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c70e4e9c9e
Since the x86-64 assembly version of sincosf is higly optimized with
vector instructions, there isn't much room for improvement. However
s_sincosf.c written in C with vector math and intrinsics can be
optimized by GCC with FMA.
On Skylake, bench-sincosf reports performance improvement:
Assembly FMA improvement
max 104.042 101.008 3%
min 9.426 8.586 10%
mean 20.6209 18.2238 13%
* sysdeps/x86_64/fpu/multiarch/Makefile (libm-sysdep_routines):
Add s_sincosf-sse2 and s_sincosf-fma.
(CFLAGS-s_sincosf-fma.c): New.
* sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: New file.
* sysdeps/x86_64/fpu/multiarch/s_sincosf-sse2.S: Likewise.
* sysdeps/x86_64/fpu/multiarch/s_sincosf.c: Likewise.
* sysdeps/x86_64/fpu/s_sincosf.S: Don't add alias if
__sincosf is defined.
567 lines
17 KiB
ArmAsm
567 lines
17 KiB
ArmAsm
/* Optimized sincosf function.
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Copyright (C) 2012-2018 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <sysdep.h>
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#include <errno.h>
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#include <libm-alias-float.h>
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/* Short algorithm description:
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*
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* 1) if |x|==0: sin(x)=x,
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* cos(x)=1.
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* 2) if |x|<2^-27: sin(x)=x-x*DP_SMALL, raising underflow only when needed,
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* cos(x)=1-|x|.
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* 3) if |x|<2^-5 : sin(x)=x+x*x^2*DP_SIN2_0+x^5*DP_SIN2_1,
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* cos(x)=1+1*x^2*DP_COS2_0+x^5*DP_COS2_1
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* 4) if |x|< Pi/4: sin(x)=x+x*x^2*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))),
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* cos(x)=1+1*x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).
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* 5) if |x| < 9*Pi/4:
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* 5.1) Range reduction:
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* k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+1, t=|x|-j*Pi/4.
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* 5.2) Reconstruction:
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* sign_sin = sign(x) * (-1.0)^(( n >>2)&1)
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* sign_cos = (-1.0)^(((n+2)>>2)&1)
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* poly_sin = ((((S4*t^2 + S3)*t^2 + S2)*t^2 + S1)*t^2 + S0)*t^2*t+t
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* poly_cos = ((((C4*t^2 + C3)*t^2 + C2)*t^2 + C1)*t^2 + C0)*t^2*s+s
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* if(n&2 != 0) {
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* using cos(t) and sin(t) polynomials for |t|<Pi/4, results are
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* cos(x) = poly_sin * sign_cos
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* sin(x) = poly_cos * sign_sin
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* } else {
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* sin(x) = poly_sin * sign_sin
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* cos(x) = poly_cos * sign_cos
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* }
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* 6) if |x| < 2^23, large args:
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* 6.1) Range reduction:
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* k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4
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* 6.2) Reconstruction same as (5.2).
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* 7) if |x| >= 2^23, very large args:
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* 7.1) Range reduction:
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* k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4.
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* 7.2) Reconstruction same as (5.2).
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* 8) if x is Inf, return x-x, and set errno=EDOM.
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* 9) if x is NaN, return x-x.
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*
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* Special cases:
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* sin/cos(+-0) = +-0/1 not raising inexact/underflow,
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* sin/cos(subnormal) raises inexact/underflow,
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* sin/cos(min_normalized) raises inexact/underflow,
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* sin/cos(normalized) raises inexact,
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* sin/cos(Inf) = NaN, raises invalid, sets errno to EDOM,
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* sin/cos(NaN) = NaN.
