
1940 : */
1941 : Datum
1942 904 : dsin(PG_FUNCTION_ARGS)
1943 : {
1944 904 : float8 arg1 = PG_GETARG_FLOAT8(0);
1945 : float8 result;
1946 :
1947 : /* Per the POSIX spec, return NaN if the input is NaN */
1948 904 : if (isnan(arg1))
1949 0 : PG_RETURN_FLOAT8(get_float8_nan());
1950 :
1951 : /* Be sure to throw an error if the input is infinite --- see dcos() */
1952 904 : errno = 0;
1953 904 : result = sin(arg1);
1954 904 : if (errno != 0 || isinf(arg1))
1955 0 : ereport(ERROR,
1956 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1957 : errmsg("input is out of range")));
1958 904 : if (unlikely(isinf(result)))
1959 0 : float_overflow_error();
1960 :
1961 904 : PG_RETURN_FLOAT8(result);
1962 : }
1963 :
1964 :
1965 : /*
1966 : * dtan - returns the tangent of arg1 (radians)
1967 : */
1968 : Datum
1969 0 : dtan(PG_FUNCTION_ARGS)
1970 : {
1971 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1972 : float8 result;
1973 :
1974 : /* Per the POSIX spec, return NaN if the input is NaN */
1975 0 : if (isnan(arg1))
1976 0 : PG_RETURN_FLOAT8(get_float8_nan());
1977 :
1978 : /* Be sure to throw an error if the input is infinite --- see dcos() */
1979 0 : errno = 0;
1980 0 : result = tan(arg1);
1981 0 : if (errno != 0 || isinf(arg1))
1982 0 : ereport(ERROR,
1983 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1984 : errmsg("input is out of range")));
1985 : /* Not checking for overflow because tan(pi/2) == Inf */
1986 :
1987 0 : PG_RETURN_FLOAT8(result);
1988 : }
1989 :
1990 :
1991 : /* ========== DEGREE-BASED TRIGONOMETRIC FUNCTIONS ========== */
1992 :
1993 :
1994 : /*
1995 : * Initialize the cached constants declared at the head of this file
1996 : * (sin_30 etc). The fact that we need those at all, let alone need this
1997 : * Rube-Goldberg-worthy method of initializing them, is because there are
1998 : * compilers out there that will precompute expressions such as sin(constant)
1999 : * using a sin() function different from what will be used at runtime. If we
2000 : * want exact results, we must ensure that none of the scaling constants used
2001 : * in the degree-based trig functions are computed that way. To do so, we
2002 : * compute them from the variables degree_c_thirty etc, which are also really
2003 : * constants, but the compiler cannot assume that.
2004 : *
2005 : * Other hazards we are trying to forestall with this kluge include the
2006 : * possibility that compilers will rearrange the expressions, or compute
2007 : * some intermediate results in registers wider than a standard double.
2008 : *
2009 : * In the places where we use these constants, the typical pattern is like
2010 : * volatile float8 sin_x = sin(x * RADIANS_PER_DEGREE);
2011 : * return (sin_x / sin_30);
2012 : * where we hope to get a value of exactly 1.0 from the division when x = 30.
2013 : * The volatile temporary variable is needed on machines with wide float
2014 : * registers, to ensure that the result of sin(x) is rounded to double width
2015 : * the same as the value of sin_30 has been. Experimentation with gcc shows
2016 : * that marking the temp variable volatile is necessary to make the store and
2017 : * reload actually happen; hopefully the same trick works for other compilers.
2018 : * (gcc's documentation suggests using the -ffloat-store compiler switch to
2019 : * ensure this, but that is compiler-specific and it also pessimizes code in
2020 : * many places where we don't care about this.)
2021 : */
2022 : static void
2023 4 : init_degree_constants(void)
2024 : {
2025 4 : sin_30 = sin(degree_c_thirty * RADIANS_PER_DEGREE);
2026 4 : one_minus_cos_60 = 1.0 - cos(degree_c_sixty * RADIANS_PER_DEGREE);
2027 4 : asin_0_5 = asin(degree_c_one_half);
2028 4 : acos_0_5 = acos(degree_c_one_half);
2029 4 : atan_1_0 = atan(degree_c_one);
2030 4 : tan_45 = sind_q1(degree_c_forty_five) / cosd_q1(degree_c_forty_five);
2031 4 : cot_45 = cosd_q1(degree_c_forty_five) / sind_q1(degree_c_forty_five);
2032 4 : degree_consts_set = true;
2033 4 : }
2034 :
2035 : #define INIT_DEGREE_CONSTANTS() \
2036 : do { \
2037 : if (!degree_consts_set) \
2038 : init_degree_constants(); \
2039 : } while(0)
2040 :
2041 :
2042 : /*
2043 : * asind_q1 - returns the inverse sine of x in degrees, for x in
2044 : * the range [0, 1]. The result is an angle in the
2045 : * first quadrant --- [0, 90] degrees.
2046 : *
2047 : * For the 3 special case inputs (0, 0.5 and 1), this
2048 : * function will return exact values (0, 30 and 90
2049 : * degrees respectively).
2050 : */
2051 : static double
2052 56 : asind_q1(double x)
2053 : {
2054 : /*
2055 : * Stitch together inverse sine and cosine functions for the ranges [0,
2056 : * 0.5] and (0.5, 1]. Each expression below is guaranteed to return
2057 : * exactly 30 for x=0.5, so the result is a continuous monotonic function
2058 : * over the full range.
2059 : */
2060 56 : if (x <= 0.5)
2061 : {
2062 32 : volatile float8 asin_x = asin(x);
2063 :
2064 32 : return (asin_x / asin_0_5) * 30.0;
2065 : }
2066 : else
2067 : {
2068 24 : volatile float8 acos_x = acos(x);
2069 :
2070 24 : return 90.0 - (acos_x / acos_0_5) * 60.0;
2071 : }
2072 : }
2073 :
2074 :
2075 : /*
2076 : * acosd_q1 - returns the inverse cosine of x in degrees, for x in
2077 : * the range [0, 1]. The result is an angle in the
2078 : * first quadrant --- [0, 90] degrees.
2079 : *
2080 : * For the 3 special case inputs (0, 0.5 and 1), this
2081 : * function will return exact values (0, 60 and 90
2082 : * degrees respectively).
2083 : */
2084 : static double
2085 24 : acosd_q1(double x)
2086 : {
2087 : /*
2088 : * Stitch together inverse sine and cosine functions for the ranges [0,
2089 : * 0.5] and (0.5, 1]. Each expression below is guaranteed to return
2090 : * exactly 60 for x=0.5, so the result is a continuous monotonic function
2091 : * over the full range.
2092 : */
2093 24 : if (x <= 0.5)
2094 : {
2095 16 : volatile float8 asin_x = asin(x);
2096 :
2097 16 : return 90.0 - (asin_x / asin_0_5) * 30.0;
2098 : }
2099 : else
2100 : {
2101 8 : volatile float8 acos_x = acos(x);
2102 :
2103 8 : return (acos_x / acos_0_5) * 60.0;
2104 : }
2105 : }
2106 :
2107 :
2108 : /*
2109 : * dacosd - returns the arccos of arg1 (degrees)
2110 : */
2111 : Datum
2112 40 : dacosd(PG_FUNCTION_ARGS)
2113 : {
2114 40 : float8 arg1 = PG_GETARG_FLOAT8(0);
2115 : float8 result;
2116 :
2117 : /* Per the POSIX spec, return NaN if the input is NaN */
2118 40 : if (isnan(arg1))
2119 0 : PG_RETURN_FLOAT8(get_float8_nan());
2120 :
2121 40 : INIT_DEGREE_CONSTANTS();
2122 :
2123 : /*
2124 : * The principal branch of the inverse cosine function maps values in the
2125 : * range [-1, 1] to values in the range [0, 180], so we should reject any
2126 : * inputs outside that range and the result will always be finite.
2127 : */
2128 40 : if (arg1 < -1.0 || arg1 > 1.0)
2129 0 : ereport(ERROR,
2130 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2131 : errmsg("input is out of range")));
2132 :
2133 40 : if (arg1 >= 0.0)
2134 24 : result = acosd_q1(arg1);
2135 : else
2136 16 : result = 90.0 + asind_q1(-arg1);
2137 :
2138 40 : if (unlikely(isinf(result)))
2139 0 : float_overflow_error();
2140 :
2141 40 : PG_RETURN_FLOAT8(result);
2142 : }
2143 :
2144 :
2145 : /*
2146 : * dasind - returns the arcsin of arg1 (degrees)
2147 : */
2148 : Datum
2149 40 : dasind(PG_FUNCTION_ARGS)
2150 : {
2151 40 : float8 arg1 = PG_GETARG_FLOAT8(0);
2152 : float8 result;
2153 :
2154 : /* Per the POSIX spec, return NaN if the input is NaN */
2155 40 : if (isnan(arg1))
2156 0 : PG_RETURN_FLOAT8(get_float8_nan());
2157 :
2158 40 : INIT_DEGREE_CONSTANTS();
2159 :
2160 : /*
2161 : * The principal branch of the inverse sine function maps values in the
2162 : * range [-1, 1] to values in the range [-90, 90], so we should reject any
2163 : * inputs outside that range and the result will always be finite.
2164 : */
2165 40 : if (arg1 < -1.0 || arg1 > 1.0)
2166 0 : ereport(ERROR,
2167 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2168 : errmsg("input is out of range")));
2169 :
2170 40 : if (arg1 >= 0.0)
2171 24 : result = asind_q1(arg1);
2172 : else
2173 16 : result = -asind_q1(-arg1);
2174 :
2175 40 : if (unlikely(isinf(result)))
2176 0 : float_overflow_error();
2177 :
2178 40 : PG_RETURN_FLOAT8(result);
2179 : }
2180 :
2181 :
2182 : /*
2183 : * datand - returns the arctan of arg1 (degrees)
2184 : */
2185 : Datum
2186 40 : datand(PG_FUNCTION_ARGS)
2187 : {
2188 40 : float8 arg1 = PG_GETARG_FLOAT8(0);
2189 : float8 result;
2190 : volatile float8 atan_arg1;
2191 :
2192 : /* Per the POSIX spec, return NaN if the input is NaN */
2193 40 : if (isnan(arg1))
2194 0 : PG_RETURN_FLOAT8(get_float8_nan());
2195 :
2196 40 : INIT_DEGREE_CONSTANTS();
2197 :
2198 : /*
2199 : * The principal branch of the inverse tangent function maps all inputs to
2200 : * values in the range [-90, 90], so the result should always be finite,
2201 : * even if the input is infinite. Additionally, we take care to ensure
2202 : * than when arg1 is 1, the result is exactly 45.
