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powerpc: Remove powerpc specific sinf and cosf optimization

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New generic optimization of sinf and cosf introduced by commit
599cf39766 shows improvement
compared to powerpc specific assembly version.  Hence removing
the powerpc assembly versions to make use of generic code.
This commit is contained in:
Rajalakshmi Srinivasaraghavan 2018-08-20 08:47:43 +05:30
parent 86a6c75a29
commit fa78896b1f
14 changed files with 18 additions and 1453 deletions
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18
ChangeLog
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@ -1,3 +1,21 @@
2018-08-20 Rajalakshmi Srinivasaraghavan <raji@linux.vnet.ibm.com>
* sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile
(libm-sysdep_routines): Remove s_sinf-ppc64, s_sinf-power8,
s_cosf-ppc64 and s_cosf-power8.
* sysdeps/powerpc/fpu/s_cosf.c: Remove file.
* sysdeps/powerpc/fpu/s_sinf.c: Likewise.
* sysdeps/powerpc/fpu/k_sinf.c: Likewise.
* sysdeps/powerpc/fpu/k_cosf.c: Likewise.
* sysdeps/powerpc/powerpc64/fpu/multiarch/s_cosf-power8.S: Likewise.
* sysdeps/powerpc/powerpc64/fpu/multiarch/s_cosf-ppc64.c: Likewise.
* sysdeps/powerpc/powerpc64/fpu/multiarch/s_cosf.c: Likewise.
* sysdeps/powerpc/powerpc64/fpu/multiarch/s_sinf-power8.S: Likewise.
* sysdeps/powerpc/powerpc64/fpu/multiarch/s_sinf-ppc64.c: Likewise.
* sysdeps/powerpc/powerpc64/fpu/multiarch/s_sinf.c: Likewise.
* sysdeps/powerpc/powerpc64/power8/fpu/s_cosf.S: Likewise.
* sysdeps/powerpc/powerpc64/power8/fpu/s_sinf.S: Likewise.
2018-08-17 Florian Weimer <fweimer@redhat.com>
* sysdeps/s390/fpu/libm-test-ulps: Regenerate.

65
sysdeps/powerpc/fpu/k_cosf.c
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@ -1,65 +0,0 @@
/* k_cosf.c -- float version of k_cos.c
Copyright (C) 2011-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If
not, see <http://www.gnu.org/licenses/>. */
#include <math.h>
#include <fenv.h>
#include <math_private.h>
static const float twom27 = 7.4505806e-09;
static const float dot3 = 3.0000001e-01;
static const float dot78125 = 7.8125000e-01;
static const float one = 1.0000000000e+00;
static const float C1 = 4.1666667908e-02;
static const float C2 = -1.3888889225e-03;
static const float C3 = 2.4801587642e-05;
static const float C4 = -2.7557314297e-07;
static const float C5 = 2.0875723372e-09;
static const float C6 = -1.1359647598e-11;
float
__kernel_cosf (float x, float y)
{
float a, hz, z, r, qx;
float ix;
ix = __builtin_fabsf (x);
if (ix < twom27)
{ /* |x| < 2**-27 */
__feraiseexcept (FE_INEXACT);
return one;
}
z = x * x;
r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
if (ix < dot3) /* if |x| < 0.3 */
return one - ((float) 0.5 * z - (z * r - x * y));
else
{
if (ix > dot78125)
{ /* x > 0.78125 */
qx = (float) 0.28125;
}
else
{
qx = ix / 4.0;
}
hz = (float) 0.5 *z - qx;
a = one - qx;
return a - (hz - (z * r - x * y));
}
}

57
sysdeps/powerpc/fpu/k_sinf.c
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@ -1,57 +0,0 @@
/* k_sinf.c -- float version of k_sin.c
Copyright (C) 2011-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If
not, see <http://www.gnu.org/licenses/>. */
#include <float.h>
#include <math.h>
#include <fenv.h>
#include <math_private.h>
static const float twom27 = 7.4505806000e-09;
static const float half = 5.0000000000e-01;
static const float S1 = -1.6666667163e-01;
static const float S2 = 8.3333337680e-03;
static const float S3 = -1.9841270114e-04;
static const float S4 = 2.7557314297e-06;
static const float S5 = -2.5050759689e-08;
static const float S6 = 1.5896910177e-10;
float
__kernel_sinf (float x, float y, int iy)
{
float z, r, v;
float ix;
ix = __builtin_fabsf (x);
if (ix < twom27)
{ /* |x| < 2**-27 */
if (ix < FLT_MIN && ix != 0.0f)
__feraiseexcept (FE_UNDERFLOW|FE_INEXACT);
else
__feraiseexcept (FE_INEXACT);
return x;
}
z = x * x;
v = z * x;
r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
if (iy == 0)
return x + v * (S1 + z * r);
else
return x - ((z * (half * y - v * r) - y) - v * S1);
}

70
sysdeps/powerpc/fpu/s_cosf.c
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@ -1,70 +0,0 @@
/* s_cosf.c -- float version of s_cos.c.
Copyright (C) 2011-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If
not, see <http://www.gnu.org/licenses/>. */
#include <errno.h>
#include <math.h>
#include <math_private.h>
#include <libm-alias-float.h>
static const float pio4 = 7.8539801e-1;
float
__cosf (float x)
{
float y[2], z = 0.0;
float ix;
int32_t n;
ix = __builtin_fabsf (x);
/* |x| ~< pi/4 */
if (ix <= pio4)
{
return __kernel_cosf (x, z);
/* cos(Inf or NaN) is NaN */
}
else if (isnanf (ix))
{
return x - x;
}
else if (isinff (ix))
{
__set_errno (EDOM);
return x - x;
}
/* argument reduction needed */
else
{
n = __ieee754_rem_pio2f (x, y);
switch (n & 3)
{
case 0:
return __kernel_cosf (y[0], y[1]);
case 1:
return -__kernel_sinf (y[0], y[1], 1);
case 2:
return -__kernel_cosf (y[0], y[1]);
default:
return __kernel_sinf (y[0], y[1], 1);
}
}
}
libm_alias_float (__cos, cos)

