1# -*- mode: perl; -*-
2
3# Test blog function (and bpow, since it uses blog), as well as bexp().
4
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 Math::BigInt::BareCalc, which
7# shouldn't make any difference since there is no $LIB->_log() function, and
8# one time under a subclass, which *should* work.
9
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).
13
14use strict;
15use warnings;
16
17use Test::More tests => 73;
18
19use Math::BigFloat only => 'FastCalc';
20use Math::BigInt;
21
22my $class = "Math::BigInt";
23
24###############################################################################
25# test $n->blog() in Math::BigInt (broken until 1.80)
26
27is($class->new(2)->blog(),    '0', "$class->new(2)->blog()");
28is($class->new(288)->blog(),  '5', "$class->new(288)->blog()");
29is($class->new(2000)->blog(), '7', "$class->new(2000)->blog()");
30
31###############################################################################
32# test $n->bexp() in Math::BigInt
33
34is($class->new(1)->bexp(), '2',  "$class->new(1)->bexp()");
35is($class->new(2)->bexp(), '7',  "$class->new(2)->bexp()");
36is($class->new(3)->bexp(), '20', "$class->new(3)->bexp()");
37
38###############################################################################
39# Math::BigFloat tests
40
41###############################################################################
42# test $n->blog(undef, N) where N > 67 (broken until 1.82)
43
44$class = "Math::BigFloat";
45
46# These tests can take quite a while, but are necessary. Maybe protect them
47# with some alarm()?
48
49# this triggers the calculation and caching of ln(2):
50is($class->new(5)->blog(undef, 71),
51   '1.6094379124341003746007593332261876395256013542685177219126478914741790',
52   "$class->new(5)->blog(undef, 71)");
53
54# if the cache was correct, we should get this result, fast:
55is($class->new(2)->blog(undef, 71),
56   '0.69314718055994530941723212145817656807550013436025525412068000949339362',
57   "$class->new(2)->blog(undef, 71)");
58
59is($class->new(11)->blog(undef, 71),
60   '2.3978952727983705440619435779651292998217068539374171752185677091305736',
61   "$class->new(11)->blog(undef, 71)");
62
63is($class->new(21)->blog(undef, 71),
64   '3.0445224377234229965005979803657054342845752874046106401940844835750742',
65   "$class->new(21)->blog(undef, 71)");
66
67###############################################################################
68
69# These tests are now really fast, since they collapse to blog(10), basically
70# Don't attempt to run them with older versions. You are warned.
71
72# $x < 0 => NaN
73is($class->new(-2)->blog(),    'NaN', "$class->new(-2)->blog()");
74is($class->new(-1)->blog(),    'NaN', "$class->new(-1)->blog()");
75is($class->new(-10)->blog(),   'NaN', "$class->new(-10)->blog()");
76is($class->new(-2, 2)->blog(), 'NaN', "$class->new(-2, 2)->blog()");
77
78my $ten = $class->new(10)->blog();
79
80# 10 is cached (up to 75 digits)
81is($class->new(10)->blog(),
82   '2.302585092994045684017991454684364207601',
83   qq|$class->new(10)->blog()|);
84
85# 0.1 is using the cached value for log(10), too
86
87is($class->new("0.1")->blog(), -$ten,
88   qq|$class->new("0.1")->blog()|);
89is($class->new("0.01")->blog(), -$ten * 2,
90   qq|$class->new("0.01")->blog()|);
91is($class->new("0.001")->blog(), -$ten * 3,
92   qq|$class->new("0.001")->blog()|);
93is($class->new("0.0001")->blog(), -$ten * 4,
94   qq|$class->new("0.0001")->blog()|);
95
96# also cached
97is($class->new(2)->blog(),
98   '0.6931471805599453094172321214581765680755',
99   qq|$class->new(2)->blog()|);
100is($class->new(4)->blog(), $class->new(2)->blog * 2,
101   qq|$class->new(4)->blog()|);
102
103# These are still slow, so do them only to 10 digits
104
105is($class->new("0.2")->blog(undef, 10), "-1.609437912",
106   qq|$class->new("0.2")->blog(undef, 10)|);
107is($class->new("0.3")->blog(undef, 10), "-1.203972804",
108   qq|$class->new("0.3")->blog(undef, 10)|);
109is($class->new("0.4")->blog(undef, 10), "-0.9162907319",
110   qq|$class->new("0.4")->blog(undef, 10)|);
111is($class->new("0.5")->blog(undef, 10), "-0.6931471806",
112   qq|$class->new("0.5")->blog(undef, 10)|);
113is($class->new("0.6")->blog(undef, 10), "-0.5108256238",
114   qq|$class->new("0.6")->blog(undef, 10)|);
115is($class->new("0.7")->blog(undef, 10), "-0.3566749439",
116   qq|$class->new("0.7")->blog(undef, 10)|);
117is($class->new("0.8")->blog(undef, 10), "-0.2231435513",
118   qq|$class->new("0.8")->blog(undef, 10)|);
119is($class->new("0.9")->blog(undef, 10), "-0.1053605157",
120   qq|$class->new("0.9")->blog(undef, 10)|);
121
122is($class->new("9")->blog(undef, 10), "2.197224577",
123   qq|$class->new("9")->blog(undef, 10)|);
124
125is($class->new("10")->blog(10, 10), "1.000000000",