2203 : */
2204 40 : atan_arg1 = atan(arg1);
2205 40 : result = (atan_arg1 / atan_1_0) * 45.0;
2206 :
2207 40 : if (unlikely(isinf(result)))
2208 0 : float_overflow_error();
2209 :
2210 40 : PG_RETURN_FLOAT8(result);
2211 : }
2212 :
2213 :
2214 : /*
2215 : * atan2d - returns the arctan of arg1/arg2 (degrees)
2216 : */
2217 : Datum
2218 40 : datan2d(PG_FUNCTION_ARGS)
2219 : {
2220 40 : float8 arg1 = PG_GETARG_FLOAT8(0);
2221 40 : float8 arg2 = PG_GETARG_FLOAT8(1);
2222 : float8 result;
2223 : volatile float8 atan2_arg1_arg2;
2224 :
2225 : /* Per the POSIX spec, return NaN if either input is NaN */
2226 40 : if (isnan(arg1) || isnan(arg2))
2227 0 : PG_RETURN_FLOAT8(get_float8_nan());
2228 :
2229 40 : INIT_DEGREE_CONSTANTS();
2230 :
2231 : /*
2232 : * atan2d maps all inputs to values in the range [-180, 180], so the
2233 : * result should always be finite, even if the inputs are infinite.
2234 : *
2235 : * Note: this coding assumes that atan(1.0) is a suitable scaling constant
2236 : * to get an exact result from atan2(). This might well fail on us at
2237 : * some point, requiring us to decide exactly what inputs we think we're
2238 : * going to guarantee an exact result for.
2239 : */
2240 40 : atan2_arg1_arg2 = atan2(arg1, arg2);
2241 40 : result = (atan2_arg1_arg2 / atan_1_0) * 45.0;
2242 :
2243 40 : if (unlikely(isinf(result)))
2244 0 : float_overflow_error();
2245 :
2246 40 : PG_RETURN_FLOAT8(result);
2247 : }
2248 :
2249 :
2250 : /*
2251 : * sind_0_to_30 - returns the sine of an angle that lies between 0 and
2252 : * 30 degrees. This will return exactly 0 when x is 0,
2253 : * and exactly 0.5 when x is 30 degrees.
2254 : */
2255 : static double
2256 212 : sind_0_to_30(double x)
2257 : {
2258 212 : volatile float8 sin_x = sin(x * RADIANS_PER_DEGREE);
2259 :
2260 212 : return (sin_x / sin_30) / 2.0;
2261 : }
2262 :
2263 :
2264 : /*
2265 : * cosd_0_to_60 - returns the cosine of an angle that lies between 0
2266 : * and 60 degrees. This will return exactly 1 when x
2267 : * is 0, and exactly 0.5 when x is 60 degrees.
2268 : */
2269 : static double
2270 356 : cosd_0_to_60(double x)
2271 : {
2272 356 : volatile float8 one_minus_cos_x = 1.0 - cos(x * RADIANS_PER_DEGREE);
2273 :
2274 356 : return 1.0 - (one_minus_cos_x / one_minus_cos_60) / 2.0;
2275 : }
2276 :
2277 :
2278 : /*
2279 : * sind_q1 - returns the sine of an angle in the first quadrant
2280 : * (0 to 90 degrees).
2281 : */
2282 : static double
2283 284 : sind_q1(double x)
2284 : {
2285 : /*
2286 : * Stitch together the sine and cosine functions for the ranges [0, 30]
2287 : * and (30, 90]. These guarantee to return exact answers at their
2288 : * endpoints, so the overall result is a continuous monotonic function
2289 : * that gives exact results when x = 0, 30 and 90 degrees.
2290 : */
2291 284 : if (x <= 30.0)
2292 140 : return sind_0_to_30(x);
2293 : else
2294 144 : return cosd_0_to_60(90.0 - x);
2295 : }
2296 :
2297 :
2298 : /*
2299 : * cosd_q1 - returns the cosine of an angle in the first quadrant
2300 : * (0 to 90 degrees).
2301 : */
2302 : static double
2303 284 : cosd_q1(double x)
2304 : {
2305 : /*
2306 : * Stitch together the sine and cosine functions for the ranges [0, 60]
2307 : * and (60, 90]. These guarantee to return exact answers at their
2308 : * endpoints, so the overall result is a continuous monotonic function
2309 : * that gives exact results when x = 0, 60 and 90 degrees.
2310 : */
2311 284 : if (x <= 60.0)
2312 212 : return cosd_0_to_60(x);
2313 : else
2314 72 : return sind_0_to_30(90.0 - x);
2315 : }
2316 :
2317 :
2318 : /*
2319 : * dcosd - returns the cosine of arg1 (degrees)
2320 : */
2321 : Datum
2322 132 : dcosd(PG_FUNCTION_ARGS)
2323 : {
2324 132 : float8 arg1 = PG_GETARG_FLOAT8(0);
2325 : float8 result;
2326 132 : int sign = 1;
2327 :
2328 : /*
2329 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2330 : * if the input is infinite.
2331 : */
2332 132 : if (isnan(arg1))
2333 0 : PG_RETURN_FLOAT8(get_float8_nan());
2334 :
2335 132 : if (isinf(arg1))
2336 0 : ereport(ERROR,
2337 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2338 : errmsg("input is out of range")));
2339 :
2340 132 : INIT_DEGREE_CONSTANTS();
2341 :
2342 : /* Reduce the range of the input to [0,90] degrees */
2343 132 : arg1 = fmod(arg1, 360.0);
2344 :
2345 132 : if (arg1 < 0.0)
2346 : {
2347 : /* cosd(-x) = cosd(x) */
2348 0 : arg1 = -arg1;
2349 : }
2350 :
2351 132 : if (arg1 > 180.0)
2352 : {
2353 : /* cosd(360-x) = cosd(x) */
2354 36 : arg1 = 360.0 - arg1;
2355 : }
2356 :
2357 132 : if (arg1 > 90.0)
2358 : {
2359 : /* cosd(180-x) = -cosd(x) */
2360 36 : arg1 = 180.0 - arg1;
2361 36 : sign = -sign;
2362 : }
2363 :
2364 132 : result = sign * cosd_q1(arg1);
2365 :
2366 132 : if (unlikely(isinf(result)))
2367 0 : float_overflow_error();
2368 :
2369 132 : PG_RETURN_FLOAT8(result);
2370 : }
2371 :
2372 :
2373 : /*
2374 : * dcotd - returns the cotangent of arg1 (degrees)
2375 : */
2376 : Datum
2377 72 : dcotd(PG_FUNCTION_ARGS)
2378 : {
2379 72 : float8 arg1 = PG_GETARG_FLOAT8(0);
2380 : float8 result;
2381 : volatile float8 cot_arg1;
2382 72 : int sign = 1;
2383 :
2384 : /*
2385 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2386 : * if the input is infinite.
2387 : */
2388 72 : if (isnan(arg1))
2389 0 : PG_RETURN_FLOAT8(get_float8_nan());
2390 :
2391 72 : if (isinf(arg1))
2392 0 : ereport(ERROR,
2393 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2394 : errmsg("input is out of range")));
2395 :
2396 72 : INIT_DEGREE_CONSTANTS();
2397 :
2398 : /* Reduce the range of the input to [0,90] degrees */
2399 72 : arg1 = fmod(arg1, 360.0);
2400 :
2401 72 : if (arg1 < 0.0)
2402 : {
2403 : /* cotd(-x) = -cotd(x) */
2404 0 : arg1 = -arg1;
2405 0 : sign = -sign;
2406 : }
2407 :
2408 72 : if (arg1 > 180.0)
2409 : {
2410 : /* cotd(360-x) = -cotd(x) */
2411 24 : arg1 = 360.0 - arg1;
2412 24 : sign = -sign;
2413 : }
2414 :
2415 72 : if (arg1 > 90.0)
2416 : {
2417 : /* cotd(180-x) = -cotd(x) */
2418 24 : arg1 = 180.0 - arg1;
2419 24 : sign = -sign;
2420 : }
2421 :
2422 72 : cot_arg1 = cosd_q1(arg1) / sind_q1(arg1);
2423 72 : result = sign * (cot_arg1 / cot_45);
2424 :
2425 : /*
2426 : * On some machines we get cotd(270) = minus zero, but this isn't always
2427 : * true. For portability, and because the user constituency for this
2428 : * function probably doesn't want minus zero, force it to plain zero.
2429 : */
2430 72 : if (result == 0.0)
2431 16 : result = 0.0;
2432 :
2433 : /* Not checking for overflow because cotd(0) == Inf */
2434 :
2435 72 : PG_RETURN_FLOAT8(result);
2436 : }
2437 :
2438 :
2439 : /*
2440 : * dsind - returns the sine of arg1 (degrees)
2441 : */
2442 : Datum
2443 132 : dsind(PG_FUNCTION_ARGS)
2444 : {
2445 132 : float8 arg1 = PG_GETARG_FLOAT8(0);
2446 : float8 result;
2447 132 : int sign = 1;
2448 :
2449 : /*
2450 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2451 : * if the input is infinite.
2452 : */
2453 132 : if (isnan(arg1))
2454 0 : PG_RETURN_FLOAT8(get_float8_nan());
2455 :
2456 132 : if (isinf(arg1))
2457 0 : ereport(ERROR,
2458 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2459 : errmsg("input is out of range")));
2460 :
2461 132 : INIT_DEGREE_CONSTANTS();
2462 :
2463 : /* Reduce the range of the input to [0,90] degrees */
2464 132 : arg1 = fmod(arg1, 360.0);
2465 :
2466 132 : if (arg1 < 0.0)
2467 : {
2468 : /* sind(-x) = -sind(x) */
2469 0 : arg1 = -arg1;
2470 0 : sign = -sign;
2471 : }
2472 :
2473 132 : if (arg1 > 180.0)
2474 : {
2475 : /* sind(360-x) = -sind(x) */
2476 36 : arg1 = 360.0 - arg1;
2477 36 : sign = -sign;
2478 : }
2479 :
2480 132 : if (arg1 > 90.0)
2481 : {
2482 : /* sind(180-x) = sind(x) */
2483 36 : arg1 = 180.0 - arg1;
2484 : }
2485 :
2486 132 : result = sign * sind_q1(arg1);
2487 :
2488 132 : if (unlikely(isinf(result)))
2489 0 : float_overflow_error();
2490 :
2491 132 : PG_RETURN_FLOAT8(result);
2492 : }
2493 :
2494 :
2495 : /*
2496 : * dtand - returns the tangent of arg1 (degrees)
2497 : */
2498 : Datum
2499 72 : dtand(PG_FUNCTION_ARGS)
2500 : {
2501 72 : float8 arg1 = PG_GETARG_FLOAT8(0);
2502 : float8 result;
2503 : volatile float8 tan_arg1;
2504 72 : int sign = 1;
2505 :
2506 : /*
2507 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2508 : * if the input is infinite.