70
sysdeps/powerpc/fpu/s_sinf.c
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@ -1,70 +0,0 @@
/* s_sinf.c -- float version of s_sin.c.
Copyright (C) 2011-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If
not, see <http://www.gnu.org/licenses/>. */
#include <errno.h>
#include <math.h>
#include <math_private.h>
#include <libm-alias-float.h>
static const float pio4 = 7.8539801e-1;
float
__sinf (float x)
{
float y[2], z = 0.0;
float ix;
int32_t n;
ix = __builtin_fabsf (x);
/* |x| ~< pi/4 */
if (ix <= pio4)
{
return __kernel_sinf (x, z, 0);
/* sin(Inf or NaN) is NaN */
}
else if (isnanf (ix))
{
return x - x;
}
else if (isinff (ix))
{
__set_errno (EDOM);
return x - x;
}
/* argument reduction needed */
else
{
n = __ieee754_rem_pio2f (x, y);
switch (n & 3)
{
case 0:
return __kernel_sinf (y[0], y[1], 1);
case 1:
return __kernel_cosf (y[0], y[1]);
case 2:
return -__kernel_sinf (y[0], y[1], 1);
default:
return -__kernel_cosf (y[0], y[1]);
}
}
}
libm_alias_float (__sin, sin)

2
sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile
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@ -27,8 +27,6 @@ libm-sysdep_routines += s_llround-power6x \
e_hypot-power7 e_hypotf-ppc64 e_hypotf-power7 \
s_llrint-power8 s_llround-power8 s_llroundf-ppc64 \
e_expf-power8 e_expf-ppc64 \
s_sinf-ppc64 s_sinf-power8 \
s_cosf-ppc64 s_cosf-power8 \
$(sysdep_calls:s_%=m_%)
CFLAGS-s_logbf-power7.c = -mcpu=power7

24
sysdeps/powerpc/powerpc64/fpu/multiarch/s_cosf-power8.S
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@ -1,24 +0,0 @@
/* cosf function. PowerPC64/power8 version.
Copyright (C) 2017-2018 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
<http://www.gnu.org/licenses/>. */
#undef weak_alias
#define weak_alias(a,b)
#define __cosf __cosf_power8
#include <sysdeps/powerpc/powerpc64/power8/fpu/s_cosf.S>

24
sysdeps/powerpc/powerpc64/fpu/multiarch/s_cosf-ppc64.c
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@ -1,24 +0,0 @@
/* cosf function. PowerPC64 default version.
Copyright (C) 2017-2018 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
<http://www.gnu.org/licenses/>. */
#undef weak_alias
#define weak_alias(a, b)
#define __cosf __cosf_ppc64
#include <sysdeps/powerpc/fpu/s_cosf.c>

32
sysdeps/powerpc/powerpc64/fpu/multiarch/s_cosf.c
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@ -1,32 +0,0 @@
/* Multiple versions of cosf.
Copyright (C) 2017-2018 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
<http://www.gnu.org/licenses/>. */
#include <math.h>
#include <shlib-compat.h>
#include "init-arch.h"
#include <libm-alias-float.h>
extern __typeof (__cosf) __cosf_ppc64 attribute_hidden;
extern __typeof (__cosf) __cosf_power8 attribute_hidden;
libc_ifunc (__cosf,
(hwcap2 & PPC_FEATURE2_ARCH_2_07)
? __cosf_power8
: __cosf_ppc64);
libm_alias_float (__cos, cos)

24
sysdeps/powerpc/powerpc64/fpu/multiarch/s_sinf-power8.S
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@ -1,24 +0,0 @@
/* sinf(). PowerPC64/POWER8 version.
Copyright (C) 2016-2018 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
<http://www.gnu.org/licenses/>. */
#undef weak_alias
#define weak_alias(a, b)
#define __sinf __sinf_power8
#include <sysdeps/powerpc/powerpc64/power8/fpu/s_sinf.S>

24
sysdeps/powerpc/powerpc64/fpu/multiarch/s_sinf-ppc64.c
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@ -1,24 +0,0 @@
/* sinf(). PowerPC64 default version.
Copyright (C) 2016-2018 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
<http://www.gnu.org/licenses/>. */
#undef weak_alias
#define weak_alias(a, b)
#define __sinf __sinf_ppc64
#include <sysdeps/powerpc/fpu/s_sinf.c>

32
sysdeps/powerpc/powerpc64/fpu/multiarch/s_sinf.c
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@ -1,32 +0,0 @@
/* Multiple versions of sinf.
Copyright (C) 2016-2018 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
<http://www.gnu.org/licenses/>. */
#include <math.h>
#include <shlib-compat.h>
#include "init-arch.h"
#include <libm-alias-float.h>
extern __typeof (__sinf) __sinf_ppc64 attribute_hidden;
extern __typeof (__sinf) __sinf_power8 attribute_hidden;
libc_ifunc (__sinf,
(hwcap2 & PPC_FEATURE2_ARCH_2_07)
? __sinf_power8
: __sinf_ppc64);
libm_alias_float (__sin, sin)

