File: | Modules/mathmodule.c |
Location: | line 1090, column 9 |
Description: | Assigned value is garbage or undefined |
1 | /* Math module -- standard C math library functions, pi and e */ | ||
2 | |||
3 | /* Here are some comments from Tim Peters, extracted from the | ||
4 | discussion attached to http://bugs.python.org/issue1640. They | ||
5 | describe the general aims of the math module with respect to | ||
6 | special values, IEEE-754 floating-point exceptions, and Python | ||
7 | exceptions. | ||
8 | |||
9 | These are the "spirit of 754" rules: | ||
10 | |||
11 | 1. If the mathematical result is a real number, but of magnitude too | ||
12 | large to approximate by a machine float, overflow is signaled and the | ||
13 | result is an infinity (with the appropriate sign). | ||
14 | |||
15 | 2. If the mathematical result is a real number, but of magnitude too | ||
16 | small to approximate by a machine float, underflow is signaled and the | ||
17 | result is a zero (with the appropriate sign). | ||
18 | |||
19 | 3. At a singularity (a value x such that the limit of f(y) as y | ||
20 | approaches x exists and is an infinity), "divide by zero" is signaled | ||
21 | and the result is an infinity (with the appropriate sign). This is | ||
22 | complicated a little by that the left-side and right-side limits may | ||
23 | not be the same; e.g., 1/x approaches +inf or -inf as x approaches 0 | ||
24 | from the positive or negative directions. In that specific case, the | ||
25 | sign of the zero determines the result of 1/0. | ||
26 | |||
27 | 4. At a point where a function has no defined result in the extended | ||
28 | reals (i.e., the reals plus an infinity or two), invalid operation is | ||
29 | signaled and a NaN is returned. | ||
30 | |||
31 | And these are what Python has historically /tried/ to do (but not | ||
32 | always successfully, as platform libm behavior varies a lot): | ||
33 | |||
34 | For #1, raise OverflowError. | ||
35 | |||
36 | For #2, return a zero (with the appropriate sign if that happens by | ||
37 | accident ;-)). | ||
38 | |||
39 | For #3 and #4, raise ValueError. It may have made sense to raise | ||
40 | Python's ZeroDivisionError in #3, but historically that's only been | ||
41 | raised for division by zero and mod by zero. | ||
42 | |||
43 | */ | ||
44 | |||
45 | /* | ||
46 | In general, on an IEEE-754 platform the aim is to follow the C99 | ||
47 | standard, including Annex 'F', whenever possible. Where the | ||
48 | standard recommends raising the 'divide-by-zero' or 'invalid' | ||
49 | floating-point exceptions, Python should raise a ValueError. Where | ||
50 | the standard recommends raising 'overflow', Python should raise an | ||
51 | OverflowError. In all other circumstances a value should be | ||
52 | returned. | ||
53 | */ | ||
54 | |||
55 | #include "Python.h" | ||
56 | #include "_math.h" | ||
57 | |||
58 | #ifdef _OSF_SOURCE | ||
59 | /* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */ | ||
60 | extern double copysign(double, double); | ||
61 | #endif | ||
62 | |||
63 | /* | ||
64 | sin(pi*x), giving accurate results for all finite x (especially x | ||
65 | integral or close to an integer). This is here for use in the | ||
66 | reflection formula for the gamma function. It conforms to IEEE | ||
67 | 754-2008 for finite arguments, but not for infinities or nans. | ||
68 | */ | ||
69 | |||
70 | static const double pi = 3.141592653589793238462643383279502884197; | ||
71 | static const double sqrtpi = 1.772453850905516027298167483341145182798; | ||
72 | static const double logpi = 1.144729885849400174143427351353058711647; | ||
73 | |||
74 | static double | ||
75 | sinpi(double x) | ||
76 | { | ||
77 | double y, r; | ||
78 | int n; | ||
79 | /* this function should only ever be called for finite arguments */ | ||
80 | assert(Py_IS_FINITE(x))(__builtin_expect(!(( sizeof (x) == sizeof(float ) ? __inline_isfinitef ((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isfinited ((double)(x)) : __inline_isfinite ((long double)(x)))), 0) ? __assert_rtn (__func__, "/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 80, "Py_IS_FINITE(x)") : (void)0); | ||
81 | y = fmod(fabs(x), 2.0); | ||
82 | n = (int)round(2.0*y); | ||
83 | assert(0 <= n && n <= 4)(__builtin_expect(!(0 <= n && n <= 4), 0) ? __assert_rtn (__func__, "/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 83, "0 <= n && n <= 4") : (void)0); | ||
84 | switch (n) { | ||
85 | case 0: | ||
86 | r = sin(pi*y); | ||
87 | break; | ||
88 | case 1: | ||
89 | r = cos(pi*(y-0.5)); | ||
90 | break; | ||
91 | case 2: | ||
92 | /* N.B. -sin(pi*(y-1.0)) is *not* equivalent: it would give | ||
93 | -0.0 instead of 0.0 when y == 1.0. */ | ||
94 | r = sin(pi*(1.0-y)); | ||
95 | break; | ||
96 | case 3: | ||
97 | r = -cos(pi*(y-1.5)); | ||
98 | break; | ||
99 | case 4: | ||
100 | r = sin(pi*(y-2.0)); | ||
101 | break; | ||
102 | default: | ||
103 | assert(0)(__builtin_expect(!(0), 0) ? __assert_rtn(__func__, "/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 103, "0") : (void)0); /* should never get here */ | ||
104 | r = -1.23e200; /* silence gcc warning */ | ||
105 | } | ||
106 | return copysign(1.0, x)*r; | ||
107 | } | ||
108 | |||
109 | /* Implementation of the real gamma function. In extensive but non-exhaustive | ||
110 | random tests, this function proved accurate to within <= 10 ulps across the | ||
111 | entire float domain. Note that accuracy may depend on the quality of the | ||
112 | system math functions, the pow function in particular. Special cases | ||
113 | follow C99 annex F. The parameters and method are tailored to platforms | ||
114 | whose double format is the IEEE 754 binary64 format. | ||
115 | |||
116 | Method: for x > 0.0 we use the Lanczos approximation with parameters N=13 | ||
117 | and g=6.024680040776729583740234375; these parameters are amongst those | ||
118 | used by the Boost library. Following Boost (again), we re-express the | ||
119 | Lanczos sum as a rational function, and compute it that way. The | ||
120 | coefficients below were computed independently using MPFR, and have been | ||
121 | double-checked against the coefficients in the Boost source code. | ||
122 | |||
123 | For x < 0.0 we use the reflection formula. | ||
124 | |||
125 | There's one minor tweak that deserves explanation: Lanczos' formula for | ||
126 | Gamma(x) involves computing pow(x+g-0.5, x-0.5) / exp(x+g-0.5). For many x | ||
127 | values, x+g-0.5 can be represented exactly. However, in cases where it | ||
128 | can't be represented exactly the small error in x+g-0.5 can be magnified | ||
129 | significantly by the pow and exp calls, especially for large x. A cheap | ||
130 | correction is to multiply by (1 + e*g/(x+g-0.5)), where e is the error | ||
131 | involved in the computation of x+g-0.5 (that is, e = computed value of | ||
132 | x+g-0.5 - exact value of x+g-0.5). Here's the proof: | ||
133 | |||
134 | Correction factor | ||
135 | ----------------- | ||
136 | Write x+g-0.5 = y-e, where y is exactly representable as an IEEE 754 | ||
137 | double, and e is tiny. Then: | ||
138 | |||
139 | pow(x+g-0.5,x-0.5)/exp(x+g-0.5) = pow(y-e, x-0.5)/exp(y-e) | ||
140 | = pow(y, x-0.5)/exp(y) * C, | ||
141 | |||
142 | where the correction_factor C is given by | ||
143 | |||
144 | C = pow(1-e/y, x-0.5) * exp(e) | ||
145 | |||
146 | Since e is tiny, pow(1-e/y, x-0.5) ~ 1-(x-0.5)*e/y, and exp(x) ~ 1+e, so: | ||
147 | |||
148 | C ~ (1-(x-0.5)*e/y) * (1+e) ~ 1 + e*(y-(x-0.5))/y | ||
149 | |||
150 | But y-(x-0.5) = g+e, and g+e ~ g. So we get C ~ 1 + e*g/y, and | ||
151 | |||
152 | pow(x+g-0.5,x-0.5)/exp(x+g-0.5) ~ pow(y, x-0.5)/exp(y) * (1 + e*g/y), | ||
153 | |||
154 | Note that for accuracy, when computing r*C it's better to do | ||
155 | |||
156 | r + e*g/y*r; | ||
157 | |||
158 | than | ||
159 | |||
160 | r * (1 + e*g/y); | ||
161 | |||
162 | since the addition in the latter throws away most of the bits of | ||
163 | information in e*g/y. | ||
164 | */ | ||
165 | |||
166 | #define LANCZOS_N13 13 | ||
167 | static const double lanczos_g = 6.024680040776729583740234375; | ||
168 | static const double lanczos_g_minus_half = 5.524680040776729583740234375; | ||
169 | static const double lanczos_num_coeffs[LANCZOS_N13] = { | ||
170 | 23531376880.410759688572007674451636754734846804940, | ||
171 | 42919803642.649098768957899047001988850926355848959, | ||
172 | 35711959237.355668049440185451547166705960488635843, | ||
173 | 17921034426.037209699919755754458931112671403265390, | ||
174 | 6039542586.3520280050642916443072979210699388420708, | ||
175 | 1439720407.3117216736632230727949123939715485786772, | ||
176 | 248874557.86205415651146038641322942321632125127801, | ||
177 | 31426415.585400194380614231628318205362874684987640, | ||
178 | 2876370.6289353724412254090516208496135991145378768, | ||
179 | 186056.26539522349504029498971604569928220784236328, | ||
180 | 8071.6720023658162106380029022722506138218516325024, | ||
181 | 210.82427775157934587250973392071336271166969580291, | ||
182 | 2.5066282746310002701649081771338373386264310793408 | ||
183 | }; | ||
184 | |||
185 | /* denominator is x*(x+1)*...*(x+LANCZOS_N-2) */ | ||
186 | static const double lanczos_den_coeffs[LANCZOS_N13] = { | ||
187 | 0.0, 39916800.0, 120543840.0, 150917976.0, 105258076.0, 45995730.0, | ||
188 | 13339535.0, 2637558.0, 357423.0, 32670.0, 1925.0, 66.0, 1.0}; | ||
189 | |||
190 | /* gamma values for small positive integers, 1 though NGAMMA_INTEGRAL */ | ||
191 | #define NGAMMA_INTEGRAL23 23 | ||
192 | static const double gamma_integral[NGAMMA_INTEGRAL23] = { | ||
193 | 1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0, | ||
194 | 3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0, | ||
195 | 1307674368000.0, 20922789888000.0, 355687428096000.0, | ||
196 | 6402373705728000.0, 121645100408832000.0, 2432902008176640000.0, | ||
197 | 51090942171709440000.0, 1124000727777607680000.0, | ||
198 | }; | ||
199 | |||
200 | /* Lanczos' sum L_g(x), for positive x */ | ||
201 | |||
202 | static double | ||
203 | lanczos_sum(double x) | ||
204 | { | ||
205 | double num = 0.0, den = 0.0; | ||
206 | int i; | ||
207 | assert(x > 0.0)(__builtin_expect(!(x > 0.0), 0) ? __assert_rtn(__func__, "/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 207, "x > 0.0") : (void)0); | ||
208 | /* evaluate the rational function lanczos_sum(x). For large | ||
209 | x, the obvious algorithm risks overflow, so we instead | ||
210 | rescale the denominator and numerator of the rational | ||
211 | function by x**(1-LANCZOS_N) and treat this as a | ||
212 | rational function in 1/x. This also reduces the error for | ||
213 | larger x values. The choice of cutoff point (5.0 below) is | ||
214 | somewhat arbitrary; in tests, smaller cutoff values than | ||
215 | this resulted in lower accuracy. */ | ||
216 | if (x < 5.0) { | ||
217 | for (i = LANCZOS_N13; --i >= 0; ) { | ||
218 | num = num * x + lanczos_num_coeffs[i]; | ||
219 | den = den * x + lanczos_den_coeffs[i]; | ||
220 | } | ||
221 | } | ||
222 | else { | ||
223 | for (i = 0; i < LANCZOS_N13; i++) { | ||
224 | num = num / x + lanczos_num_coeffs[i]; | ||
225 | den = den / x + lanczos_den_coeffs[i]; | ||
226 | } | ||
227 | } | ||
228 | return num/den; | ||
229 | } | ||
230 | |||
231 | static double | ||
232 | m_tgamma(double x) | ||
233 | { | ||
234 | double absx, r, y, z, sqrtpow; | ||
235 | |||
236 | /* special cases */ | ||
237 | if (!Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))) { | ||
238 | if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x))) || x > 0.0) | ||
239 | return x; /* tgamma(nan) = nan, tgamma(inf) = inf */ | ||
240 | else { | ||
241 | errno(*__error()) = EDOM33; | ||
242 | return Py_NAN(__builtin_huge_val() * 0.); /* tgamma(-inf) = nan, invalid */ | ||
243 | } | ||
244 | } | ||
245 | if (x == 0.0) { | ||
246 | errno(*__error()) = EDOM33; | ||
247 | return 1.0/x; /* tgamma(+-0.0) = +-inf, divide-by-zero */ | ||
248 | } | ||
249 | |||
250 | /* integer arguments */ | ||
251 | if (x == floor(x)) { | ||
252 | if (x < 0.0) { | ||
253 | errno(*__error()) = EDOM33; /* tgamma(n) = nan, invalid for */ | ||
254 | return Py_NAN(__builtin_huge_val() * 0.); /* negative integers n */ | ||
255 | } | ||
256 | if (x <= NGAMMA_INTEGRAL23) | ||
257 | return gamma_integral[(int)x - 1]; | ||
258 | } | ||
259 | absx = fabs(x); | ||
260 | |||
261 | /* tiny arguments: tgamma(x) ~ 1/x for x near 0 */ | ||
262 | if (absx < 1e-20) { | ||
263 | r = 1.0/x; | ||
264 | if (Py_IS_INFINITY(r)( sizeof (r) == sizeof(float ) ? __inline_isinff((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isinfd((double)(r)) : __inline_isinf ((long double)(r)))) | ||
265 | errno(*__error()) = ERANGE34; | ||
266 | return r; | ||
267 | } | ||
268 | |||
269 | /* large arguments: assuming IEEE 754 doubles, tgamma(x) overflows for | ||
270 | x > 200, and underflows to +-0.0 for x < -200, not a negative | ||
271 | integer. */ | ||
272 | if (absx > 200.0) { | ||
273 | if (x < 0.0) { | ||
274 | return 0.0/sinpi(x); | ||
275 | } | ||
276 | else { | ||
277 | errno(*__error()) = ERANGE34; | ||
278 | return Py_HUGE_VAL__builtin_huge_val(); | ||
279 | } | ||
280 | } | ||
281 | |||
282 | y = absx + lanczos_g_minus_half; | ||
283 | /* compute error in sum */ | ||
284 | if (absx > lanczos_g_minus_half) { | ||
285 | /* note: the correction can be foiled by an optimizing | ||
286 | compiler that (incorrectly) thinks that an expression like | ||
287 | a + b - a - b can be optimized to 0.0. This shouldn't | ||
288 | happen in a standards-conforming compiler. */ | ||
289 | double q = y - absx; | ||
290 | z = q - lanczos_g_minus_half; | ||
291 | } | ||
292 | else { | ||
293 | double q = y - lanczos_g_minus_half; | ||
294 | z = q - absx; | ||
295 | } | ||
296 | z = z * lanczos_g / y; | ||
297 | if (x < 0.0) { | ||
298 | r = -pi / sinpi(absx) / absx * exp(y) / lanczos_sum(absx); | ||
