Révision 162
pobysoPythonSage/src/sollya_lib.sage (revision 162) | ||
---|---|---|
78 | 78 |
sollya_lib_on = sollya.sollya_lib_on |
79 | 79 |
sollya_lib_parse_string = sollya.sollya_lib_parse_string |
80 | 80 |
sollya_lib_range = sollya.sollya_lib_range |
81 |
sollya_lib_range_from_bounds = sollya.sollya_lib_range_from_bounds |
|
82 |
sollya_lib_range_from_interval = \ |
|
83 |
sollya.sollya_lib_range_from_interval |
|
81 | 84 |
sollya_lib_relative = sollya.sollya_lib_relative |
82 | 85 |
sollya_lib_remez = sollya.sollya_lib_remez |
83 | 86 |
sollya_lib_set_canonical = sollya.sollya_lib_set_canonical |
... | ... | |
104 | 107 |
# Set the argument type of several functions. |
105 | 108 |
# |
106 | 109 |
try: |
110 |
sollya_lib_autoprint.argtypes = [c_ulong] |
|
111 |
sollya_lib_constant.argtypes = [c_ulong] |
|
112 |
sollya_lib_constant.restype = c_ulong |
|
113 |
sollya_lib_get_constant.argtypes = [c_ulong, c_ulong] |
|
107 | 114 |
sollya_lib_get_constant_as_int.argtypes = [POINTER(c_int), c_int] |
108 | 115 |
sollya_lib_get_function_arity.argtypes = [POINTER(c_int), c_int] |
109 | 116 |
sollya_lib_get_head_function.argtypes = [POINTER(c_int), c_int] |
117 |
sollya_lib_get_interval_from_range.argtypes = [c_ulong, c_ulong] |
|
110 | 118 |
sollya_lib_get_list_elements.argtypes = [POINTER(POINTER(c_longlong)), \ |
111 | 119 |
POINTER(c_int),\ |
112 | 120 |
POINTER(c_int), c_int] |
... | ... | |
116 | 124 |
POINTER(c_int), POINTER(c_int), POINTER(c_int), POINTER(c_int), \ |
117 | 125 |
POINTER(c_int), POINTER(c_int), POINTER(c_int), POINTER(c_int), \ |
118 | 126 |
POINTER(c_int), POINTER(c_int)] |
127 |
sollya_lib_guessdegree.argtypes = [c_ulong, c_ulong, c_ulong, \ |
|
128 |
c_ulong, c_ulong] |
|
129 |
sollya_lib_guessdegree.restype = c_ulong |
|
119 | 130 |
sollya_lib_name_free_variable.argtypes = [POINTER(c_char)] |
131 |
sollya_lib_parse_string.restype = c_long |
|
132 |
sollya_lib_range.argtypes = [c_ulong, c_ulong] |
|
133 |
sollya_lib_range.restype = c_ulong |
|
134 |
sollya_lib_range_from_bounds.argtypes = [c_ulong, c_ulong] |
|
135 |
sollya_lib_range_from_bounds.restype = c_ulong |
|
136 |
sollya_lib_range_from_interval.argtypes = [c_ulong] |
|
137 |
sollya_lib_range_from_interval.restype = c_ulong |
|
120 | 138 |
except : |
121 | 139 |
print "\nOne of the Python-Sollya argument type setting command has \ |
122 | 140 |
failed.\n" |
pobysoPythonSage/src/testPobyso.sage (revision 162) | ||
---|---|---|
76 | 76 |
pointSo = pobyso_constant_sa_so(RR("1.5")) |
77 | 77 |
intervalSo = pobyso_interval_to_range_sa_so(intervalSa) |
78 | 78 |
# |
79 |
def test(lowerBoundSa, upperBoundSa):
|
|
79 |
def test(functionSo, degreeSo, pointSo, intervalSo):
|
|
80 | 80 |
taylorformSo = pobyso_taylorform_so_so(functionSo, |
81 | 81 |
degreeSo, |
82 | 82 |
pointSo, |
83 | 83 |
intervalSo) |
84 |
sollya_lib_clear_obj(rangeSo)
|
|
84 |
pobyso_clear_taylorform_sa_so(taylorformSo)
|
|
85 | 85 |
# |
86 |
wrapped = test_pobyso_wrapper(test,lowerBoundSa, upperBoundSa) |