509
sysdeps/powerpc/powerpc64/power8/fpu/s_cosf.S
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@ -1,509 +0,0 @@
/* Optimized cosf(). PowerPC64/POWER8 version.
Copyright (C) 2017-2018 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
<http://www.gnu.org/licenses/>. */
#include <sysdep.h>
#define _ERRNO_H 1
#include <bits/errno.h>
#include <libm-alias-float.h>
#define FRAMESIZE (FRAME_MIN_SIZE+16)
#define FLOAT_EXPONENT_SHIFT 23
#define FLOAT_EXPONENT_BIAS 127
#define INTEGER_BITS 3
#define PI_4 0x3f490fdb /* PI/4 */
#define NINEPI_4 0x40e231d6 /* 9 * PI/4 */
#define TWO_PN5 0x3d000000 /* 2^-5 */
#define TWO_PN27 0x32000000 /* 2^-27 */
#define INFINITY 0x7f800000
#define TWO_P23 0x4b000000 /* 2^23 */
#define FX_FRACTION_1_28 0x9249250 /* 0x100000000 / 28 + 1 */
/* Implements the function
float [fp1] cosf (float [fp1] x) */
.machine power8
ENTRY (__cosf, 4)
addis r9,r2,L(anchor)@toc@ha
addi r9,r9,L(anchor)@toc@l
lis r4,PI_4@h
ori r4,r4,PI_4@l
xscvdpspn v0,v1
mfvsrd r8,v0
rldicl r3,r8,32,33 /* Remove sign bit. */
cmpw r3,r4
bge L(greater_or_equal_pio4)
lis r4,TWO_PN5@h
ori r4,r4,TWO_PN5@l
cmpw r3,r4
blt L(less_2pn5)
/* Chebyshev polynomial of the form:
* 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
lfd fp9,(L(C0)-L(anchor))(r9)
lfd fp10,(L(C1)-L(anchor))(r9)
lfd fp11,(L(C2)-L(anchor))(r9)
lfd fp12,(L(C3)-L(anchor))(r9)
lfd fp13,(L(C4)-L(anchor))(r9)
fmul fp2,fp1,fp1 /* x^2 */
lfd fp3,(L(DPone)-L(anchor))(r9)
fmadd fp4,fp2,fp13,fp12 /* C3+x^2*C4 */
fmadd fp4,fp2,fp4,fp11 /* C2+x^2*(C3+x^2*C4) */
fmadd fp4,fp2,fp4,fp10 /* C1+x^2*(C2+x^2*(C3+x^2*C4)) */
fmadd fp4,fp2,fp4,fp9 /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))) */
fmadd fp1,fp2,fp4,fp3 /* 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))) */
frsp fp1,fp1 /* Round to single precision. */
blr
.balign 16
L(greater_or_equal_pio4):
lis r4,NINEPI_4@h
ori r4,r4,NINEPI_4@l
cmpw r3,r4
bge L(greater_or_equal_9pio4)
/* Calculate quotient of |x|/(PI/4). */
lfd fp2,(L(invpio4)-L(anchor))(r9)
fabs fp1,fp1 /* |x| */
fmul fp2,fp1,fp2 /* |x|/(PI/4) */
fctiduz fp2,fp2
mfvsrd r3,v2 /* n = |x| mod PI/4 */
/* Now use that quotient to find |x| mod (PI/2). */
addi r7,r3,1
rldicr r5,r7,2,60 /* ((n+1) >> 1) << 3 */
addi r6,r9,(L(pio2_table)-L(anchor))
lfdx fp4,r5,r6
fsub fp1,fp1,fp4
.balign 16
L(reduced):
/* Now we are in the range -PI/4 to PI/4. */
/* Work out if we are in a positive or negative primary interval. */
addi r7,r7,2
rldicl r4,r7,62,63 /* ((n+3) >> 2) & 1 */
/* Load a 1.0 or -1.0. */
addi r5,r9,(L(ones)-L(anchor))
sldi r4,r4,3
lfdx fp0,r4,r5
/* Are we in the primary interval of sin or cos? */
andi. r4,r7,0x2
bne L(cos)
/* Chebyshev polynomial of the form:
x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
lfd fp9,(L(S0)-L(anchor))(r9)
lfd fp10,(L(S1)-L(anchor))(r9)
lfd fp11,(L(S2)-L(anchor))(r9)
lfd fp12,(L(S3)-L(anchor))(r9)
lfd fp13,(L(S4)-L(anchor))(r9)
fmul fp2,fp1,fp1 /* x^2 */
fmul fp3,fp2,fp1 /* x^3 */
fmadd fp4,fp2,fp13,fp12 /* S3+x^2*S4 */
fmadd fp4,fp2,fp4,fp11 /* S2+x^2*(S3+x^2*S4) */
fmadd fp4,fp2,fp4,fp10 /* S1+x^2*(S2+x^2*(S3+x^2*S4)) */
fmadd fp4,fp2,fp4,fp9 /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))) */
fmadd fp4,fp3,fp4,fp1 /* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))) */
fmul fp4,fp4,fp0 /* Add in the sign. */
frsp fp1,fp4 /* Round to single precision. */
blr
.balign 16
L(cos):
/* Chebyshev polynomial of the form:
1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
lfd fp9,(L(C0)-L(anchor))(r9)
lfd fp10,(L(C1)-L(anchor))(r9)
lfd fp11,(L(C2)-L(anchor))(r9)
lfd fp12,(L(C3)-L(anchor))(r9)
lfd fp13,(L(C4)-L(anchor))(r9)
fmul fp2,fp1,fp1 /* x^2 */
lfd fp3,(L(DPone)-L(anchor))(r9)
fmadd fp4,fp2,fp13,fp12 /* C3+x^2*C4 */
fmadd fp4,fp2,fp4,fp11 /* C2+x^2*(C3+x^2*C4) */
fmadd fp4,fp2,fp4,fp10 /* C1+x^2*(C2+x^2*(C3+x^2*C4)) */