299 | r -= z * r; | ||
300 | if (absx < 140.0) { | ||
301 | r /= pow(y, absx - 0.5); | ||
302 | } | ||
303 | else { | ||
304 | sqrtpow = pow(y, absx / 2.0 - 0.25); | ||
305 | r /= sqrtpow; | ||
306 | r /= sqrtpow; | ||
307 | } | ||
308 | } | ||
309 | else { | ||
310 | r = lanczos_sum(absx) / exp(y); | ||
311 | r += z * r; | ||
312 | if (absx < 140.0) { | ||
313 | r *= pow(y, absx - 0.5); | ||
314 | } | ||
315 | else { | ||
316 | sqrtpow = pow(y, absx / 2.0 - 0.25); | ||
317 | r *= sqrtpow; | ||
318 | r *= sqrtpow; | ||
319 | } | ||
320 | } | ||
321 | if (Py_IS_INFINITY(r)( sizeof (r) == sizeof(float ) ? __inline_isinff((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isinfd((double)(r)) : __inline_isinf ((long double)(r)))) | ||
322 | errno(*__error()) = ERANGE34; | ||
323 | return r; | ||
324 | } | ||
325 | |||
326 | /* | ||
327 | lgamma: natural log of the absolute value of the Gamma function. | ||
328 | For large arguments, Lanczos' formula works extremely well here. | ||
329 | */ | ||
330 | |||
331 | static double | ||
332 | m_lgamma(double x) | ||
333 | { | ||
334 | double r, absx; | ||
335 | |||
336 | /* special cases */ | ||
337 | if (!Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))) { | ||
338 | if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x)))) | ||
339 | return x; /* lgamma(nan) = nan */ | ||
340 | else | ||
341 | return Py_HUGE_VAL__builtin_huge_val(); /* lgamma(+-inf) = +inf */ | ||
342 | } | ||
343 | |||
344 | /* integer arguments */ | ||
345 | if (x == floor(x) && x <= 2.0) { | ||
346 | if (x <= 0.0) { | ||
347 | errno(*__error()) = EDOM33; /* lgamma(n) = inf, divide-by-zero for */ | ||
348 | return Py_HUGE_VAL__builtin_huge_val(); /* integers n <= 0 */ | ||
349 | } | ||
350 | else { | ||
351 | return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */ | ||
352 | } | ||
353 | } | ||
354 | |||
355 | absx = fabs(x); | ||
356 | /* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */ | ||
357 | if (absx < 1e-20) | ||
358 | return -log(absx); | ||
359 | |||
360 | /* Lanczos' formula. We could save a fraction of a ulp in accuracy by | ||
361 | having a second set of numerator coefficients for lanczos_sum that | ||
362 | absorbed the exp(-lanczos_g) term, and throwing out the lanczos_g | ||
363 | subtraction below; it's probably not worth it. */ | ||
364 | r = log(lanczos_sum(absx)) - lanczos_g; | ||
365 | r += (absx - 0.5) * (log(absx + lanczos_g - 0.5) - 1); | ||
366 | if (x < 0.0) | ||
367 | /* Use reflection formula to get value for negative x. */ | ||
368 | r = logpi - log(fabs(sinpi(absx))) - log(absx) - r; | ||
369 | if (Py_IS_INFINITY(r)( sizeof (r) == sizeof(float ) ? __inline_isinff((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isinfd((double)(r)) : __inline_isinf ((long double)(r)))) | ||
370 | errno(*__error()) = ERANGE34; | ||
371 | return r; | ||
372 | } | ||
373 | |||
374 | /* | ||
375 | Implementations of the error function erf(x) and the complementary error | ||
376 | function erfc(x). | ||
377 | |||
378 | Method: following 'Numerical Recipes' by Flannery, Press et. al. (2nd ed., | ||
379 | Cambridge University Press), we use a series approximation for erf for | ||
380 | small x, and a continued fraction approximation for erfc(x) for larger x; | ||
381 | combined with the relations erf(-x) = -erf(x) and erfc(x) = 1.0 - erf(x), | ||
382 | this gives us erf(x) and erfc(x) for all x. | ||
383 | |||
384 | The series expansion used is: | ||
385 | |||
386 | erf(x) = x*exp(-x*x)/sqrt(pi) * [ | ||
387 | 2/1 + 4/3 x**2 + 8/15 x**4 + 16/105 x**6 + ...] | ||
388 | |||
389 | The coefficient of x**(2k-2) here is 4**k*factorial(k)/factorial(2*k). | ||
390 | This series converges well for smallish x, but slowly for larger x. | ||
391 | |||
392 | The continued fraction expansion used is: | ||
393 | |||
394 | erfc(x) = x*exp(-x*x)/sqrt(pi) * [1/(0.5 + x**2 -) 0.5/(2.5 + x**2 - ) | ||
395 | 3.0/(4.5 + x**2 - ) 7.5/(6.5 + x**2 - ) ...] | ||
396 | |||
397 | after the first term, the general term has the form: | ||
398 | |||
399 | k*(k-0.5)/(2*k+0.5 + x**2 - ...). | ||
400 | |||
401 | This expansion converges fast for larger x, but convergence becomes | ||
402 | infinitely slow as x approaches 0.0. The (somewhat naive) continued | ||
403 | fraction evaluation algorithm used below also risks overflow for large x; | ||
404 | but for large x, erfc(x) == 0.0 to within machine precision. (For | ||
405 | example, erfc(30.0) is approximately 2.56e-393). | ||
406 | |||
407 | Parameters: use series expansion for abs(x) < ERF_SERIES_CUTOFF and | ||
408 | continued fraction expansion for ERF_SERIES_CUTOFF <= abs(x) < | ||
409 | ERFC_CONTFRAC_CUTOFF. ERFC_SERIES_TERMS and ERFC_CONTFRAC_TERMS are the | ||
410 | numbers of terms to use for the relevant expansions. */ | ||
411 | |||
412 | #define ERF_SERIES_CUTOFF1.5 1.5 | ||
413 | #define ERF_SERIES_TERMS25 25 | ||
414 | #define ERFC_CONTFRAC_CUTOFF30.0 30.0 | ||
415 | #define ERFC_CONTFRAC_TERMS50 50 | ||
416 | |||
417 | /* | ||
418 | Error function, via power series. | ||
419 | |||
420 | Given a finite float x, return an approximation to erf(x). | ||
421 | Converges reasonably fast for small x. | ||
422 | */ | ||
423 | |||
424 | static double | ||
425 | m_erf_series(double x) | ||
426 | { | ||
427 | double x2, acc, fk, result; | ||
428 | int i, saved_errno; | ||
429 | |||
430 | x2 = x * x; | ||
431 | acc = 0.0; | ||
432 | fk = (double)ERF_SERIES_TERMS25 + 0.5; | ||
433 | for (i = 0; i < ERF_SERIES_TERMS25; i++) { | ||
434 | acc = 2.0 + x2 * acc / fk; | ||
435 | fk -= 1.0; | ||
436 | } | ||
437 | /* Make sure the exp call doesn't affect errno; | ||
438 | see m_erfc_contfrac for more. */ | ||
439 | saved_errno = errno(*__error()); | ||
440 | result = acc * x * exp(-x2) / sqrtpi; | ||
441 | errno(*__error()) = saved_errno; | ||
442 | return result; | ||
443 | } | ||
444 | |||
445 | /* | ||
446 | Complementary error function, via continued fraction expansion. | ||
447 | |||
448 | Given a positive float x, return an approximation to erfc(x). Converges | ||
449 | reasonably fast for x large (say, x > 2.0), and should be safe from | ||
450 | overflow if x and nterms are not too large. On an IEEE 754 machine, with x | ||
451 | <= 30.0, we're safe up to nterms = 100. For x >= 30.0, erfc(x) is smaller | ||
452 | than the smallest representable nonzero float. */ | ||
453 | |||
454 | static double | ||
455 | m_erfc_contfrac(double x) | ||
456 | { | ||
457 | double x2, a, da, p, p_last, q, q_last, b, result; | ||
458 | int i, saved_errno; | ||
459 | |||
460 | if (x >= ERFC_CONTFRAC_CUTOFF30.0) | ||
461 | return 0.0; | ||
462 | |||
463 | x2 = x*x; | ||
464 | a = 0.0; | ||
465 | da = 0.5; | ||
466 | p = 1.0; p_last = 0.0; | ||
467 | q = da + x2; q_last = 1.0; | ||
468 | for (i = 0; i < ERFC_CONTFRAC_TERMS50; i++) { | ||
469 | double temp; | ||
470 | a += da; | ||
471 | da += 2.0; | ||
472 | b = da + x2; | ||
473 | temp = p; p = b*p - a*p_last; p_last = temp; | ||
474 | temp = q; q = b*q - a*q_last; q_last = temp; | ||
475 | } | ||
476 | /* Issue #8986: On some platforms, exp sets errno on underflow to zero; | ||
477 | save the current errno value so that we can restore it later. */ | ||
478 | saved_errno = errno(*__error()); | ||
479 | result = p / q * x * exp(-x2) / sqrtpi; | ||
480 | errno(*__error()) = saved_errno; | ||
481 | return result; | ||
482 | } | ||
483 | |||
484 | /* Error function erf(x), for general x */ | ||
485 | |||
486 | static double | ||
487 | m_erf(double x) | ||
488 | { | ||
489 | double absx, cf; | ||
490 | |||
491 | if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x)))) | ||
492 | return x; | ||
493 | absx = fabs(x); | ||
494 | if (absx < ERF_SERIES_CUTOFF1.5) | ||
495 | return m_erf_series(x); | ||
496 | else { | ||
497 | cf = m_erfc_contfrac(absx); | ||
498 | return x > 0.0 ? 1.0 - cf : cf - 1.0; | ||
499 | } | ||
500 | } | ||
501 | |||
502 | /* Complementary error function erfc(x), for general x. */ | ||
503 | |||
504 | static double | ||
505 | m_erfc(double x) | ||
506 | { | ||
507 | double absx, cf; | ||
508 | |||
509 | if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x)))) | ||
510 | return x; | ||
511 | absx = fabs(x); | ||
512 | if (absx < ERF_SERIES_CUTOFF1.5) | ||
513 | return 1.0 - m_erf_series(x); | ||
514 | else { | ||
515 | cf = m_erfc_contfrac(absx); | ||
516 | return x > 0.0 ? cf : 2.0 - cf; | ||
517 | } | ||
518 | } | ||
519 | |||
520 | /* | ||
521 | wrapper for atan2 that deals directly with special cases before | ||
522 | delegating to the platform libm for the remaining cases. This | ||
523 | is necessary to get consistent behaviour across platforms. | ||
524 | Windows, FreeBSD and alpha Tru64 are amongst platforms that don't | ||
525 | always follow C99. | ||
526 | */ | ||
527 | |||
528 | static double | ||
529 | m_atan2(double y, double x) | ||
530 | { | ||
531 | if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x))) || Py_IS_NAN(y)( sizeof (y) == sizeof(float ) ? __inline_isnanf((float)(y)) : sizeof (y) == sizeof(double) ? __inline_isnand((double)(y)) : __inline_isnan ((long double)(y)))) | ||
532 | return Py_NAN(__builtin_huge_val() * 0.); | ||
533 | if (Py_IS_INFINITY(y)( sizeof (y) == sizeof(float ) ? __inline_isinff((float)(y)) : sizeof (y) == sizeof(double) ? __inline_isinfd((double)(y)) : __inline_isinf ((long double)(y)))) { | ||
534 | if (Py_IS_INFINITY(x)( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isinfd((double)(x)) : __inline_isinf ((long double)(x)))) { | ||
535 | if (copysign(1., x) == 1.) | ||
536 | /* atan2(+-inf, +inf) == +-pi/4 */ | ||
537 | return copysign(0.25*Py_MATH_PI3.14159265358979323846, y); | ||
538 | else | ||
539 | /* atan2(+-inf, -inf) == +-pi*3/4 */ | ||
540 | return copysign(0.75*Py_MATH_PI3.14159265358979323846, y); | ||
541 | } | ||
542 | /* atan2(+-inf, x) == +-pi/2 for finite x */ | ||
543 | return copysign(0.5*Py_MATH_PI3.14159265358979323846, y); | ||
544 | } | ||
545 | if (Py_IS_INFINITY(x)( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isinfd((double)(x)) : __inline_isinf ((long double)(x))) || y == 0.) { | ||
546 | if (copysign(1., x) == 1.) | ||
547 | /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */ | ||
548 | return copysign(0., y); | ||
549 | else | ||
550 | /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */ | ||
551 | return copysign(Py_MATH_PI3.14159265358979323846, y); | ||
552 | } | ||
553 | return atan2(y, x); | ||
554 | } | ||
555 | |||
556 | /* | ||
557 | Various platforms (Solaris, OpenBSD) do nonstandard things for log(0), | ||
558 | log(-ve), log(NaN). Here are wrappers for log and log10 that deal with | ||
559 | special values directly, passing positive non-special values through to | ||
560 | the system log/log10. | ||
561 | */ | ||
562 | |||
563 | static double | ||
564 | m_log(double x) | ||
565 | { | ||
566 | if (Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))) { | ||
567 | if (x > 0.0) | ||
568 | return log(x); | ||
569 | errno(*__error()) = EDOM33; | ||
570 | if (x == 0.0) | ||
571 | return -Py_HUGE_VAL__builtin_huge_val(); /* log(0) = -inf */ | ||
572 | else | ||
573 | return Py_NAN(__builtin_huge_val() * 0.); /* log(-ve) = nan */ | ||
574 | } | ||
575 | else if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x)))) | ||
576 | return x; /* log(nan) = nan */ | ||
577 | else if (x > 0.0) | ||
578 | return x; /* log(inf) = inf */ | ||
579 | else { | ||
580 | errno(*__error()) = EDOM33; | ||
581 | return Py_NAN(__builtin_huge_val() * 0.); /* log(-inf) = nan */ | ||
582 | } | ||
583 | } | ||
584 | |||
585 | static double | ||
586 | m_log10(double x) | ||
587 | { | ||
588 | if (Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))) { | ||
589 | if (x > 0.0) | ||
590 | return log10(x); | ||
591 | errno(*__error()) = EDOM33; | ||
592 | if (x == 0.0) | ||
593 | return -Py_HUGE_VAL__builtin_huge_val(); /* log10(0) = -inf */ | ||
594 | else | ||
595 | return Py_NAN(__builtin_huge_val() * 0.); /* log10(-ve) = nan */ | ||
596 | } | ||
597 | else if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x)))) | ||
598 | return x; /* log10(nan) = nan */ | ||
599 | else if (x > 0.0) | ||
600 | return x; /* log10(inf) = inf */ | ||
601 | else { | ||
602 | errno(*__error()) = EDOM33; | ||
603 | return Py_NAN(__builtin_huge_val() * 0.); /* log10(-inf) = nan */ | ||
604 | } | ||
605 | } | ||
606 | |||
607 | |||
608 | /* Call is_error when errno != 0, and where x is the result libm | ||
609 | * returned. is_error will usually set up an exception and return | ||
610 | * true (1), but may return false (0) without setting up an exception. | ||
611 | */ | ||
612 | static int | ||
613 | is_error(double x) | ||
614 | { | ||
615 | int result = 1; /* presumption of guilt */ | ||
616 | assert(errno)(__builtin_expect(!((*__error())), 0) ? __assert_rtn(__func__ , "/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 616 , "errno") : (void)0); /* non-zero errno is a precondition for calling */ | ||
617 | if (errno(*__error()) == EDOM33) | ||
618 | PyErr_SetString(PyExc_ValueError, "math domain error"); | ||
619 | |||
620 | else if (errno(*__error()) == ERANGE34) { | ||
621 | /* ANSI C generally requires libm functions to set ERANGE | ||
622 | * on overflow, but also generally *allows* them to set | ||
623 | * ERANGE on underflow too. There's no consistency about | ||
624 | * the latter across platforms. | ||
625 | * Alas, C99 never requires that errno be set. | ||
626 | * Here we suppress the underflow errors (libm functions | ||
627 | * should return a zero on underflow, and +- HUGE_VAL on | ||
628 | * overflow, so testing the result for zero suffices to | ||
629 | * distinguish the cases). | ||
630 | * | ||
631 | * On some platforms (Ubuntu/ia64) it seems that errno can be | ||
632 | * set to ERANGE for subnormal results that do *not* underflow | ||
633 | * to zero. So to be safe, we'll ignore ERANGE whenever the | ||