2509 : */
2510 72 : if (isnan(arg1))
2511 0 : PG_RETURN_FLOAT8(get_float8_nan());
2512 :
2513 72 : if (isinf(arg1))
2514 0 : ereport(ERROR,
2515 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2516 : errmsg("input is out of range")));
2517 :
2518 72 : INIT_DEGREE_CONSTANTS();
2519 :
2520 : /* Reduce the range of the input to [0,90] degrees */
2521 72 : arg1 = fmod(arg1, 360.0);
2522 :
2523 72 : if (arg1 < 0.0)
2524 : {
2525 : /* tand(-x) = -tand(x) */
2526 0 : arg1 = -arg1;
2527 0 : sign = -sign;
2528 : }
2529 :
2530 72 : if (arg1 > 180.0)
2531 : {
2532 : /* tand(360-x) = -tand(x) */
2533 24 : arg1 = 360.0 - arg1;
2534 24 : sign = -sign;
2535 : }
2536 :
2537 72 : if (arg1 > 90.0)
2538 : {
2539 : /* tand(180-x) = -tand(x) */
2540 24 : arg1 = 180.0 - arg1;
2541 24 : sign = -sign;
2542 : }
2543 :
2544 72 : tan_arg1 = sind_q1(arg1) / cosd_q1(arg1);
2545 72 : result = sign * (tan_arg1 / tan_45);
2546 :
2547 : /*
2548 : * On some machines we get tand(180) = minus zero, but this isn't always
2549 : * true. For portability, and because the user constituency for this
2550 : * function probably doesn't want minus zero, force it to plain zero.
2551 : */
2552 72 : if (result == 0.0)
2553 24 : result = 0.0;
2554 :
2555 : /* Not checking for overflow because tand(90) == Inf */
2556 :
2557 72 : PG_RETURN_FLOAT8(result);
2558 : }
2559 :
2560 :
2561 : /*
2562 : * degrees - returns degrees converted from radians
2563 : */
2564 : Datum
2565 80 : degrees(PG_FUNCTION_ARGS)
2566 : {
2567 80 : float8 arg1 = PG_GETARG_FLOAT8(0);
2568 :
2569 80 : PG_RETURN_FLOAT8(float8_div(arg1, RADIANS_PER_DEGREE));
2570 : }
2571 :
2572 :
2573 : /*
2574 : * dpi - returns the constant PI
2575 : */
2576 : Datum
2577 182 : dpi(PG_FUNCTION_ARGS)
2578 : {
2579 182 : PG_RETURN_FLOAT8(M_PI);
2580 : }
2581 :
2582 :
2583 : /*
2584 : * radians - returns radians converted from degrees
2585 : */
2586 : Datum
2587 1910 : radians(PG_FUNCTION_ARGS)
2588 : {
2589 1910 : float8 arg1 = PG_GETARG_FLOAT8(0);
2590 :
2591 1910 : PG_RETURN_FLOAT8(float8_mul(arg1, RADIANS_PER_DEGREE));
2592 : }
2593 :
2594 :
2595 : /* ========== HYPERBOLIC FUNCTIONS ========== */
2596 :
2597 :
2598 : /*
2599 : * dsinh - returns the hyperbolic sine of arg1
2600 : */
2601 : Datum
2602 16 : dsinh(PG_FUNCTION_ARGS)
2603 : {
2604 16 : float8 arg1 = PG_GETARG_FLOAT8(0);
2605 : float8 result;
2606 :
2607 16 : errno = 0;
2608 16 : result = sinh(arg1);
2609 :
2610 : /*
2611 : * if an ERANGE error occurs, it means there is an overflow. For sinh,
2612 : * the result should be either -infinity or infinity, depending on the
2613 : * sign of arg1.
2614 : */
2615 16 : if (errno == ERANGE)
2616 : {
2617 0 : if (arg1 < 0)
2618 0 : result = -get_float8_infinity();
2619 : else
2620 0 : result = get_float8_infinity();
2621 : }
2622 :
2623 16 : PG_RETURN_FLOAT8(result);
2624 : }
2625 :
2626 :
2627 : /*
2628 : * dcosh - returns the hyperbolic cosine of arg1
2629 : */
2630 : Datum
2631 16 : dcosh(PG_FUNCTION_ARGS)
2632 : {
2633 16 : float8 arg1 = PG_GETARG_FLOAT8(0);
2634 : float8 result;
2635 :
2636 16 : errno = 0;
2637 16 : result = cosh(arg1);
2638 :
2639 : /*
2640 : * if an ERANGE error occurs, it means there is an overflow. As cosh is
2641 : * always positive, it always means the result is positive infinity.
2642 : */
2643 16 : if (errno == ERANGE)
2644 0 : result = get_float8_infinity();
2645 :
2646 16 : if (unlikely(result == 0.0))
2647 0 : float_underflow_error();
2648 :
2649 16 : PG_RETURN_FLOAT8(result);
2650 : }
2651 :
2652 : /*
2653 : * dtanh - returns the hyperbolic tangent of arg1
2654 : */
2655 : Datum
2656 16 : dtanh(PG_FUNCTION_ARGS)
2657 : {
2658 16 : float8 arg1 = PG_GETARG_FLOAT8(0);
2659 : float8 result;
2660 :
2661 : /*
2662 : * For tanh, we don't need an errno check because it never overflows.
2663 : */
2664 16 : result = tanh(arg1);
2665 :
2666 16 : if (unlikely(isinf(result)))
2667 0 : float_overflow_error();
2668 :
2669 16 : PG_RETURN_FLOAT8(result);
2670 : }
2671 :
2672 : /*
2673 : * dasinh - returns the inverse hyperbolic sine of arg1
2674 : */
2675 : Datum
2676 16 : dasinh(PG_FUNCTION_ARGS)
2677 : {
2678 16 : float8 arg1 = PG_GETARG_FLOAT8(0);
2679 : float8 result;
2680 :
2681 : /*
2682 : * For asinh, we don't need an errno check because it never overflows.
2683 : */
2684 16 : result = asinh(arg1);
2685 :
2686 16 : PG_RETURN_FLOAT8(result);
2687 : }
2688 :
2689 : /*
2690 : * dacosh - returns the inverse hyperbolic cosine of arg1
2691 : */
2692 : Datum
2693 12 : dacosh(PG_FUNCTION_ARGS)
2694 : {
2695 12 : float8 arg1 = PG_GETARG_FLOAT8(0);
2696 : float8 result;
2697 :
2698 : /*
2699 : * acosh is only defined for inputs >= 1.0. By checking this ourselves,
2700 : * we need not worry about checking for an EDOM error, which is a good
2701 : * thing because some implementations will report that for NaN. Otherwise,
2702 : * no error is possible.
2703 : */
2704 12 : if (arg1 < 1.0)
2705 4 : ereport(ERROR,
2706 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2707 : errmsg("input is out of range")));
2708 :
2709 8 : result = acosh(arg1);
2710 :
2711 8 : PG_RETURN_FLOAT8(result);
2712 : }
2713 :
2714 : /*
2715 : * datanh - returns the inverse hyperbolic tangent of arg1
2716 : */
2717 : Datum
2718 16 : datanh(PG_FUNCTION_ARGS)
2719 : {
2720 16 : float8 arg1 = PG_GETARG_FLOAT8(0);
2721 : float8 result;
2722 :
2723 : /*
2724 : * atanh is only defined for inputs between -1 and 1. By checking this
2725 : * ourselves, we need not worry about checking for an EDOM error, which is
2726 : * a good thing because some implementations will report that for NaN.
2727 : */
2728 16 : if (arg1 < -1.0 || arg1 > 1.0)
2729 8 : ereport(ERROR,
2730 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2731 : errmsg("input is out of range")));
2732 :
2733 : /*
2734 : * Also handle the infinity cases ourselves; this is helpful because old
2735 : * glibc versions may produce the wrong errno for this. All other inputs
2736 : * cannot produce an error.
2737 : */
2738 8 : if (arg1 == -1.0)
2739 0 : result = -get_float8_infinity();
2740 8 : else if (arg1 == 1.0)
2741 0 : result = get_float8_infinity();
2742 : else
2743 8 : result = atanh(arg1);
2744 :
2745 8 : PG_RETURN_FLOAT8(result);
2746 : }
2747 :
2748 :
2749 : /*
2750 : * drandom - returns a random number
2751 : */
2752 : Datum
2753 663884 : drandom(PG_FUNCTION_ARGS)
2754 : {
2755 : float8 result;
2756 :
2757 : /* Initialize random seed, if not done yet in this process */
2758 663884 : if (unlikely(!drandom_seed_set))
2759 : {
2760 : /*
2761 : * If possible, initialize the seed using high-quality random bits.
2762 : * Should that fail for some reason, we fall back on a lower-quality
2763 : * seed based on current time and PID.
