Coverage for /var/srv/projects/api.amasfac.comuna18.com/tmp/venv/lib/python3.9/site-packages/numpy/core/_machar.py: 5%
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1"""
2Machine arithmetic - determine the parameters of the
3floating-point arithmetic system
5Author: Pearu Peterson, September 2003
7"""
8__all__ = ['MachAr']
10from numpy.core.fromnumeric import any
11from numpy.core._ufunc_config import errstate
12from numpy.core.overrides import set_module
14# Need to speed this up...especially for longfloat
16# Deprecated 2021-10-20, NumPy 1.22
17@set_module('numpy')
18class MachAr:
19 """
20 Diagnosing machine parameters.
22 Attributes
23 ----------
24 ibeta : int
25 Radix in which numbers are represented.
26 it : int
27 Number of base-`ibeta` digits in the floating point mantissa M.
28 machep : int
29 Exponent of the smallest (most negative) power of `ibeta` that,
30 added to 1.0, gives something different from 1.0
31 eps : float
32 Floating-point number ``beta**machep`` (floating point precision)
33 negep : int
34 Exponent of the smallest power of `ibeta` that, subtracted
35 from 1.0, gives something different from 1.0.
36 epsneg : float
37 Floating-point number ``beta**negep``.
38 iexp : int
39 Number of bits in the exponent (including its sign and bias).
40 minexp : int
41 Smallest (most negative) power of `ibeta` consistent with there
42 being no leading zeros in the mantissa.
43 xmin : float
44 Floating-point number ``beta**minexp`` (the smallest [in
45 magnitude] positive floating point number with full precision).
46 maxexp : int
47 Smallest (positive) power of `ibeta` that causes overflow.
48 xmax : float
49 ``(1-epsneg) * beta**maxexp`` (the largest [in magnitude]
50 usable floating value).
51 irnd : int
52 In ``range(6)``, information on what kind of rounding is done
53 in addition, and on how underflow is handled.
54 ngrd : int
55 Number of 'guard digits' used when truncating the product
56 of two mantissas to fit the representation.
57 epsilon : float
58 Same as `eps`.
59 tiny : float
60 An alias for `smallest_normal`, kept for backwards compatibility.
61 huge : float
62 Same as `xmax`.
63 precision : float
64 ``- int(-log10(eps))``
65 resolution : float
66 ``- 10**(-precision)``
67 smallest_normal : float
68 The smallest positive floating point number with 1 as leading bit in
69 the mantissa following IEEE-754. Same as `xmin`.
70 smallest_subnormal : float
71 The smallest positive floating point number with 0 as leading bit in
72 the mantissa following IEEE-754.
74 Parameters
75 ----------
76 float_conv : function, optional
77 Function that converts an integer or integer array to a float
78 or float array. Default is `float`.
79 int_conv : function, optional
80 Function that converts a float or float array to an integer or
81 integer array. Default is `int`.
82 float_to_float : function, optional
83 Function that converts a float array to float. Default is `float`.
84 Note that this does not seem to do anything useful in the current
85 implementation.
86 float_to_str : function, optional
87 Function that converts a single float to a string. Default is
88 ``lambda v:'%24.16e' %v``.
89 title : str, optional
90 Title that is printed in the string representation of `MachAr`.
92 See Also
93 --------
94 finfo : Machine limits for floating point types.
95 iinfo : Machine limits for integer types.
97 References
98 ----------
99 .. [1] Press, Teukolsky, Vetterling and Flannery,
100 "Numerical Recipes in C++," 2nd ed,
101 Cambridge University Press, 2002, p. 31.
103 """
105 def __init__(self, float_conv=float,int_conv=int, 105 ↛ exitline 105 didn't jump to the function exit
106 float_to_float=float,
107 float_to_str=lambda v:'%24.16e' % v,
108 title='Python floating point number'):
109 """
111 float_conv - convert integer to float (array)
112 int_conv - convert float (array) to integer
113 float_to_float - convert float array to float
114 float_to_str - convert array float to str
115 title - description of used floating point numbers
117 """
118 # We ignore all errors here because we are purposely triggering
119 # underflow to detect the properties of the runninng arch.