634 | * function result is less than one in absolute value. | ||
635 | */ | ||
636 | if (fabs(x) < 1.0) | ||
637 | result = 0; | ||
638 | else | ||
639 | PyErr_SetString(PyExc_OverflowError, | ||
640 | "math range error"); | ||
641 | } | ||
642 | else | ||
643 | /* Unexpected math error */ | ||
644 | PyErr_SetFromErrno(PyExc_ValueError); | ||
645 | return result; | ||
646 | } | ||
647 | |||
648 | /* | ||
649 | math_1 is used to wrap a libm function f that takes a double | ||
650 | arguments and returns a double. | ||
651 | |||
652 | The error reporting follows these rules, which are designed to do | ||
653 | the right thing on C89/C99 platforms and IEEE 754/non IEEE 754 | ||
654 | platforms. | ||
655 | |||
656 | - a NaN result from non-NaN inputs causes ValueError to be raised | ||
657 | - an infinite result from finite inputs causes OverflowError to be | ||
658 | raised if can_overflow is 1, or raises ValueError if can_overflow | ||
659 | is 0. | ||
660 | - if the result is finite and errno == EDOM then ValueError is | ||
661 | raised | ||
662 | - if the result is finite and nonzero and errno == ERANGE then | ||
663 | OverflowError is raised | ||
664 | |||
665 | The last rule is used to catch overflow on platforms which follow | ||
666 | C89 but for which HUGE_VAL is not an infinity. | ||
667 | |||
668 | For the majority of one-argument functions these rules are enough | ||
669 | to ensure that Python's functions behave as specified in 'Annex F' | ||
670 | of the C99 standard, with the 'invalid' and 'divide-by-zero' | ||
671 | floating-point exceptions mapping to Python's ValueError and the | ||
672 | 'overflow' floating-point exception mapping to OverflowError. | ||
673 | math_1 only works for functions that don't have singularities *and* | ||
674 | the possibility of overflow; fortunately, that covers everything we | ||
675 | care about right now. | ||
676 | */ | ||
677 | |||
678 | static PyObject * | ||
679 | math_1_to_whatever(PyObject *arg, double (*func) (double), | ||
680 | PyObject *(*from_double_func) (double), | ||
681 | int can_overflow) | ||
682 | { | ||
683 | double x, r; | ||
684 | x = PyFloat_AsDouble(arg); | ||
685 | if (x == -1.0 && PyErr_Occurred()) | ||
686 | return NULL((void *)0); | ||
687 | errno(*__error()) = 0; | ||
688 | PyFPE_START_PROTECT("in math_1", return 0); | ||
689 | r = (*func)(x); | ||
690 | PyFPE_END_PROTECT(r); | ||
691 | if (Py_IS_NAN(r)( sizeof (r) == sizeof(float ) ? __inline_isnanf((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isnand((double)(r)) : __inline_isnan ((long double)(r))) && !Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x)))) { | ||
692 | PyErr_SetString(PyExc_ValueError, | ||
693 | "math domain error"); /* invalid arg */ | ||
694 | return NULL((void *)0); | ||
695 | } | ||
696 | if (Py_IS_INFINITY(r)( sizeof (r) == sizeof(float ) ? __inline_isinff((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isinfd((double)(r)) : __inline_isinf ((long double)(r))) && Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))) { | ||
697 | if (can_overflow) | ||
698 | PyErr_SetString(PyExc_OverflowError, | ||
699 | "math range error"); /* overflow */ | ||
700 | else | ||
701 | PyErr_SetString(PyExc_ValueError, | ||
702 | "math domain error"); /* singularity */ | ||
703 | return NULL((void *)0); | ||
704 | } | ||
705 | if (Py_IS_FINITE(r)( sizeof (r) == sizeof(float ) ? __inline_isfinitef((float)(r )) : sizeof (r) == sizeof(double) ? __inline_isfinited((double )(r)) : __inline_isfinite ((long double)(r))) && errno(*__error()) && is_error(r)) | ||
706 | /* this branch unnecessary on most platforms */ | ||
707 | return NULL((void *)0); | ||
708 | |||
709 | return (*from_double_func)(r); | ||
710 | } | ||
711 | |||
712 | /* variant of math_1, to be used when the function being wrapped is known to | ||
713 | set errno properly (that is, errno = EDOM for invalid or divide-by-zero, | ||
714 | errno = ERANGE for overflow). */ | ||
715 | |||
716 | static PyObject * | ||
717 | math_1a(PyObject *arg, double (*func) (double)) | ||
718 | { | ||
719 | double x, r; | ||
720 | x = PyFloat_AsDouble(arg); | ||
721 | if (x == -1.0 && PyErr_Occurred()) | ||
722 | return NULL((void *)0); | ||
723 | errno(*__error()) = 0; | ||
724 | PyFPE_START_PROTECT("in math_1a", return 0); | ||
725 | r = (*func)(x); | ||
726 | PyFPE_END_PROTECT(r); | ||
727 | if (errno(*__error()) && is_error(r)) | ||
728 | return NULL((void *)0); | ||
729 | return PyFloat_FromDouble(r); | ||
730 | } | ||
731 | |||
732 | /* | ||
733 | math_2 is used to wrap a libm function f that takes two double | ||
734 | arguments and returns a double. | ||
735 | |||
736 | The error reporting follows these rules, which are designed to do | ||
737 | the right thing on C89/C99 platforms and IEEE 754/non IEEE 754 | ||
738 | platforms. | ||
739 | |||
740 | - a NaN result from non-NaN inputs causes ValueError to be raised | ||
741 | - an infinite result from finite inputs causes OverflowError to be | ||
742 | raised. | ||
743 | - if the result is finite and errno == EDOM then ValueError is | ||
744 | raised | ||
745 | - if the result is finite and nonzero and errno == ERANGE then | ||
746 | OverflowError is raised | ||
747 | |||
748 | The last rule is used to catch overflow on platforms which follow | ||
749 | C89 but for which HUGE_VAL is not an infinity. | ||
750 | |||
751 | For most two-argument functions (copysign, fmod, hypot, atan2) | ||
752 | these rules are enough to ensure that Python's functions behave as | ||
753 | specified in 'Annex F' of the C99 standard, with the 'invalid' and | ||
754 | 'divide-by-zero' floating-point exceptions mapping to Python's | ||
755 | ValueError and the 'overflow' floating-point exception mapping to | ||
756 | OverflowError. | ||
757 | */ | ||
758 | |||
759 | static PyObject * | ||
760 | math_1(PyObject *arg, double (*func) (double), int can_overflow) | ||
761 | { | ||
762 | return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow); | ||
763 | } | ||
764 | |||
765 | static PyObject * | ||
766 | math_1_to_int(PyObject *arg, double (*func) (double), int can_overflow) | ||
767 | { | ||
768 | return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow); | ||
769 | } | ||
770 | |||
771 | static PyObject * | ||
772 | math_2(PyObject *args, double (*func) (double, double), char *funcname) | ||
773 | { | ||
774 | PyObject *ox, *oy; | ||
775 | double x, y, r; | ||
776 | if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy)) | ||
777 | return NULL((void *)0); | ||
778 | x = PyFloat_AsDouble(ox); | ||
779 | y = PyFloat_AsDouble(oy); | ||
780 | if ((x == -1.0 || y == -1.0) && PyErr_Occurred()) | ||
781 | return NULL((void *)0); | ||
782 | errno(*__error()) = 0; | ||
783 | PyFPE_START_PROTECT("in math_2", return 0); | ||
784 | r = (*func)(x, y); | ||
785 | PyFPE_END_PROTECT(r); | ||
786 | if (Py_IS_NAN(r)( sizeof (r) == sizeof(float ) ? __inline_isnanf((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isnand((double)(r)) : __inline_isnan ((long double)(r)))) { | ||
787 | if (!Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x))) && !Py_IS_NAN(y)( sizeof (y) == sizeof(float ) ? __inline_isnanf((float)(y)) : sizeof (y) == sizeof(double) ? __inline_isnand((double)(y)) : __inline_isnan ((long double)(y)))) | ||
788 | errno(*__error()) = EDOM33; | ||
789 | else | ||
790 | errno(*__error()) = 0; | ||
791 | } | ||
792 | else if (Py_IS_INFINITY(r)( sizeof (r) == sizeof(float ) ? __inline_isinff((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isinfd((double)(r)) : __inline_isinf ((long double)(r)))) { | ||
793 | if (Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x))) && Py_IS_FINITE(y)( sizeof (y) == sizeof(float ) ? __inline_isfinitef((float)(y )) : sizeof (y) == sizeof(double) ? __inline_isfinited((double )(y)) : __inline_isfinite ((long double)(y)))) | ||
794 | errno(*__error()) = ERANGE34; | ||
795 | else | ||
796 | errno(*__error()) = 0; | ||
797 | } | ||
798 | if (errno(*__error()) && is_error(r)) | ||
799 | return NULL((void *)0); | ||
800 | else | ||
801 | return PyFloat_FromDouble(r); | ||
802 | } | ||
803 | |||
804 | #define FUNC1(funcname, func, can_overflow, docstring)static PyObject * math_funcname(PyObject *self, PyObject *args ) { return math_1(args, func, can_overflow); } static char math_funcname_doc [] = docstring; \ | ||
805 | static PyObject * math_##funcname(PyObject *self, PyObject *args) { \ | ||
806 | return math_1(args, func, can_overflow); \ | ||
807 | }\ | ||
808 | PyDoc_STRVAR(math_##funcname##_doc, docstring)static char math_##funcname##_doc[] = docstring; | ||
809 | |||
810 | #define FUNC1A(funcname, func, docstring)static PyObject * math_funcname(PyObject *self, PyObject *args ) { return math_1a(args, func); } static char math_funcname_doc [] = docstring; \ | ||
811 | static PyObject * math_##funcname(PyObject *self, PyObject *args) { \ | ||
812 | return math_1a(args, func); \ | ||
813 | }\ | ||
814 | PyDoc_STRVAR(math_##funcname##_doc, docstring)static char math_##funcname##_doc[] = docstring; | ||
815 | |||
816 | #define FUNC2(funcname, func, docstring)static PyObject * math_funcname(PyObject *self, PyObject *args ) { return math_2(args, func, "funcname"); } static char math_funcname_doc [] = docstring; \ | ||
817 | static PyObject * math_##funcname(PyObject *self, PyObject *args) { \ | ||
818 | return math_2(args, func, #funcname); \ | ||
819 | }\ | ||
820 | PyDoc_STRVAR(math_##funcname##_doc, docstring)static char math_##funcname##_doc[] = docstring; | ||
821 | |||
822 | FUNC1(acos, acos, 0,static PyObject * math_acos(PyObject *self, PyObject *args) { return math_1(args, acos, 0); } static char math_acos_doc[] = "acos(x)\n\nReturn the arc cosine (measured in radians) of x." ; | ||
823 | "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")static PyObject * math_acos(PyObject *self, PyObject *args) { return math_1(args, acos, 0); } static char math_acos_doc[] = "acos(x)\n\nReturn the arc cosine (measured in radians) of x." ; | ||
824 | FUNC1(acosh, m_acosh, 0,static PyObject * math_acosh(PyObject *self, PyObject *args) { return math_1(args, acosh, 0); } static char math_acosh_doc[ ] = "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x." ; | ||
825 | "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")static PyObject * math_acosh(PyObject *self, PyObject *args) { return math_1(args, acosh, 0); } static char math_acosh_doc[ ] = "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x." ; | ||
826 | FUNC1(asin, asin, 0,static PyObject * math_asin(PyObject *self, PyObject *args) { return math_1(args, asin, 0); } static char math_asin_doc[] = "asin(x)\n\nReturn the arc sine (measured in radians) of x." ; | ||
827 | "asin(x)\n\nReturn the arc sine (measured in radians) of x.")static PyObject * math_asin(PyObject *self, PyObject *args) { return math_1(args, asin, 0); } static char math_asin_doc[] = "asin(x)\n\nReturn the arc sine (measured in radians) of x." ; | ||
828 | FUNC1(asinh, m_asinh, 0,static PyObject * math_asinh(PyObject *self, PyObject *args) { return math_1(args, asinh, 0); } static char math_asinh_doc[ ] = "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x." ; | ||
829 | "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")static PyObject * math_asinh(PyObject *self, PyObject *args) { return math_1(args, asinh, 0); } static char math_asinh_doc[ ] = "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x." ; | ||
830 | FUNC1(atan, atan, 0,static PyObject * math_atan(PyObject *self, PyObject *args) { return math_1(args, atan, 0); } static char math_atan_doc[] = "atan(x)\n\nReturn the arc tangent (measured in radians) of x." ; | ||
831 | "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")static PyObject * math_atan(PyObject *self, PyObject *args) { return math_1(args, atan, 0); } static char math_atan_doc[] = "atan(x)\n\nReturn the arc tangent (measured in radians) of x." ; | ||
832 | FUNC2(atan2, m_atan2,static PyObject * math_atan2(PyObject *self, PyObject *args) { return math_2(args, m_atan2, "atan2"); } static char math_atan2_doc [] = "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n" "Unlike atan(y/x), the signs of both x and y are considered." ; | ||
833 | "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"static PyObject * math_atan2(PyObject *self, PyObject *args) { return math_2(args, m_atan2, "atan2"); } static char math_atan2_doc [] = "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n" "Unlike atan(y/x), the signs of both x and y are considered." ; | ||
834 | "Unlike atan(y/x), the signs of both x and y are considered.")static PyObject * math_atan2(PyObject *self, PyObject *args) { return math_2(args, m_atan2, "atan2"); } static char math_atan2_doc [] = "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n" "Unlike atan(y/x), the signs of both x and y are considered." ; | ||
835 | FUNC1(atanh, m_atanh, 0,static PyObject * math_atanh(PyObject *self, PyObject *args) { return math_1(args, atanh, 0); } static char math_atanh_doc[ ] = "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x." ; | ||
836 | "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")static PyObject * math_atanh(PyObject *self, PyObject *args) { return math_1(args, atanh, 0); } static char math_atanh_doc[ ] = "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x." ; | ||
837 | |||
838 | static PyObject * math_ceil(PyObject *self, PyObject *number) { | ||
839 | static PyObject *ceil_str = NULL((void *)0); | ||
840 | PyObject *method, *result; | ||
841 | |||
842 | method = _PyObject_LookupSpecial(number, "__ceil__", &ceil_str); | ||
843 | if (method == NULL((void *)0)) { | ||
844 | if (PyErr_Occurred()) | ||
845 | return NULL((void *)0); | ||
846 | return math_1_to_int(number, ceil, 0); | ||
847 | } | ||
848 | result = PyObject_CallFunctionObjArgs(method, NULL((void *)0)); | ||