2764 : */
2765 62 : if (!pg_strong_random(drandom_seed, sizeof(drandom_seed)))
2766 : {
2767 0 : TimestampTz now = GetCurrentTimestamp();
2768 : uint64 iseed;
2769 :
2770 : /* Mix the PID with the most predictable bits of the timestamp */
2771 0 : iseed = (uint64) now ^ ((uint64) MyProcPid << 32);
2772 0 : drandom_seed[0] = (unsigned short) iseed;
2773 0 : drandom_seed[1] = (unsigned short) (iseed >> 16);
2774 0 : drandom_seed[2] = (unsigned short) (iseed >> 32);
2775 : }
2776 62 : drandom_seed_set = true;
2777 : }
2778 :
2779 : /* pg_erand48 produces desired result range [0.0 - 1.0) */
2780 663884 : result = pg_erand48(drandom_seed);
2781 :
2782 663884 : PG_RETURN_FLOAT8(result);
2783 : }
2784 :
2785 :
2786 : /*
2787 : * setseed - set seed for the random number generator
2788 : */
2789 : Datum
2790 2 : setseed(PG_FUNCTION_ARGS)
2791 : {
2792 2 : float8 seed = PG_GETARG_FLOAT8(0);
2793 : uint64 iseed;
2794 :
2795 2 : if (seed < -1 || seed > 1 || isnan(seed))
2796 0 : ereport(ERROR,
2797 : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
2798 : errmsg("setseed parameter %g is out of allowed range [-1,1]",
2799 : seed)));
2800 :
2801 : /* Use sign bit + 47 fractional bits to fill drandom_seed[] */
2802 2 : iseed = (int64) (seed * (float8) UINT64CONST(0x7FFFFFFFFFFF));
2803 2 : drandom_seed[0] = (unsigned short) iseed;
2804 2 : drandom_seed[1] = (unsigned short) (iseed >> 16);
2805 2 : drandom_seed[2] = (unsigned short) (iseed >> 32);
2806 2 : drandom_seed_set = true;
2807 :
2808 2 : PG_RETURN_VOID();
2809 : }
2810 :
2811 :
2812 :
2813 : /*
2814 : * =========================
2815 : * FLOAT AGGREGATE OPERATORS
2816 : * =========================
2817 : *
2818 : * float8_accum - accumulate for AVG(), variance aggregates, etc.
2819 : * float4_accum - same, but input data is float4
2820 : * float8_avg - produce final result for float AVG()
2821 : * float8_var_samp - produce final result for float VAR_SAMP()
2822 : * float8_var_pop - produce final result for float VAR_POP()
2823 : * float8_stddev_samp - produce final result for float STDDEV_SAMP()
2824 : * float8_stddev_pop - produce final result for float STDDEV_POP()
2825 : *
2826 : * The naive schoolbook implementation of these aggregates works by
2827 : * accumulating sum(X) and sum(X^2). However, this approach suffers from
2828 : * large rounding errors in the final computation of quantities like the
2829 : * population variance (N*sum(X^2) - sum(X)^2) / N^2, since each of the
2830 : * intermediate terms is potentially very large, while the difference is often
2831 : * quite small.
2832 : *
2833 : * Instead we use the Youngs-Cramer algorithm [1] which works by accumulating
2834 : * Sx=sum(X) and Sxx=sum((X-Sx/N)^2), using a numerically stable algorithm to
2835 : * incrementally update those quantities. The final computations of each of
2836 : * the aggregate values is then trivial and gives more accurate results (for
2837 : * example, the population variance is just Sxx/N). This algorithm is also
2838 : * fairly easy to generalize to allow parallel execution without loss of
2839 : * precision (see, for example, [2]). For more details, and a comparison of
2840 : * this with other algorithms, see [3].
2841 : *
2842 : * The transition datatype for all these aggregates is a 3-element array
2843 : * of float8, holding the values N, Sx, Sxx in that order.
2844 : *
2845 : * Note that we represent N as a float to avoid having to build a special
2846 : * datatype. Given a reasonable floating-point implementation, there should
2847 : * be no accuracy loss unless N exceeds 2 ^ 52 or so (by which time the
2848 : * user will have doubtless lost interest anyway...)
2849 : *
2850 : * [1] Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms,
2851 : * E. A. Youngs and E. M. Cramer, Technometrics Vol 13, No 3, August 1971.
2852 : *
2853 : * [2] Updating Formulae and a Pairwise Algorithm for Computing Sample
2854 : * Variances, T. F. Chan, G. H. Golub & R. J. LeVeque, COMPSTAT 1982.
2855 : *
2856 : * [3] Numerically Stable Parallel Computation of (Co-)Variance, Erich
2857 : * Schubert and Michael Gertz, Proceedings of the 30th International
2858 : * Conference on Scientific and Statistical Database Management, 2018.
2859 : */
2860 :
2861 : static float8 *
2862 1062 : check_float8_array(ArrayType *transarray, const char *caller, int n)
2863 : {
2864 : /*
2865 : * We expect the input to be an N-element float array; verify that. We
2866 : * don't need to use deconstruct_array() since the array data is just
2867 : * going to look like a C array of N float8 values.
2868 : */
2869 1062 : if (ARR_NDIM(transarray) != 1 ||
2870 1062 : ARR_DIMS(transarray)[0] != n ||
2871 1062 : ARR_HASNULL(transarray) ||
2872 1062 : ARR_ELEMTYPE(transarray) != FLOAT8OID)
2873 0 : elog(ERROR, "%s: expected %d-element float8 array", caller, n);
2874 1062 : return (float8 *) ARR_DATA_PTR(transarray);
2875 : }
2876 :
2877 : /*
2878 : * float8_combine
2879 : *
2880 : * An aggregate combine function used to combine two 3 fields
2881 : * aggregate transition data into a single transition data.
2882 : * This function is used only in two stage aggregation and
2883 : * shouldn't be called outside aggregate context.
2884 : */
2885 : Datum
2886 12 : float8_combine(PG_FUNCTION_ARGS)
2887 : {
2888 12 : ArrayType *transarray1 = PG_GETARG_ARRAYTYPE_P(0);
2889 12 : ArrayType *transarray2 = PG_GETARG_ARRAYTYPE_P(1);
2890 : float8 *transvalues1;
2891 : float8 *transvalues2;
2892 : float8 N1,
2893 : Sx1,
2894 : Sxx1,
2895 : N2,
2896 : Sx2,
2897 : Sxx2,
2898 : tmp,
2899 : N,
2900 : Sx,
2901 : Sxx;
2902 :
2903 12 : transvalues1 = check_float8_array(transarray1, "float8_combine", 3);
2904 12 : transvalues2 = check_float8_array(transarray2, "float8_combine", 3);
2905 :
2906 12 : N1 = transvalues1[0];
2907 12 : Sx1 = transvalues1[1];
2908 12 : Sxx1 = transvalues1[2];
2909 :
2910 12 : N2 = transvalues2[0];
2911 12 : Sx2 = transvalues2[1];
2912 12 : Sxx2 = transvalues2[2];
2913 :
2914 : /*--------------------
2915 : * The transition values combine using a generalization of the
2916 : * Youngs-Cramer algorithm as follows:
2917 : *
2918 : * N = N1 + N2
2919 : * Sx = Sx1 + Sx2
2920 : * Sxx = Sxx1 + Sxx2 + N1 * N2 * (Sx1/N1 - Sx2/N2)^2 / N;
2921 : *
2922 : * It's worth handling the special cases N1 = 0 and N2 = 0 separately
2923 : * since those cases are trivial, and we then don't need to worry about
2924 : * division-by-zero errors in the general case.
2925 : *--------------------
2926 : */
2927 12 : if (N1 == 0.0)
2928 : {
2929 4 : N = N2;
2930 4 : Sx = Sx2;
2931 4 : Sxx = Sxx2;
2932 : }
2933 8 : else if (N2 == 0.0)
2934 : {
2935 4 : N = N1;
2936 4 : Sx = Sx1;
2937 4 : Sxx = Sxx1;
2938 : }
2939 : else
2940 : {
2941 4 : N = N1 + N2;
2942 4 : Sx = float8_pl(Sx1, Sx2);
2943 4 : tmp = Sx1 / N1 - Sx2 / N2;
2944 4 : Sxx = Sxx1 + Sxx2 + N1 * N2 * tmp * tmp / N;
2945 4 : if (unlikely(isinf(Sxx)) && !isinf(Sxx1) && !isinf(Sxx2))
2946 0 : float_overflow_error();
2947 : }
2948 :
2949 : /*
2950 : * If we're invoked as an aggregate, we can cheat and modify our first
2951 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
2952 : * new array with the updated transition data and return it.
2953 : */
2954 12 : if (AggCheckCallContext(fcinfo, NULL))
2955 : {
2956 0 : transvalues1[0] = N;
2957 0 : transvalues1[1] = Sx;
2958 0 : transvalues1[2] = Sxx;
2959 :
2960 0 : PG_RETURN_ARRAYTYPE_P(transarray1);
2961 : }
2962 : else
2963 : {
2964 : Datum transdatums[3];
2965 : ArrayType *result;
2966 :
2967 12 : transdatums[0] = Float8GetDatumFast(N);
2968 12 : transdatums[1] = Float8GetDatumFast(Sx);
2969 12 : transdatums[2] = Float8GetDatumFast(Sxx);
2970 :
2971 12 : result = construct_array(transdatums, 3,
2972 : FLOAT8OID,
2973 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
2974 :
2975 12 : PG_RETURN_ARRAYTYPE_P(result);
2976 : }
2977 : }
2978 :
2979 : Datum
2980 308 : float8_accum(PG_FUNCTION_ARGS)
2981 : {
2982 308 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
2983 308 : float8 newval = PG_GETARG_FLOAT8(1);
2984 : float8 *transvalues;
2985 : float8 N,
2986 : Sx,
2987 : Sxx,
2988 : tmp;
2989 :
2990 308 : transvalues = check_float8_array(transarray, "float8_accum", 3);
2991 308 : N = transvalues[0];
2992 308 : Sx = transvalues[1];
2993 308 : Sxx = transvalues[2];
2994 :
2995 : /*
2996 : * Use the Youngs-Cramer algorithm to incorporate the new value into the
2997 : * transition values.
2998 : */
2999 308 : N += 1.0;
3000 308 : Sx += newval;
3001 308 : if (transvalues[0] > 0.0)
3002 : {
3003 242 : tmp = newval * N - Sx;
3004 242 : Sxx += tmp * tmp / (N * transvalues[0]);
3005 :
3006 : /*
3007 : * Overflow check. We only report an overflow error when finite
3008 : * inputs lead to infinite results. Note also that Sxx should be NaN
3009 : * if any of the inputs are infinite, so we intentionally prevent Sxx
3010 : * from becoming infinite.
3011 : */
3012 242 : if (isinf(Sx) || isinf(Sxx))
3013 : {
3014 16 : if (!isinf(transvalues[1]) && !isinf(newval))
3015 0 : float_overflow_error();
3016 :
3017 16 : Sxx = get_float8_nan();
3018 : }
3019 : }
3020 : else
3021 : {
3022 : /*
3023 : * At the first input, we normally can leave Sxx as 0. However, if
3024 : * the first input is Inf or NaN, we'd better force Sxx to NaN;
3025 : * otherwise we will falsely report variance zero when there are no
3026 : * more inputs.