120 with errstate(under='ignore'):
121 self._do_init(float_conv, int_conv, float_to_float, float_to_str, title)
123 def _do_init(self, float_conv, int_conv, float_to_float, float_to_str, title):
124 max_iterN = 10000
125 msg = "Did not converge after %d tries with %s"
126 one = float_conv(1)
127 two = one + one
128 zero = one - one
130 # Do we really need to do this? Aren't they 2 and 2.0?
131 # Determine ibeta and beta
132 a = one
133 for _ in range(max_iterN):
134 a = a + a
135 temp = a + one
136 temp1 = temp - a
137 if any(temp1 - one != zero):
138 break
139 else:
140 raise RuntimeError(msg % (_, one.dtype))
141 b = one
142 for _ in range(max_iterN):
143 b = b + b
144 temp = a + b
145 itemp = int_conv(temp-a)
146 if any(itemp != 0):
147 break
148 else:
149 raise RuntimeError(msg % (_, one.dtype))
150 ibeta = itemp
151 beta = float_conv(ibeta)
153 # Determine it and irnd
154 it = -1
155 b = one
156 for _ in range(max_iterN):
157 it = it + 1
158 b = b * beta
159 temp = b + one
160 temp1 = temp - b
161 if any(temp1 - one != zero):
162 break
163 else:
164 raise RuntimeError(msg % (_, one.dtype))
166 betah = beta / two
167 a = one
168 for _ in range(max_iterN):
169 a = a + a
170 temp = a + one
171 temp1 = temp - a
172 if any(temp1 - one != zero):
173 break
174 else:
175 raise RuntimeError(msg % (_, one.dtype))
176 temp = a + betah
177 irnd = 0
178 if any(temp-a != zero):
179 irnd = 1
180 tempa = a + beta
181 temp = tempa + betah
182 if irnd == 0 and any(temp-tempa != zero):
183 irnd = 2
185 # Determine negep and epsneg
186 negep = it + 3
187 betain = one / beta
188 a = one
189 for i in range(negep):
190 a = a * betain
191 b = a
192 for _ in range(max_iterN):
193 temp = one - a
194 if any(temp-one != zero):
195 break
196 a = a * beta
197 negep = negep - 1
198 # Prevent infinite loop on PPC with gcc 4.0:
199 if negep < 0:
200 raise RuntimeError("could not determine machine tolerance "
201 "for 'negep', locals() -> %s" % (locals()))
202 else:
203 raise RuntimeError(msg % (_, one.dtype))
204 negep = -negep
205 epsneg = a
207 # Determine machep and eps
208 machep = - it - 3
209 a = b
211 for _ in range(max_iterN):
212 temp = one + a
213 if any(temp-one != zero):
214 break
215 a = a * beta
216 machep = machep + 1
217 else:
218 raise RuntimeError(msg % (_, one.dtype))
219 eps = a
221 # Determine ngrd
222 ngrd = 0
223 temp = one + eps
224 if irnd == 0 and any(temp*one - one != zero):
225 ngrd = 1
227 # Determine iexp
228 i = 0
229 k = 1
230 z = betain
231 t = one + eps
232 nxres = 0
233 for _ in range(max_iterN):
234 y = z
235 z = y*y
236 a = z*one # Check here for underflow
237 temp = z*t
238 if any(a+a == zero) or any(abs(z) >= y):
239 break
240 temp1 = temp * betain
241 if any(temp1*beta == z):
242 break
243 i = i + 1
244 k = k + k
245 else:
246 raise RuntimeError(msg % (_, one.dtype))
247 if ibeta != 10:
248 iexp = i + 1
249 mx = k + k
250 else:
251 iexp = 2
252 iz = ibeta
253 while k >= iz:
254 iz = iz * ibeta
255 iexp = iexp + 1
256 mx = iz + iz - 1
258 # Determine minexp and xmin