849 | Py_DECREF(method)do { if (_Py_RefTotal-- , --((PyObject*)(method))->ob_refcnt != 0) { if (((PyObject*)method)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 849 , (PyObject *)(method)); } else _Py_Dealloc((PyObject *)(method )); } while (0); | ||
850 | return result; | ||
851 | } | ||
852 | |||
853 | PyDoc_STRVAR(math_ceil_doc,static char math_ceil_doc[] = "ceil(x)\n\nReturn the ceiling of x as an int.\n" "This is the smallest integral value >= x." | ||
854 | "ceil(x)\n\nReturn the ceiling of x as an int.\n"static char math_ceil_doc[] = "ceil(x)\n\nReturn the ceiling of x as an int.\n" "This is the smallest integral value >= x." | ||
855 | "This is the smallest integral value >= x.")static char math_ceil_doc[] = "ceil(x)\n\nReturn the ceiling of x as an int.\n" "This is the smallest integral value >= x."; | ||
856 | |||
857 | FUNC2(copysign, copysign,static PyObject * math_copysign(PyObject *self, PyObject *args ) { return math_2(args, copysign, "copysign"); } static char math_copysign_doc [] = "copysign(x, y)\n\nReturn x with the sign of y."; | ||
858 | "copysign(x, y)\n\nReturn x with the sign of y.")static PyObject * math_copysign(PyObject *self, PyObject *args ) { return math_2(args, copysign, "copysign"); } static char math_copysign_doc [] = "copysign(x, y)\n\nReturn x with the sign of y."; | ||
859 | FUNC1(cos, cos, 0,static PyObject * math_cos(PyObject *self, PyObject *args) { return math_1(args, cos, 0); } static char math_cos_doc[] = "cos(x)\n\nReturn the cosine of x (measured in radians)." ; | ||
860 | "cos(x)\n\nReturn the cosine of x (measured in radians).")static PyObject * math_cos(PyObject *self, PyObject *args) { return math_1(args, cos, 0); } static char math_cos_doc[] = "cos(x)\n\nReturn the cosine of x (measured in radians)." ; | ||
861 | FUNC1(cosh, cosh, 1,static PyObject * math_cosh(PyObject *self, PyObject *args) { return math_1(args, cosh, 1); } static char math_cosh_doc[] = "cosh(x)\n\nReturn the hyperbolic cosine of x."; | ||
862 | "cosh(x)\n\nReturn the hyperbolic cosine of x.")static PyObject * math_cosh(PyObject *self, PyObject *args) { return math_1(args, cosh, 1); } static char math_cosh_doc[] = "cosh(x)\n\nReturn the hyperbolic cosine of x."; | ||
863 | FUNC1A(erf, m_erf,static PyObject * math_erf(PyObject *self, PyObject *args) { return math_1a(args, m_erf); } static char math_erf_doc[] = "erf(x)\n\nError function at x." ; | ||
864 | "erf(x)\n\nError function at x.")static PyObject * math_erf(PyObject *self, PyObject *args) { return math_1a(args, m_erf); } static char math_erf_doc[] = "erf(x)\n\nError function at x." ; | ||
865 | FUNC1A(erfc, m_erfc,static PyObject * math_erfc(PyObject *self, PyObject *args) { return math_1a(args, m_erfc); } static char math_erfc_doc[] = "erfc(x)\n\nComplementary error function at x."; | ||
866 | "erfc(x)\n\nComplementary error function at x.")static PyObject * math_erfc(PyObject *self, PyObject *args) { return math_1a(args, m_erfc); } static char math_erfc_doc[] = "erfc(x)\n\nComplementary error function at x."; | ||
867 | FUNC1(exp, exp, 1,static PyObject * math_exp(PyObject *self, PyObject *args) { return math_1(args, exp, 1); } static char math_exp_doc[] = "exp(x)\n\nReturn e raised to the power of x." ; | ||
868 | "exp(x)\n\nReturn e raised to the power of x.")static PyObject * math_exp(PyObject *self, PyObject *args) { return math_1(args, exp, 1); } static char math_exp_doc[] = "exp(x)\n\nReturn e raised to the power of x." ; | ||
869 | FUNC1(expm1, m_expm1, 1,static PyObject * math_expm1(PyObject *self, PyObject *args) { return math_1(args, expm1, 1); } static char math_expm1_doc[ ] = "expm1(x)\n\nReturn exp(x)-1.\n" "This function avoids the loss of precision involved in the direct " "evaluation of exp(x)-1 for small x."; | ||
870 | "expm1(x)\n\nReturn exp(x)-1.\n"static PyObject * math_expm1(PyObject *self, PyObject *args) { return math_1(args, expm1, 1); } static char math_expm1_doc[ ] = "expm1(x)\n\nReturn exp(x)-1.\n" "This function avoids the loss of precision involved in the direct " "evaluation of exp(x)-1 for small x."; | ||
871 | "This function avoids the loss of precision involved in the direct "static PyObject * math_expm1(PyObject *self, PyObject *args) { return math_1(args, expm1, 1); } static char math_expm1_doc[ ] = "expm1(x)\n\nReturn exp(x)-1.\n" "This function avoids the loss of precision involved in the direct " "evaluation of exp(x)-1 for small x."; | ||
872 | "evaluation of exp(x)-1 for small x.")static PyObject * math_expm1(PyObject *self, PyObject *args) { return math_1(args, expm1, 1); } static char math_expm1_doc[ ] = "expm1(x)\n\nReturn exp(x)-1.\n" "This function avoids the loss of precision involved in the direct " "evaluation of exp(x)-1 for small x."; | ||
873 | FUNC1(fabs, fabs, 0,static PyObject * math_fabs(PyObject *self, PyObject *args) { return math_1(args, fabs, 0); } static char math_fabs_doc[] = "fabs(x)\n\nReturn the absolute value of the float x."; | ||
874 | "fabs(x)\n\nReturn the absolute value of the float x.")static PyObject * math_fabs(PyObject *self, PyObject *args) { return math_1(args, fabs, 0); } static char math_fabs_doc[] = "fabs(x)\n\nReturn the absolute value of the float x."; | ||
875 | |||
876 | static PyObject * math_floor(PyObject *self, PyObject *number) { | ||
877 | static PyObject *floor_str = NULL((void *)0); | ||
878 | PyObject *method, *result; | ||
879 | |||
880 | method = _PyObject_LookupSpecial(number, "__floor__", &floor_str); | ||
881 | if (method == NULL((void *)0)) { | ||
882 | if (PyErr_Occurred()) | ||
883 | return NULL((void *)0); | ||
884 | return math_1_to_int(number, floor, 0); | ||
885 | } | ||
886 | result = PyObject_CallFunctionObjArgs(method, NULL((void *)0)); | ||
887 | Py_DECREF(method)do { if (_Py_RefTotal-- , --((PyObject*)(method))->ob_refcnt != 0) { if (((PyObject*)method)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 887 , (PyObject *)(method)); } else _Py_Dealloc((PyObject *)(method )); } while (0); | ||
888 | return result; | ||
889 | } | ||
890 | |||
891 | PyDoc_STRVAR(math_floor_doc,static char math_floor_doc[] = "floor(x)\n\nReturn the floor of x as an int.\n" "This is the largest integral value <= x." | ||
892 | "floor(x)\n\nReturn the floor of x as an int.\n"static char math_floor_doc[] = "floor(x)\n\nReturn the floor of x as an int.\n" "This is the largest integral value <= x." | ||
893 | "This is the largest integral value <= x.")static char math_floor_doc[] = "floor(x)\n\nReturn the floor of x as an int.\n" "This is the largest integral value <= x."; | ||
894 | |||
895 | FUNC1A(gamma, m_tgamma,static PyObject * math_gamma(PyObject *self, PyObject *args) { return math_1a(args, m_tgamma); } static char math_gamma_doc [] = "gamma(x)\n\nGamma function at x."; | ||
896 | "gamma(x)\n\nGamma function at x.")static PyObject * math_gamma(PyObject *self, PyObject *args) { return math_1a(args, m_tgamma); } static char math_gamma_doc [] = "gamma(x)\n\nGamma function at x."; | ||
897 | FUNC1A(lgamma, m_lgamma,static PyObject * math_lgamma(PyObject *self, PyObject *args) { return math_1a(args, m_lgamma); } static char math_lgamma_doc [] = "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x." ; | ||
898 | "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.")static PyObject * math_lgamma(PyObject *self, PyObject *args) { return math_1a(args, m_lgamma); } static char math_lgamma_doc [] = "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x." ; | ||
899 | FUNC1(log1p, m_log1p, 0,static PyObject * math_log1p(PyObject *self, PyObject *args) { return math_1(args, log1p, 0); } static char math_log1p_doc[ ] = "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n" "The result is computed in a way which is accurate for x near zero." ; | ||
900 | "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"static PyObject * math_log1p(PyObject *self, PyObject *args) { return math_1(args, log1p, 0); } static char math_log1p_doc[ ] = "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n" "The result is computed in a way which is accurate for x near zero." ; | ||
901 | "The result is computed in a way which is accurate for x near zero.")static PyObject * math_log1p(PyObject *self, PyObject *args) { return math_1(args, log1p, 0); } static char math_log1p_doc[ ] = "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n" "The result is computed in a way which is accurate for x near zero." ; | ||
902 | FUNC1(sin, sin, 0,static PyObject * math_sin(PyObject *self, PyObject *args) { return math_1(args, sin, 0); } static char math_sin_doc[] = "sin(x)\n\nReturn the sine of x (measured in radians)." ; | ||
903 | "sin(x)\n\nReturn the sine of x (measured in radians).")static PyObject * math_sin(PyObject *self, PyObject *args) { return math_1(args, sin, 0); } static char math_sin_doc[] = "sin(x)\n\nReturn the sine of x (measured in radians)." ; | ||
904 | FUNC1(sinh, sinh, 1,static PyObject * math_sinh(PyObject *self, PyObject *args) { return math_1(args, sinh, 1); } static char math_sinh_doc[] = "sinh(x)\n\nReturn the hyperbolic sine of x."; | ||
905 | "sinh(x)\n\nReturn the hyperbolic sine of x.")static PyObject * math_sinh(PyObject *self, PyObject *args) { return math_1(args, sinh, 1); } static char math_sinh_doc[] = "sinh(x)\n\nReturn the hyperbolic sine of x."; | ||
906 | FUNC1(sqrt, sqrt, 0,static PyObject * math_sqrt(PyObject *self, PyObject *args) { return math_1(args, sqrt, 0); } static char math_sqrt_doc[] = "sqrt(x)\n\nReturn the square root of x."; | ||
907 | "sqrt(x)\n\nReturn the square root of x.")static PyObject * math_sqrt(PyObject *self, PyObject *args) { return math_1(args, sqrt, 0); } static char math_sqrt_doc[] = "sqrt(x)\n\nReturn the square root of x."; | ||
908 | FUNC1(tan, tan, 0,static PyObject * math_tan(PyObject *self, PyObject *args) { return math_1(args, tan, 0); } static char math_tan_doc[] = "tan(x)\n\nReturn the tangent of x (measured in radians)." ; | ||
909 | "tan(x)\n\nReturn the tangent of x (measured in radians).")static PyObject * math_tan(PyObject *self, PyObject *args) { return math_1(args, tan, 0); } static char math_tan_doc[] = "tan(x)\n\nReturn the tangent of x (measured in radians)." ; | ||
910 | FUNC1(tanh, tanh, 0,static PyObject * math_tanh(PyObject *self, PyObject *args) { return math_1(args, tanh, 0); } static char math_tanh_doc[] = "tanh(x)\n\nReturn the hyperbolic tangent of x."; | ||
911 | "tanh(x)\n\nReturn the hyperbolic tangent of x.")static PyObject * math_tanh(PyObject *self, PyObject *args) { return math_1(args, tanh, 0); } static char math_tanh_doc[] = "tanh(x)\n\nReturn the hyperbolic tangent of x."; | ||
912 | |||
913 | /* Precision summation function as msum() by Raymond Hettinger in | ||
914 | <http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090>, | ||
915 | enhanced with the exact partials sum and roundoff from Mark | ||
916 | Dickinson's post at <http://bugs.python.org/file10357/msum4.py>. | ||
917 | See those links for more details, proofs and other references. | ||
918 | |||
919 | Note 1: IEEE 754R floating point semantics are assumed, | ||
920 | but the current implementation does not re-establish special | ||
921 | value semantics across iterations (i.e. handling -Inf + Inf). | ||
922 | |||
923 | Note 2: No provision is made for intermediate overflow handling; | ||
924 | therefore, sum([1e+308, 1e-308, 1e+308]) returns 1e+308 while | ||
925 | sum([1e+308, 1e+308, 1e-308]) raises an OverflowError due to the | ||
926 | overflow of the first partial sum. | ||
927 | |||
928 | Note 3: The intermediate values lo, yr, and hi are declared volatile so | ||
929 | aggressive compilers won't algebraically reduce lo to always be exactly 0.0. | ||
930 | Also, the volatile declaration forces the values to be stored in memory as | ||
931 | regular doubles instead of extended long precision (80-bit) values. This | ||
932 | prevents double rounding because any addition or subtraction of two doubles | ||
933 | can be resolved exactly into double-sized hi and lo values. As long as the | ||
934 | hi value gets forced into a double before yr and lo are computed, the extra | ||
935 | bits in downstream extended precision operations (x87 for example) will be | ||
936 | exactly zero and therefore can be losslessly stored back into a double, | ||
937 | thereby preventing double rounding. | ||
938 | |||
939 | Note 4: A similar implementation is in Modules/cmathmodule.c. | ||
940 | Be sure to update both when making changes. | ||
941 | |||
942 | Note 5: The signature of math.fsum() differs from __builtin__.sum() | ||
943 | because the start argument doesn't make sense in the context of | ||
944 | accurate summation. Since the partials table is collapsed before | ||
945 | returning a result, sum(seq2, start=sum(seq1)) may not equal the | ||
946 | accurate result returned by sum(itertools.chain(seq1, seq2)). | ||
947 | */ | ||
948 | |||
949 | #define NUM_PARTIALS 32 /* initial partials array size, on stack */ | ||
950 | |||
951 | /* Extend the partials array p[] by doubling its size. */ | ||
952 | static int /* non-zero on error */ | ||
953 | _fsum_realloc(double **p_ptr, Py_ssize_t n, | ||
954 | double *ps, Py_ssize_t *m_ptr) | ||
955 | { | ||
956 | void *v = NULL((void *)0); | ||
957 | Py_ssize_t m = *m_ptr; | ||
958 | |||
959 | m += m; /* double */ | ||
960 | if (n < m && m < (PY_SSIZE_T_MAX((Py_ssize_t)(((size_t)-1)>>1)) / sizeof(double))) { | ||
961 | double *p = *p_ptr; | ||
962 | if (p == ps) { | ||
963 | v = PyMem_Malloc(sizeof(double) * m); | ||
964 | if (v != NULL((void *)0)) | ||
965 | memcpy(v, ps, sizeof(double) * n)((__builtin_object_size (v, 0) != (size_t) -1) ? __builtin___memcpy_chk (v, ps, sizeof(double) * n, __builtin_object_size (v, 0)) : __inline_memcpy_chk (v, ps, sizeof(double) * n)); | ||
966 | } | ||
967 | else | ||
968 | v = PyMem_Realloc(p, sizeof(double) * m); | ||
969 | } | ||
970 | if (v == NULL((void *)0)) { /* size overflow or no memory */ | ||