fmadd fp4,fp2,fp4,fp9 /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))) */
fmadd fp4,fp2,fp4,fp3 /* 1.0 + x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))) */
fmul fp4,fp4,fp0 /* Add in the sign. */
frsp fp1,fp4 /* Round to single precision. */
blr
.balign 16
L(greater_or_equal_9pio4):
lis r4,INFINITY@h
ori r4,r4,INFINITY@l
cmpw r3,r4
bge L(inf_or_nan)
lis r4,TWO_P23@h
ori r4,r4,TWO_P23@l
cmpw r3,r4
bge L(greater_or_equal_2p23)
fabs fp1,fp1 /* |x| */
/* Calculate quotient of |x|/(PI/4). */
lfd fp2,(L(invpio4)-L(anchor))(r9)
lfd fp3,(L(DPone)-L(anchor))(r9)
lfd fp4,(L(DPhalf)-L(anchor))(r9)
fmul fp2,fp1,fp2 /* |x|/(PI/4) */
friz fp2,fp2 /* n = floor(|x|/(PI/4)) */
/* Calculate (n + 1) / 2. */
fadd fp2,fp2,fp3 /* n + 1 */
fmul fp3,fp2,fp4 /* (n + 1) / 2 */
friz fp3,fp3
lfd fp4,(L(pio2hi)-L(anchor))(r9)
lfd fp5,(L(pio2lo)-L(anchor))(r9)
fmul fp6,fp4,fp3
fadd fp6,fp6,fp1
fmadd fp1,fp5,fp3,fp6
fctiduz fp2,fp2
mfvsrd r7,v2 /* n + 1 */
b L(reduced)
.balign 16
L(inf_or_nan):
bne L(skip_errno_setting) /* Is a NAN? */
/* We delayed the creation of the stack frame, as well as the saving of
the link register, because only at this point, we are sure that
doing so is actually needed. */
stfd fp1,-8(r1)
/* Save the link register. */
mflr r0
std r0,16(r1)
cfi_offset(lr, 16)
/* Create the stack frame. */
stdu r1,-FRAMESIZE(r1)
cfi_adjust_cfa_offset(FRAMESIZE)
bl JUMPTARGET(__errno_location)
nop
/* Restore the stack frame. */
addi r1,r1,FRAMESIZE
cfi_adjust_cfa_offset(-FRAMESIZE)
/* Restore the link register. */
ld r0,16(r1)
mtlr r0
lfd fp1,-8(r1)
/* errno = EDOM */
li r4,EDOM
stw r4,0(r3)
L(skip_errno_setting):
fsub fp1,fp1,fp1 /* x - x */
blr
.balign 16
L(greater_or_equal_2p23):
fabs fp1,fp1
srwi r4,r3,FLOAT_EXPONENT_SHIFT
subi r4,r4,FLOAT_EXPONENT_BIAS
/* We reduce the input modulo pi/4, so we need 3 bits of integer
to determine where in 2*pi we are. Index into our array
accordingly. */
addi r4,r4,INTEGER_BITS
/* To avoid an expensive divide, for the range we care about (0 - 127)
we can transform x/28 into:
x/28 = (x * ((0x100000000 / 28) + 1)) >> 32
mulhwu returns the top 32 bits of the 64 bit result, doing the
shift for us in the same instruction. The top 32 bits are undefined,
so we have to mask them. */
lis r6,FX_FRACTION_1_28@h
ori r6,r6,FX_FRACTION_1_28@l
mulhwu r5,r4,r6
clrldi r5,r5,32
/* Get our pointer into the invpio4_table array. */
sldi r4,r5,3
addi r6,r9,(L(invpio4_table)-L(anchor))
add r4,r4,r6
lfd fp2,0(r4)
lfd fp3,8(r4)
lfd fp4,16(r4)
lfd fp5,24(r4)
fmul fp6,fp2,fp1
fmul fp7,fp3,fp1
fmul fp8,fp4,fp1
fmul fp9,fp5,fp1
/* Mask off larger integer bits in highest double word that we don't
care about to avoid losing precision when combining with smaller
values. */
fctiduz fp10,fp6
mfvsrd r7,v10
rldicr r7,r7,0,(63-INTEGER_BITS)
mtvsrd v10,r7
fcfidu fp10,fp10 /* Integer bits. */
fsub fp6,fp6,fp10 /* highest -= integer bits */
/* Work out the integer component, rounded down. Use the top two
limbs for this. */
fadd fp10,fp6,fp7 /* highest + higher */
fctiduz fp10,fp10
mfvsrd r7,v10
andi. r0,r7,1
fcfidu fp10,fp10
/* Subtract integer component from highest limb. */
fsub fp12,fp6,fp10
beq L(even_integer)
/* Our integer component is odd, so we are in the -PI/4 to 0 primary
region. We need to shift our result down by PI/4, and to do this
in the mod (4/PI) space we simply subtract 1. */
lfd fp11,(L(DPone)-L(anchor))(r9)
fsub fp12,fp12,fp11
/* Now add up all the limbs in order. */
fadd fp12,fp12,fp7
fadd fp12,fp12,fp8
fadd fp12,fp12,fp9
/* And finally multiply by pi/4. */
lfd fp13,(L(pio4)-L(anchor))(r9)
fmul fp1,fp12,fp13
addi r7,r7,1
b L(reduced)
L(even_integer):
lfd fp11,(L(DPone)-L(anchor))(r9)
/* Now add up all the limbs in order. */
fadd fp12,fp12,fp7
fadd fp12,r12,fp8
fadd fp12,r12,fp9
