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/* Compute cubic root of float value.
Copyright (C) 1997-2021 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 <machine/asm.h>
#include <libm-alias-float.h>
.section .rodata
.align ALIGNARG(4)
.type f3,@object
f3: .double 0.191502161678719066
ASM_SIZE_DIRECTIVE(f3)
.type f2,@object
f2: .double 0.697570460207922770
ASM_SIZE_DIRECTIVE(f2)
.type f1,@object
f1: .double 0.492659620528969547
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
.align ALIGNARG(4)
factor: .double ONE_SQR_CBRT2
.double ONE_CBRT2
.double 1.0
.double CBRT2
.double SQR_CBRT2
ASM_SIZE_DIRECTIVE(factor)
.type two25,@object
two25: .byte 0, 0, 0, 0x4c
ASM_SIZE_DIRECTIVE(two25)
#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(__cbrtf)
movl 4(%esp), %eax
xorl %ecx, %ecx
movl %eax, %edx
andl $0x7fffffff, %eax
jz 1f
cmpl $0x7f800000, %eax
jae 1f
#ifdef PIC
pushl %ebx
cfi_adjust_cfa_offset (4)
cfi_rel_offset (ebx, 0)
LOAD_PIC_REG (bx)
#endif
cmpl $0x00800000, %eax
jae 2f
#ifdef PIC
flds 8(%esp)
#else
flds 4(%esp)
#endif
fmuls MO(two25)
movl $-25, %ecx
#ifdef PIC
fstps 8(%esp)
movl 8(%esp), %eax
#else
fstps 4(%esp)
movl 4(%esp), %eax
#endif
movl %eax, %edx
andl $0x7fffffff, %eax
2: shrl $23, %eax
andl $0x807fffff, %edx
subl $126, %eax
orl $0x3f000000, %edx
addl %eax, %ecx
#ifdef PIC
movl %edx, 8(%esp)
flds 8(%esp) /* xm */
#else
movl %edx, 4(%esp)
flds 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(f3) /* f3*xm : xm */
movl $1431655766, %eax
fsubrl MO(f2) /* f2-f3*xm : xm */
imull %ecx
fmul %st(1) /* (f2-f3*xm)*xm : xm */
movl %ecx, %eax
faddl MO(f1) /* u:=f1+(f2-f3*xm)*xm : xm */
sarl $31, %eax
fld %st /* u : u : xm */
subl %eax, %edx
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 8(%esp), %eax
popl %ebx
cfi_adjust_cfa_offset (-4)
cfi_restore (ebx)
#else
movl 4(%esp), %eax
#endif
testl %eax, %eax
fstp %st(1)
jns 4f
fchs
4: ret
/* Return the argument. */
1: flds 4(%esp)
ret
END(__cbrtf)
libm_alias_float (__cbrt, cbrt)
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