3027 : */
3028 66 : if (isnan(newval) || isinf(newval))
3029 32 : Sxx = get_float8_nan();
3030 : }
3031 :
3032 : /*
3033 : * If we're invoked as an aggregate, we can cheat and modify our first
3034 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3035 : * new array with the updated transition data and return it.
3036 : */
3037 308 : if (AggCheckCallContext(fcinfo, NULL))
3038 : {
3039 304 : transvalues[0] = N;
3040 304 : transvalues[1] = Sx;
3041 304 : transvalues[2] = Sxx;
3042 :
3043 304 : PG_RETURN_ARRAYTYPE_P(transarray);
3044 : }
3045 : else
3046 : {
3047 : Datum transdatums[3];
3048 : ArrayType *result;
3049 :
3050 4 : transdatums[0] = Float8GetDatumFast(N);
3051 4 : transdatums[1] = Float8GetDatumFast(Sx);
3052 4 : transdatums[2] = Float8GetDatumFast(Sxx);
3053 :
3054 4 : result = construct_array(transdatums, 3,
3055 : FLOAT8OID,
3056 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
3057 :
3058 4 : PG_RETURN_ARRAYTYPE_P(result);
3059 : }
3060 : }
3061 :
3062 : Datum
3063 192 : float4_accum(PG_FUNCTION_ARGS)
3064 : {
3065 192 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3066 :
3067 : /* do computations as float8 */
3068 192 : float8 newval = PG_GETARG_FLOAT4(1);
3069 : float8 *transvalues;
3070 : float8 N,
3071 : Sx,
3072 : Sxx,
3073 : tmp;
3074 :
3075 192 : transvalues = check_float8_array(transarray, "float4_accum", 3);
3076 192 : N = transvalues[0];
3077 192 : Sx = transvalues[1];
3078 192 : Sxx = transvalues[2];
3079 :
3080 : /*
3081 : * Use the Youngs-Cramer algorithm to incorporate the new value into the
3082 : * transition values.
3083 : */
3084 192 : N += 1.0;
3085 192 : Sx += newval;
3086 192 : if (transvalues[0] > 0.0)
3087 : {
3088 136 : tmp = newval * N - Sx;
3089 136 : Sxx += tmp * tmp / (N * transvalues[0]);
3090 :
3091 : /*
3092 : * Overflow check. We only report an overflow error when finite
3093 : * inputs lead to infinite results. Note also that Sxx should be NaN
3094 : * if any of the inputs are infinite, so we intentionally prevent Sxx
3095 : * from becoming infinite.
3096 : */
3097 136 : if (isinf(Sx) || isinf(Sxx))
3098 : {
3099 0 : if (!isinf(transvalues[1]) && !isinf(newval))
3100 0 : float_overflow_error();
3101 :
3102 0 : Sxx = get_float8_nan();
3103 : }
3104 : }
3105 : else
3106 : {
3107 : /*
3108 : * At the first input, we normally can leave Sxx as 0. However, if
3109 : * the first input is Inf or NaN, we'd better force Sxx to NaN;
3110 : * otherwise we will falsely report variance zero when there are no
3111 : * more inputs.
3112 : */
3113 56 : if (isnan(newval) || isinf(newval))
3114 16 : Sxx = get_float8_nan();
3115 : }
3116 :
3117 : /*
3118 : * If we're invoked as an aggregate, we can cheat and modify our first
3119 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3120 : * new array with the updated transition data and return it.
3121 : */
3122 192 : if (AggCheckCallContext(fcinfo, NULL))
3123 : {
3124 192 : transvalues[0] = N;
3125 192 : transvalues[1] = Sx;
3126 192 : transvalues[2] = Sxx;
3127 :
3128 192 : PG_RETURN_ARRAYTYPE_P(transarray);
3129 : }
3130 : else
3131 : {
3132 : Datum transdatums[3];
3133 : ArrayType *result;
3134 :
3135 0 : transdatums[0] = Float8GetDatumFast(N);
3136 0 : transdatums[1] = Float8GetDatumFast(Sx);
3137 0 : transdatums[2] = Float8GetDatumFast(Sxx);
3138 :
3139 0 : result = construct_array(transdatums, 3,
3140 : FLOAT8OID,
3141 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
3142 :
3143 0 : PG_RETURN_ARRAYTYPE_P(result);
3144 : }
3145 : }
3146 :
3147 : Datum
3148 42 : float8_avg(PG_FUNCTION_ARGS)
3149 : {
3150 42 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3151 : float8 *transvalues;
3152 : float8 N,
3153 : Sx;
3154 :
3155 42 : transvalues = check_float8_array(transarray, "float8_avg", 3);
3156 42 : N = transvalues[0];
3157 42 : Sx = transvalues[1];
3158 : /* ignore Sxx */
3159 :
3160 : /* SQL defines AVG of no values to be NULL */
3161 42 : if (N == 0.0)
3162 4 : PG_RETURN_NULL();
3163 :
3164 38 : PG_RETURN_FLOAT8(Sx / N);
3165 : }
3166 :
3167 : Datum
3168 56 : float8_var_pop(PG_FUNCTION_ARGS)
3169 : {
3170 56 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3171 : float8 *transvalues;
3172 : float8 N,
3173 : Sxx;
3174 :
3175 56 : transvalues = check_float8_array(transarray, "float8_var_pop", 3);
3176 56 : N = transvalues[0];
3177 : /* ignore Sx */
3178 56 : Sxx = transvalues[2];
3179 :
3180 : /* Population variance is undefined when N is 0, so return NULL */
3181 56 : if (N == 0.0)
3182 0 : PG_RETURN_NULL();
3183 :
3184 : /* Note that Sxx is guaranteed to be non-negative */
3185 :
3186 56 : PG_RETURN_FLOAT8(Sxx / N);
3187 : }
3188 :
3189 : Datum
3190 28 : float8_var_samp(PG_FUNCTION_ARGS)
3191 : {
3192 28 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3193 : float8 *transvalues;
3194 : float8 N,
3195 : Sxx;
3196 :
3197 28 : transvalues = check_float8_array(transarray, "float8_var_samp", 3);
3198 28 : N = transvalues[0];
3199 : /* ignore Sx */
3200 28 : Sxx = transvalues[2];
3201 :
3202 : /* Sample variance is undefined when N is 0 or 1, so return NULL */
3203 28 : if (N <= 1.0)
3204 24 : PG_RETURN_NULL();
3205 :
3206 : /* Note that Sxx is guaranteed to be non-negative */
3207 :
3208 4 : PG_RETURN_FLOAT8(Sxx / (N - 1.0));
3209 : }
3210 :
3211 : Datum
3212 28 : float8_stddev_pop(PG_FUNCTION_ARGS)
3213 : {
3214 28 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3215 : float8 *transvalues;
3216 : float8 N,
3217 : Sxx;
3218 :
3219 28 : transvalues = check_float8_array(transarray, "float8_stddev_pop", 3);
3220 28 : N = transvalues[0];
3221 : /* ignore Sx */
3222 28 : Sxx = transvalues[2];
3223 :
3224 : /* Population stddev is undefined when N is 0, so return NULL */
3225 28 : if (N == 0.0)
3226 0 : PG_RETURN_NULL();
3227 :
3228 : /* Note that Sxx is guaranteed to be non-negative */
3229 :
3230 28 : PG_RETURN_FLOAT8(sqrt(Sxx / N));
3231 : }
3232 :
3233 : Datum
3234 32 : float8_stddev_samp(PG_FUNCTION_ARGS)
3235 : {
3236 32 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3237 : float8 *transvalues;
3238 : float8 N,
3239 : Sxx;
3240 :
3241 32 : transvalues = check_float8_array(transarray, "float8_stddev_samp", 3);
3242 32 : N = transvalues[0];
3243 : /* ignore Sx */
3244 32 : Sxx = transvalues[2];
3245 :
3246 : /* Sample stddev is undefined when N is 0 or 1, so return NULL */
3247 32 : if (N <= 1.0)
3248 24 : PG_RETURN_NULL();
3249 :
3250 : /* Note that Sxx is guaranteed to be non-negative */
3251 :
3252 8 : PG_RETURN_FLOAT8(sqrt(Sxx / (N - 1.0)));
3253 : }
3254 :
3255 : /*
3256 : * =========================
3257 : * SQL2003 BINARY AGGREGATES
3258 : * =========================
3259 : *
3260 : * As with the preceding aggregates, we use the Youngs-Cramer algorithm to
3261 : * reduce rounding errors in the aggregate final functions.
3262 : *
3263 : * The transition datatype for all these aggregates is a 6-element array of
3264 : * float8, holding the values N, Sx=sum(X), Sxx=sum((X-Sx/N)^2), Sy=sum(Y),
3265 : * Syy=sum((Y-Sy/N)^2), Sxy=sum((X-Sx/N)*(Y-Sy/N)) in that order.
3266 : *
3267 : * Note that Y is the first argument to all these aggregates!
3268 : *
3269 : * It might seem attractive to optimize this by having multiple accumulator
3270 : * functions that only calculate the sums actually needed. But on most
3271 : * modern machines, a couple of extra floating-point multiplies will be
3272 : * insignificant compared to the other per-tuple overhead, so I've chosen
3273 : * to minimize code space instead.
3274 : */
3275 :
3276 : Datum
3277 212 : float8_regr_accum(PG_FUNCTION_ARGS)
3278 : {
3279 212 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3280 212 : float8 newvalY = PG_GETARG_FLOAT8(1);
3281 212 : float8 newvalX = PG_GETARG_FLOAT8(2);
3282 : float8 *transvalues;
3283 : float8 N,
3284 : Sx,
3285 : Sxx,
3286 : Sy,
3287 : Syy,
3288 : Sxy,
3289 : tmpX,
3290 : tmpY,
3291 : scale;
3292 :
3293 212 : transvalues = check_float8_array(transarray, "float8_regr_accum", 6);
3294 212 : N = transvalues[0];
3295 212 : Sx = transvalues[1];
3296 212 : Sxx = transvalues[2];
3297 212 : Sy = transvalues[3];
3298 212 : Syy = transvalues[4];
3299 212 : Sxy = transvalues[5];
3300 :
3301 : /*
3302 : * Use the Youngs-Cramer algorithm to incorporate the new values into the
3303 : * transition values.