/* We need to check if the addition of all the limbs resulted in us
overflowing 1.0. */
fcmpu 0,fp12,fp11
bgt L(greater_than_one)
/* And finally multiply by pi/4. */
lfd fp13,(L(pio4)-L(anchor))(r9)
fmul fp1,fp12,fp13
addi r7,r7,1
b L(reduced)
L(greater_than_one):
/* We did overflow 1.0 when adding up all the limbs. Add 1.0 to our
integer, and subtract 1.0 from our result. Since that makes the
integer component odd, we need to subtract another 1.0 as
explained above. */
addi r7,r7,1
lfd fp11,(L(DPtwo)-L(anchor))(r9)
fsub fp12,fp12,fp11
/* And finally multiply by pi/4. */
lfd fp13,(L(pio4)-L(anchor))(r9)
fmul fp1,fp12,fp13
addi r7,r7,1
b L(reduced)
.balign 16
L(less_2pn5):
lis r4,TWO_PN27@h
ori r4,r4,TWO_PN27@l
cmpw r3,r4
blt L(less_2pn27)
/* A simpler Chebyshev approximation is close enough for this range:
1.0+x^2*(CC0+x^3*CC1). */
lfd fp10,(L(CC0)-L(anchor))(r9)
lfd fp11,(L(CC1)-L(anchor))(r9)
fmul fp2,fp1,fp1 /* x^2 */
fmul fp3,fp2,fp1 /* x^3 */
lfd fp1,(L(DPone)-L(anchor))(r9)
fmadd fp4,fp3,fp11,fp10 /* CC0+x^3*CC1 */
fmadd fp1,fp2,fp4,fp1 /* 1.0+x^2*(CC0+x^3*CC1) */
frsp fp1,fp1 /* Round to single precision. */
blr
.balign 16
L(less_2pn27):
/* Handle some special cases:
cosf(subnormal) raises inexact
cosf(min_normalized) raises inexact
cosf(normalized) raises inexact. */
lfd fp2,(L(DPone)-L(anchor))(r9)
fabs fp1,fp1 /* |x| */
fsub fp1,fp2,fp1 /* 1.0-|x| */
frsp fp1,fp1
blr
END (__cosf)
.section .rodata, "a"
.balign 8
L(anchor):
/* Chebyshev constants for sin, range -PI/4 - PI/4. */
L(S0): .8byte 0xbfc5555555551cd9
L(S1): .8byte 0x3f81111110c2688b
L(S2): .8byte 0xbf2a019f8b4bd1f9
L(S3): .8byte 0x3ec71d7264e6b5b4
L(S4): .8byte 0xbe5a947e1674b58a
/* Chebyshev constants for cos, range 2^-27 - 2^-5. */
L(CC0): .8byte 0xbfdfffffff5cc6fd
L(CC1): .8byte 0x3fa55514b178dac5
/* Chebyshev constants for cos, range -PI/4 - PI/4. */
L(C0): .8byte 0xbfdffffffffe98ae
L(C1): .8byte 0x3fa55555545c50c7
L(C2): .8byte 0xbf56c16b348b6874
L(C3): .8byte 0x3efa00eb9ac43cc0
L(C4): .8byte 0xbe923c97dd8844d7
L(invpio2):
.8byte 0x3fe45f306dc9c883 /* 2/PI */
L(invpio4):
.8byte 0x3ff45f306dc9c883 /* 4/PI */
L(invpio4_table):
.8byte 0x0000000000000000
.8byte 0x3ff45f306c000000
.8byte 0x3e3c9c882a000000
.8byte 0x3c54fe13a8000000
.8byte 0x3aaf47d4d0000000
.8byte 0x38fbb81b6c000000
.8byte 0x3714acc9e0000000
.8byte 0x3560e4107c000000
.8byte 0x33bca2c756000000
.8byte 0x31fbd778ac000000
.8byte 0x300b7246e0000000
.8byte 0x2e5d2126e8000000
.8byte 0x2c97003248000000
.8byte 0x2ad77504e8000000
.8byte 0x290921cfe0000000
.8byte 0x274deb1cb0000000
.8byte 0x25829a73e0000000
.8byte 0x23fd1046be000000
.8byte 0x2224baed10000000
.8byte 0x20709d338e000000
.8byte 0x1e535a2f80000000
.8byte 0x1cef904e64000000
.8byte 0x1b0d639830000000
.8byte 0x1964ce7d24000000
.8byte 0x17b908bf16000000
L(pio4):
.8byte 0x3fe921fb54442d18 /* PI/4 */
/* PI/2 as a sum of two doubles. We only use 32 bits of the upper limb
to avoid losing significant bits when multiplying with up to
(2^22)/(pi/2). */
L(pio2hi):
.8byte 0xbff921fb54400000
L(pio2lo):
.8byte 0xbdd0b4611a626332
L(pio2_table):
.8byte 0
.8byte 0x3ff921fb54442d18 /* 1 * PI/2 */
.8byte 0x400921fb54442d18 /* 2 * PI/2 */
.8byte 0x4012d97c7f3321d2 /* 3 * PI/2 */
.8byte 0x401921fb54442d18 /* 4 * PI/2 */
.8byte 0x401f6a7a2955385e /* 5 * PI/2 */
.8byte 0x4022d97c7f3321d2 /* 6 * PI/2 */
.8byte 0x4025fdbbe9bba775 /* 7 * PI/2 */
.8byte 0x402921fb54442d18 /* 8 * PI/2 */
.8byte 0x402c463abeccb2bb /* 9 * PI/2 */
.8byte 0x402f6a7a2955385e /* 10 * PI/2 */
L(small):
.8byte 0x3cd0000000000000 /* 2^-50 */
L(ones):
.8byte 0x3ff0000000000000 /* +1.0 */
.8byte 0xbff0000000000000 /* -1.0 */
L(DPhalf):
.8byte 0x3fe0000000000000 /* 0.5 */
L(DPone):
.8byte 0x3ff0000000000000 /* 1.0 */
L(DPtwo):
.8byte 0x4000000000000000 /* 2.0 */
libm_alias_float (__cos, cos)

