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/* Compute cubic root of double value.
Copyright (C) 1997-2020 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)
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