|
86 |
wrapped = test_pobyso_wrapper(test, |
|
87 |
functionSo, |
|
88 |
degreeSo, |
|
89 |
pointSo, |
|
90 |
intervalSo) |
|
87 | 91 |
timing = min(timeit.repeat(wrapped, repeat=repeat, number=number)) |
88 | 92 |
# |
89 |
precSo = pobyso_get_prec_so() |
|
90 |
#pobyso_autoprint(precSo) |
|
91 |
sollya_lib_clear_obj(precSo) |
|
93 |
sollya_lib_clear_obj(functionSo) |
|
94 |
sollya_lib_clear_obj(degreeSo) |
|
95 |
sollya_lib_clear_obj(pointSo) |
|
96 |
sollya_lib_clear_obj(intervalSo) |
|
92 | 97 |
print "\t...", functionName, "done." |
93 | 98 |
return timing |
94 | 99 |
# End test_pobyso_bounds_to_range_sa_so |
pobysoPythonSage/src/pobyso.py (revision 162) | ||
---|---|---|
99 | 99 |
""" |
100 | 100 |
Return a Sollya range from to 2 RealField Sage elements. |
101 | 101 |
The Sollya range element has a sufficient precision to hold all |
102 |
the digits of the Sage bounds. |
|
102 |
the digits of the widest of the Sage bounds.
|
|
103 | 103 |
""" |
104 | 104 |
# Sanity check. |
105 | 105 |
if rnLowerBoundSa > rnUpperBoundSa: |
... | ... | |
113 | 113 |
else: |
114 | 114 |
maxPrecSa = precisionSa |
115 | 115 |
# From Sage to Sollya bounds. |
116 |
lowerBoundSo = sollya_lib_constant(get_rn_value(rnLowerBoundSa), |
|
116 |
# lowerBoundSo = sollya_lib_constant(get_rn_value(rnLowerBoundSa), |
|
117 |
# maxPrecSa) |
|
118 |
lowerBoundSo = pobyso_constant_sa_so(rnLowerBoundSa, |
|
119 |
maxPrecSa) |
|
120 |
upperBoundSo = pobyso_constant_sa_so(rnUpperBoundSa, |
|
117 | 121 |
maxPrecSa) |
118 |
upperBoundSo = sollya_lib_constant(get_rn_value(rnUpperBoundSa), |
|
119 |
maxPrecSa) |
|
122 |
|
|
120 | 123 |
# From Sollya bounds to range. |
121 | 124 |
rangeSo = sollya_lib_range(lowerBoundSo, upperBoundSo) |
122 | 125 |
# Back to original precision. |
... | ... | |
798 | 801 |
else: |
799 | 802 |
degreeBoundSo = None |
800 | 803 |
guessedDegreeSa = pobyso_guess_degree_so_sa(functionSo, |
801 |
rangeSo, |
|
802 |
approxErrorSo, |
|
803 |
weightSo, |
|
804 |
degreeBoundSo) |
|
804 |
rangeSo,
|
|
805 |
approxErrorSo,
|
|
806 |
weightSo,
|
|
807 |
degreeBoundSo)
|
|
805 | 808 |
sollya_lib_clear_obj(functionSo) |
806 | 809 |
sollya_lib_clear_obj(rangeSo) |
807 | 810 |
sollya_lib_clear_obj(approxErrorSo) |
... | ... | |
831 | 834 |
if neededPrecisionSa > currentPrecSa: |
832 | 835 |
currentPrecSo = pobyso_get_prec_so() |
833 | 836 |
pobyso_set_prec_sa_so(neededPrecisionSa) |
837 |
print "Guessing degree..." |
|
834 | 838 |
# weightSo and degreeBoundsSo are optional arguments. |
839 |
# As declared, sollya_lib_guessdegree must take 5 arguments. |
|
835 | 840 |
if weightSo is None: |
836 |
degreeRangeSo = sollya_lib_guessdegree(functionSo, rangeSo, errorSo, None) |
|
841 |
degreeRangeSo = sollya_lib_guessdegree(functionSo, rangeSo, errorSo, |
|
842 |
0, 0, None) |
|
837 | 843 |
elif degreeBoundSo is None: |
838 | 844 |
degreeRangeSo = sollya_lib_guessdegree(functionSo, rangeSo, \ |
839 |
errorSo, weightSo, None) |
|
845 |
