1 /* Compute cubic root of float value.
2 Copyright (C) 1997-2014 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
5 Ulrich Drepper <drepper@cygnus.com>, 1997.
7 The GNU C Library is free software; you can redistribute it and/or
8 modify it under the terms of the GNU Lesser General Public
9 License as published by the Free Software Foundation; either
10 version 2.1 of the License, or (at your option) any later version.
12 The GNU C Library is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 Lesser General Public License for more details.
17 You should have received a copy of the GNU Lesser General Public
18 License along with the GNU C Library; if not, see
19 <http://www.gnu.org/licenses/>. */
21 #include <machine/asm.h>
27 f3: .double 0.191502161678719066
28 ASM_SIZE_DIRECTIVE(f3)
30 f2: .double 0.697570460207922770
31 ASM_SIZE_DIRECTIVE(f2)
33 f1: .double 0.492659620528969547
34 ASM_SIZE_DIRECTIVE(f1)
36 #define CBRT2 1.2599210498948731648
37 #define ONE_CBRT2 0.793700525984099737355196796584
38 #define SQR_CBRT2 1.5874010519681994748
39 #define ONE_SQR_CBRT2 0.629960524947436582364439673883
43 factor: .double ONE_SQR_CBRT2
48 ASM_SIZE_DIRECTIVE(factor)
51 two25: .byte 0, 0, 0, 0x4c
52 ASM_SIZE_DIRECTIVE(two25)
55 #define MO(op) op##@GOTOFF(%ebx)
56 #define MOX(op,x) op##@GOTOFF(%ebx,x,1)
59 #define MOX(op,x) op(x)
67 andl $0x7fffffff, %eax
69 cmpl $0x7f800000, %eax
74 cfi_adjust_cfa_offset (4)
75 cfi_rel_offset (ebx, 0)
79 cmpl $0x00800000, %eax
97 andl $0x7fffffff, %eax
100 andl $0x807fffff, %edx
102 orl $0x3f000000, %edx
107 flds 8(%esp) /* xm */
111 flds 4(%esp) /* xm */
115 /* The following code has two tracks:
116 a) compute the normalized cbrt value
117 b) compute xe/3 and xe%3
118 The right track computes the value for b) and this is done
119 in an optimized way by avoiding division.
121 But why two tracks at all? Very easy: efficiency. Some FP
122 instruction can overlap with a certain amount of integer (and
123 FP) instructions. So we get (except for the imull) all
124 instructions for free. */
126 fld %st(0) /* xm : xm */
127 fmull MO(f3) /* f3*xm : xm */
128 movl $1431655766, %eax
129 fsubrl MO(f2) /* f2-f3*xm : xm */
131 fmul %st(1) /* (f2-f3*xm)*xm : xm */
133 faddl MO(f1) /* u:=f1+(f2-f3*xm)*xm : xm */
135 fld %st /* u : u : xm */
137 fmul %st(1) /* u*u : u : xm */
138 fld %st(2) /* xm : u*u : u : xm */
139 fadd %st /* 2*xm : u*u : u : xm */
140 fxch %st(1) /* u*u : 2*xm : u : xm */
141 fmul %st(2) /* t2:=u*u*u : 2*xm : u : xm */
143 fadd %st, %st(1) /* t2 : t2+2*xm : u : xm */
144 leal (%edx,%edx,2),%edx
145 fadd %st(0) /* 2*t2 : t2+2*xm : u : xm */
147 faddp %st, %st(3) /* t2+2*xm : u : 2*t2+xm */
149 fmulp /* u*(t2+2*xm) : 2*t2+xm */
150 fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */
151 fmull MOX(16+factor,%ecx) /* u*(t2+2*xm)/(2*t2+xm)*FACT */
153 cfi_adjust_cfa_offset (4)
154 fildl (%esp) /* xe/3 : u*(t2+2*xm)/(2*t2+xm)*FACT */
155 fxch /* u*(t2+2*xm)/(2*t2+xm)*FACT : xe/3 */
156 fscale /* u*(t2+2*xm)/(2*t2+xm)*FACT*2^xe/3 */
158 cfi_adjust_cfa_offset (-4)
162 cfi_adjust_cfa_offset (-4)
173 /* Return the argument. */
177 weak_alias (__cbrtf, cbrtf)