BC开方（乙）

1function bcroot($幂, $指 = '3', $scale = 0){
2	#开方
3	$d = false;
4	if($幂 == '0'){
5		return '0';
6	}elseif($幂 == '1'){
7		return '1';
8	}
9
10	$指数 = intval($指);
11	$底扩位数 = $scale;
12	$幂扩位数 = $指数 * $底扩位数;
13
14	$幂 = bcmul($幂,str_pad('1',$幂扩位数+1,'0'));
15
16	$小数点位 = strpos($幂,'.');
17	if($小数点位 !== FALSE){
18		$幂 = substr($幂,0,$小数点位);
19	}
20
21	$幂长 = strlen($幂);
22	$底数长 = ceil($幂长 / $指数);
23
24	#初次逆序
25	$幂 = strrev($幂);
26	$幂段 = array_reverse(str_split($幂,$指数));
27	$底数 = '';
28	$小余 = '0';
29	foreach($幂段 as $小幂){
30		#再次逆序，则正过来
31		$小幂 = strrev($小幂);
32
33		# （底 . 小底）^指数  - 小底^指数 <= 小余 . 小幂
34
35		if($小余 != '0'){
36			$此幂 = $小余.$小幂;
37		}else{
38			$此幂 = $小幂;
39		}
40
41		$小余 = '0';
42
43		$小底 = '1';
44		${'试幂'.$小底} = bcpow_sub($底数,$小底,$指);
45		$比较 = bccomp(${'试幂'.$小底},$此幂);
46		if($比较 == '1'){
47			# x<1
48			$小底 = '0';
49			$小余 = $此幂;
50		}else{
51			# 1<x
52			$小底 = '9';
53			${'试幂'.$小底} = bcpow_sub($底数,$小底,$指);
54			$比较 = bccomp(${'试幂'.$小底},$此幂);
55			if($比较 == '-1'){
56				# 9<x
57				$小底 = '9';
58				$小余 = bcsub($此幂,${'试幂'.$小底});
59			}else{
60				# 1<x<9
61				$小底 = '5';
62				${'试幂'.$小底} = bcpow_sub($底数,$小底,$指);
63				$比较 = bccomp(${'试幂'.$小底},$此幂);
64				if($比较 == '1'){
65					# 1<x<5
66					$小底 = '3';
67					${'试幂'.$小底} = bcpow_sub($底数,$小底,$指);
68					$比较 = bccomp(${'试幂'.$小底},$此幂);
69					if($比较 == '1'){
70						# 1<x<3
71						$小底 = '2';
72						${'试幂'.$小底} = bcpow_sub($底数,$小底,$指);
73						$比较 = bccomp(${'试幂'.$小底},$此幂);
74						if($比较 == '1'){
75							# 1<x<2
76							$小底 = '1';
77							$小余 = bcsub($此幂,${'试幂'.$小底});
78						}else{
79							# 2<x<3
80							$小底 = '2';
81							$小余 = bcsub($此幂,${'试幂'.$小底});
82						}
83					}else{
84						# 3<x<5
85						$小底 = '4';
86						${'试幂'.$小底} = bcpow_sub($底数,$小底,$指);
87						$比较 = bccomp(${'试幂'.$小底},$此幂);
88						if($比较 == '1'){
89							# 3<x<4
90							$小底 = '3';
91							$小余 = bcsub($此幂,${'试幂'.$小底});
92						}else{
93							# 4<x<5
94							$小底 = '4';
95							$小余 = bcsub($此幂,${'试幂'.$小底});
96						}
97					}
98				}else{
99					# 5<x<9
100					$小底 = '7';
101					${'试幂'.$小底} = bcpow_sub($底数,$小底,$指);
102					$比较 = bccomp(${'试幂'.$小底},$此幂);
103					if($比较 == '1'){
104						# 5<x<7
105						$小底 = '6';
106						${'试幂'.$小底} = bcpow_sub($底数,$小底,$指);
107						$比较 = bccomp(${'试幂'.$小底},$此幂);
108						if($比较 == '1'){
109							# 5<x<6
110							$小底 = '5';
111							$小余 = bcsub($此幂,${'试幂'.$小底});
112						}else{
113							# 6<x<7
114							$小底 = '6';
115							$小余 = bcsub($此幂,${'试幂'.$小底});
116						}
117					}else{
118						# 7<x<9
119						$小底 = '8';
120						${'试幂'.$小底} = bcpow_sub($底数,$小底,$指);
121						$比较 = bccomp(${'试幂'.$小底},$此幂);
122						if($比较 == '1'){
123							# 7<x<8
124							$小底 = '7';
125							$小余 = bcsub($此幂,${'试幂'.$小底});
126						}else{
127							# 8<x<9
128							$小底 = '8';
129							$小余 = bcsub($此幂,${'试幂'.$小底});
130						}
131					}
132				}
133			}
134		}
135		$底数 .= $小底;
136	}
137
138	$底数 = bcdiv($底数,str_pad('1',$底扩位数+1,'0'),$scale);
139	return $底数;
140}
141
142function bcpow_sub($底,$小底,$指){
143	if($底 == '0' or $底 == ''){
144		return bcpow($小底,$指);
145	}else{
146		return bcsub(bcpow($底 . $小底,$指),bcpow($底 .'0',$指));
147	}
148}