errorSo, weightSo, 0, None)
|
|
840 | 846 |
else: |
841 | 847 |
degreeRangeSo = sollya_lib_guessdegree(functionSo, rangeSo, errorSo, \ |
842 | 848 |
weightSo, degreeBoundSo, None) |
849 |
print "Degree guess done." |
|
843 | 850 |
# Restore internal precision, if applicable. |
844 | 851 |
if neededPrecisionSa > currentPrecSa: |
845 | 852 |
pobyso_set_prec_so_so(currentPrecSo) |
... | ... | |
1117 | 1124 |
return resultSo |
1118 | 1125 |
# End pobyso_supnorm_so_so |
1119 | 1126 |
|
1120 |
def pobyso_taylor_expansion_with_change_var_so_so(functionSo, degreeSo, \ |
|
1121 |
rangeSo, \ |
|
1122 |
errorTypeSo=None, \ |
|
1123 |
sollyaPrecSo=None): |
|
1127 |
def pobyso_taylor_expansion_no_change_var_so_so(functionSo, |
|
1128 |
degreeSo, |
|
1129 |
rangeSo, |
|
1130 |
errorTypeSo=None, |
|
1131 |
sollyaPrecSo=None): |
|
1124 | 1132 |
""" |
1125 |
Compute the Taylor expansion with the variable change |
|
1126 |
x -> (x-intervalCenter) included.
|
|
1133 |
Compute the Taylor expansion without the variable change
|
|
1134 |
x -> x-intervalCenter.
|
|
1127 | 1135 |
""" |
1128 | 1136 |
# No global change of the working precision. |
1129 | 1137 |
if not sollyaPrecSo is None: |
1130 | 1138 |
initialPrecSo = sollya_lib_get_prec(None) |
1131 | 1139 |
sollya_lib_set_prec(sollyaPrecSo) |
1132 |
# |
|
1133 | 1140 |
# Error type stuff: default to absolute. |
1134 | 1141 |
if errorTypeSo is None: |
1135 | 1142 |
errorTypeIsNone = True |
1136 | 1143 |
errorTypeSo = sollya_lib_absolute(None) |
1137 | 1144 |
else: |
1138 | 1145 |
errorTypeIsNone = False |
1139 |
intervalCenterSo = sollya_lib_mid(rangeSo) |
|
1140 |
taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo, \
|
|
1141 |
intervalCenterSo, \
|
|
1146 |
intervalCenterSo = sollya_lib_mid(rangeSo, None)
|
|
1147 |
taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo, |
|
1148 |
intervalCenterSo, |
|
1142 | 1149 |
rangeSo, errorTypeSo, None) |
1143 | 1150 |
# taylorFormListSaSo is a Python list of Sollya objects references that |
1144 | 1151 |
# are copies of the elements of taylorFormSo. |
1145 | 1152 |
# pobyso_get_list_elements_so_so clears taylorFormSo. |
1146 |
(taylorFormListSo, numElements, isEndElliptic) = \
|
|
1153 |
(taylorFormListSaSo, numElementsSa, isEndEllipticSa) = \
|
|
1147 | 1154 |
pobyso_get_list_elements_so_so(taylorFormSo) |
1148 |
polySo = taylorFormListSo[0] |
|
1149 |
errorRangeSo = taylorFormListSo[2] |
|
1155 |
polySo = sollya_lib_copy_obj(taylorFormListSaSo[0]) |
|
1156 |
#print "Num elements:", numElementsSa |
|
1157 |
sollya_lib_clear_obj(taylorFormSo) |
|
1158 |
#polySo = taylorFormListSaSo[0] |
|
1159 |
#errorRangeSo = sollya_lib_copy_obj(taylorFormListSaSo[2]) |
|
1160 |
errorRangeSo = taylorFormListSaSo[2] |
|
1161 |
# No copy_obj needed here: a new object is created. |
|
1150 | 1162 |
maxErrorSo = sollya_lib_sup(errorRangeSo) |
1151 |
changeVarExpSo = sollya_lib_build_function_sub(\ |
|
1152 |
sollya_lib_build_function_free_variable(),\ |
|
1153 |