3304 : */
3305 212 : N += 1.0;
3306 212 : Sx += newvalX;
3307 212 : Sy += newvalY;
3308 212 : if (transvalues[0] > 0.0)
3309 : {
3310 140 : tmpX = newvalX * N - Sx;
3311 140 : tmpY = newvalY * N - Sy;
3312 140 : scale = 1.0 / (N * transvalues[0]);
3313 140 : Sxx += tmpX * tmpX * scale;
3314 140 : Syy += tmpY * tmpY * scale;
3315 140 : Sxy += tmpX * tmpY * scale;
3316 :
3317 : /*
3318 : * Overflow check. We only report an overflow error when finite
3319 : * inputs lead to infinite results. Note also that Sxx, Syy and Sxy
3320 : * should be NaN if any of the relevant inputs are infinite, so we
3321 : * intentionally prevent them from becoming infinite.
3322 : */
3323 140 : if (isinf(Sx) || isinf(Sxx) || isinf(Sy) || isinf(Syy) || isinf(Sxy))
3324 : {
3325 0 : if (((isinf(Sx) || isinf(Sxx)) &&
3326 0 : !isinf(transvalues[1]) && !isinf(newvalX)) ||
3327 0 : ((isinf(Sy) || isinf(Syy)) &&
3328 0 : !isinf(transvalues[3]) && !isinf(newvalY)) ||
3329 0 : (isinf(Sxy) &&
3330 0 : !isinf(transvalues[1]) && !isinf(newvalX) &&
3331 0 : !isinf(transvalues[3]) && !isinf(newvalY)))
3332 0 : float_overflow_error();
3333 :
3334 0 : if (isinf(Sxx))
3335 0 : Sxx = get_float8_nan();
3336 0 : if (isinf(Syy))
3337 0 : Syy = get_float8_nan();
3338 0 : if (isinf(Sxy))
3339 0 : Sxy = get_float8_nan();
3340 : }
3341 : }
3342 : else
3343 : {
3344 : /*
3345 : * At the first input, we normally can leave Sxx et al as 0. However,
3346 : * if the first input is Inf or NaN, we'd better force the dependent
3347 : * sums to NaN; otherwise we will falsely report variance zero when
3348 : * there are no more inputs.
3349 : */
3350 72 : if (isnan(newvalX) || isinf(newvalX))
3351 16 : Sxx = Sxy = get_float8_nan();
3352 72 : if (isnan(newvalY) || isinf(newvalY))
3353 0 : Syy = Sxy = get_float8_nan();
3354 : }
3355 :
3356 : /*
3357 : * If we're invoked as an aggregate, we can cheat and modify our first
3358 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3359 : * new array with the updated transition data and return it.
3360 : */
3361 212 : if (AggCheckCallContext(fcinfo, NULL))
3362 : {
3363 208 : transvalues[0] = N;
3364 208 : transvalues[1] = Sx;
3365 208 : transvalues[2] = Sxx;
3366 208 : transvalues[3] = Sy;
3367 208 : transvalues[4] = Syy;
3368 208 : transvalues[5] = Sxy;
3369 :
3370 208 : PG_RETURN_ARRAYTYPE_P(transarray);
3371 : }
3372 : else
3373 : {
3374 : Datum transdatums[6];
3375 : ArrayType *result;
3376 :
3377 4 : transdatums[0] = Float8GetDatumFast(N);
3378 4 : transdatums[1] = Float8GetDatumFast(Sx);
3379 4 : transdatums[2] = Float8GetDatumFast(Sxx);
3380 4 : transdatums[3] = Float8GetDatumFast(Sy);
3381 4 : transdatums[4] = Float8GetDatumFast(Syy);
3382 4 : transdatums[5] = Float8GetDatumFast(Sxy);
3383 :
3384 4 : result = construct_array(transdatums, 6,
3385 : FLOAT8OID,
3386 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
3387 :
3388 4 : PG_RETURN_ARRAYTYPE_P(result);
3389 : }
3390 : }
3391 :
3392 : /*
3393 : * float8_regr_combine
3394 : *
3395 : * An aggregate combine function used to combine two 6 fields
3396 : * aggregate transition data into a single transition data.
3397 : * This function is used only in two stage aggregation and
3398 : * shouldn't be called outside aggregate context.
3399 : */
3400 : Datum
3401 12 : float8_regr_combine(PG_FUNCTION_ARGS)
3402 : {
3403 12 : ArrayType *transarray1 = PG_GETARG_ARRAYTYPE_P(0);
3404 12 : ArrayType *transarray2 = PG_GETARG_ARRAYTYPE_P(1);
3405 : float8 *transvalues1;
3406 : float8 *transvalues2;
3407 : float8 N1,
3408 : Sx1,
3409 : Sxx1,
3410 : Sy1,
3411 : Syy1,
3412 : Sxy1,
3413 : N2,
3414 : Sx2,
3415 : Sxx2,
3416 : Sy2,
3417 : Syy2,
3418 : Sxy2,
3419 : tmp1,
3420 : tmp2,
3421 : N,
3422 : Sx,
3423 : Sxx,
3424 : Sy,
3425 : Syy,
3426 : Sxy;
3427 :
3428 12 : transvalues1 = check_float8_array(transarray1, "float8_regr_combine", 6);
3429 12 : transvalues2 = check_float8_array(transarray2, "float8_regr_combine", 6);
3430 :
3431 12 : N1 = transvalues1[0];
3432 12 : Sx1 = transvalues1[1];
3433 12 : Sxx1 = transvalues1[2];
3434 12 : Sy1 = transvalues1[3];
3435 12 : Syy1 = transvalues1[4];
3436 12 : Sxy1 = transvalues1[5];
3437 :
3438 12 : N2 = transvalues2[0];
3439 12 : Sx2 = transvalues2[1];
3440 12 : Sxx2 = transvalues2[2];
3441 12 : Sy2 = transvalues2[3];
3442 12 : Syy2 = transvalues2[4];
3443 12 : Sxy2 = transvalues2[5];
3444 :
3445 : /*--------------------
3446 : * The transition values combine using a generalization of the
3447 : * Youngs-Cramer algorithm as follows:
3448 : *
3449 : * N = N1 + N2
3450 : * Sx = Sx1 + Sx2
3451 : * Sxx = Sxx1 + Sxx2 + N1 * N2 * (Sx1/N1 - Sx2/N2)^2 / N
3452 : * Sy = Sy1 + Sy2
3453 : * Syy = Syy1 + Syy2 + N1 * N2 * (Sy1/N1 - Sy2/N2)^2 / N
3454 : * Sxy = Sxy1 + Sxy2 + N1 * N2 * (Sx1/N1 - Sx2/N2) * (Sy1/N1 - Sy2/N2) / N
3455 : *
3456 : * It's worth handling the special cases N1 = 0 and N2 = 0 separately
3457 : * since those cases are trivial, and we then don't need to worry about
3458 : * division-by-zero errors in the general case.
3459 : *--------------------
3460 : */
3461 12 : if (N1 == 0.0)
3462 : {
3463 4 : N = N2;
3464 4 : Sx = Sx2;
3465 4 : Sxx = Sxx2;
3466 4 : Sy = Sy2;
3467 4 : Syy = Syy2;
3468 4 : Sxy = Sxy2;
3469 : }
3470 8 : else if (N2 == 0.0)
3471 : {
3472 4 : N = N1;
3473 4 : Sx = Sx1;
3474 4 : Sxx = Sxx1;
3475 4 : Sy = Sy1;
3476 4 : Syy = Syy1;
3477 4 : Sxy = Sxy1;
3478 : }
3479 : else
3480 : {
3481 4 : N = N1 + N2;
3482 4 : Sx = float8_pl(Sx1, Sx2);
3483 4 : tmp1 = Sx1 / N1 - Sx2 / N2;
3484 4 : Sxx = Sxx1 + Sxx2 + N1 * N2 * tmp1 * tmp1 / N;
3485 4 : if (unlikely(isinf(Sxx)) && !isinf(Sxx1) && !isinf(Sxx2))
3486 0 : float_overflow_error();
3487 4 : Sy = float8_pl(Sy1, Sy2);
3488 4 : tmp2 = Sy1 / N1 - Sy2 / N2;
3489 4 : Syy = Syy1 + Syy2 + N1 * N2 * tmp2 * tmp2 / N;
3490 4 : if (unlikely(isinf(Syy)) && !isinf(Syy1) && !isinf(Syy2))
3491 0 : float_overflow_error();
3492 4 : Sxy = Sxy1 + Sxy2 + N1 * N2 * tmp1 * tmp2 / N;
3493 4 : if (unlikely(isinf(Sxy)) && !isinf(Sxy1) && !isinf(Sxy2))
3494 0 : float_overflow_error();
3495 : }
3496 :
3497 : /*
3498 : * If we're invoked as an aggregate, we can cheat and modify our first
3499 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3500 : * new array with the updated transition data and return it.
