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/* Compute cubic root of long double value.
Copyright (C) 1997-2022 Free Software Foundation, Inc.
This file is part of the GNU C Library.
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 <libm-alias-ldouble.h>
#include <machine/asm.h>
.section .rodata
.align ALIGNARG(4)
.type f8,@object
f8: .quad 0xa57ef3d83a542839 /* 0.161617097923756032 */
.short 0x3ffc
ASM_SIZE_DIRECTIVE(f8)
.align ALIGNARG(4)
.type f7,@object
f7: .quad 0xfd11da7820029014 /* -0.988553671195413709 */
.short 0xbffe
ASM_SIZE_DIRECTIVE(f7)
.align ALIGNARG(4)
.type f6,@object
f6: .quad 0xa9ca93fcade3b4ad /* 2.65298938441952296 */
.short 0x4000
ASM_SIZE_DIRECTIVE(f6)
.align ALIGNARG(4)
.type f5,@object
f5: .quad 0x839186562c931c34 /* -4.11151425200350531 */
.short 0xc001
ASM_SIZE_DIRECTIVE(f5)
.align ALIGNARG(4)
.type f4,@object
f4: .quad 0x830f25c9ee304594 /* 4.09559907378707839 */
.short 0x4001
ASM_SIZE_DIRECTIVE(f4)
.align ALIGNARG(4)
.type f3,@object
f3: .quad 0xb4bedd1d5fa2f0c6 /* -2.82414939754975962 */
.short 0xc000
ASM_SIZE_DIRECTIVE(f3)
.align ALIGNARG(4)
.type f2,@object
f2: .quad 0xd685a163b08586e3 /* 1.67595307700780102 */
.short 0x3fff
ASM_SIZE_DIRECTIVE(f2)
.align ALIGNARG(4)
.type f1,@object
f1: .quad 0xad16073ed4ec3b45 /* 0.338058687610520237 */
.short 0x3ffd
ASM_SIZE_DIRECTIVE(f1)
/* We make the entries in the following table all 16 bytes
wide to avoid having to implement a multiplication by 10. */
.type factor,@object
.align ALIGNARG(4)
factor: /* 1.0 / cbrt (2.0) ^ 2 = 0.629960524947436582364439673883 */
.quad 0xa14517cc6b945711
.short 0x3ffe
.byte 0, 0, 0, 0, 0, 0
/* 1.0 / cbrt (2.0) = 0.793700525984099737355196796584 */
.quad 0xcb2ff529eb71e415
.short 0x3ffe
.byte 0, 0, 0, 0, 0, 0
/* 1.0L */
.quad 0x8000000000000000
.short 0x3fff
.byte 0, 0, 0, 0, 0, 0
/* cbrt (2.0) = 1.2599210498948731648 */
.quad 0xa14517cc6b945711
.short 0x3fff
.byte 0, 0, 0, 0, 0, 0
/* cbrt (2.0) ^ 2 = 1.5874010519681994748 */
.quad 0xcb2ff529eb71e416
.short 0x3fff
ASM_SIZE_DIRECTIVE(factor)
.type two64,@object
.align ALIGNARG(4)
two64: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43
ASM_SIZE_DIRECTIVE(two64)
#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(__cbrtl)
movl 4(%esp), %ecx
movl 12(%esp), %eax
orl 8(%esp), %ecx
movl %eax, %edx
andl $0x7fff, %eax
orl %eax, %ecx
jz 1f
xorl %ecx, %ecx
cmpl $0x7fff, %eax
je 1f
#ifdef PIC
pushl %ebx
cfi_adjust_cfa_offset (4)
cfi_rel_offset (ebx, 0)
LOAD_PIC_REG (bx)
#endif
cmpl $0, %eax
jne 2f
#ifdef PIC
fldt 8(%esp)
#else
fldt 4(%esp)
#endif
fmull MO(two64)
movl $-64, %ecx
#ifdef PIC
fstpt 8(%esp)
movl 16(%esp), %eax
#else
fstpt 4(%esp)
movl 12(%esp), %eax
#endif
movl %eax, %edx
andl $0x7fff, %eax
2: andl $0x8000, %edx
subl $16382, %eax
orl $0x3ffe, %edx
addl %eax, %ecx
#ifdef PIC
movl %edx, 16(%esp)
fldt 8(%esp) /* xm */
#else
movl %edx, 12(%esp)
fldt 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. */
fldt MO(f8) /* f8 : xm */
fmul %st(1) /* f8*xm : xm */
fldt MO(f7)
faddp /* f7+f8*xm : xm */
fmul %st(1) /* (f7+f8*xm)*xm : xm */
movl $1431655766, %eax
fldt MO(f6)
faddp /* f6+(f7+f8*xm)*xm : xm */
imull %ecx
fmul %st(1) /* (f6+(f7+f8*xm)*xm)*xm : xm */
movl %ecx, %eax
fldt MO(f5)
faddp /* f5+(f6+(f7+f8*xm)*xm)*xm : xm */
sarl $31, %eax
fmul %st(1) /* (f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */
subl %eax, %edx
fldt MO(f4)
faddp /* f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */
fmul %st(1) /* (f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */
fldt MO(f3)
faddp /* f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */
fmul %st(1) /* (f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */
fldt MO(f2)
faddp /* f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */
fmul %st(1) /* (f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm)*xm : xm */
fldt MO(f1)
faddp /* u:=f1+(f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*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 $4, %ecx
fmulp /* u*(t2+2*xm) : 2*t2+xm */
fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */
fldt MOX(32+factor,%ecx)
fmulp /* 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 16(%esp), %eax
popl %ebx
cfi_adjust_cfa_offset (-4)
cfi_restore (ebx)
#else
movl 12(%esp), %eax
#endif
testl $0x8000, %eax
fstp %st(1)
jz 4f
fchs
4: ret
/* Return the argument. */
1: fldt 4(%esp)
fadd %st
ret
END(__cbrtl)
libm_alias_ldouble (__cbrt, cbrt)
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