aboutsummaryrefslogtreecommitdiff
path: root/sysdeps/i386/fpu/s_cbrt.S
blob: 4e612f149b78b077d36eccbc6b9d95932e1c1c15 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
/* Compute cubic root of double value.
   Copyright (C) 1997-2021 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
   Ulrich Drepper <drepper@cygnus.com>, 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <https://www.gnu.org/licenses/>.  */

#include <machine/asm.h>
#include <libm-alias-double.h>

        .section .rodata

        .align ALIGNARG(4)
        .type f7,@object
f7:	.double -0.145263899385486377
	ASM_SIZE_DIRECTIVE(f7)
        .type f6,@object
f6:	.double 0.784932344976639262
	ASM_SIZE_DIRECTIVE(f6)
        .type f5,@object
f5:	.double -1.83469277483613086
	ASM_SIZE_DIRECTIVE(f5)
        .type f4,@object
f4:	.double 2.44693122563534430
	ASM_SIZE_DIRECTIVE(f4)
        .type f3,@object
f3:	.double -2.11499494167371287
	ASM_SIZE_DIRECTIVE(f3)
        .type f2,@object
f2:	.double 1.50819193781584896
	ASM_SIZE_DIRECTIVE(f2)
        .type f1,@object
f1:	.double 0.354895765043919860
	ASM_SIZE_DIRECTIVE(f1)

#define CBRT2		1.2599210498948731648
#define ONE_CBRT2	0.793700525984099737355196796584
#define SQR_CBRT2	1.5874010519681994748
#define ONE_SQR_CBRT2	0.629960524947436582364439673883

	.type factor,@object
factor:	.double ONE_SQR_CBRT2
	.double ONE_CBRT2
	.double 1.0
	.double CBRT2
	.double SQR_CBRT2
	ASM_SIZE_DIRECTIVE(factor)

        .type two54,@object
two54:  .byte 0, 0, 0, 0, 0, 0, 0x50, 0x43
        ASM_SIZE_DIRECTIVE(two54)

#ifdef PIC
#define MO(op) op##@GOTOFF(%ebx)
#define MOX(op,x) op##@GOTOFF(%ebx,x,1)
#else
#define MO(op) op
#define MOX(op,x) op(x)
#endif

	.text
ENTRY(__cbrt)
	movl	4(%esp), %ecx
	movl	8(%esp), %eax
	movl	%eax, %edx
	andl	$0x7fffffff, %eax
	orl	%eax, %ecx
	jz	1f
	xorl	%ecx, %ecx
	cmpl	$0x7ff00000, %eax
	jae	1f

#ifdef PIC
	pushl	%ebx
	cfi_adjust_cfa_offset (4)
	cfi_rel_offset (ebx, 0)
	LOAD_PIC_REG (bx)
#endif

	cmpl	$0x00100000, %eax
	jae	2f

#ifdef PIC
	fldl	8(%esp)
#else
	fldl	4(%esp)
#endif
	fmull	MO(two54)
	movl	$-54, %ecx
#ifdef PIC
	fstpl	8(%esp)
	movl	12(%esp), %eax
#else
	fstpl	4(%esp)
	movl	8(%esp), %eax
#endif
	movl	%eax, %edx
	andl	$0x7fffffff, %eax

2:	shrl	$20, %eax
	andl	$0x800fffff, %edx
	subl	$1022, %eax
	orl	$0x3fe00000, %edx
	addl	%eax, %ecx
#ifdef PIC
	movl	%edx, 12(%esp)

	fldl	8(%esp)			/* xm */
#else
	movl	%edx, 8(%esp)

	fldl	4(%esp)			/* xm */
#endif
	fabs

	/* The following code has two tracks:
	    a) compute the normalized cbrt value
	    b) compute xe/3 and xe%3
	   The right track computes the value for b) and this is done
	   in an optimized way by avoiding division.

	   But why two tracks at all?  Very easy: efficiency.  Some FP
	   instruction can overlap with a certain amount of integer (and
	   FP) instructions.  So we get (except for the imull) all
	   instructions for free.  */

	fld	%st(0)			/* xm : xm */

	fmull	MO(f7)			/* f7*xm : xm */
			movl	$1431655766, %eax
	faddl	MO(f6)			/* f6+f7*xm : xm */
			imull	%ecx
	fmul	%st(1)			/* (f6+f7*xm)*xm : xm */
			movl	%ecx, %eax
	faddl	MO(f5)			/* f5+(f6+f7*xm)*xm : xm */
			sarl	$31, %eax
	fmul	%st(1)			/* (f5+(f6+f7*xm)*xm)*xm : xm */
			subl	%eax, %edx
	faddl	MO(f4)			/* f4+(f5+(f6+f7*xm)*xm)*xm : xm */
	fmul	%st(1)			/* (f4+(f5+(f6+f7*xm)*xm)*xm)*xm : xm */
	faddl	MO(f3)			/* f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm : xm */
	fmul	%st(1)			/* (f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm : xm */
	faddl	MO(f2)			/* f2+(f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm : xm */
	fmul	%st(1)			/* (f2+(f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm)*xm : xm */
	faddl	MO(f1)			/* u:=f1+(f2+(f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm)*xm : xm */

	fld	%st			/* u : u : xm */
	fmul	%st(1)			/* u*u : u : xm */
	fld	%st(2)			/* xm : u*u : u : xm */
	fadd	%st			/* 2*xm : u*u : u : xm */
	fxch	%st(1)			/* u*u : 2*xm : u : xm */
	fmul	%st(2)			/* t2:=u*u*u : 2*xm : u : xm */
			movl	%edx, %eax
	fadd	%st, %st(1)		/* t2 : t2+2*xm : u : xm */
			leal	(%edx,%edx,2),%edx
	fadd	%st(0)			/* 2*t2 : t2+2*xm : u : xm */
			subl	%edx, %ecx
	faddp	%st, %st(3)		/* t2+2*xm : u : 2*t2+xm */
			shll	$3, %ecx
	fmulp				/* u*(t2+2*xm) : 2*t2+xm */
	fdivp	%st, %st(1)		/* u*(t2+2*xm)/(2*t2+xm) */
	fmull	MOX(16+factor,%ecx)	/* u*(t2+2*xm)/(2*t2+xm)*FACT */
	pushl	%eax
	cfi_adjust_cfa_offset (4)
	fildl	(%esp)			/* xe/3 : u*(t2+2*xm)/(2*t2+xm)*FACT */
	fxch				/* u*(t2+2*xm)/(2*t2+xm)*FACT : xe/3 */
	fscale				/* u*(t2+2*xm)/(2*t2+xm)*FACT*2^xe/3 */
	popl	%edx
	cfi_adjust_cfa_offset (-4)
#ifdef PIC
	movl	12(%esp), %eax
	popl	%ebx
	cfi_adjust_cfa_offset (-4)
	cfi_restore (ebx)
#else
	movl	8(%esp), %eax
#endif
	testl	%eax, %eax
	fstp	%st(1)
	jns	4f
	fchs
4:	ret

	/* Return the argument.  */
1:	fldl	4(%esp)
	ret
END(__cbrt)
libm_alias_double (__cbrt, cbrt)