520
sysdeps/powerpc/powerpc64/power8/fpu/s_sinf.S
View File

@ -1,520 +0,0 @@
/* Optimized sinf(). PowerPC64/POWER8 version.
Copyright (C) 2016-2018 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
<http://www.gnu.org/licenses/>. */
#include <sysdep.h>
#define _ERRNO_H 1
#include <bits/errno.h>
#include <libm-alias-float.h>
#define FRAMESIZE (FRAME_MIN_SIZE+16)
#define FLOAT_EXPONENT_SHIFT 23
#define FLOAT_EXPONENT_BIAS 127
#define INTEGER_BITS 3
#define PI_4 0x3f490fdb /* PI/4 */
#define NINEPI_4 0x40e231d6 /* 9 * PI/4 */
#define TWO_PN5 0x3d000000 /* 2^-5 */
#define TWO_PN27 0x32000000 /* 2^-27 */
#define INFINITY 0x7f800000
#define TWO_P23 0x4b000000 /* 2^27 */
#define FX_FRACTION_1_28 0x9249250 /* 0x100000000 / 28 + 1 */
/* Implements the function
float [fp1] sinf (float [fp1] x) */
.machine power8
ENTRY (__sinf, 4)
addis r9,r2,L(anchor)@toc@ha
addi r9,r9,L(anchor)@toc@l
lis r4,PI_4@h
ori r4,r4,PI_4@l
xscvdpspn v0,v1
mfvsrd r8,v0
rldicl r3,r8,32,33 /* Remove sign bit. */
cmpw r3,r4
bge L(greater_or_equal_pio4)
lis r4,TWO_PN5@h
ori r4,r4,TWO_PN5@l
cmpw r3,r4
blt L(less_2pn5)
/* Chebyshev polynomial of the form:
* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
lfd fp9,(L(S0)-L(anchor))(r9)
lfd fp10,(L(S1)-L(anchor))(r9)
lfd fp11,(L(S2)-L(anchor))(r9)
lfd fp12,(L(S3)-L(anchor))(r9)
lfd fp13,(L(S4)-L(anchor))(r9)
fmul fp2,fp1,fp1 /* x^2 */
fmul fp3,fp2,fp1 /* x^3 */
fmadd fp4,fp2,fp13,fp12 /* S3+x^2*S4 */
fmadd fp4,fp2,fp4,fp11 /* S2+x^2*(S3+x^2*S4) */
fmadd fp4,fp2,fp4,fp10 /* S1+x^2*(S2+x^2*(S3+x^2*S4)) */
fmadd fp4,fp2,fp4,fp9 /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))) */
fmadd fp1,fp3,fp4,fp1 /* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))) */
frsp fp1,fp1 /* Round to single precision. */
blr
.balign 16
L(greater_or_equal_pio4):
lis r4,NINEPI_4@h
ori r4,r4,NINEPI_4@l
cmpw r3,r4
bge L(greater_or_equal_9pio4)
/* Calculate quotient of |x|/(PI/4). */
lfd fp2,(L(invpio4)-L(anchor))(r9)
fabs fp1,fp1 /* |x| */
fmul fp2,fp1,fp2 /* |x|/(PI/4) */
fctiduz fp2,fp2
mfvsrd r3,v2 /* n = |x| mod PI/4 */
/* Now use that quotient to find |x| mod (PI/2). */
addi r7,r3,1
rldicr r5,r7,2,60 /* ((n+1) >> 1) << 3 */
addi r6,r9,(L(pio2_table)-L(anchor))
lfdx fp4,r5,r6
fsub fp1,fp1,fp4
.balign 16
L(reduced):
/* Now we are in the range -PI/4 to PI/4. */
/* Work out if we are in a positive or negative primary interval. */
rldicl r4,r7,62,63 /* ((n+1) >> 2) & 1 */
/* We are operating on |x|, so we need to add back the original
sign. */
rldicl r8,r8,33,63 /* (x >> 31) & 1, ie the sign bit. */
xor r4,r4,r8 /* 0 if result should be positive,
1 if negative. */
/* Load a 1.0 or -1.0. */
addi r5,r9,(L(ones)-L(anchor))
sldi r4,r4,3
lfdx fp0,r4,r5
/* Are we in the primary interval of sin or cos? */
andi. r4,r7,0x2
bne L(cos)
/* Chebyshev polynomial of the form:
x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
lfd fp9,(L(S0)-L(anchor))(r9)
lfd fp10,(L(S1)-L(anchor))(r9)
lfd fp11,(L(S2)-L(anchor))(r9)
lfd fp12,(L(S3)-L(anchor))(r9)
lfd fp13,(L(S4)-L(anchor))(r9)
fmul fp2,fp1,fp1 /* x^2 */
fmul fp3,fp2,fp1 /* x^3 */
fmadd fp4,fp2,fp13,fp12 /* S3+x^2*S4 */
fmadd fp4,fp2,fp4,fp11 /* S2+x^2*(S3+x^2*S4) */
fmadd fp4,fp2,fp4,fp10 /* S1+x^2*(S2+x^2*(S3+x^2*S4)) */
fmadd fp4,fp2,fp4,fp9 /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))) */
fmadd fp4,fp3,fp4,fp1 /* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))) */
fmul fp4,fp4,fp0 /* Add in the sign. */
frsp fp1,fp4 /* Round to single precision. */
blr
.balign 16
L(cos):
/* Chebyshev polynomial of the form:
1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
lfd fp9,(L(C0)-L(anchor))(r9)
lfd fp10,(L(C1)-L(anchor))(r9)
lfd fp11,(L(C2)-L(anchor))(r9)
lfd fp12,(L(C3)-L(anchor))(r9)
lfd fp13,(L(C4)-L(anchor))(r9)
fmul fp2,fp1,fp1 /* x^2 */
lfd fp3,(L(DPone)-L(anchor))(r9)
fmadd fp4,fp2,fp13,fp12 /* C3+x^2*C4 */