3501 : */
3502 12 : if (AggCheckCallContext(fcinfo, NULL))
3503 : {
3504 0 : transvalues1[0] = N;
3505 0 : transvalues1[1] = Sx;
3506 0 : transvalues1[2] = Sxx;
3507 0 : transvalues1[3] = Sy;
3508 0 : transvalues1[4] = Syy;
3509 0 : transvalues1[5] = Sxy;
3510 :
3511 0 : PG_RETURN_ARRAYTYPE_P(transarray1);
3512 : }
3513 : else
3514 : {
3515 : Datum transdatums[6];
3516 : ArrayType *result;
3517 :
3518 12 : transdatums[0] = Float8GetDatumFast(N);
3519 12 : transdatums[1] = Float8GetDatumFast(Sx);
3520 12 : transdatums[2] = Float8GetDatumFast(Sxx);
3521 12 : transdatums[3] = Float8GetDatumFast(Sy);
3522 12 : transdatums[4] = Float8GetDatumFast(Syy);
3523 12 : transdatums[5] = Float8GetDatumFast(Sxy);
3524 :
3525 12 : result = construct_array(transdatums, 6,
3526 : FLOAT8OID,
3527 : sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
3528 :
3529 12 : PG_RETURN_ARRAYTYPE_P(result);
3530 : }
3531 : }
3532 :
3533 :
3534 : Datum
3535 20 : float8_regr_sxx(PG_FUNCTION_ARGS)
3536 : {
3537 20 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3538 : float8 *transvalues;
3539 : float8 N,
3540 : Sxx;
3541 :
3542 20 : transvalues = check_float8_array(transarray, "float8_regr_sxx", 6);
3543 20 : N = transvalues[0];
3544 20 : Sxx = transvalues[2];
3545 :
3546 : /* if N is 0 we should return NULL */
3547 20 : if (N < 1.0)
3548 0 : PG_RETURN_NULL();
3549 :
3550 : /* Note that Sxx is guaranteed to be non-negative */
3551 :
3552 20 : PG_RETURN_FLOAT8(Sxx);
3553 : }
3554 :
3555 : Datum
3556 20 : float8_regr_syy(PG_FUNCTION_ARGS)
3557 : {
3558 20 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3559 : float8 *transvalues;
3560 : float8 N,
3561 : Syy;
3562 :
3563 20 : transvalues = check_float8_array(transarray, "float8_regr_syy", 6);
3564 20 : N = transvalues[0];
3565 20 : Syy = transvalues[4];
3566 :
3567 : /* if N is 0 we should return NULL */
3568 20 : if (N < 1.0)
3569 0 : PG_RETURN_NULL();
3570 :
3571 : /* Note that Syy is guaranteed to be non-negative */
3572 :
3573 20 : PG_RETURN_FLOAT8(Syy);
3574 : }
3575 :
3576 : Datum
3577 20 : float8_regr_sxy(PG_FUNCTION_ARGS)
3578 : {
3579 20 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3580 : float8 *transvalues;
3581 : float8 N,
3582 : Sxy;
3583 :
3584 20 : transvalues = check_float8_array(transarray, "float8_regr_sxy", 6);
3585 20 : N = transvalues[0];
3586 20 : Sxy = transvalues[5];
3587 :
3588 : /* if N is 0 we should return NULL */
3589 20 : if (N < 1.0)
3590 0 : PG_RETURN_NULL();
3591 :
3592 : /* A negative result is valid here */
3593 :
3594 20 : PG_RETURN_FLOAT8(Sxy);
3595 : }
3596 :
3597 : Datum
3598 4 : float8_regr_avgx(PG_FUNCTION_ARGS)
3599 : {
3600 4 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3601 : float8 *transvalues;
3602 : float8 N,
3603 : Sx;
3604 :
3605 4 : transvalues = check_float8_array(transarray, "float8_regr_avgx", 6);
3606 4 : N = transvalues[0];
3607 4 : Sx = transvalues[1];
3608 :
3609 : /* if N is 0 we should return NULL */
3610 4 : if (N < 1.0)
3611 0 : PG_RETURN_NULL();
3612 :
3613 4 : PG_RETURN_FLOAT8(Sx / N);
3614 : }
3615 :
3616 : Datum
3617 4 : float8_regr_avgy(PG_FUNCTION_ARGS)
3618 : {
3619 4 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3620 : float8 *transvalues;
3621 : float8 N,
3622 : Sy;
3623 :
3624 4 : transvalues = check_float8_array(transarray, "float8_regr_avgy", 6);
3625 4 : N = transvalues[0];
3626 4 : Sy = transvalues[3];
3627 :
3628 : /* if N is 0 we should return NULL */
3629 4 : if (N < 1.0)
3630 0 : PG_RETURN_NULL();
3631 :
3632 4 : PG_RETURN_FLOAT8(Sy / N);
3633 : }
3634 :
3635 : Datum
3636 16 : float8_covar_pop(PG_FUNCTION_ARGS)
3637 : {
3638 16 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3639 : float8 *transvalues;
3640 : float8 N,
3641 : Sxy;
3642 :
3643 16 : transvalues = check_float8_array(transarray, "float8_covar_pop", 6);
3644 16 : N = transvalues[0];
3645 16 : Sxy = transvalues[5];
3646 :
3647 : /* if N is 0 we should return NULL */
3648 16 : if (N < 1.0)
3649 0 : PG_RETURN_NULL();
3650 :
3651 16 : PG_RETURN_FLOAT8(Sxy / N);
3652 : }
3653 :
3654 : Datum
3655 16 : float8_covar_samp(PG_FUNCTION_ARGS)
3656 : {
3657 16 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3658 : float8 *transvalues;
3659 : float8 N,
3660 : Sxy;
3661 :
3662 16 : transvalues = check_float8_array(transarray, "float8_covar_samp", 6);
3663 16 : N = transvalues[0];
3664 16 : Sxy = transvalues[5];
3665 :
3666 : /* if N is <= 1 we should return NULL */
3667 16 : if (N < 2.0)
3668 12 : PG_RETURN_NULL();
3669 :
3670 4 : PG_RETURN_FLOAT8(Sxy / (N - 1.0));
3671 : }
3672 :
3673 : Datum
3674 4 : float8_corr(PG_FUNCTION_ARGS)
3675 : {
3676 4 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3677 : float8 *transvalues;
3678 : float8 N,
3679 : Sxx,
3680 : Syy,
3681 : Sxy;
3682 :
3683 4 : transvalues = check_float8_array(transarray, "float8_corr", 6);
3684 4 : N = transvalues[0];
3685 4 : Sxx = transvalues[2];
3686 4 : Syy = transvalues[4];
3687 4 : Sxy = transvalues[5];
3688 :
3689 : /* if N is 0 we should return NULL */
3690 4 : if (N < 1.0)
3691 0 : PG_RETURN_NULL();
3692 :
3693 : /* Note that Sxx and Syy are guaranteed to be non-negative */
3694 :
3695 : /* per spec, return NULL for horizontal and vertical lines */
3696 4 : if (Sxx == 0 || Syy == 0)
3697 0 : PG_RETURN_NULL();
3698 :
3699 4 : PG_RETURN_FLOAT8(Sxy / sqrt(Sxx * Syy));
3700 : }
3701 :
3702 : Datum
3703 4 : float8_regr_r2(PG_FUNCTION_ARGS)
3704 : {
3705 4 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3706 : float8 *transvalues;
3707 : float8 N,
3708 : Sxx,
3709 : Syy,
3710 : Sxy;
3711 :
3712 4 : transvalues = check_float8_array(transarray, "float8_regr_r2", 6);
3713 4 : N = transvalues[0];
3714 4 : Sxx = transvalues[2];
3715 4 : Syy = transvalues[4];
3716 4 : Sxy = transvalues[5];
3717 :
3718 : /* if N is 0 we should return NULL */
3719 4 : if (N < 1.0)
3720 0 : PG_RETURN_NULL();
3721 :
3722 : /* Note that Sxx and Syy are guaranteed to be non-negative */
3723 :
3724 : /* per spec, return NULL for a vertical line */
3725 4 : if (Sxx == 0)
3726 0 : PG_RETURN_NULL();
3727 :
3728 : /* per spec, return 1.0 for a horizontal line */
3729 4 : if (Syy == 0)
3730 0 : PG_RETURN_FLOAT8(1.0);
3731 :
3732 4 : PG_RETURN_FLOAT8((Sxy * Sxy) / (Sxx * Syy));
3733 : }
3734 :
3735 : Datum
3736 4 : float8_regr_slope(PG_FUNCTION_ARGS)
3737 : {
3738 4 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3739 : float8 *transvalues;
3740 : float8 N,
3741 : Sxx,
3742 : Sxy;
3743 :
3744 4 : transvalues = check_float8_array(transarray, "float8_regr_slope", 6);
3745 4 : N = transvalues[0];
3746 4 : Sxx = transvalues[2];
3747 4 : Sxy = transvalues[5];
3748 :
3749 : /* if N is 0 we should return NULL */
3750 4 : if (N < 1.0)
3751 0 : PG_RETURN_NULL();
3752 :
3753 : /* Note that Sxx is guaranteed to be non-negative */
3754 :
3755 : /* per spec, return NULL for a vertical line */
3756 4 : if (Sxx == 0)
3757 0 : PG_RETURN_NULL();
3758 :
3759 4 : PG_RETURN_FLOAT8(Sxy / Sxx);
3760 : }
3761 :
3762 : Datum
3763 4 : float8_regr_intercept(PG_FUNCTION_ARGS)
3764 : {
3765 4 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3766 : float8 *transvalues;
3767 : float8 N,
3768 : Sx,
3769 : Sxx,
3770 : Sy,
3771 : Sxy;
3772 :
3773 4 : transvalues = check_float8_array(transarray, "float8_regr_intercept", 6);
3774 4 : N = transvalues[0];
3775 4 : Sx = transvalues[1];
3776 4 : Sxx = transvalues[2];
3777 4 : Sy = transvalues[3];
3778 4 : Sxy = transvalues[5];
3779 :
3780 : /* if N is 0 we should return NULL */
3781 4 : if (N < 1.0)
3782 0 : PG_RETURN_NULL();
3783 :
3784 : /* Note that Sxx is guaranteed to be non-negative */
3785 :
3786 : /* per spec, return NULL for a vertical line */
3787 4 : if (Sxx == 0)
3788 0 : PG_RETURN_NULL();
3789 :
3790 4 : PG_RETURN_FLOAT8((Sy - Sx * Sxy / Sxx) / N);
3791 : }
3792 :
3793 :
3794 : /*
3795 : * ====================================
3796 : * MIXED-PRECISION ARITHMETIC OPERATORS
3797 : * ====================================
3798 : */
3799 :
3800 : /*
3801 : * float48pl - returns arg1 + arg2
3802 : * float48mi - returns arg1 - arg2
3803 : * float48mul - returns arg1 * arg2
3804 : * float48div - returns arg1 / arg2
3805 : */
3806 : Datum
3807 4 : float48pl(PG_FUNCTION_ARGS)