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*/
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# define ARG_SIN_PTR %rdi
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# define ARG_COS_PTR %rsi
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.text
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ENTRY(__sincosf)
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/* Input: %xmm0 contains single precision argument x */
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/* %rdi points to sin result */
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/* %rsi points to cos result */
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movd %xmm0, %eax /* Bits of x */
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movaps %xmm0, %xmm7 /* Copy of x */
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cvtss2sd %xmm0, %xmm0 /* DP x */
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movss L(SP_ABS_MASK)(%rip), %xmm3
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movl %eax, %r8d /* Copy of x bits */
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andl $0x7fffffff, %eax /* |x| */
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cmpl $0x3f490fdb, %eax /* |x|<Pi/4 ? */
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jb L(arg_less_pio4)
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/* Here if |x|>=Pi/4 */
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andps %xmm7, %xmm3 /* SP |x| */
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andpd L(DP_ABS_MASK)(%rip),%xmm0 /* DP |x| */
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movss L(SP_INVPIO4)(%rip), %xmm2 /* SP 1/(Pi/4) */
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cmpl $0x40e231d6, %eax /* |x|<9*Pi/4 ? */
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jae L(large_args)
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/* Here if Pi/4<=|x|<9*Pi/4 */
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mulss %xmm3, %xmm2 /* SP |x|/(Pi/4) */
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movl %r8d, %ecx /* Load x */
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cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */
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lea L(PIO4J)(%rip), %r9
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shrl $29, %ecx /* (sign of x) << 2 */
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addl $1, %eax /* k+1 */
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movl $0x0e, %edx
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andl %eax, %edx /* j = (k+1)&0x0e */
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subsd (%r9,%rdx,8), %xmm0 /* t = |x| - j * Pi/4 */
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L(reconstruction):
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/* Input: %eax=n, %xmm0=t, %ecx=sign(x) */
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movaps %xmm0, %xmm4 /* t */
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movhpd L(DP_ONES)(%rip), %xmm4 /* 1|t */
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mulsd %xmm0, %xmm0 /* y=t^2 */
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movl $2, %edx
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unpcklpd %xmm0, %xmm0 /* y|y */
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addl %eax, %edx /* k+2 */
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movaps %xmm0, %xmm1 /* y|y */
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mulpd %xmm0, %xmm0 /* z=t^4|z=t^4 */
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movaps L(DP_SC4)(%rip), %xmm2 /* S4 */
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mulpd %xmm0, %xmm2 /* z*S4 */
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movaps L(DP_SC3)(%rip), %xmm3 /* S3 */
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mulpd %xmm0, %xmm3 /* z*S3 */
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xorl %eax, %ecx /* (sign_x ^ (k>>2))<<2 */
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addpd L(DP_SC2)(%rip), %xmm2 /* S2+z*S4 */
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mulpd %xmm0, %xmm2 /* z*(S2+z*S4) */
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shrl $2, %edx /* (k+2)>>2 */
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addpd L(DP_SC1)(%rip), %xmm3 /* S1+z*S3 */
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mulpd %xmm0, %xmm3 /* z*(S1+z*S3) */
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shrl $2, %ecx /* sign_x ^ k>>2 */
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addpd L(DP_SC0)(%rip), %xmm2 /* S0+z*(S2+z*S4) */
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andl $1, %edx /* sign_cos = ((k+2)>>2)&1 */
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mulpd %xmm1, %xmm2 /* y*(S0+z*(S2+z*S4)) */
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andl $1, %ecx /* sign_sin = sign_x ^ ((k>>2)&1) */
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addpd %xmm2, %xmm3 /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */
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lea L(DP_ONES)(%rip), %r9
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mulpd %xmm4, %xmm3 /*t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
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testl $2, %eax /* n&2 != 0 ? */
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addpd %xmm4, %xmm3 /*t+t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
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jnz L(sin_result_sin_poly)
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/*L(sin_result_cos_poly):*/
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/*
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* Here if
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* cos(x) = poly_sin * sign_cos
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* sin(x) = poly_cos * sign_sin
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*/
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movsd (%r9,%rcx,8), %xmm4 /* 0|sign_sin */
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movhpd (%r9,%rdx,8), %xmm4 /* sign_cos|sign_sin */
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mulpd %xmm4, %xmm3 /* result_cos|result_sin */
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cvtpd2ps %xmm3, %xmm0 /* SP results */
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movss %xmm0, (ARG_SIN_PTR) /* store sin(x) from xmm0[0] */
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shufps $1, %xmm0, %xmm0 /* move cos(x) to xmm0[0] */
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movss %xmm0, (ARG_COS_PTR) /* store cos(x) */
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ret
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.p2align 4
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L(sin_result_sin_poly):
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/*
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* Here if