971 | PyErr_SetString(PyExc_MemoryError, "math.fsum partials"); | ||
972 | return 1; | ||
973 | } | ||
974 | *p_ptr = (double*) v; | ||
975 | *m_ptr = m; | ||
976 | return 0; | ||
977 | } | ||
978 | |||
979 | /* Full precision summation of a sequence of floats. | ||
980 | |||
981 | def msum(iterable): | ||
982 | partials = [] # sorted, non-overlapping partial sums | ||
983 | for x in iterable: | ||
984 | i = 0 | ||
985 | for y in partials: | ||
986 | if abs(x) < abs(y): | ||
987 | x, y = y, x | ||
988 | hi = x + y | ||
989 | lo = y - (hi - x) | ||
990 | if lo: | ||
991 | partials[i] = lo | ||
992 | i += 1 | ||
993 | x = hi | ||
994 | partials[i:] = [x] | ||
995 | return sum_exact(partials) | ||
996 | |||
997 | Rounded x+y stored in hi with the roundoff stored in lo. Together hi+lo | ||
998 | are exactly equal to x+y. The inner loop applies hi/lo summation to each | ||
999 | partial so that the list of partial sums remains exact. | ||
1000 | |||
1001 | Sum_exact() adds the partial sums exactly and correctly rounds the final | ||
1002 | result (using the round-half-to-even rule). The items in partials remain | ||
1003 | non-zero, non-special, non-overlapping and strictly increasing in | ||
1004 | magnitude, but possibly not all having the same sign. | ||
1005 | |||
1006 | Depends on IEEE 754 arithmetic guarantees and half-even rounding. | ||
1007 | */ | ||
1008 | |||
1009 | static PyObject* | ||
1010 | math_fsum(PyObject *self, PyObject *seq) | ||
1011 | { | ||
1012 | PyObject *item, *iter, *sum = NULL((void *)0); | ||
1013 | Py_ssize_t i, j, n = 0, m = NUM_PARTIALS; | ||
1014 | double x, y, t, ps[NUM_PARTIALS], *p = ps; | ||
1015 | double xsave, special_sum = 0.0, inf_sum = 0.0; | ||
1016 | volatile double hi, yr, lo; | ||
1017 | |||
1018 | iter = PyObject_GetIter(seq); | ||
1019 | if (iter == NULL((void *)0)) | ||
| |||
1020 | return NULL((void *)0); | ||
1021 | |||
1022 | PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL) | ||
1023 | |||
1024 | for(;;) { /* for x in iterable */ | ||
| |||
| |||
1025 | assert(0 <= n && n <= m)(__builtin_expect(!(0 <= n && n <= m), 0) ? __assert_rtn (__func__, "/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 1025, "0 <= n && n <= m") : (void)0); | ||
1026 | assert((m == NUM_PARTIALS && p == ps) ||(__builtin_expect(!((m == NUM_PARTIALS && p == ps) || (m > NUM_PARTIALS && p != ((void *)0))), 0) ? __assert_rtn (__func__, "/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 1027, "(m == NUM_PARTIALS && p == ps) || (m > NUM_PARTIALS && p != NULL)" ) : (void)0) | ||
1027 | (m > NUM_PARTIALS && p != NULL))(__builtin_expect(!((m == NUM_PARTIALS && p == ps) || (m > NUM_PARTIALS && p != ((void *)0))), 0) ? __assert_rtn (__func__, "/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 1027, "(m == NUM_PARTIALS && p == ps) || (m > NUM_PARTIALS && p != NULL)" ) : (void)0); | ||
1028 | |||
1029 | item = PyIter_Next(iter); | ||
1030 | if (item == NULL((void *)0)) { | ||
| |||
| |||
1031 | if (PyErr_Occurred()) | ||
| |||
1032 | goto _fsum_error; | ||
1033 | break; | ||
| |||
1034 | } | ||
1035 | x = PyFloat_AsDouble(item); | ||
1036 | Py_DECREF(item)do { if (_Py_RefTotal-- , --((PyObject*)(item))->ob_refcnt != 0) { if (((PyObject*)item)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1036 , (PyObject *)(item)); } else _Py_Dealloc((PyObject *)(item)) ; } while (0); | ||
1037 | if (PyErr_Occurred()) | ||
| |||
1038 | goto _fsum_error; | ||
1039 | |||
1040 | xsave = x; | ||
1041 | for (i = j = 0; j < n; j++) { /* for y in partials */ | ||
| |||
1042 | y = p[j]; | ||
1043 | if (fabs(x) < fabs(y)) { | ||
1044 | t = x; x = y; y = t; | ||
1045 | } | ||
1046 | hi = x + y; | ||
1047 | yr = hi - x; | ||
1048 | lo = y - yr; | ||
1049 | if (lo != 0.0) | ||
1050 | p[i++] = lo; | ||
1051 | x = hi; | ||
1052 | } | ||
1053 | |||
1054 | n = i; /* ps[i:] = [x] */ | ||
1055 | if (x != 0.0) { | ||
| |||
1056 | if (! Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))) { | ||
| |||
1057 | /* a nonfinite x could arise either as | ||
1058 | a result of intermediate overflow, or | ||
1059 | as a result of a nan or inf in the | ||
1060 | summands */ | ||
1061 | if (Py_IS_FINITE(xsave)( sizeof (xsave) == sizeof(float ) ? __inline_isfinitef((float )(xsave)) : sizeof (xsave) == sizeof(double) ? __inline_isfinited ((double)(xsave)) : __inline_isfinite ((long double)(xsave)))) { | ||
1062 | PyErr_SetString(PyExc_OverflowError, | ||
1063 | "intermediate overflow in fsum"); | ||
1064 | goto _fsum_error; | ||
1065 | } | ||
1066 | if (Py_IS_INFINITY(xsave)( sizeof (xsave) == sizeof(float ) ? __inline_isinff((float)( xsave)) : sizeof (xsave) == sizeof(double) ? __inline_isinfd( (double)(xsave)) : __inline_isinf ((long double)(xsave)))) | ||
1067 | inf_sum += xsave; | ||
1068 | special_sum += xsave; | ||
1069 | /* reset partials */ | ||
1070 | n = 0; | ||
1071 | } | ||
1072 | else if (n >= m && _fsum_realloc(&p, n, ps, &m)) | ||
| |||
1073 | goto _fsum_error; | ||
1074 | else | ||
1075 | p[n++] = x; | ||
1076 | } | ||
1077 | } | ||
1078 | |||
1079 | if (special_sum != 0.0) { | ||
| |||
1080 | if (Py_IS_NAN(inf_sum)( sizeof (inf_sum) == sizeof(float ) ? __inline_isnanf((float )(inf_sum)) : sizeof (inf_sum) == sizeof(double) ? __inline_isnand ((double)(inf_sum)) : __inline_isnan ((long double)(inf_sum)) )) | ||
1081 | PyErr_SetString(PyExc_ValueError, | ||
1082 | "-inf + inf in fsum"); | ||
1083 | else | ||
1084 | sum = PyFloat_FromDouble(special_sum); | ||
1085 | goto _fsum_error; | ||
1086 | } | ||
1087 | |||
1088 | hi = 0.0; | ||
1089 | if (n > 0) { | ||
| |||
1090 | hi = p[--n]; | ||
| |||
1091 | /* sum_exact(ps, hi) from the top, stop when the sum becomes | ||
1092 | inexact. */ | ||
1093 | while (n > 0) { | ||
1094 | x = hi; | ||
1095 | y = p[--n]; | ||
1096 | assert(fabs(y) < fabs(x))(__builtin_expect(!(fabs(y) < fabs(x)), 0) ? __assert_rtn( __func__, "/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 1096, "fabs(y) < fabs(x)") : (void)0); | ||
1097 | hi = x + y; | ||
1098 | yr = hi - x; | ||
1099 | lo = y - yr; | ||
1100 | if (lo != 0.0) | ||
1101 | break; | ||
1102 | } | ||
1103 | /* Make half-even rounding work across multiple partials. | ||
1104 | Needed so that sum([1e-16, 1, 1e16]) will round-up the last | ||
1105 | digit to two instead of down to zero (the 1e-16 makes the 1 | ||
1106 | slightly closer to two). With a potential 1 ULP rounding | ||
1107 | error fixed-up, math.fsum() can guarantee commutativity. */ | ||
1108 | if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) || | ||
1109 | (lo > 0.0 && p[n-1] > 0.0))) { | ||
1110 | y = lo * 2.0; | ||
1111 | x = hi + y; | ||
1112 | yr = x - hi; | ||
1113 | if (y == yr) | ||
1114 | hi = x; | ||
1115 | } | ||
1116 | } | ||
1117 | sum = PyFloat_FromDouble(hi); | ||
1118 | |||
1119 | _fsum_error: | ||
1120 | PyFPE_END_PROTECT(hi) | ||
1121 | Py_DECREF(iter)do { if (_Py_RefTotal-- , --((PyObject*)(iter))->ob_refcnt != 0) { if (((PyObject*)iter)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1121 , (PyObject *)(iter)); } else _Py_Dealloc((PyObject *)(iter)) ; } while (0); | ||
1122 | if (p != ps) | ||
1123 | PyMem_Free(p); | ||
1124 | return sum; | ||
1125 | } | ||
1126 | |||
1127 | #undef NUM_PARTIALS | ||
1128 | |||
1129 | PyDoc_STRVAR(math_fsum_doc,static char math_fsum_doc[] = "fsum(iterable)\n\nReturn an accurate floating point sum of values in the iterable.\nAssumes IEEE-754 floating point arithmetic." | ||
1130 | "fsum(iterable)\n\n\static char math_fsum_doc[] = "fsum(iterable)\n\nReturn an accurate floating point sum of values in the iterable.\nAssumes IEEE-754 floating point arithmetic." | ||
1131 | Return an accurate floating point sum of values in the iterable.\n\static char math_fsum_doc[] = "fsum(iterable)\n\nReturn an accurate floating point sum of values in the iterable.\nAssumes IEEE-754 floating point arithmetic." | ||
1132 | Assumes IEEE-754 floating point arithmetic.")static char math_fsum_doc[] = "fsum(iterable)\n\nReturn an accurate floating point sum of values in the iterable.\nAssumes IEEE-754 floating point arithmetic."; | ||
1133 | |||
1134 | /* Return the smallest integer k such that n < 2**k, or 0 if n == 0. | ||
1135 | * Equivalent to floor(lg(x))+1. Also equivalent to: bitwidth_of_type - | ||
1136 | * count_leading_zero_bits(x) | ||
1137 | */ | ||
1138 | |||
1139 | /* XXX: This routine does more or less the same thing as | ||
1140 | * bits_in_digit() in Objects/longobject.c. Someday it would be nice to | ||
1141 | * consolidate them. On BSD, there's a library function called fls() | ||
1142 | * that we could use, and GCC provides __builtin_clz(). | ||
1143 | */ | ||
1144 | |||
1145 | static unsigned long | ||
1146 | bit_length(unsigned long n) | ||
1147 | { | ||
1148 | unsigned long len = 0; | ||
1149 | while (n != 0) { | ||
1150 | ++len; | ||
1151 | n >>= 1; | ||
1152 | } | ||
1153 | return len; | ||
1154 | } | ||
1155 | |||
1156 | static unsigned long | ||
1157 | count_set_bits(unsigned long n) | ||
1158 | { | ||
1159 | unsigned long count = 0; | ||
1160 | while (n != 0) { | ||
1161 | ++count; | ||
1162 | n &= n - 1; /* clear least significant bit */ | ||
1163 | } | ||
1164 | return count; | ||
1165 | } | ||
1166 | |||
1167 | /* Divide-and-conquer factorial algorithm | ||
1168 | * | ||
1169 | * Based on the formula and psuedo-code provided at: | ||
1170 | * http://www.luschny.de/math/factorial/binarysplitfact.html | ||
1171 | * | ||
1172 | * Faster algorithms exist, but they're more complicated and depend on | ||
1173 | * a fast prime factorization algorithm. | ||
1174 | * | ||
1175 | * Notes on the algorithm | ||
1176 | * ---------------------- | ||
1177 | * | ||
1178 | * factorial(n) is written in the form 2**k * m, with m odd. k and m are | ||
1179 | * computed separately, and then combined using a left shift. | ||
1180 | * | ||
1181 | * The function factorial_odd_part computes the odd part m (i.e., the greatest | ||
1182 | * odd divisor) of factorial(n), using the formula: | ||
1183 | * | ||
1184 | * factorial_odd_part(n) = | ||
1185 | * | ||
1186 | * product_{i >= 0} product_{0 < j <= n / 2**i, j odd} j | ||
1187 | * | ||
1188 | * Example: factorial_odd_part(20) = | ||
1189 | * | ||
1190 | * (1) * | ||
1191 | * (1) * | ||
1192 | * (1 * 3 * 5) * | ||
1193 | * (1 * 3 * 5 * 7 * 9) | ||
1194 | * (1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19) | ||
1195 | * | ||
1196 | * Here i goes from large to small: the first term corresponds to i=4 (any | ||
1197 | * larger i gives an empty product), and the last term corresponds to i=0. | ||
1198 | * Each term can be computed from the last by multiplying by the extra odd | ||
1199 | * numbers required: e.g., to get from the penultimate term to the last one, | ||
1200 | * we multiply by (11 * 13 * 15 * 17 * 19). | ||
1201 | * | ||
1202 | * To see a hint of why this formula works, here are the same numbers as above | ||
1203 | * but with the even parts (i.e., the appropriate powers of 2) included. For | ||
1204 | * each subterm in the product for i, we multiply that subterm by 2**i: | ||
1205 | * | ||
1206 | * factorial(20) = | ||
1207 | * | ||
1208 | * (16) * | ||
1209 | * (8) * | ||
1210 | * (4 * 12 * 20) * | ||
1211 | * (2 * 6 * 10 * 14 * 18) * | ||
1212 | * (1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19) | ||
1213 | * | ||
1214 | * The factorial_partial_product function computes the product of all odd j in | ||
1215 | * range(start, stop) for given start and stop. It's used to compute the | ||
1216 | * partial products like (11 * 13 * 15 * 17 * 19) in the example above. It | ||
1217 | * operates recursively, repeatedly splitting the range into two roughly equal | ||
1218 | * pieces until the subranges are small enough to be computed using only C | ||
1219 | * integer arithmetic. | ||
1220 | * | ||
1221 | * The two-valuation k (i.e., the exponent of the largest power of 2 dividing | ||
1222 | * the factorial) is computed independently in the main math_factorial | ||
1223 | * function. By standard results, its value is: | ||
1224 | * | ||
1225 | * two_valuation = n//2 + n//4 + n//8 + .... | ||
1226 | * | ||
1227 | * It can be shown (e.g., by complete induction on n) that two_valuation is | ||
1228 | * equal to n - count_set_bits(n), where count_set_bits(n) gives the number of | ||
1229 | * '1'-bits in the binary expansion of n. | ||
1230 | */ | ||
1231 | |||
1232 | /* factorial_partial_product: Compute product(range(start, stop, 2)) using | ||
1233 | * divide and conquer. Assumes start and stop are odd and stop > start. | ||
1234 | * max_bits must be >= bit_length(stop - 2). */ | ||
1235 | |||
1236 | static PyObject * | ||
1237 | factorial_partial_product(unsigned long start, unsigned long stop, | ||
1238 | unsigned long max_bits) | ||
1239 | { | ||
1240 | unsigned long midpoint, num_operands; | ||
1241 | PyObject *left = NULL((void *)0), *right = NULL((void *)0), *result = NULL((void *)0); | ||
1242 | |||
1243 | /* If the return value will fit an unsigned long, then we can | ||
1244 | * multiply in a tight, fast loop where each multiply is O(1). | ||
1245 | * Compute an upper bound on the number of bits required to store | ||
1246 | * the answer. | ||
1247 | * | ||
1248 | * Storing some integer z requires floor(lg(z))+1 bits, which is | ||
1249 | * conveniently the value returned by bit_length(z). The | ||
1250 | * product x*y will require at most | ||
1251 | * bit_length(x) + bit_length(y) bits to store, based | ||
1252 | * on the idea that lg product = lg x + lg y. | ||
1253 | * | ||
1254 | * We know that stop - 2 is the largest number to be multiplied. From | ||
1255 | * there, we have: bit_length(answer) <= num_operands * | ||
1256 | * bit_length(stop - 2) | ||
1257 | */ | ||
1258 | |||
1259 | num_operands = (stop - start) / 2; | ||
1260 | /* The "num_operands <= 8 * SIZEOF_LONG" check guards against the | ||
1261 | * unlikely case of an overflow in num_operands * max_bits. */ | ||
