1 | /* Compute cubic root of long double value. |
2 | Copyright (C) 1997-2022 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Lesser General Public |
7 | License as published by the Free Software Foundation; either |
8 | version 2.1 of the License, or (at your option) any later version. |
9 | |
10 | The GNU C Library is distributed in the hope that it will be useful, |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | Lesser General Public License for more details. |
14 | |
15 | You should have received a copy of the GNU Lesser General Public |
16 | License along with the GNU C Library; if not, see |
17 | <https://www.gnu.org/licenses/>. */ |
18 | |
19 | #include <libm-alias-ldouble.h> |
20 | #include <machine/asm.h> |
21 | |
22 | .section .rodata |
23 | |
24 | .align ALIGNARG(4) |
25 | .type f8,@object |
26 | f8: .tfloat 0.161617097923756032 |
27 | ASM_SIZE_DIRECTIVE(f8) |
28 | .align ALIGNARG(4) |
29 | .type f7,@object |
30 | f7: .tfloat -0.988553671195413709 |
31 | ASM_SIZE_DIRECTIVE(f7) |
32 | .align ALIGNARG(4) |
33 | .type f6,@object |
34 | f6: .tfloat 2.65298938441952296 |
35 | ASM_SIZE_DIRECTIVE(f6) |
36 | .align ALIGNARG(4) |
37 | .type f5,@object |
38 | f5: .tfloat -4.11151425200350531 |
39 | ASM_SIZE_DIRECTIVE(f5) |
40 | .align ALIGNARG(4) |
41 | .type f4,@object |
42 | f4: .tfloat 4.09559907378707839 |
43 | ASM_SIZE_DIRECTIVE(f4) |
44 | .align ALIGNARG(4) |
45 | .type f3,@object |
46 | f3: .tfloat -2.82414939754975962 |
47 | ASM_SIZE_DIRECTIVE(f3) |
48 | .align ALIGNARG(4) |
49 | .type f2,@object |
50 | f2: .tfloat 1.67595307700780102 |
51 | ASM_SIZE_DIRECTIVE(f2) |
52 | .align ALIGNARG(4) |
53 | .type f1,@object |
54 | f1: .tfloat 0.338058687610520237 |
55 | ASM_SIZE_DIRECTIVE(f1) |
56 | |
57 | #define CBRT2 1.2599210498948731648 |
58 | #define ONE_CBRT2 0.793700525984099737355196796584 |
59 | #define SQR_CBRT2 1.5874010519681994748 |
60 | #define ONE_SQR_CBRT2 0.629960524947436582364439673883 |
61 | |
62 | /* We make the entries in the following table all 16 bytes |
63 | wide to avoid having to implement a multiplication by 10. */ |
64 | .type factor,@object |
65 | .align ALIGNARG(4) |
66 | factor: .tfloat ONE_SQR_CBRT2 |
67 | .byte 0, 0, 0, 0, 0, 0 |
68 | .tfloat ONE_CBRT2 |
69 | .byte 0, 0, 0, 0, 0, 0 |
70 | .tfloat 1.0 |
71 | .byte 0, 0, 0, 0, 0, 0 |
72 | .tfloat CBRT2 |
73 | .byte 0, 0, 0, 0, 0, 0 |
74 | .tfloat SQR_CBRT2 |
75 | ASM_SIZE_DIRECTIVE(factor) |
76 | |
77 | .type two64,@object |
78 | .align ALIGNARG(4) |
79 | two64: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43 |
80 | ASM_SIZE_DIRECTIVE(two64) |
81 | |
82 | #ifdef PIC |
83 | #define MO(op) op##@GOTOFF(%ebx) |
84 | #define MOX(op,x) op##@GOTOFF(%ebx,x,1) |
85 | #else |
86 | #define MO(op) op |
87 | #define MOX(op,x) op(x) |
88 | #endif |
89 | |
90 | .text |
91 | ENTRY(__cbrtl) |
92 | movl 4(%esp), %ecx |
93 | movl 12(%esp), %eax |
94 | orl 8(%esp), %ecx |
95 | movl %eax, %edx |
96 | andl $0x7fff, %eax |
97 | orl %eax, %ecx |
98 | jz 1f |
99 | xorl %ecx, %ecx |
100 | cmpl $0x7fff, %eax |
101 | je 1f |
102 | |
103 | #ifdef PIC |
104 | pushl %ebx |
105 | cfi_adjust_cfa_offset (4) |
106 | cfi_rel_offset (ebx, 0) |
107 | LOAD_PIC_REG (bx) |
108 | #endif |
109 | |
110 | cmpl $0, %eax |
111 | jne 2f |
112 | |
113 | #ifdef PIC |
114 | fldt 8(%esp) |
115 | #else |
116 | fldt 4(%esp) |
117 | #endif |
118 | fmull MO(two64) |
119 | movl $-64, %ecx |
120 | #ifdef PIC |
121 | fstpt 8(%esp) |
122 | movl 16(%esp), %eax |
123 | #else |
124 | fstpt 4(%esp) |
125 | movl 12(%esp), %eax |