3808 : {
3809 4 : float4 arg1 = PG_GETARG_FLOAT4(0);
3810 4 : float8 arg2 = PG_GETARG_FLOAT8(1);
3811 :
3812 4 : PG_RETURN_FLOAT8(float8_pl((float8) arg1, arg2));
3813 : }
3814 :
3815 : Datum
3816 0 : float48mi(PG_FUNCTION_ARGS)
3817 : {
3818 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
3819 0 : float8 arg2 = PG_GETARG_FLOAT8(1);
3820 :
3821 0 : PG_RETURN_FLOAT8(float8_mi((float8) arg1, arg2));
3822 : }
3823 :
3824 : Datum
3825 0 : float48mul(PG_FUNCTION_ARGS)
3826 : {
3827 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
3828 0 : float8 arg2 = PG_GETARG_FLOAT8(1);
3829 :
3830 0 : PG_RETURN_FLOAT8(float8_mul((float8) arg1, arg2));
3831 : }
3832 :
3833 : Datum
3834 4 : float48div(PG_FUNCTION_ARGS)
3835 : {
3836 4 : float4 arg1 = PG_GETARG_FLOAT4(0);
3837 4 : float8 arg2 = PG_GETARG_FLOAT8(1);
3838 :
3839 4 : PG_RETURN_FLOAT8(float8_div((float8) arg1, arg2));
3840 : }
3841 :
3842 : /*
3843 : * float84pl - returns arg1 + arg2
3844 : * float84mi - returns arg1 - arg2
3845 : * float84mul - returns arg1 * arg2
3846 : * float84div - returns arg1 / arg2
3847 : */
3848 : Datum
3849 8 : float84pl(PG_FUNCTION_ARGS)
3850 : {
3851 8 : float8 arg1 = PG_GETARG_FLOAT8(0);
3852 8 : float4 arg2 = PG_GETARG_FLOAT4(1);
3853 :
3854 8 : PG_RETURN_FLOAT8(float8_pl(arg1, (float8) arg2));
3855 : }
3856 :
3857 : Datum
3858 0 : float84mi(PG_FUNCTION_ARGS)
3859 : {
3860 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
3861 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
3862 :
3863 0 : PG_RETURN_FLOAT8(float8_mi(arg1, (float8) arg2));
3864 : }
3865 :
3866 : Datum
3867 0 : float84mul(PG_FUNCTION_ARGS)
3868 : {
3869 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
3870 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
3871 :
3872 0 : PG_RETURN_FLOAT8(float8_mul(arg1, (float8) arg2));
3873 : }
3874 :
3875 : Datum
3876 4 : float84div(PG_FUNCTION_ARGS)
3877 : {
3878 4 : float8 arg1 = PG_GETARG_FLOAT8(0);
3879 4 : float4 arg2 = PG_GETARG_FLOAT4(1);
3880 :
3881 4 : PG_RETURN_FLOAT8(float8_div(arg1, (float8) arg2));
3882 : }
3883 :
3884 : /*
3885 : * ====================
3886 : * COMPARISON OPERATORS
3887 : * ====================
3888 : */
3889 :
3890 : /*
3891 : * float48{eq,ne,lt,le,gt,ge} - float4/float8 comparison operations
3892 : */
3893 : Datum
3894 1514 : float48eq(PG_FUNCTION_ARGS)
3895 : {
3896 1514 : float4 arg1 = PG_GETARG_FLOAT4(0);
3897 1514 : float8 arg2 = PG_GETARG_FLOAT8(1);
3898 :
3899 1514 : PG_RETURN_BOOL(float8_eq((float8) arg1, arg2));
3900 : }
3901 :
3902 : Datum
3903 11872 : float48ne(PG_FUNCTION_ARGS)
3904 : {
3905 11872 : float4 arg1 = PG_GETARG_FLOAT4(0);
3906 11872 : float8 arg2 = PG_GETARG_FLOAT8(1);
3907 :
3908 11872 : PG_RETURN_BOOL(float8_ne((float8) arg1, arg2));
3909 : }
3910 :
3911 : Datum
3912 2278 : float48lt(PG_FUNCTION_ARGS)
3913 : {
3914 2278 : float4 arg1 = PG_GETARG_FLOAT4(0);
3915 2278 : float8 arg2 = PG_GETARG_FLOAT8(1);
3916 :
3917 2278 : PG_RETURN_BOOL(float8_lt((float8) arg1, arg2));
3918 : }
3919 :
3920 : Datum
3921 15326 : float48le(PG_FUNCTION_ARGS)
3922 : {
3923 15326 : float4 arg1 = PG_GETARG_FLOAT4(0);
3924 15326 : float8 arg2 = PG_GETARG_FLOAT8(1);
3925 :
3926 15326 : PG_RETURN_BOOL(float8_le((float8) arg1, arg2));
3927 : }
3928 :
3929 : Datum
3930 2430 : float48gt(PG_FUNCTION_ARGS)
3931 : {
3932 2430 : float4 arg1 = PG_GETARG_FLOAT4(0);
3933 2430 : float8 arg2 = PG_GETARG_FLOAT8(1);
3934 :
3935 2430 : PG_RETURN_BOOL(float8_gt((float8) arg1, arg2));
3936 : }
3937 :
3938 : Datum
3939 2694 : float48ge(PG_FUNCTION_ARGS)
3940 : {
3941 2694 : float4 arg1 = PG_GETARG_FLOAT4(0);
3942 2694 : float8 arg2 = PG_GETARG_FLOAT8(1);
3943 :
3944 2694 : PG_RETURN_BOOL(float8_ge((float8) arg1, arg2));
3945 : }
3946 :
3947 : /*
3948 : * float84{eq,ne,lt,le,gt,ge} - float8/float4 comparison operations
3949 : */
3950 : Datum
3951 404 : float84eq(PG_FUNCTION_ARGS)
3952 : {
3953 404 : float8 arg1 = PG_GETARG_FLOAT8(0);
3954 404 : float4 arg2 = PG_GETARG_FLOAT4(1);
3955 :
3956 404 : PG_RETURN_BOOL(float8_eq(arg1, (float8) arg2));
3957 : }
3958 :
3959 : Datum
3960 0 : float84ne(PG_FUNCTION_ARGS)
3961 : {
3962 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
3963 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
3964 :
3965 0 : PG_RETURN_BOOL(float8_ne(arg1, (float8) arg2));
3966 : }
3967 :
3968 : Datum
3969 1200 : float84lt(PG_FUNCTION_ARGS)
3970 : {
3971 1200 : float8 arg1 = PG_GETARG_FLOAT8(0);
3972 1200 : float4 arg2 = PG_GETARG_FLOAT4(1);
3973 :
3974 1200 : PG_RETURN_BOOL(float8_lt(arg1, (float8) arg2));
3975 : }
3976 :
3977 : Datum
3978 1600 : float84le(PG_FUNCTION_ARGS)
3979 : {
3980 1600 : float8 arg1 = PG_GETARG_FLOAT8(0);
3981 1600 : float4 arg2 = PG_GETARG_FLOAT4(1);
3982 :
3983 1600 : PG_RETURN_BOOL(float8_le(arg1, (float8) arg2));
3984 : }
3985 :
3986 : Datum
3987 1196 : float84gt(PG_FUNCTION_ARGS)
3988 : {
3989 1196 : float8 arg1 = PG_GETARG_FLOAT8(0);
3990 1196 : float4 arg2 = PG_GETARG_FLOAT4(1);
3991 :
3992 1196 : PG_RETURN_BOOL(float8_gt(arg1, (float8) arg2));
3993 : }
3994 :
3995 : Datum
3996 1204 : float84ge(PG_FUNCTION_ARGS)
3997 : {
3998 1204 : float8 arg1 = PG_GETARG_FLOAT8(0);
3999 1204 : float4 arg2 = PG_GETARG_FLOAT4(1);
4000 :
4001 1204 : PG_RETURN_BOOL(float8_ge(arg1, (float8) arg2));
4002 : }
4003 :
4004 : /*
4005 : * Implements the float8 version of the width_bucket() function
4006 : * defined by SQL2003. See also width_bucket_numeric().
4007 : *
4008 : * 'bound1' and 'bound2' are the lower and upper bounds of the
4009 : * histogram's range, respectively. 'count' is the number of buckets
4010 : * in the histogram. width_bucket() returns an integer indicating the
4011 : * bucket number that 'operand' belongs to in an equiwidth histogram
4012 : * with the specified characteristics. An operand smaller than the
4013 : * lower bound is assigned to bucket 0. An operand greater than the
4014 : * upper bound is assigned to an additional bucket (with number
4015 : * count+1). We don't allow "NaN" for any of the float8 inputs, and we
4016 : * don't allow either of the histogram bounds to be +/- infinity.
4017 : */
4018 : Datum
4019 512 : width_bucket_float8(PG_FUNCTION_ARGS)
4020 : {
4021 512 : float8 operand = PG_GETARG_FLOAT8(0);
4022 512 : float8 bound1 = PG_GETARG_FLOAT8(1);
4023 512 : float8 bound2 = PG_GETARG_FLOAT8(2);
4024 512 : int32 count = PG_GETARG_INT32(3);
4025 : int32 result;
4026 :
4027 512 : if (count <= 0.0)
4028 8 : ereport(ERROR,
4029 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4030 : errmsg("count must be greater than zero")));
4031 :
4032 504 : if (isnan(operand) || isnan(bound1) || isnan(bound2))
4033 4 : ereport(ERROR,
4034 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4035 : errmsg("operand, lower bound, and upper bound cannot be NaN")));
4036 :
4037 : /* Note that we allow "operand" to be infinite */
4038 500 : if (isinf(bound1) || isinf(bound2))
4039 12 : ereport(ERROR,
4040 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4041 : errmsg("lower and upper bounds must be finite")));
4042 :
4043 488 : if (bound1 < bound2)
4044 : {
4045 360 : if (operand < bound1)
4046 76 : result = 0;
4047 284 : else if (operand >= bound2)
4048 : {
4049 72 : if (pg_add_s32_overflow(count, 1, &result))
4050 0 : ereport(ERROR,
4051 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
4052 : errmsg("integer out of range")));
4053 : }
4054 : else
4055 212 : result = ((float8) count * (operand - bound1) / (bound2 - bound1)) + 1;
4056 : }
4057 128 : else if (bound1 > bound2)
4058 : {
4059 124 : if (operand > bound1)
4060 8 : result = 0;
4061 116 : else if (operand <= bound2)
4062 : {
4063 16 : if (pg_add_s32_overflow(count, 1, &result))
4064 0 : ereport(ERROR,
4065 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
4066 : errmsg("integer out of range")));
4067 : }
4068 : else
4069 100 : result = ((float8) count * (bound1 - operand) / (bound1 - bound2)) + 1;
4070 : }
4071 : else
4072 : {
4073 4 : ereport(ERROR,
4074 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4075 : errmsg("lower bound cannot equal upper bound")));
4076 : result = 0; /* keep the compiler quiet */
4077 : }
4078 :
4079 484 : PG_RETURN_INT32(result);
4080 : }
|