1262 | if (num_operands <= 8 * SIZEOF_LONG8 && | ||
1263 | num_operands * max_bits <= 8 * SIZEOF_LONG8) { | ||
1264 | unsigned long j, total; | ||
1265 | for (total = start, j = start + 2; j < stop; j += 2) | ||
1266 | total *= j; | ||
1267 | return PyLong_FromUnsignedLong(total); | ||
1268 | } | ||
1269 | |||
1270 | /* find midpoint of range(start, stop), rounded up to next odd number. */ | ||
1271 | midpoint = (start + num_operands) | 1; | ||
1272 | left = factorial_partial_product(start, midpoint, | ||
1273 | bit_length(midpoint - 2)); | ||
1274 | if (left == NULL((void *)0)) | ||
1275 | goto error; | ||
1276 | right = factorial_partial_product(midpoint, stop, max_bits); | ||
1277 | if (right == NULL((void *)0)) | ||
1278 | goto error; | ||
1279 | result = PyNumber_Multiply(left, right); | ||
1280 | |||
1281 | error: | ||
1282 | Py_XDECREF(left)do { if ((left) == ((void *)0)) ; else do { if (_Py_RefTotal-- , --((PyObject*)(left))->ob_refcnt != 0) { if (((PyObject *)left)->ob_refcnt < 0) _Py_NegativeRefcount("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 1282, (PyObject *)(left)); } else _Py_Dealloc((PyObject *)( left)); } while (0); } while (0); | ||
1283 | Py_XDECREF(right)do { if ((right) == ((void *)0)) ; else do { if (_Py_RefTotal -- , --((PyObject*)(right))->ob_refcnt != 0) { if (((PyObject *)right)->ob_refcnt < 0) _Py_NegativeRefcount("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 1283, (PyObject *)(right)); } else _Py_Dealloc((PyObject *) (right)); } while (0); } while (0); | ||
1284 | return result; | ||
1285 | } | ||
1286 | |||
1287 | /* factorial_odd_part: compute the odd part of factorial(n). */ | ||
1288 | |||
1289 | static PyObject * | ||
1290 | factorial_odd_part(unsigned long n) | ||
1291 | { | ||
1292 | long i; | ||
1293 | unsigned long v, lower, upper; | ||
1294 | PyObject *partial, *tmp, *inner, *outer; | ||
1295 | |||
1296 | inner = PyLong_FromLong(1); | ||
1297 | if (inner == NULL((void *)0)) | ||
1298 | return NULL((void *)0); | ||
1299 | outer = inner; | ||
1300 | Py_INCREF(outer)( _Py_RefTotal++ , ((PyObject*)(outer))->ob_refcnt++); | ||
1301 | |||
1302 | upper = 3; | ||
1303 | for (i = bit_length(n) - 2; i >= 0; i--) { | ||
1304 | v = n >> i; | ||
1305 | if (v <= 2) | ||
1306 | continue; | ||
1307 | lower = upper; | ||
1308 | /* (v + 1) | 1 = least odd integer strictly larger than n / 2**i */ | ||
1309 | upper = (v + 1) | 1; | ||
1310 | /* Here inner is the product of all odd integers j in the range (0, | ||
1311 | n/2**(i+1)]. The factorial_partial_product call below gives the | ||
1312 | product of all odd integers j in the range (n/2**(i+1), n/2**i]. */ | ||
1313 | partial = factorial_partial_product(lower, upper, bit_length(upper-2)); | ||
1314 | /* inner *= partial */ | ||
1315 | if (partial == NULL((void *)0)) | ||
1316 | goto error; | ||
1317 | tmp = PyNumber_Multiply(inner, partial); | ||
1318 | Py_DECREF(partial)do { if (_Py_RefTotal-- , --((PyObject*)(partial))->ob_refcnt != 0) { if (((PyObject*)partial)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1318 , (PyObject *)(partial)); } else _Py_Dealloc((PyObject *)(partial )); } while (0); | ||
1319 | if (tmp == NULL((void *)0)) | ||
1320 | goto error; | ||
1321 | Py_DECREF(inner)do { if (_Py_RefTotal-- , --((PyObject*)(inner))->ob_refcnt != 0) { if (((PyObject*)inner)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1321 , (PyObject *)(inner)); } else _Py_Dealloc((PyObject *)(inner )); } while (0); | ||
1322 | inner = tmp; | ||
1323 | /* Now inner is the product of all odd integers j in the range (0, | ||
1324 | n/2**i], giving the inner product in the formula above. */ | ||
1325 | |||
1326 | /* outer *= inner; */ | ||
1327 | tmp = PyNumber_Multiply(outer, inner); | ||
1328 | if (tmp == NULL((void *)0)) | ||
1329 | goto error; | ||
1330 | Py_DECREF(outer)do { if (_Py_RefTotal-- , --((PyObject*)(outer))->ob_refcnt != 0) { if (((PyObject*)outer)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1330 , (PyObject *)(outer)); } else _Py_Dealloc((PyObject *)(outer )); } while (0); | ||
1331 | outer = tmp; | ||
1332 | } | ||
1333 | |||
1334 | goto done; | ||
1335 | |||
1336 | error: | ||
1337 | Py_DECREF(outer)do { if (_Py_RefTotal-- , --((PyObject*)(outer))->ob_refcnt != 0) { if (((PyObject*)outer)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1337 , (PyObject *)(outer)); } else _Py_Dealloc((PyObject *)(outer )); } while (0); | ||
1338 | done: | ||
1339 | Py_DECREF(inner)do { if (_Py_RefTotal-- , --((PyObject*)(inner))->ob_refcnt != 0) { if (((PyObject*)inner)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1339 , (PyObject *)(inner)); } else _Py_Dealloc((PyObject *)(inner )); } while (0); | ||
1340 | return outer; | ||
1341 | } | ||
1342 | |||
1343 | /* Lookup table for small factorial values */ | ||
1344 | |||
1345 | static const unsigned long SmallFactorials[] = { | ||
1346 | 1, 1, 2, 6, 24, 120, 720, 5040, 40320, | ||
1347 | 362880, 3628800, 39916800, 479001600, | ||
1348 | #if SIZEOF_LONG8 >= 8 | ||
1349 | 6227020800, 87178291200, 1307674368000, | ||
1350 | 20922789888000, 355687428096000, 6402373705728000, | ||
1351 | 121645100408832000, 2432902008176640000 | ||
1352 | #endif | ||
1353 | }; | ||
1354 | |||
1355 | static PyObject * | ||
1356 | math_factorial(PyObject *self, PyObject *arg) | ||
1357 | { | ||
1358 | long x; | ||
1359 | PyObject *result, *odd_part, *two_valuation; | ||
1360 | |||
1361 | if (PyFloat_Check(arg)((((PyObject*)(arg))->ob_type) == (&PyFloat_Type) || PyType_IsSubtype ((((PyObject*)(arg))->ob_type), (&PyFloat_Type)))) { | ||
1362 | PyObject *lx; | ||
1363 | double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg)(((PyFloatObject *)((PyFloatObject *)arg))->ob_fval); | ||
1364 | if (!(Py_IS_FINITE(dx)( sizeof (dx) == sizeof(float ) ? __inline_isfinitef((float)( dx)) : sizeof (dx) == sizeof(double) ? __inline_isfinited((double )(dx)) : __inline_isfinite ((long double)(dx))) && dx == floor(dx))) { | ||
1365 | PyErr_SetString(PyExc_ValueError, | ||
1366 | "factorial() only accepts integral values"); | ||
1367 | return NULL((void *)0); | ||
1368 | } | ||
1369 | lx = PyLong_FromDouble(dx); | ||
1370 | if (lx == NULL((void *)0)) | ||
1371 | return NULL((void *)0); | ||
1372 | x = PyLong_AsLong(lx); | ||
1373 | Py_DECREF(lx)do { if (_Py_RefTotal-- , --((PyObject*)(lx))->ob_refcnt != 0) { if (((PyObject*)lx)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1373 , (PyObject *)(lx)); } else _Py_Dealloc((PyObject *)(lx)); } while (0); | ||
1374 | } | ||
1375 | else | ||
1376 | x = PyLong_AsLong(arg); | ||
1377 | |||
1378 | if (x == -1 && PyErr_Occurred()) | ||
1379 | return NULL((void *)0); | ||
1380 | if (x < 0) { | ||
1381 | PyErr_SetString(PyExc_ValueError, | ||
1382 | "factorial() not defined for negative values"); | ||
1383 | return NULL((void *)0); | ||
1384 | } | ||
1385 | |||
1386 | /* use lookup table if x is small */ | ||
1387 | if (x < (long)(sizeof(SmallFactorials)/sizeof(SmallFactorials[0]))) | ||
1388 | return PyLong_FromUnsignedLong(SmallFactorials[x]); | ||
1389 | |||
1390 | /* else express in the form odd_part * 2**two_valuation, and compute as | ||
1391 | odd_part << two_valuation. */ | ||
1392 | odd_part = factorial_odd_part(x); | ||
1393 | if (odd_part == NULL((void *)0)) | ||
1394 | return NULL((void *)0); | ||
1395 | two_valuation = PyLong_FromLong(x - count_set_bits(x)); | ||
1396 | if (two_valuation == NULL((void *)0)) { | ||
1397 | Py_DECREF(odd_part)do { if (_Py_RefTotal-- , --((PyObject*)(odd_part))->ob_refcnt != 0) { if (((PyObject*)odd_part)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1397 , (PyObject *)(odd_part)); } else _Py_Dealloc((PyObject *)(odd_part )); } while (0); | ||
1398 | return NULL((void *)0); | ||
1399 | } | ||
1400 | result = PyNumber_Lshift(odd_part, two_valuation); | ||
1401 | Py_DECREF(two_valuation)do { if (_Py_RefTotal-- , --((PyObject*)(two_valuation))-> ob_refcnt != 0) { if (((PyObject*)two_valuation)->ob_refcnt < 0) _Py_NegativeRefcount("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c" , 1401, (PyObject *)(two_valuation)); } else _Py_Dealloc((PyObject *)(two_valuation)); } while (0); | ||
1402 | Py_DECREF(odd_part)do { if (_Py_RefTotal-- , --((PyObject*)(odd_part))->ob_refcnt != 0) { if (((PyObject*)odd_part)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1402 , (PyObject *)(odd_part)); } else _Py_Dealloc((PyObject *)(odd_part )); } while (0); | ||
1403 | return result; | ||
1404 | } | ||
1405 | |||
1406 | PyDoc_STRVAR(math_factorial_doc,static char math_factorial_doc[] = "factorial(x) -> Integral\n" "\n""Find x!. Raise a ValueError if x is negative or non-integral." | ||
1407 | "factorial(x) -> Integral\n"static char math_factorial_doc[] = "factorial(x) -> Integral\n" "\n""Find x!. Raise a ValueError if x is negative or non-integral." | ||
1408 | "\n"static char math_factorial_doc[] = "factorial(x) -> Integral\n" "\n""Find x!. Raise a ValueError if x is negative or non-integral." | ||
1409 | "Find x!. Raise a ValueError if x is negative or non-integral.")static char math_factorial_doc[] = "factorial(x) -> Integral\n" "\n""Find x!. Raise a ValueError if x is negative or non-integral."; | ||
1410 | |||
1411 | static PyObject * | ||
1412 | math_trunc(PyObject *self, PyObject *number) | ||
1413 | { | ||
1414 | static PyObject *trunc_str = NULL((void *)0); | ||
1415 | PyObject *trunc, *result; | ||
1416 | |||
1417 | if (Py_TYPE(number)(((PyObject*)(number))->ob_type)->tp_dict == NULL((void *)0)) { | ||
1418 | if (PyType_Ready(Py_TYPE(number)(((PyObject*)(number))->ob_type)) < 0) | ||
1419 | return NULL((void *)0); | ||
1420 | } | ||
1421 | |||
1422 | trunc = _PyObject_LookupSpecial(number, "__trunc__", &trunc_str); | ||
1423 | if (trunc == NULL((void *)0)) { | ||
1424 | if (!PyErr_Occurred()) | ||
1425 | PyErr_Format(PyExc_TypeError, | ||
1426 | "type %.100s doesn't define __trunc__ method", | ||
1427 | Py_TYPE(number)(((PyObject*)(number))->ob_type)->tp_name); | ||
1428 | return NULL((void *)0); | ||
1429 | } | ||
1430 | result = PyObject_CallFunctionObjArgs(trunc, NULL((void *)0)); | ||
1431 | Py_DECREF(trunc)do { if (_Py_RefTotal-- , --((PyObject*)(trunc))->ob_refcnt != 0) { if (((PyObject*)trunc)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1431 , (PyObject *)(trunc)); } else _Py_Dealloc((PyObject *)(trunc )); } while (0); | ||
1432 | return result; | ||
1433 | } | ||
1434 | |||
1435 | PyDoc_STRVAR(math_trunc_doc,static char math_trunc_doc[] = "trunc(x:Real) -> Integral\n" "\n""Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method." | ||
1436 | "trunc(x:Real) -> Integral\n"static char math_trunc_doc[] = "trunc(x:Real) -> Integral\n" "\n""Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method." | ||
1437 | "\n"static char math_trunc_doc[] = "trunc(x:Real) -> Integral\n" "\n""Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method." | ||
1438 | "Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.")static char math_trunc_doc[] = "trunc(x:Real) -> Integral\n" "\n""Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method."; | ||
1439 | |||
1440 | static PyObject * | ||
1441 | math_frexp(PyObject *self, PyObject *arg) | ||
1442 | { | ||
1443 | int i; | ||
1444 | double x = PyFloat_AsDouble(arg); | ||
1445 | if (x == -1.0 && PyErr_Occurred()) | ||
1446 | return NULL((void *)0); | ||
1447 | /* deal with special cases directly, to sidestep platform | ||
1448 | differences */ | ||
1449 | if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x))) || Py_IS_INFINITY(x)( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isinfd((double)(x)) : __inline_isinf ((long double)(x))) || !x) { | ||
1450 | i = 0; | ||
1451 | } | ||
1452 | else { | ||
1453 | PyFPE_START_PROTECT("in math_frexp", return 0); | ||
1454 | x = frexp(x, &i); | ||
1455 | PyFPE_END_PROTECT(x); | ||
1456 | } | ||
1457 | return Py_BuildValue("(di)", x, i); | ||
1458 | } | ||
1459 | |||
1460 | PyDoc_STRVAR(math_frexp_doc,static char math_frexp_doc[] = "frexp(x)\n""\n""Return the mantissa and exponent of x, as pair (m, e).\n" "m is a float and e is an int, such that x = m * 2.**e.\n""If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0." | ||
1461 | "frexp(x)\n"static char math_frexp_doc[] = "frexp(x)\n""\n""Return the mantissa and exponent of x, as pair (m, e).\n" "m is a float and e is an int, such that x = m * 2.**e.\n""If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0." | ||
1462 | "\n"static char math_frexp_doc[] = "frexp(x)\n""\n""Return the mantissa and exponent of x, as pair (m, e).\n" "m is a float and e is an int, such that x = m * 2.**e.\n""If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0." | ||
1463 | "Return the mantissa and exponent of x, as pair (m, e).\n"static char math_frexp_doc[] = "frexp(x)\n""\n""Return the mantissa and exponent of x, as pair (m, e).\n" "m is a float and e is an int, such that x = m * 2.**e.\n""If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0." | ||
1464 | "m is a float and e is an int, such that x = m * 2.**e.\n"static char math_frexp_doc[] = "frexp(x)\n""\n""Return the mantissa and exponent of x, as pair (m, e).\n" "m is a float and e is an int, such that x = m * 2.**e.\n""If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0." | ||
1465 | "If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.")static char math_frexp_doc[] = "frexp(x)\n""\n""Return the mantissa and exponent of x, as pair (m, e).\n" "m is a float and e is an int, such that x = m * 2.**e.\n""If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0."; | ||
1466 | |||
1467 | static PyObject * | ||
1468 | math_ldexp(PyObject *self, PyObject *args) | ||
1469 | { | ||
1470 | double x, r; | ||
1471 | PyObject *oexp; | ||
1472 | long exp; | ||
1473 | int overflow; | ||
1474 | if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp)) | ||
1475 | return NULL((void *)0); | ||
1476 | |||