126 | #endif |
127 | movl %eax, %edx |
128 | andl $0x7fff, %eax |
129 | |
130 | 2: andl $0x8000, %edx |
131 | subl $16382, %eax |
132 | orl $0x3ffe, %edx |
133 | addl %eax, %ecx |
134 | #ifdef PIC |
135 | movl %edx, 16(%esp) |
136 | |
137 | fldt 8(%esp) /* xm */ |
138 | #else |
139 | movl %edx, 12(%esp) |
140 | |
141 | fldt 4(%esp) /* xm */ |
142 | #endif |
143 | fabs |
144 | |
145 | /* The following code has two tracks: |
146 | a) compute the normalized cbrt value |
147 | b) compute xe/3 and xe%3 |
148 | The right track computes the value for b) and this is done |
149 | in an optimized way by avoiding division. |
150 | |
151 | But why two tracks at all? Very easy: efficiency. Some FP |
152 | instruction can overlap with a certain amount of integer (and |
153 | FP) instructions. So we get (except for the imull) all |
154 | instructions for free. */ |
155 | |
156 | fldt MO(f8) /* f8 : xm */ |
157 | fmul %st(1) /* f8*xm : xm */ |
158 | |
159 | fldt MO(f7) |
160 | faddp /* f7+f8*xm : xm */ |
161 | fmul %st(1) /* (f7+f8*xm)*xm : xm */ |
162 | movl $1431655766, %eax |
163 | fldt MO(f6) |
164 | faddp /* f6+(f7+f8*xm)*xm : xm */ |
165 | imull %ecx |
166 | fmul %st(1) /* (f6+(f7+f8*xm)*xm)*xm : xm */ |
167 | movl %ecx, %eax |
168 | fldt MO(f5) |
169 | faddp /* f5+(f6+(f7+f8*xm)*xm)*xm : xm */ |
170 | sarl $31, %eax |
171 | fmul %st(1) /* (f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */ |
172 | subl %eax, %edx |
173 | fldt MO(f4) |
174 | faddp /* f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */ |
175 | fmul %st(1) /* (f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */ |
176 | fldt MO(f3) |
177 | faddp /* f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */ |
178 | fmul %st(1) /* (f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */ |
179 | fldt MO(f2) |
180 | faddp /* f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */ |
181 | fmul %st(1) /* (f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm)*xm : xm */ |
182 | fldt MO(f1) |
183 | faddp /* u:=f1+(f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm)*xm : xm */ |
184 | |
185 | fld %st /* u : u : xm */ |
186 | fmul %st(1) /* u*u : u : xm */ |
187 | fld %st(2) /* xm : u*u : u : xm */ |
188 | fadd %st /* 2*xm : u*u : u : xm */ |
189 | fxch %st(1) /* u*u : 2*xm : u : xm */ |
190 | fmul %st(2) /* t2:=u*u*u : 2*xm : u : xm */ |
191 | movl %edx, %eax |
192 | fadd %st, %st(1) /* t2 : t2+2*xm : u : xm */ |
193 | leal (%edx,%edx,2),%edx |
194 | fadd %st(0) /* 2*t2 : t2+2*xm : u : xm */ |
195 | subl %edx, %ecx |
196 | faddp %st, %st(3) /* t2+2*xm : u : 2*t2+xm */ |
197 | shll $4, %ecx |
198 | fmulp /* u*(t2+2*xm) : 2*t2+xm */ |
199 | fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */ |
200 | fldt MOX(32+factor,%ecx) |
201 | fmulp /* u*(t2+2*xm)/(2*t2+xm)*FACT */ |
202 | pushl %eax |
203 | cfi_adjust_cfa_offset (4) |
204 | fildl (%esp) /* xe/3 : u*(t2+2*xm)/(2*t2+xm)*FACT */ |
205 | fxch /* u*(t2+2*xm)/(2*t2+xm)*FACT : xe/3 */ |
206 | fscale /* u*(t2+2*xm)/(2*t2+xm)*FACT*2^xe/3 */ |
207 | popl %edx |
208 | cfi_adjust_cfa_offset (-4) |
209 | #ifdef PIC |
210 | movl 16(%esp), %eax |
211 | popl %ebx |
212 | cfi_adjust_cfa_offset (-4) |
213 | cfi_restore (ebx) |
214 | #else |
215 | movl 12(%esp), %eax |
216 | #endif |
217 | testl $0x8000, %eax |
218 | fstp %st(1) |
219 | jz 4f |
220 | fchs |
221 | 4: ret |
222 | |
223 | /* Return the argument. */ |
224 | 1: fldt 4(%esp) |
225 | fadd %st |
226 | ret |
227 | END(__cbrtl) |
228 | libm_alias_ldouble (__cbrt, cbrt) |
229 | |