259 for _ in range(max_iterN):
260 xmin = y
261 y = y * betain
262 a = y * one
263 temp = y * t
264 if any((a + a) != zero) and any(abs(y) < xmin):
265 k = k + 1
266 temp1 = temp * betain
267 if any(temp1*beta == y) and any(temp != y):
268 nxres = 3
269 xmin = y
270 break
271 else:
272 break
273 else:
274 raise RuntimeError(msg % (_, one.dtype))
275 minexp = -k
277 # Determine maxexp, xmax
278 if mx <= k + k - 3 and ibeta != 10:
279 mx = mx + mx
280 iexp = iexp + 1
281 maxexp = mx + minexp
282 irnd = irnd + nxres
283 if irnd >= 2:
284 maxexp = maxexp - 2
285 i = maxexp + minexp
286 if ibeta == 2 and not i:
287 maxexp = maxexp - 1
288 if i > 20:
289 maxexp = maxexp - 1
290 if any(a != y):
291 maxexp = maxexp - 2
292 xmax = one - epsneg
293 if any(xmax*one != xmax):
294 xmax = one - beta*epsneg
295 xmax = xmax / (xmin*beta*beta*beta)
296 i = maxexp + minexp + 3
297 for j in range(i):
298 if ibeta == 2:
299 xmax = xmax + xmax
300 else:
301 xmax = xmax * beta
303 smallest_subnormal = abs(xmin / beta ** (it))
305 self.ibeta = ibeta
306 self.it = it
307 self.negep = negep
308 self.epsneg = float_to_float(epsneg)
309 self._str_epsneg = float_to_str(epsneg)
310 self.machep = machep
311 self.eps = float_to_float(eps)
312 self._str_eps = float_to_str(eps)
313 self.ngrd = ngrd
314 self.iexp = iexp
315 self.minexp = minexp
316 self.xmin = float_to_float(xmin)
317 self._str_xmin = float_to_str(xmin)
318 self.maxexp = maxexp
319 self.xmax = float_to_float(xmax)
320 self._str_xmax = float_to_str(xmax)
321 self.irnd = irnd
323 self.title = title
324 # Commonly used parameters
325 self.epsilon = self.eps
326 self.tiny = self.xmin
327 self.huge = self.xmax
328 self.smallest_normal = self.xmin
329 self._str_smallest_normal = float_to_str(self.xmin)
330 self.smallest_subnormal = float_to_float(smallest_subnormal)
331 self._str_smallest_subnormal = float_to_str(smallest_subnormal)
333 import math
334 self.precision = int(-math.log10(float_to_float(self.eps)))
335 ten = two + two + two + two + two
336 resolution = ten ** (-self.precision)
337 self.resolution = float_to_float(resolution)
338 self._str_resolution = float_to_str(resolution)
340 def __str__(self):
341 fmt = (
342 'Machine parameters for %(title)s\n'
343 '---------------------------------------------------------------------\n'
344 'ibeta=%(ibeta)s it=%(it)s iexp=%(iexp)s ngrd=%(ngrd)s irnd=%(irnd)s\n'
345 'machep=%(machep)s eps=%(_str_eps)s (beta**machep == epsilon)\n'
346 'negep =%(negep)s epsneg=%(_str_epsneg)s (beta**epsneg)\n'
347 'minexp=%(minexp)s xmin=%(_str_xmin)s (beta**minexp == tiny)\n'
348 'maxexp=%(maxexp)s xmax=%(_str_xmax)s ((1-epsneg)*beta**maxexp == huge)\n'
349 'smallest_normal=%(smallest_normal)s '
350 'smallest_subnormal=%(smallest_subnormal)s\n'
351 '---------------------------------------------------------------------\n'
352 )
353 return fmt % self.__dict__
356if __name__ == '__main__': 356 ↛ 357line 356 didn't jump to line 357, because the condition on line 356 was never true
357 print(MachAr())