sollya_lib_copy_obj(intervalCenterSo)) |
|
1154 |
polyVarChangedSo = sollya_lib_evaluate(polySo, changeVarExpSo) |
|
1155 |
sollya_lib_clear_obj(changeVarExpSo) |
|
1156 | 1163 |
# If changed, reset the Sollya working precision. |
1157 | 1164 |
if not sollyaPrecSo is None: |
1158 | 1165 |
sollya_lib_set_prec(initialPrecSo) |
1159 | 1166 |
sollya_lib_clear_obj(initialPrecSo) |
1160 | 1167 |
if errorTypeIsNone: |
1161 | 1168 |
sollya_lib_clear_obj(errorTypeSo) |
1162 |
sollya_lib_clear_obj(taylorFormSo) |
|
1163 |
# Do not clear maxErrorSo. |
|
1164 |
return((polyVarChangedSo, intervalCenterSo, maxErrorSo)) |
|
1165 |
# end pobyso_taylor_expansion_with_change_var_so_so |
|
1169 |
pobyso_clear_taylorform_sa_so(taylorFormListSaSo) |
|
1170 |
return((polySo, intervalCenterSo, maxErrorSo)) |
|
1171 |
# end pobyso_taylor_expansion_no_change_var_so_so |
|
1166 | 1172 |
|
1167 |
def pobyso_taylor_expansion_no_change_var_so_so(functionSo, degreeSo, rangeSo, |
|
1168 |
errorTypeSo=None, |
|
1169 |
sollyaPrecSo=None): |
|
1173 |
def pobyso_taylor_expansion_with_change_var_so_so(functionSo, degreeSo, \ |
|
1174 |
rangeSo, \ |
|
1175 |
errorTypeSo=None, \ |
|
1176 |
sollyaPrecSo=None): |
|
1170 | 1177 |
""" |
1171 |
Compute the Taylor expansion without the variable change
|
|
1172 |
x -> x-intervalCenter.
|
|
1178 |
Compute the Taylor expansion with the variable change |
|
1179 |
x -> (x-intervalCenter) included.
|
|
1173 | 1180 |
""" |
1174 | 1181 |
# No global change of the working precision. |
1175 | 1182 |
if not sollyaPrecSo is None: |
1176 | 1183 |
initialPrecSo = sollya_lib_get_prec(None) |
1177 | 1184 |
sollya_lib_set_prec(sollyaPrecSo) |
1185 |
# |
|
1178 | 1186 |
# Error type stuff: default to absolute. |
1179 | 1187 |
if errorTypeSo is None: |
1180 | 1188 |
errorTypeIsNone = True |
1181 | 1189 |
errorTypeSo = sollya_lib_absolute(None) |
1182 | 1190 |
else: |
1183 | 1191 |
errorTypeIsNone = False |
1184 |
intervalCenterSo = sollya_lib_mid(rangeSo, None)
|
|
1185 |
taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo, |
|
1186 |
intervalCenterSo, |
|
1192 |
intervalCenterSo = sollya_lib_mid(rangeSo) |
|
1193 |
taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo, \
|
|
1194 |
intervalCenterSo, \
|
|
1187 | 1195 |
rangeSo, errorTypeSo, None) |
1188 | 1196 |
# taylorFormListSaSo is a Python list of Sollya objects references that |
1189 | 1197 |
# are copies of the elements of taylorFormSo. |
1190 | 1198 |
# pobyso_get_list_elements_so_so clears taylorFormSo. |
1191 |
(taylorFormListSaSo, numElementsSa, isEndEllipticSa) = \
|
|
1199 |
(taylorFormListSo, numElements, isEndElliptic) = \
|
|
1192 | 1200 |
pobyso_get_list_elements_so_so(taylorFormSo) |
1193 |
polySo = sollya_lib_copy_obj(taylorFormListSaSo[0]) |
|
1194 |
#print "Num elements:", numElementsSa |
|
1195 |
sollya_lib_clear_obj(taylorFormSo) |
|
1196 |
#polySo = taylorFormListSaSo[0] |
|
1197 |
#errorRangeSo = sollya_lib_copy_obj(taylorFormListSaSo[2]) |
|
1198 |