126   qq|$class->new("10")->blog(10, 10)|);
127is($class->new("20")->blog(20, 10), "1.000000000",
128   qq|$class->new("20")->blog(20, 10)|);
129is($class->new("100")->blog(100, 10), "1.000000000",
130   qq|$class->new("100")->blog(100, 10)|);
131
132is($class->new("100")->blog(10, 10), "2.000000000",     # 10 ** 2 == 100
133   qq|$class->new("100")->blog(10, 10)|);
134is($class->new("400")->blog(20, 10), "2.000000000",     # 20 ** 2 == 400
135   qq|$class->new("400")->blog(20, 10)|);
136
137is($class->new("4")->blog(2, 10), "2.000000000",        # 2 ** 2 == 4
138   qq|$class->new("4")->blog(2, 10)|);
139is($class->new("16")->blog(2, 10), "4.000000000",       # 2 ** 4 == 16
140   qq|$class->new("16")->blog(2, 10)|);
141
142is($class->new("1.2")->bpow("0.3", 10), "1.056219968",
143   qq|$class->new("1.2")->bpow("0.3", 10)|);
144is($class->new("10")->bpow("0.6", 10), "3.981071706",
145   qq|$class->new("10")->bpow("0.6", 10)|);
146
147# blog should handle bigint input
148is(Math::BigFloat->blog(Math::BigInt->new(100), 10), 2, "blog(100)");
149
150###############################################################################
151# some integer results
152is($class->new(2)->bpow(32)->blog(2), "32", "2 ** 32");
153is($class->new(3)->bpow(32)->blog(3), "32", "3 ** 32");
154is($class->new(2)->bpow(65)->blog(2), "65", "2 ** 65");
155
156my $x = Math::BigInt->new('777') ** 256;
157my $base = Math::BigInt->new('12345678901234');
158is($x->copy()->blog($base), 56, 'blog(777**256, 12345678901234)');
159
160$x = Math::BigInt->new('777') ** 777;
161$base = Math::BigInt->new('777');
162is($x->copy()->blog($base), 777, 'blog(777**777, 777)');
163
164###############################################################################
165# test for bug in bsqrt() not taking negative _e into account
166test_bpow('200', '0.5', 10, '14.14213562');
167test_bpow('20', '0.5', 10, '4.472135955');
168test_bpow('2', '0.5', 10, '1.414213562');
169test_bpow('0.2', '0.5', 10, '0.4472135955');
170test_bpow('0.02', '0.5', 10, '0.1414213562');
171test_bpow('0.49', '0.5', undef, '0.7');
172test_bpow('0.49', '0.5', 10, '0.7000000000');
173test_bpow('0.002', '0.5', 10, '0.04472135955');
174test_bpow('0.0002', '0.5', 10, '0.01414213562');
175test_bpow('0.0049', '0.5', undef, '0.07');
176test_bpow('0.0049', '0.5', 10, '0.07000000000');
177test_bpow('0.000002', '0.5', 10, '0.001414213562');
178test_bpow('0.021', '0.5', 10, '0.1449137675');
179test_bpow('1.2', '0.5', 10, '1.095445115');
180test_bpow('1.23', '0.5', 10, '1.109053651');
181test_bpow('12.3', '0.5', 10, '3.507135583');
182
183test_bpow('9.9', '0.5', 10, '3.146426545');
184test_bpow('9.86902225', '0.5', 10, '3.141500000');
185test_bpow('9.86902225', '0.5', undef, '3.1415');
186
187###############################################################################
188# other tests for bpow()
189
190test_bpow('0.2', '0.41', 10, '0.5169187652');
191
192is($class->new("0.1")->bpow("28.4", 40)->bsstr(),
193   '3981071705534972507702523050877520434877e-68',
194   qq|$class->new("0.1")->bpow("28.4", 40)->bsstr()|);
195
196# The following test takes too long.
197#is($class->new("2")->bpow("-1034.5", 40)->bsstr(),
198#   '3841222690408590466868250378242558090957e-351',
199#   qq|$class->new("2")->bpow("-1034.5", 40)|);
200
201###############################################################################
202# test bexp() with cached results
203
204is($class->new(1)->bexp(), '2.718281828459045235360287471352662497757',
205    'bexp(1)');
206is($class->new(2)->bexp(40), $class->new(1)->bexp(45)->bpow(2, 40),
207    'bexp(2)');
208
209is($class->new("12.5")->bexp(61), $class->new(1)->bexp(65)->bpow(12.5, 61),
210    'bexp(12.5)');
211
212###############################################################################
213# test bexp() with big values (non-cached)
214
215is($class->new(1)->bexp(100),
216   '2.7182818284590452353602874713526624977572470936999'
217   . '59574966967627724076630353547594571382178525166427',
218   qq|$class->new(1)->bexp(100)|);
219
220is($class->new("12.5")->bexp(91), $class->new(1)->bexp(95)->bpow(12.5, 91),
221   qq|$class->new("12.5")->bexp(91)|);
222
223is($class->new("-118.5")->bexp(20)->bsstr(),
224   '34364014567198602057e-71',
225   qq|$class->new("-118.5")->bexp(20)->bsstr()|);
226
227is($class->new("-394.84010945715266885")->bexp(20)->bsstr(),
228   '33351796227864913873e-191',
229   qq|$class->new("-118.5")->bexp(20)->bsstr()|);
230
231# all done
232
233###############################################################################
234
235sub test_bpow {
236    my ($x, $y, $scale, $result) = @_;
237    is($class->new($x)->bpow($y, $scale), $result,
238         qq|$class->new($x)->bpow($y, |
239       . (defined($scale) ? $scale : 'undef')
240       . qq|)|);
241}
242