3 # Test blog function (and bpow, since it uses blog), as well as bexp().
5 # It is too slow to be simple included in bigfltpm.inc, where it would get
6 # executed 3 times. One time would be under BareCalc, which shouldn't make any
7 # difference since there is no CALC->_log() function, and one time under a
8 # subclass, which *should* work.
10 # But it is better to test the numerical functionality, instead of not testing
11 # it at all (which did lead to wrong answers for 0 < $x < 1 in blog() in
12 # versions up to v1.63, and for bsqrt($x) when $x << 1 for instance).
20 # to locate the testing files
21 my $location = $0; $location =~ s/biglog.t//i;
24 # testing with the core distribution
27 unshift @INC, '../lib';
32 unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
36 unshift @INC, $location;
38 print "# INC = @INC\n";
46 my $cl = "Math::BigInt";
48 #############################################################################
49 # test log($n) in BigInt (broken until 1.80)
51 is ($cl->new(2)->blog(), '0', "blog(2)");
52 is ($cl->new(288)->blog(), '5',"blog(288)");
53 is ($cl->new(2000)->blog(), '7', "blog(2000)");
55 #############################################################################
56 # test exp($n) in BigInt
58 is ($cl->new(1)->bexp(), '2', "bexp(1)");
59 is ($cl->new(2)->bexp(), '7',"bexp(2)");
60 is ($cl->new(3)->bexp(), '20', "bexp(3)");
62 #############################################################################
63 #############################################################################
66 #############################################################################
67 # test log(2, N) where N > 67 (broken until 1.82)
69 $cl = "Math::BigFloat";
71 # These tests can take quite a while, but are nec. Maybe protect them with
74 # this triggers the calculation and caching of ln(2):
75 ok ($cl->new(5)->blog(undef,71),
76 '1.6094379124341003746007593332261876395256013542685177219126478914741790');
78 # if the cache was correct, we should get this result, fast:
79 ok ($cl->new(2)->blog(undef,71),
80 '0.69314718055994530941723212145817656807550013436025525412068000949339362');
82 ok ($cl->new(10)->blog(undef,71),
83 '2.3025850929940456840179914546843642076011014886287729760333279009675726');
85 ok ($cl->new(21)->blog(undef,71),
86 '3.0445224377234229965005979803657054342845752874046106401940844835750742');
88 #############################################################################
90 # These tests are now really fast, since they collapse to blog(10), basically
91 # Don't attempt to run them with older versions. You are warned.
94 ok ($cl->new(-2)->blog(), 'NaN');
95 ok ($cl->new(-1)->blog(), 'NaN');
96 ok ($cl->new(-10)->blog(), 'NaN');
97 ok ($cl->new(-2,2)->blog(), 'NaN');
99 my $ten = $cl->new(10)->blog();
101 # 10 is cached (up to 75 digits)
102 ok ($cl->new(10)->blog(), '2.302585092994045684017991454684364207601');
104 # 0.1 is using the cached value for log(10), too
106 ok ($cl->new(0.1)->blog(), -$ten);
107 ok ($cl->new(0.01)->blog(), -$ten * 2);
108 ok ($cl->new(0.001)->blog(), -$ten * 3);
109 ok ($cl->new(0.0001)->blog(), -$ten * 4);
112 ok ($cl->new(2)->blog(), '0.6931471805599453094172321214581765680755');
113 ok ($cl->new(4)->blog(), $cl->new(2)->blog * 2);
115 # These are still slow, so do them only to 10 digits
117 ok ($cl->new('0.2')->blog(undef,10), '-1.609437912');
118 ok ($cl->new('0.3')->blog(undef,10), '-1.203972804');
119 ok ($cl->new('0.4')->blog(undef,10), '-0.9162907319');
120 ok ($cl->new('0.5')->blog(undef,10), '-0.6931471806');