errorRangeSo = taylorFormListSaSo[2] |
|
1199 |
# No copy_obj needed here: a new object is created. |
|
1201 |
polySo = taylorFormListSo[0] |
|
1202 |
errorRangeSo = taylorFormListSo[2] |
|
1200 | 1203 |
maxErrorSo = sollya_lib_sup(errorRangeSo) |
1204 |
changeVarExpSo = sollya_lib_build_function_sub(\ |
|
1205 |
sollya_lib_build_function_free_variable(),\ |
|
1206 |
sollya_lib_copy_obj(intervalCenterSo)) |
|
1207 |
polyVarChangedSo = sollya_lib_evaluate(polySo, changeVarExpSo) |
|
1208 |
sollya_lib_clear_obj(changeVarExpSo) |
|
1201 | 1209 |
# If changed, reset the Sollya working precision. |
1202 | 1210 |
if not sollyaPrecSo is None: |
1203 | 1211 |
sollya_lib_set_prec(initialPrecSo) |
1204 | 1212 |
sollya_lib_clear_obj(initialPrecSo) |
1205 | 1213 |
if errorTypeIsNone: |
1206 | 1214 |
sollya_lib_clear_obj(errorTypeSo) |
1207 |
pobyso_clear_taylorform_sa_so(taylorFormListSaSo) |
|
1208 |
return((polySo, intervalCenterSo, maxErrorSo)) |
|
1209 |
# end pobyso_taylor_expansion_no_change_var_so_so |
|
1215 |
sollya_lib_clear_obj(taylorFormSo) |
|
1216 |
# Do not clear maxErrorSo. |
|
1217 |
return((polyVarChangedSo, intervalCenterSo, maxErrorSo)) |
|
1218 |
# end pobyso_taylor_expansion_with_change_var_so_so |
|
1210 | 1219 |
|
1211 | 1220 |
def pobyso_taylor(function, degree, point): |
1212 | 1221 |
""" Legacy function. See pobysoTaylor_so_so. """ |
pobysoPythonSage/src/testSageMpfr.sage (revision 162) | ||
---|---|---|
10 | 10 |
|
11 | 11 |
""" |
12 | 12 |
print "\ntestSageMpfr loading..." |
13 |
load(str('/home/storres/recherche/arithmetique/pobysoPythonSage/src/ppsTestFunctions.sage')) |
|
14 |
# |
|
15 |
|
|
16 |
def test_cmp_rn_values(repeat=10, number=100): |
|
17 |
functionName = inspect.stack()[0][3] |
|
18 |
print "Running", inspect.stack()[0][3], "..." |
|
19 |
rn1Sa = RR(1) |
|
20 |
rn1bisSa = RR(1) |
|
21 |
rn2Sa = RR(2) |
|
22 |
# |
|
23 |
def test(rn1Sa, rn1bisSa, rn2Sa): |
|
24 |
if cmp_rn_values(rn1Sa, rn1bisSa) != 0: |
|
25 |
exit() |
|
26 |
if cmp_rn_values(rn1Sa, rn2Sa) >= 0: |
|
27 |
exit() |
|
28 |
if cmp_rn_values(rn2Sa, rn1Sa) <= 0: |
|
29 |
exit() |
|
30 |
wrapped = pps_test_wrapper(test, rn1Sa, rn1bisSa, rn2Sa) |
|
31 |
timing = min(timeit.repeat(wrapped, repeat=repeat, number=number)) |
|
32 |
print "\t...", functionName, "done." |
|
33 |
return timing |
|
34 |
# End test_cmp_rn_values |
|
35 |
|
|
36 |
def test_get_set_interval_value(repeat=10, number=100): |
|
37 |
functionName = inspect.stack()[0][3] |
|
38 |
print "Running", inspect.stack()[0][3], "..." |
|
39 |
interval1Sa = RIF(1,2) |
|
40 |
interval2Sa = RIF(2,3) |
|
41 |
# |
|
42 |
def test(interval1Sa, interval2Sa): |
|
43 |
interval1SaValue = get_interval_value(interval1Sa) |
|
44 |
interval2SaValue = get_interval_value(interval2Sa) |
|
45 |
set_interval_value(interval2Sa, interval1SaValue) |
|
46 |
if cmp_interval_values(interval1Sa, interval2Sa) != 0: |
|
47 |
exit() |
|
48 |
set_interval_value(interval2Sa, interval2SaValue) |
|
49 |
# |
|
50 |