1477 | if (PyLong_Check(oexp)((((((PyObject*)(oexp))->ob_type))->tp_flags & ((1L <<24))) != 0)) { | ||
1478 | /* on overflow, replace exponent with either LONG_MAX | ||
1479 | or LONG_MIN, depending on the sign. */ | ||
1480 | exp = PyLong_AsLongAndOverflow(oexp, &overflow); | ||
1481 | if (exp == -1 && PyErr_Occurred()) | ||
1482 | return NULL((void *)0); | ||
1483 | if (overflow) | ||
1484 | exp = overflow < 0 ? LONG_MIN(-9223372036854775807L -1L) : LONG_MAX9223372036854775807L; | ||
1485 | } | ||
1486 | else { | ||
1487 | PyErr_SetString(PyExc_TypeError, | ||
1488 | "Expected an int or long as second argument " | ||
1489 | "to ldexp."); | ||
1490 | return NULL((void *)0); | ||
1491 | } | ||
1492 | |||
1493 | if (x == 0. || !Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))) { | ||
1494 | /* NaNs, zeros and infinities are returned unchanged */ | ||
1495 | r = x; | ||
1496 | errno(*__error()) = 0; | ||
1497 | } else if (exp > INT_MAX2147483647) { | ||
1498 | /* overflow */ | ||
1499 | r = copysign(Py_HUGE_VAL__builtin_huge_val(), x); | ||
1500 | errno(*__error()) = ERANGE34; | ||
1501 | } else if (exp < INT_MIN(-2147483647 -1)) { | ||
1502 | /* underflow to +-0 */ | ||
1503 | r = copysign(0., x); | ||
1504 | errno(*__error()) = 0; | ||
1505 | } else { | ||
1506 | errno(*__error()) = 0; | ||
1507 | PyFPE_START_PROTECT("in math_ldexp", return 0); | ||
1508 | r = ldexp(x, (int)exp); | ||
1509 | PyFPE_END_PROTECT(r); | ||
1510 | if (Py_IS_INFINITY(r)( sizeof (r) == sizeof(float ) ? __inline_isinff((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isinfd((double)(r)) : __inline_isinf ((long double)(r)))) | ||
1511 | errno(*__error()) = ERANGE34; | ||
1512 | } | ||
1513 | |||
1514 | if (errno(*__error()) && is_error(r)) | ||
1515 | return NULL((void *)0); | ||
1516 | return PyFloat_FromDouble(r); | ||
1517 | } | ||
1518 | |||
1519 | PyDoc_STRVAR(math_ldexp_doc,static char math_ldexp_doc[] = "ldexp(x, i)\n\nReturn x * (2**i)." | ||
1520 | "ldexp(x, i)\n\n\static char math_ldexp_doc[] = "ldexp(x, i)\n\nReturn x * (2**i)." | ||
1521 | Return x * (2**i).")static char math_ldexp_doc[] = "ldexp(x, i)\n\nReturn x * (2**i)."; | ||
1522 | |||
1523 | static PyObject * | ||
1524 | math_modf(PyObject *self, PyObject *arg) | ||
1525 | { | ||
1526 | double y, x = PyFloat_AsDouble(arg); | ||
1527 | if (x == -1.0 && PyErr_Occurred()) | ||
1528 | return NULL((void *)0); | ||
1529 | /* some platforms don't do the right thing for NaNs and | ||
1530 | infinities, so we take care of special cases directly. */ | ||
1531 | if (!Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))) { | ||
1532 | if (Py_IS_INFINITY(x)( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isinfd((double)(x)) : __inline_isinf ((long double)(x)))) | ||
1533 | return Py_BuildValue("(dd)", copysign(0., x), x); | ||
1534 | else if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x)))) | ||
1535 | return Py_BuildValue("(dd)", x, x); | ||
1536 | } | ||
1537 | |||
1538 | errno(*__error()) = 0; | ||
1539 | PyFPE_START_PROTECT("in math_modf", return 0); | ||
1540 | x = modf(x, &y); | ||
1541 | PyFPE_END_PROTECT(x); | ||
1542 | return Py_BuildValue("(dd)", x, y); | ||
1543 | } | ||
1544 | |||
1545 | PyDoc_STRVAR(math_modf_doc,static char math_modf_doc[] = "modf(x)\n""\n""Return the fractional and integer parts of x. Both results carry the sign\n" "of x and are floats." | ||
1546 | "modf(x)\n"static char math_modf_doc[] = "modf(x)\n""\n""Return the fractional and integer parts of x. Both results carry the sign\n" "of x and are floats." | ||
1547 | "\n"static char math_modf_doc[] = "modf(x)\n""\n""Return the fractional and integer parts of x. Both results carry the sign\n" "of x and are floats." | ||
1548 | "Return the fractional and integer parts of x. Both results carry the sign\n"static char math_modf_doc[] = "modf(x)\n""\n""Return the fractional and integer parts of x. Both results carry the sign\n" "of x and are floats." | ||
1549 | "of x and are floats.")static char math_modf_doc[] = "modf(x)\n""\n""Return the fractional and integer parts of x. Both results carry the sign\n" "of x and are floats."; | ||
1550 | |||
1551 | /* A decent logarithm is easy to compute even for huge longs, but libm can't | ||
1552 | do that by itself -- loghelper can. func is log or log10, and name is | ||
1553 | "log" or "log10". Note that overflow of the result isn't possible: a long | ||
1554 | can contain no more than INT_MAX * SHIFT bits, so has value certainly less | ||
1555 | than 2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is | ||
1556 | small enough to fit in an IEEE single. log and log10 are even smaller. | ||
1557 | However, intermediate overflow is possible for a long if the number of bits | ||
1558 | in that long is larger than PY_SSIZE_T_MAX. */ | ||
1559 | |||
1560 | static PyObject* | ||
1561 | loghelper(PyObject* arg, double (*func)(double), char *funcname) | ||
1562 | { | ||
1563 | /* If it is long, do it ourselves. */ | ||
1564 | if (PyLong_Check(arg)((((((PyObject*)(arg))->ob_type))->tp_flags & ((1L<< 24))) != 0)) { | ||
1565 | double x, result; | ||
1566 | Py_ssize_t e; | ||
1567 | |||
1568 | /* Negative or zero inputs give a ValueError. */ | ||
1569 | if (Py_SIZE(arg)(((PyVarObject*)(arg))->ob_size) <= 0) { | ||
1570 | PyErr_SetString(PyExc_ValueError, | ||
1571 | "math domain error"); | ||
1572 | return NULL((void *)0); | ||
1573 | } | ||
1574 | |||
1575 | x = PyLong_AsDouble(arg); | ||
1576 | if (x == -1.0 && PyErr_Occurred()) { | ||
1577 | if (!PyErr_ExceptionMatches(PyExc_OverflowError)) | ||
1578 | return NULL((void *)0); | ||
1579 | /* Here the conversion to double overflowed, but it's possible | ||
1580 | to compute the log anyway. Clear the exception and continue. */ | ||
1581 | PyErr_Clear(); | ||
1582 | x = _PyLong_Frexp((PyLongObject *)arg, &e); | ||
1583 | if (x == -1.0 && PyErr_Occurred()) | ||
1584 | return NULL((void *)0); | ||
1585 | /* Value is ~= x * 2**e, so the log ~= log(x) + log(2) * e. */ | ||
1586 | result = func(x) + func(2.0) * e; | ||
1587 | } | ||
1588 | else | ||
1589 | /* Successfully converted x to a double. */ | ||
1590 | result = func(x); | ||
1591 | return PyFloat_FromDouble(result); | ||
1592 | } | ||
1593 | |||
1594 | /* Else let libm handle it by itself. */ | ||
1595 | return math_1(arg, func, 0); | ||
1596 | } | ||
1597 | |||
1598 | static PyObject * | ||
1599 | math_log(PyObject *self, PyObject *args) | ||
1600 | { | ||
1601 | PyObject *arg; | ||
1602 | PyObject *base = NULL((void *)0); | ||
1603 | PyObject *num, *den; | ||
1604 | PyObject *ans; | ||
1605 | |||
1606 | if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base)) | ||
1607 | return NULL((void *)0); | ||
1608 | |||
1609 | num = loghelper(arg, m_log, "log"); | ||
1610 | if (num == NULL((void *)0) || base == NULL((void *)0)) | ||
1611 | return num; | ||
1612 | |||
1613 | den = loghelper(base, m_log, "log"); | ||
1614 | if (den == NULL((void *)0)) { | ||
1615 | Py_DECREF(num)do { if (_Py_RefTotal-- , --((PyObject*)(num))->ob_refcnt != 0) { if (((PyObject*)num)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1615 , (PyObject *)(num)); } else _Py_Dealloc((PyObject *)(num)); } while (0); | ||
1616 | return NULL((void *)0); | ||
1617 | } | ||
1618 | |||
1619 | ans = PyNumber_TrueDivide(num, den); | ||
1620 | Py_DECREF(num)do { if (_Py_RefTotal-- , --((PyObject*)(num))->ob_refcnt != 0) { if (((PyObject*)num)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1620 , (PyObject *)(num)); } else _Py_Dealloc((PyObject *)(num)); } while (0); | ||
1621 | Py_DECREF(den)do { if (_Py_RefTotal-- , --((PyObject*)(den))->ob_refcnt != 0) { if (((PyObject*)den)->ob_refcnt < 0) _Py_NegativeRefcount ("/Users/brett/Dev/python/3.x/py3k/Modules/mathmodule.c", 1621 , (PyObject *)(den)); } else _Py_Dealloc((PyObject *)(den)); } while (0); | ||
1622 | return ans; | ||
1623 | } | ||
1624 | |||
1625 | PyDoc_STRVAR(math_log_doc,static char math_log_doc[] = "log(x[, base])\n\nReturn the logarithm of x to the given base.\nIf the base not specified, returns the natural logarithm (base e) of x." | ||
1626 | "log(x[, base])\n\n\static char math_log_doc[] = "log(x[, base])\n\nReturn the logarithm of x to the given base.\nIf the base not specified, returns the natural logarithm (base e) of x." | ||
1627 | Return the logarithm of x to the given base.\n\static char math_log_doc[] = "log(x[, base])\n\nReturn the logarithm of x to the given base.\nIf the base not specified, returns the natural logarithm (base e) of x." | ||
1628 | If the base not specified, returns the natural logarithm (base e) of x.")static char math_log_doc[] = "log(x[, base])\n\nReturn the logarithm of x to the given base.\nIf the base not specified, returns the natural logarithm (base e) of x."; | ||
1629 | |||
1630 | static PyObject * | ||
1631 | math_log10(PyObject *self, PyObject *arg) | ||
1632 | { | ||
1633 | return loghelper(arg, m_log10, "log10"); | ||
1634 | } | ||
1635 | |||
1636 | PyDoc_STRVAR(math_log10_doc,static char math_log10_doc[] = "log10(x)\n\nReturn the base 10 logarithm of x." | ||
1637 | "log10(x)\n\nReturn the base 10 logarithm of x.")static char math_log10_doc[] = "log10(x)\n\nReturn the base 10 logarithm of x."; | ||
1638 | |||
1639 | static PyObject * | ||
1640 | math_fmod(PyObject *self, PyObject *args) | ||
1641 | { | ||
1642 | PyObject *ox, *oy; | ||
1643 | double r, x, y; | ||
1644 | if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy)) | ||
1645 | return NULL((void *)0); | ||
1646 | x = PyFloat_AsDouble(ox); | ||
1647 | y = PyFloat_AsDouble(oy); | ||
1648 | if ((x == -1.0 || y == -1.0) && PyErr_Occurred()) | ||
1649 | return NULL((void *)0); | ||
1650 | /* fmod(x, +/-Inf) returns x for finite x. */ | ||
1651 | if (Py_IS_INFINITY(y)( sizeof (y) == sizeof(float ) ? __inline_isinff((float)(y)) : sizeof (y) == sizeof(double) ? __inline_isinfd((double)(y)) : __inline_isinf ((long double)(y))) && Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))) | ||
1652 | return PyFloat_FromDouble(x); | ||
1653 | errno(*__error()) = 0; | ||
1654 | PyFPE_START_PROTECT("in math_fmod", return 0); | ||
1655 | r = fmod(x, y); | ||
1656 | PyFPE_END_PROTECT(r); | ||
1657 | if (Py_IS_NAN(r)( sizeof (r) == sizeof(float ) ? __inline_isnanf((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isnand((double)(r)) : __inline_isnan ((long double)(r)))) { | ||
1658 | if (!Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x))) && !Py_IS_NAN(y)( sizeof (y) == sizeof(float ) ? __inline_isnanf((float)(y)) : sizeof (y) == sizeof(double) ? __inline_isnand((double)(y)) : __inline_isnan ((long double)(y)))) | ||
1659 | errno(*__error()) = EDOM33; | ||
1660 | else | ||
1661 | errno(*__error()) = 0; | ||
1662 | } | ||
1663 | if (errno(*__error()) && is_error(r)) | ||
1664 | return NULL((void *)0); | ||
1665 | else | ||
1666 | return PyFloat_FromDouble(r); | ||
1667 | } | ||
1668 | |||
1669 | PyDoc_STRVAR(math_fmod_doc,static char math_fmod_doc[] = "fmod(x, y)\n\nReturn fmod(x, y), according to platform C." " x % y may differ." | ||
1670 | "fmod(x, y)\n\nReturn fmod(x, y), according to platform C."static char math_fmod_doc[] = "fmod(x, y)\n\nReturn fmod(x, y), according to platform C." " x % y may differ." | ||
1671 | " x % y may differ.")static char math_fmod_doc[] = "fmod(x, y)\n\nReturn fmod(x, y), according to platform C." " x % y may differ."; | ||
1672 | |||
1673 | static PyObject * | ||
1674 | math_hypot(PyObject *self, PyObject *args) | ||
1675 | { | ||
1676 | PyObject *ox, *oy; | ||
1677 | double r, x, y; | ||
1678 | if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy)) | ||
1679 | return NULL((void *)0); | ||
1680 | x = PyFloat_AsDouble(ox); | ||
1681 | y = PyFloat_AsDouble(oy); | ||
1682 | if ((x == -1.0 || y == -1.0) && PyErr_Occurred()) | ||
1683 | return NULL((void *)0); | ||
1684 | /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */ | ||
1685 | if (Py_IS_INFINITY(x)( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isinfd((double)(x)) : __inline_isinf ((long double)(x)))) | ||
1686 | return PyFloat_FromDouble(fabs(x)); | ||
1687 | if (Py_IS_INFINITY(y)( sizeof (y) == sizeof(float ) ? __inline_isinff((float)(y)) : sizeof (y) == sizeof(double) ? __inline_isinfd((double)(y)) : __inline_isinf ((long double)(y)))) | ||
1688 | return PyFloat_FromDouble(fabs(y)); | ||
1689 | errno(*__error()) = 0; | ||
1690 | PyFPE_START_PROTECT("in math_hypot", return 0); | ||
1691 | r = hypot(x, y); | ||
1692 | PyFPE_END_PROTECT(r); | ||
1693 | if (Py_IS_NAN(r)( sizeof (r) == sizeof(float ) ? __inline_isnanf((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isnand((double)(r)) : __inline_isnan ((long double)(r)))) { | ||
1694 | if (!Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x))) && !Py_IS_NAN(y)( sizeof (y) == sizeof(float ) ? __inline_isnanf((float)(y)) : sizeof (y) == sizeof(double) ? __inline_isnand((double)(y)) : __inline_isnan ((long double)(y)))) | ||
1695 | errno(*__error()) = EDOM33; | ||
1696 | else | ||
1697 | errno(*__error()) = 0; | ||
1698 | } | ||
1699 | else if (Py_IS_INFINITY(r)( sizeof (r) == sizeof(float ) ? __inline_isinff((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isinfd((double)(r)) : __inline_isinf ((long double)(r)))) { | ||
1700 | if (Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x))) && Py_IS_FINITE(y)( sizeof (y) == sizeof(float ) ? __inline_isfinitef((float)(y )) : sizeof (y) == sizeof(double) ? __inline_isfinited((double )(y)) : __inline_isfinite ((long double)(y)))) | ||
1701 | errno(*__error()) = ERANGE34; | ||
1702 | else | ||
1703 | errno(*__error()) = 0; | ||
1704 | } | ||
1705 | if (errno(*__error()) && is_error(r)) | ||
1706 | return NULL((void *)0); | ||
1707 | else | ||
1708 | return PyFloat_FromDouble(r); | ||
1709 | } | ||
1710 | |||
1711 | PyDoc_STRVAR(math_hypot_doc,static char math_hypot_doc[] = "hypot(x, y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y)." | ||