fmadd fp4,fp2,fp4,fp11 /* C2+x^2*(C3+x^2*C4) */
fmadd fp4,fp2,fp4,fp10 /* C1+x^2*(C2+x^2*(C3+x^2*C4)) */
fmadd fp4,fp2,fp4,fp9 /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))) */
fmadd fp4,fp2,fp4,fp3 /* 1.0 + x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))) */
fmul fp4,fp4,fp0 /* Add in the sign. */
frsp fp1,fp4 /* Round to single precision. */
blr
.balign 16
L(greater_or_equal_9pio4):
lis r4,INFINITY@h
ori r4,r4,INFINITY@l
cmpw r3,r4
bge L(inf_or_nan)
lis r4,TWO_P23@h
ori r4,r4,TWO_P23@l
cmpw r3,r4
bge L(greater_or_equal_2p23)
fabs fp1,fp1 /* |x| */
/* Calculate quotient of |x|/(PI/4). */
lfd fp2,(L(invpio4)-L(anchor))(r9)
lfd fp3,(L(DPone)-L(anchor))(r9)
lfd fp4,(L(DPhalf)-L(anchor))(r9)
fmul fp2,fp1,fp2 /* |x|/(PI/4) */
friz fp2,fp2 /* n = floor(|x|/(PI/4)) */
/* Calculate (n + 1) / 2. */
fadd fp2,fp2,fp3 /* n + 1 */
fmul fp3,fp2,fp4 /* (n + 1) / 2 */
friz fp3,fp3
lfd fp4,(L(pio2hi)-L(anchor))(r9)
lfd fp5,(L(pio2lo)-L(anchor))(r9)
fmul fp6,fp4,fp3
fadd fp6,fp6,fp1
fmadd fp1,fp5,fp3,fp6
fctiduz fp2,fp2
mfvsrd r7,v2 /* n + 1 */
b L(reduced)
.balign 16
L(inf_or_nan):
bne L(skip_errno_setting) /* Is a NAN? */
/* We delayed the creation of the stack frame, as well as the saving of
the link register, because only at this point, we are sure that
doing so is actually needed. */
stfd fp1,-8(r1)
/* Save the link register. */
mflr r0
std r0,16(r1)
cfi_offset(lr, 16)
/* Create the stack frame. */
stdu r1,-FRAMESIZE(r1)
cfi_adjust_cfa_offset(FRAMESIZE)
bl JUMPTARGET(__errno_location)
nop
/* Restore the stack frame. */
addi r1,r1,FRAMESIZE
cfi_adjust_cfa_offset(-FRAMESIZE)
/* Restore the link register. */
ld r0,16(r1)
mtlr r0
lfd fp1,-8(r1)
/* errno = EDOM */
li r4,EDOM
stw r4,0(r3)
L(skip_errno_setting):
fsub fp1,fp1,fp1 /* x - x */
blr
.balign 16
L(greater_or_equal_2p23):
fabs fp1,fp1
srwi r4,r3,FLOAT_EXPONENT_SHIFT
subi r4,r4,FLOAT_EXPONENT_BIAS
/* We reduce the input modulo pi/4, so we need 3 bits of integer
to determine where in 2*pi we are. Index into our array
accordingly. */
addi r4,r4,INTEGER_BITS
/* To avoid an expensive divide, for the range we care about (0 - 127)
we can transform x/28 into:
x/28 = (x * ((0x100000000 / 28) + 1)) >> 32
mulhwu returns the top 32 bits of the 64 bit result, doing the
shift for us in the same instruction. The top 32 bits are undefined,
so we have to mask them. */
lis r6,FX_FRACTION_1_28@h
ori r6,r6,FX_FRACTION_1_28@l
mulhwu r5,r4,r6
clrldi r5,r5,32
/* Get our pointer into the invpio4_table array. */
sldi r4,r5,3
addi r6,r9,(L(invpio4_table)-L(anchor))
add r4,r4,r6
lfd fp2,0(r4)
lfd fp3,8(r4)
lfd fp4,16(r4)
lfd fp5,24(r4)
fmul fp6,fp2,fp1
fmul fp7,fp3,fp1
fmul fp8,fp4,fp1
fmul fp9,fp5,fp1
/* Mask off larger integer bits in highest double word that we don't
care about to avoid losing precision when combining with smaller
values. */
fctiduz fp10,fp6
mfvsrd r7,v10
rldicr r7,r7,0,(63-INTEGER_BITS)
mtvsrd v10,r7
fcfidu fp10,fp10 /* Integer bits. */
fsub fp6,fp6,fp10 /* highest -= integer bits */
/* Work out the integer component, rounded down. Use the top two
limbs for this. */
fadd fp10,fp6,fp7 /* highest + higher */
fctiduz fp10,fp10
mfvsrd r7,v10
andi. r0,r7,1
fcfidu fp10,fp10
/* Subtract integer component from highest limb. */
fsub fp12,fp6,fp10
beq L(even_integer)
/* Our integer component is odd, so we are in the -PI/4 to 0 primary
region. We need to shift our result down by PI/4, and to do this
in the mod (4/PI) space we simply subtract 1. */
lfd fp11,(L(DPone)-L(anchor))(r9)
fsub fp12,fp12,fp11
/* Now add up all the limbs in order. */
fadd fp12,fp12,fp7
fadd fp12,fp12,fp8
fadd fp12,fp12,fp9
/* And finally multiply by pi/4. */
lfd fp13,(L(pio4)-L(anchor))(r9)
fmul fp1,fp12,fp13
addi r7,r7,1
b L(reduced)
L(even_integer):
lfd fp11,(L(DPone)-L(anchor))(r9)
/* Now add up all the limbs in order. */
fadd fp12,fp12,fp7
fadd fp12,r12,fp8