121 ok ($cl->new('0.6')->blog(undef,10), '-0.5108256238');
122 ok ($cl->new('0.7')->blog(undef,10), '-0.3566749439');
123 ok ($cl->new('0.8')->blog(undef,10), '-0.2231435513');
124 ok ($cl->new('0.9')->blog(undef,10), '-0.1053605157');
126 ok ($cl->new('9')->blog(undef,10), '2.197224577');
128 ok ($cl->new('10')->blog(10,10), '1.000000000');
129 ok ($cl->new('20')->blog(20,10), '1.000000000');
130 ok ($cl->new('100')->blog(100,10), '1.000000000');
132 ok ($cl->new('100')->blog(10,10), '2.000000000'); # 10 ** 2 == 100
133 ok ($cl->new('400')->blog(20,10), '2.000000000'); # 20 ** 2 == 400
135 ok ($cl->new('4')->blog(2,10), '2.000000000'); # 2 ** 2 == 4
136 ok ($cl->new('16')->blog(2,10), '4.000000000'); # 2 ** 4 == 16
138 ok ($cl->new('1.2')->bpow('0.3',10), '1.056219968');
139 ok ($cl->new('10')->bpow('0.6',10), '3.981071706');
141 # blog should handle bigint input
142 is (Math::BigFloat::blog(Math::BigInt->new(100),10), 2, "blog(100)");
144 #############################################################################
145 # some integer results
146 is ($cl->new(2)->bpow(32)->blog(2), '32', "2 ** 32");
147 is ($cl->new(3)->bpow(32)->blog(3), '32', "3 ** 32");
148 is ($cl->new(2)->bpow(65)->blog(2), '65', "2 ** 65");
150 my $x = Math::BigInt->new( '777' ) ** 256;
151 my $base = Math::BigInt->new( '12345678901234' );
152 is ($x->copy()->blog($base), 56, 'blog(777**256, 12345678901234)');
154 $x = Math::BigInt->new( '777' ) ** 777;
155 $base = Math::BigInt->new( '777' );
156 is ($x->copy()->blog($base), 777, 'blog(777**777, 777)');
158 #############################################################################
159 # test for bug in bsqrt() not taking negative _e into account
160 test_bpow ('200','0.5',10, '14.14213562');
161 test_bpow ('20','0.5',10, '4.472135955');
162 test_bpow ('2','0.5',10, '1.414213562');
163 test_bpow ('0.2','0.5',10, '0.4472135955');
164 test_bpow ('0.02','0.5',10, '0.1414213562');
165 test_bpow ('0.49','0.5',undef , '0.7');
166 test_bpow ('0.49','0.5',10 , '0.7000000000');
167 test_bpow ('0.002','0.5',10, '0.04472135955');
168 test_bpow ('0.0002','0.5',10, '0.01414213562');
169 test_bpow ('0.0049','0.5',undef,'0.07');
170 test_bpow ('0.0049','0.5',10 , '0.07000000000');
171 test_bpow ('0.000002','0.5',10, '0.001414213562');
172 test_bpow ('0.021','0.5',10, '0.1449137675');
173 test_bpow ('1.2','0.5',10, '1.095445115');
174 test_bpow ('1.23','0.5',10, '1.109053651');
175 test_bpow ('12.3','0.5',10, '3.507135583');
177 test_bpow ('9.9','0.5',10, '3.146426545');
178 test_bpow ('9.86902225','0.5',10, '3.141500000');
179 test_bpow ('9.86902225','0.5',undef, '3.1415');
181 test_bpow ('0.2','0.41',10, '0.5169187652');
183 #############################################################################
184 # test bexp() with cached results
186 is ($cl->new(1)->bexp(), '2.718281828459045235360287471352662497757', 'bexp(1)');
187 is ($cl->new(2)->bexp(40), $cl->new(1)->bexp(45)->bpow(2,40), 'bexp(2)');
189 is ($cl->new("12.5")->bexp(61), $cl->new(1)->bexp(65)->bpow(12.5,61), 'bexp(12.5)');
191 #############################################################################
192 # test bexp() with big values (non-cached)
194 is ($cl->new(1)->bexp(100),
195 '2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427',
198 is ($cl->new("12.5")->bexp(91), $cl->new(1)->bexp(95)->bpow(12.5,91),
199 'bexp(12.5) to 91 digits');
204 #############################################################################
207 my ($x,$y,$scale,$result) = @_;
209 print "# Tried: $x->bpow($y,$scale);\n"
210 unless ok ($cl->new($x)->bpow($y,$scale),$result);