1712 | "hypot(x, y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).")static char math_hypot_doc[] = "hypot(x, y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y)."; | ||
1713 | |||
1714 | /* pow can't use math_2, but needs its own wrapper: the problem is | ||
1715 | that an infinite result can arise either as a result of overflow | ||
1716 | (in which case OverflowError should be raised) or as a result of | ||
1717 | e.g. 0.**-5. (for which ValueError needs to be raised.) | ||
1718 | */ | ||
1719 | |||
1720 | static PyObject * | ||
1721 | math_pow(PyObject *self, PyObject *args) | ||
1722 | { | ||
1723 | PyObject *ox, *oy; | ||
1724 | double r, x, y; | ||
1725 | int odd_y; | ||
1726 | |||
1727 | if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy)) | ||
1728 | return NULL((void *)0); | ||
1729 | x = PyFloat_AsDouble(ox); | ||
1730 | y = PyFloat_AsDouble(oy); | ||
1731 | if ((x == -1.0 || y == -1.0) && PyErr_Occurred()) | ||
1732 | return NULL((void *)0); | ||
1733 | |||
1734 | /* deal directly with IEEE specials, to cope with problems on various | ||
1735 | platforms whose semantics don't exactly match C99 */ | ||
1736 | r = 0.; /* silence compiler warning */ | ||
1737 | if (!Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x))) || !Py_IS_FINITE(y)( sizeof (y) == sizeof(float ) ? __inline_isfinitef((float)(y )) : sizeof (y) == sizeof(double) ? __inline_isfinited((double )(y)) : __inline_isfinite ((long double)(y)))) { | ||
1738 | errno(*__error()) = 0; | ||
1739 | if (Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x)))) | ||
1740 | r = y == 0. ? 1. : x; /* NaN**0 = 1 */ | ||
1741 | else if (Py_IS_NAN(y)( sizeof (y) == sizeof(float ) ? __inline_isnanf((float)(y)) : sizeof (y) == sizeof(double) ? __inline_isnand((double)(y)) : __inline_isnan ((long double)(y)))) | ||
1742 | r = x == 1. ? 1. : y; /* 1**NaN = 1 */ | ||
1743 | else if (Py_IS_INFINITY(x)( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isinfd((double)(x)) : __inline_isinf ((long double)(x)))) { | ||
1744 | odd_y = Py_IS_FINITE(y)( sizeof (y) == sizeof(float ) ? __inline_isfinitef((float)(y )) : sizeof (y) == sizeof(double) ? __inline_isfinited((double )(y)) : __inline_isfinite ((long double)(y))) && fmod(fabs(y), 2.0) == 1.0; | ||
1745 | if (y > 0.) | ||
1746 | r = odd_y ? x : fabs(x); | ||
1747 | else if (y == 0.) | ||
1748 | r = 1.; | ||
1749 | else /* y < 0. */ | ||
1750 | r = odd_y ? copysign(0., x) : 0.; | ||
1751 | } | ||
1752 | else if (Py_IS_INFINITY(y)( sizeof (y) == sizeof(float ) ? __inline_isinff((float)(y)) : sizeof (y) == sizeof(double) ? __inline_isinfd((double)(y)) : __inline_isinf ((long double)(y)))) { | ||
1753 | if (fabs(x) == 1.0) | ||
1754 | r = 1.; | ||
1755 | else if (y > 0. && fabs(x) > 1.0) | ||
1756 | r = y; | ||
1757 | else if (y < 0. && fabs(x) < 1.0) { | ||
1758 | r = -y; /* result is +inf */ | ||
1759 | if (x == 0.) /* 0**-inf: divide-by-zero */ | ||
1760 | errno(*__error()) = EDOM33; | ||
1761 | } | ||
1762 | else | ||
1763 | r = 0.; | ||
1764 | } | ||
1765 | } | ||
1766 | else { | ||
1767 | /* let libm handle finite**finite */ | ||
1768 | errno(*__error()) = 0; | ||
1769 | PyFPE_START_PROTECT("in math_pow", return 0); | ||
1770 | r = pow(x, y); | ||
1771 | PyFPE_END_PROTECT(r); | ||
1772 | /* a NaN result should arise only from (-ve)**(finite | ||
1773 | non-integer); in this case we want to raise ValueError. */ | ||
1774 | if (!Py_IS_FINITE(r)( sizeof (r) == sizeof(float ) ? __inline_isfinitef((float)(r )) : sizeof (r) == sizeof(double) ? __inline_isfinited((double )(r)) : __inline_isfinite ((long double)(r)))) { | ||
1775 | if (Py_IS_NAN(r)( sizeof (r) == sizeof(float ) ? __inline_isnanf((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isnand((double)(r)) : __inline_isnan ((long double)(r)))) { | ||
1776 | errno(*__error()) = EDOM33; | ||
1777 | } | ||
1778 | /* | ||
1779 | an infinite result here arises either from: | ||
1780 | (A) (+/-0.)**negative (-> divide-by-zero) | ||
1781 | (B) overflow of x**y with x and y finite | ||
1782 | */ | ||
1783 | else if (Py_IS_INFINITY(r)( sizeof (r) == sizeof(float ) ? __inline_isinff((float)(r)) : sizeof (r) == sizeof(double) ? __inline_isinfd((double)(r)) : __inline_isinf ((long double)(r)))) { | ||
1784 | if (x == 0.) | ||
1785 | errno(*__error()) = EDOM33; | ||
1786 | else | ||
1787 | errno(*__error()) = ERANGE34; | ||
1788 | } | ||
1789 | } | ||
1790 | } | ||
1791 | |||
1792 | if (errno(*__error()) && is_error(r)) | ||
1793 | return NULL((void *)0); | ||
1794 | else | ||
1795 | return PyFloat_FromDouble(r); | ||
1796 | } | ||
1797 | |||
1798 | PyDoc_STRVAR(math_pow_doc,static char math_pow_doc[] = "pow(x, y)\n\nReturn x**y (x to the power of y)." | ||
1799 | "pow(x, y)\n\nReturn x**y (x to the power of y).")static char math_pow_doc[] = "pow(x, y)\n\nReturn x**y (x to the power of y)."; | ||
1800 | |||
1801 | static const double degToRad = Py_MATH_PI3.14159265358979323846 / 180.0; | ||
1802 | static const double radToDeg = 180.0 / Py_MATH_PI3.14159265358979323846; | ||
1803 | |||
1804 | static PyObject * | ||
1805 | math_degrees(PyObject *self, PyObject *arg) | ||
1806 | { | ||
1807 | double x = PyFloat_AsDouble(arg); | ||
1808 | if (x == -1.0 && PyErr_Occurred()) | ||
1809 | return NULL((void *)0); | ||
1810 | return PyFloat_FromDouble(x * radToDeg); | ||
1811 | } | ||
1812 | |||
1813 | PyDoc_STRVAR(math_degrees_doc,static char math_degrees_doc[] = "degrees(x)\n\nConvert angle x from radians to degrees." | ||
1814 | "degrees(x)\n\n\static char math_degrees_doc[] = "degrees(x)\n\nConvert angle x from radians to degrees." | ||
1815 | Convert angle x from radians to degrees.")static char math_degrees_doc[] = "degrees(x)\n\nConvert angle x from radians to degrees."; | ||
1816 | |||
1817 | static PyObject * | ||
1818 | math_radians(PyObject *self, PyObject *arg) | ||
1819 | { | ||
1820 | double x = PyFloat_AsDouble(arg); | ||
1821 | if (x == -1.0 && PyErr_Occurred()) | ||
1822 | return NULL((void *)0); | ||
1823 | return PyFloat_FromDouble(x * degToRad); | ||
1824 | } | ||
1825 | |||
1826 | PyDoc_STRVAR(math_radians_doc,static char math_radians_doc[] = "radians(x)\n\nConvert angle x from degrees to radians." | ||
1827 | "radians(x)\n\n\static char math_radians_doc[] = "radians(x)\n\nConvert angle x from degrees to radians." | ||
1828 | Convert angle x from degrees to radians.")static char math_radians_doc[] = "radians(x)\n\nConvert angle x from degrees to radians."; | ||
1829 | |||
1830 | static PyObject * | ||
1831 | math_isfinite(PyObject *self, PyObject *arg) | ||
1832 | { | ||
1833 | double x = PyFloat_AsDouble(arg); | ||
1834 | if (x == -1.0 && PyErr_Occurred()) | ||
1835 | return NULL((void *)0); | ||
1836 | return PyBool_FromLong((long)Py_IS_FINITE(x)( sizeof (x) == sizeof(float ) ? __inline_isfinitef((float)(x )) : sizeof (x) == sizeof(double) ? __inline_isfinited((double )(x)) : __inline_isfinite ((long double)(x)))); | ||
1837 | } | ||
1838 | |||
1839 | PyDoc_STRVAR(math_isfinite_doc,static char math_isfinite_doc[] = "isfinite(x) -> bool\n\nReturn True if x is neither an infinity nor a NaN, and False otherwise." | ||
1840 | "isfinite(x) -> bool\n\n\static char math_isfinite_doc[] = "isfinite(x) -> bool\n\nReturn True if x is neither an infinity nor a NaN, and False otherwise." | ||
1841 | Return True if x is neither an infinity nor a NaN, and False otherwise.")static char math_isfinite_doc[] = "isfinite(x) -> bool\n\nReturn True if x is neither an infinity nor a NaN, and False otherwise."; | ||
1842 | |||
1843 | static PyObject * | ||
1844 | math_isnan(PyObject *self, PyObject *arg) | ||
1845 | { | ||
1846 | double x = PyFloat_AsDouble(arg); | ||
1847 | if (x == -1.0 && PyErr_Occurred()) | ||
1848 | return NULL((void *)0); | ||
1849 | return PyBool_FromLong((long)Py_IS_NAN(x)( sizeof (x) == sizeof(float ) ? __inline_isnanf((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isnand((double)(x)) : __inline_isnan ((long double)(x)))); | ||
1850 | } | ||
1851 | |||
1852 | PyDoc_STRVAR(math_isnan_doc,static char math_isnan_doc[] = "isnan(x) -> bool\n\nReturn True if x is a NaN (not a number), and False otherwise." | ||
1853 | "isnan(x) -> bool\n\n\static char math_isnan_doc[] = "isnan(x) -> bool\n\nReturn True if x is a NaN (not a number), and False otherwise." | ||
1854 | Return True if x is a NaN (not a number), and False otherwise.")static char math_isnan_doc[] = "isnan(x) -> bool\n\nReturn True if x is a NaN (not a number), and False otherwise."; | ||
1855 | |||
1856 | static PyObject * | ||
1857 | math_isinf(PyObject *self, PyObject *arg) | ||
1858 | { | ||
1859 | double x = PyFloat_AsDouble(arg); | ||
1860 | if (x == -1.0 && PyErr_Occurred()) | ||
1861 | return NULL((void *)0); | ||
1862 | return PyBool_FromLong((long)Py_IS_INFINITY(x)( sizeof (x) == sizeof(float ) ? __inline_isinff((float)(x)) : sizeof (x) == sizeof(double) ? __inline_isinfd((double)(x)) : __inline_isinf ((long double)(x)))); | ||
1863 | } | ||
1864 | |||
1865 | PyDoc_STRVAR(math_isinf_doc,static char math_isinf_doc[] = "isinf(x) -> bool\n\nReturn True if x is a positive or negative infinity, and False otherwise." | ||
1866 | "isinf(x) -> bool\n\n\static char math_isinf_doc[] = "isinf(x) -> bool\n\nReturn True if x is a positive or negative infinity, and False otherwise." | ||
1867 | Return True if x is a positive or negative infinity, and False otherwise.")static char math_isinf_doc[] = "isinf(x) -> bool\n\nReturn True if x is a positive or negative infinity, and False otherwise."; | ||
1868 | |||
1869 | static PyMethodDef math_methods[] = { | ||
1870 | {"acos", math_acos, METH_O0x0008, math_acos_doc}, | ||
1871 | {"acosh", math_acosh, METH_O0x0008, math_acosh_doc}, | ||
1872 | {"asin", math_asin, METH_O0x0008, math_asin_doc}, | ||
1873 | {"asinh", math_asinh, METH_O0x0008, math_asinh_doc}, | ||
1874 | {"atan", math_atan, METH_O0x0008, math_atan_doc}, | ||
1875 | {"atan2", math_atan2, METH_VARARGS0x0001, math_atan2_doc}, | ||
1876 | {"atanh", math_atanh, METH_O0x0008, math_atanh_doc}, | ||
1877 | {"ceil", math_ceil, METH_O0x0008, math_ceil_doc}, | ||
1878 | {"copysign", math_copysign, METH_VARARGS0x0001, math_copysign_doc}, | ||
1879 | {"cos", math_cos, METH_O0x0008, math_cos_doc}, | ||
1880 | {"cosh", math_cosh, METH_O0x0008, math_cosh_doc}, | ||
1881 | {"degrees", math_degrees, METH_O0x0008, math_degrees_doc}, | ||
1882 | {"erf", math_erf, METH_O0x0008, math_erf_doc}, | ||
1883 | {"erfc", math_erfc, METH_O0x0008, math_erfc_doc}, | ||
1884 | {"exp", math_exp, METH_O0x0008, math_exp_doc}, | ||
1885 | {"expm1", math_expm1, METH_O0x0008, math_expm1_doc}, | ||
1886 | {"fabs", math_fabs, METH_O0x0008, math_fabs_doc}, | ||
1887 | {"factorial", math_factorial, METH_O0x0008, math_factorial_doc}, | ||
1888 | {"floor", math_floor, METH_O0x0008, math_floor_doc}, | ||
1889 | {"fmod", math_fmod, METH_VARARGS0x0001, math_fmod_doc}, | ||
1890 | {"frexp", math_frexp, METH_O0x0008, math_frexp_doc}, | ||
1891 | {"fsum", math_fsum, METH_O0x0008, math_fsum_doc}, | ||
1892 | {"gamma", math_gamma, METH_O0x0008, math_gamma_doc}, | ||
1893 | {"hypot", math_hypot, METH_VARARGS0x0001, math_hypot_doc}, | ||
1894 | {"isfinite", math_isfinite, METH_O0x0008, math_isfinite_doc}, | ||
1895 | {"isinf", math_isinf, METH_O0x0008, math_isinf_doc}, | ||
1896 | {"isnan", math_isnan, METH_O0x0008, math_isnan_doc}, | ||
1897 | {"ldexp", math_ldexp, METH_VARARGS0x0001, math_ldexp_doc}, | ||
1898 | {"lgamma", math_lgamma, METH_O0x0008, math_lgamma_doc}, | ||
1899 | {"log", math_log, METH_VARARGS0x0001, math_log_doc}, | ||
1900 | {"log1p", math_log1p, METH_O0x0008, math_log1p_doc}, | ||
1901 | {"log10", math_log10, METH_O0x0008, math_log10_doc}, | ||
1902 | {"modf", math_modf, METH_O0x0008, math_modf_doc}, | ||
1903 | {"pow", math_pow, METH_VARARGS0x0001, math_pow_doc}, | ||
1904 | {"radians", math_radians, METH_O0x0008, math_radians_doc}, | ||
1905 | {"sin", math_sin, METH_O0x0008, math_sin_doc}, | ||
1906 | {"sinh", math_sinh, METH_O0x0008, math_sinh_doc}, | ||
1907 | {"sqrt", math_sqrt, METH_O0x0008, math_sqrt_doc}, | ||
1908 | {"tan", math_tan, METH_O0x0008, math_tan_doc}, | ||
1909 | {"tanh", math_tanh, METH_O0x0008, math_tanh_doc}, | ||
1910 | {"trunc", math_trunc, METH_O0x0008, math_trunc_doc}, | ||
1911 | {NULL((void *)0), NULL((void *)0)} /* sentinel */ | ||
1912 | }; | ||
1913 | |||
1914 | |||
1915 | PyDoc_STRVAR(module_doc,static char module_doc[] = "This module is always available. It provides access to the\n" "mathematical functions defined by the C standard." | ||
1916 | "This module is always available. It provides access to the\n"static char module_doc[] = "This module is always available. It provides access to the\n" "mathematical functions defined by the C standard." | ||
1917 | "mathematical functions defined by the C standard.")static char module_doc[] = "This module is always available. It provides access to the\n" "mathematical functions defined by the C standard."; | ||
1918 | |||
1919 | |||
1920 | static struct PyModuleDef mathmodule = { | ||
1921 | PyModuleDef_HEAD_INIT{ { 0, 0, 1, ((void *)0) }, ((void *)0), 0, ((void *)0), }, | ||
1922 | "math", | ||
1923 | module_doc, | ||
1924 | -1, | ||
1925 | math_methods, | ||
1926 | NULL((void *)0), | ||
1927 | NULL((void *)0), | ||
1928 | NULL((void *)0), | ||
1929 | NULL((void *)0) | ||
1930 | }; | ||
1931 | |||
1932 | PyMODINIT_FUNCPyObject* | ||
1933 | PyInit_math(void) | ||
1934 | { | ||
1935 | PyObject *m; | ||
1936 | |||
1937 | m = PyModule_Create(&mathmodule)PyModule_Create2TraceRefs(&mathmodule, 1013); | ||
1938 | if (m == NULL((void *)0)) | ||
1939 | goto finally; | ||
1940 | |||
1941 | PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI3.14159265358979323846)); | ||
1942 | PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E2.7182818284590452354)); | ||
1943 | |||
1944 | finally: | ||
1945 | return m; | ||
1946 | } |