fadd fp12,r12,fp9
/* We need to check if the addition of all the limbs resulted in us
overflowing 1.0. */
fcmpu 0,fp12,fp11
bgt L(greater_than_one)
/* And finally multiply by pi/4. */
lfd fp13,(L(pio4)-L(anchor))(r9)
fmul fp1,fp12,fp13
addi r7,r7,1
b L(reduced)
L(greater_than_one):
/* We did overflow 1.0 when adding up all the limbs. Add 1.0 to our
integer, and subtract 1.0 from our result. Since that makes the
integer component odd, we need to subtract another 1.0 as
explained above. */
addi r7,r7,1
lfd fp11,(L(DPtwo)-L(anchor))(r9)
fsub fp12,fp12,fp11
/* And finally multiply by pi/4. */
lfd fp13,(L(pio4)-L(anchor))(r9)
fmul fp1,fp12,fp13
addi r7,r7,1
b L(reduced)
.balign 16
L(less_2pn5):
lis r4,TWO_PN27@h
ori r4,r4,TWO_PN27@l
cmpw r3,r4
blt L(less_2pn27)
/* A simpler Chebyshev approximation is close enough for this range:
x+x^3*(SS0+x^2*SS1). */
lfd fp10,(L(SS0)-L(anchor))(r9)
lfd fp11,(L(SS1)-L(anchor))(r9)
fmul fp2,fp1,fp1 /* x^2 */
fmul fp3,fp2,fp1 /* x^3 */
fmadd fp4,fp2,fp11,fp10 /* SS0+x^2*SS1 */
fmadd fp1,fp3,fp4,fp1 /* x+x^3*(SS0+x^2*SS1) */
frsp fp1,fp1 /* Round to single precision. */
blr
.balign 16
L(less_2pn27):
cmpwi r3,0
beq L(zero)
/* Handle some special cases:
sinf(subnormal) raises inexact/underflow
sinf(min_normalized) raises inexact/underflow
sinf(normalized) raises inexact. */
lfd fp2,(L(small)-L(anchor))(r9)
fmul fp2,fp1,fp2 /* x * small */
fsub fp1,fp1,fp2 /* x - x * small */
frsp fp1,fp1
blr
.balign 16
L(zero):
blr
END (__sinf)
.section .rodata, "a"
.balign 8
L(anchor):
/* Chebyshev constants for sin, range -PI/4 - PI/4. */
L(S0): .8byte 0xbfc5555555551cd9
L(S1): .8byte 0x3f81111110c2688b
L(S2): .8byte 0xbf2a019f8b4bd1f9
L(S3): .8byte 0x3ec71d7264e6b5b4
L(S4): .8byte 0xbe5a947e1674b58a
/* Chebyshev constants for sin, range 2^-27 - 2^-5. */
L(SS0): .8byte 0xbfc555555543d49d
L(SS1): .8byte 0x3f8110f475cec8c5
/* Chebyshev constants for cos, range -PI/4 - PI/4. */
L(C0): .8byte 0xbfdffffffffe98ae
L(C1): .8byte 0x3fa55555545c50c7
L(C2): .8byte 0xbf56c16b348b6874
L(C3): .8byte 0x3efa00eb9ac43cc0
L(C4): .8byte 0xbe923c97dd8844d7
L(invpio2):
.8byte 0x3fe45f306dc9c883 /* 2/PI */
L(invpio4):
.8byte 0x3ff45f306dc9c883 /* 4/PI */
L(invpio4_table):
.8byte 0x0000000000000000
.8byte 0x3ff45f306c000000
.8byte 0x3e3c9c882a000000
.8byte 0x3c54fe13a8000000
.8byte 0x3aaf47d4d0000000
.8byte 0x38fbb81b6c000000
.8byte 0x3714acc9e0000000
.8byte 0x3560e4107c000000
.8byte 0x33bca2c756000000
.8byte 0x31fbd778ac000000
.8byte 0x300b7246e0000000
.8byte 0x2e5d2126e8000000
.8byte 0x2c97003248000000
.8byte 0x2ad77504e8000000
.8byte 0x290921cfe0000000
.8byte 0x274deb1cb0000000
.8byte 0x25829a73e0000000
.8byte 0x23fd1046be000000
.8byte 0x2224baed10000000
.8byte 0x20709d338e000000
.8byte 0x1e535a2f80000000
.8byte 0x1cef904e64000000
.8byte 0x1b0d639830000000
.8byte 0x1964ce7d24000000
.8byte 0x17b908bf16000000
L(pio4):
.8byte 0x3fe921fb54442d18 /* PI/4 */
/* PI/2 as a sum of two doubles. We only use 32 bits of the upper limb
to avoid losing significant bits when multiplying with up to
(2^22)/(pi/2). */
L(pio2hi):
.8byte 0xbff921fb54400000
L(pio2lo):
.8byte 0xbdd0b4611a626332
L(pio2_table):
.8byte 0
.8byte 0x3ff921fb54442d18 /* 1 * PI/2 */
.8byte 0x400921fb54442d18 /* 2 * PI/2 */
.8byte 0x4012d97c7f3321d2 /* 3 * PI/2 */
.8byte 0x401921fb54442d18 /* 4 * PI/2 */
.8byte 0x401f6a7a2955385e /* 5 * PI/2 */
.8byte 0x4022d97c7f3321d2 /* 6 * PI/2 */
.8byte 0x4025fdbbe9bba775 /* 7 * PI/2 */
.8byte 0x402921fb54442d18 /* 8 * PI/2 */
.8byte 0x402c463abeccb2bb /* 9 * PI/2 */
.8byte 0x402f6a7a2955385e /* 10 * PI/2 */
L(small):
.8byte 0x3cd0000000000000 /* 2^-50 */
L(ones):
.8byte 0x3ff0000000000000 /* +1.0 */
.8byte 0xbff0000000000000 /* -1.0 */
L(DPhalf):
.8byte 0x3fe0000000000000 /* 0.5 */
L(DPone):
.8byte 0x3ff0000000000000 /* 1.0 */
L(DPtwo):
.8byte 0x4000000000000000 /* 2.0 */
libm_alias_float (__sin, sin)