wrapped = pps_test_wrapper(test, interval1Sa, interval2Sa) |
|
51 |
timing = min(timeit.repeat(wrapped, repeat=repeat, number=number)) |
|
52 |
print "\t...", functionName, "done." |
|
53 |
return timing |
|
54 |
# End test_get_set_interval_value |
|
55 |
|
|
56 |
print "\ntestSageMpfr loading..." |
|
13 | 57 |
attach(str('/home/storres/recherche/arithmetique/pobysoPythonSage/src/ppsTestFunctions.sage')) |
14 | 58 |
# |
15 | 59 |
|
16 |
def test_get_interval_value(repeat=10, number=100):
|
|
60 |
def test_get_set_rn_value(repeat=10, number=100):
|
|
17 | 61 |
functionName = inspect.stack()[0][3] |
18 | 62 |
print "Running", inspect.stack()[0][3], "..." |
19 |
intervalSa = RIF(1,2) |
|
63 |
rn1Sa = RR(1) |
|
64 |
rn2Sa = RR(2) |
|
20 | 65 |
# |
21 |
def test(intervalSa): |
|
22 |
intervalSaValue = get_interval_value(intervalSa) |
|
66 |
def test(rn1Sa, rn2Sa): |
|
67 |
rn1SaValue = get_rn_value(rn1Sa) |
|
68 |
rn2SaValue = get_rn_value(rn2Sa) |
|
69 |
set_rn_value(rn2Sa, rn1SaValue) |
|
70 |
if cmp_rn_values(rn1Sa, rn2Sa) != 0: |
|
71 |
exit() |
|
72 |
set_rn_value(rn2Sa, rn2SaValue) |
|
23 | 73 |
# |
24 |
wrapped = pps_test_wrapper(test,intervalSa)
|
|
74 |
wrapped = pps_test_wrapper(test, rn1Sa, rn2Sa)
|
|
25 | 75 |
timing = min(timeit.repeat(wrapped, repeat=repeat, number=number)) |
26 | 76 |
print "\t...", functionName, "done." |
27 | 77 |
return timing |
28 |
|
|
78 |
# End test_get_set_rn_value |
|
29 | 79 |
print "\t...testSageMpfr loaded" |
pobysoPythonSage/src/sageMpfr.spyx (revision 162) | ||
---|---|---|
19 | 19 |
cdef mp_rnd_t MPFR_RNDN "MPFR_RNDN" |
20 | 20 |
cdef mpfr_prec_t mpfr_min_prec(mpfr_t x) |
21 | 21 |
|
22 |
cpdef unsigned long int deref(unsigned long int p, int index): |
|
23 |
return((<unsigned long int*>p)[index]) |
|
24 |
|
|
22 | 25 |
cpdef unsigned long int get_interval_value(RealIntervalFieldElement x): |
23 | 26 |
""" |
24 | 27 |
Get the address of the value of a RealIntervalField Element. |
... | ... | |
115 | 118 |
|
116 | 119 |
# |
117 | 120 |
|
118 |
cpdef cmp_rn_value(RealNumber x, RealNumber y): |
|
119 |
""" |
|
120 |
Compare two RN with the mpfr_cmp function |
|
121 |
""" |
|
122 |
return(mpfr_cmp(x.value, y.value)) |
|
123 |
|
|
124 |
cpdef cmp_interval_value(RealIntervalFieldElement x, |
|
121 |
cpdef cmp_interval_values(RealIntervalFieldElement x, |
|
125 | 122 |
RealIntervalFieldElement y): |
126 | 123 |
""" |
127 | 124 |
Compare two intervals with the mpfi_cmp function |
128 | 125 |
""" |
129 | 126 |
return(mpfi_cmp(x.value, y.value)) |
130 | 127 |
|
128 |
cpdef cmp_rn_values(RealNumber x, RealNumber y): |
|
129 |
""" |
|
130 |
Compare two RN with the mpfr_cmp function |
|
131 |
""" |
|
132 |
return(mpfr_cmp(x.value, y.value)) |
|
133 |
|
|
131 | 134 |
# Do not use this function! |
132 | 135 |
# It changes the precision of the instance behind the curtain, but precision is |
133 | 136 |
# class attribute. If the precision is increased, memory space is wasted and |
Formats disponibles : Unified diff