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* sin(x) = poly_sin * sign_sin
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* cos(x) = poly_cos * sign_cos
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*/
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movsd (%r9,%rdx,8), %xmm4 /* 0|sign_cos */
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movhpd (%r9,%rcx,8), %xmm4 /* sign_sin|sign_cos */
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mulpd %xmm4, %xmm3 /* result_sin|result_cos */
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cvtpd2ps %xmm3, %xmm0 /* SP results */
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movss %xmm0, (ARG_COS_PTR) /* store cos(x) from xmm0[0] */
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shufps $1, %xmm0, %xmm0 /* move sin(x) to xmm0[0] */
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movss %xmm0, (ARG_SIN_PTR) /* store sin(x) */
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ret
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.p2align 4
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L(large_args):
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/* Here if |x|>=9*Pi/4 */
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cmpl $0x7f800000, %eax /* x is Inf or NaN ? */
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jae L(arg_inf_or_nan)
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/* Here if finite |x|>=9*Pi/4 */
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cmpl $0x4b000000, %eax /* |x|<2^23 ? */
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jae L(very_large_args)
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/* Here if 9*Pi/4<=|x|<2^23 */
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movsd L(DP_INVPIO4)(%rip), %xmm1 /* 1/(Pi/4) */
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mulsd %xmm0, %xmm1 /* |x|/(Pi/4) */
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cvttsd2si %xmm1, %eax /* k=trunc(|x|/(Pi/4)) */
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addl $1, %eax /* k+1 */
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movl %eax, %edx
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andl $0xfffffffe, %edx /* j=(k+1)&0xfffffffe */
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cvtsi2sdl %edx, %xmm4 /* DP j */
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movl %r8d, %ecx /* Load x */
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movsd L(DP_PIO4HI)(%rip), %xmm2 /* -PIO4HI = high part of -Pi/4 */
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shrl $29, %ecx /* (sign of x) << 2 */
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mulsd %xmm4, %xmm2 /* -j*PIO4HI */
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movsd L(DP_PIO4LO)(%rip), %xmm3 /* -PIO4LO = low part of -Pi/4 */
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addsd %xmm2, %xmm0 /* |x| - j*PIO4HI */
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mulsd %xmm3, %xmm4 /* j*PIO4LO */
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addsd %xmm4, %xmm0 /* t = |x| - j*PIO4HI - j*PIO4LO */
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jmp L(reconstruction)
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.p2align 4
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L(very_large_args):
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/* Here if finite |x|>=2^23 */
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/* bitpos = (ix>>23) - BIAS_32 + 59; */
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shrl $23, %eax /* eb = biased exponent of x */
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subl $68, %eax /* bitpos=eb-0x7f+59, where 0x7f */
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/*is exponent bias */
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movl $28, %ecx /* %cl=28 */
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movl %eax, %edx /* bitpos copy */
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/* j = bitpos/28; */
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div %cl /* j in register %al=%ax/%cl */
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movapd %xmm0, %xmm3 /* |x| */
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andl $0xff, %eax /* clear unneeded remainder from %ah*/
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imull $28, %eax, %ecx /* j*28 */
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lea L(_FPI)(%rip), %r9
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movsd L(DP_HI_MASK)(%rip), %xmm4 /* DP_HI_MASK */
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movapd %xmm0, %xmm5 /* |x| */
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mulsd -16(%r9,%rax,8), %xmm3 /* tmp3 = FPI[j-2]*|x| */
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movapd %xmm0, %xmm1 /* |x| */
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mulsd -8(%r9,%rax,8), %xmm5 /* tmp2 = FPI[j-1]*|x| */
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mulsd (%r9,%rax,8), %xmm0 /* tmp0 = FPI[j]*|x| */
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addl $19, %ecx /* j*28+19 */
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mulsd 8(%r9,%rax,8), %xmm1 /* tmp1 = FPI[j+1]*|x| */
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cmpl %ecx, %edx /* bitpos>=j*28+19 ? */
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jl L(very_large_skip1)
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/* Here if bitpos>=j*28+19 */
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andpd %xmm3, %xmm4 /* HI(tmp3) */
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subsd %xmm4, %xmm3 /* tmp3 = tmp3 - HI(tmp3) */
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L(very_large_skip1):
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movsd L(DP_2POW52)(%rip), %xmm6
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movapd %xmm5, %xmm2 /* tmp2 copy */
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addsd %xmm3, %xmm5 /* tmp5 = tmp3 + tmp2 */
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movl $1, %edx
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addsd %xmm5, %xmm6 /* tmp6 = tmp5 + 2^52 */
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movsd 8+L(DP_2POW52)(%rip), %xmm4
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movd %xmm6, %eax /* k = I64_LO(tmp6); */
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addsd %xmm6, %xmm4 /* tmp4 = tmp6 - 2^52 */
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movl %r8d, %ecx /* Load x */
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comisd %xmm5, %xmm4 /* tmp4 > tmp5 ? */
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jbe L(very_large_skip2)
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/* Here if tmp4 > tmp5 */
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subl $1, %eax /* k-- */
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addsd 8+L(DP_ONES)(%rip), %xmm4 /* tmp4 -= 1.0 */
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L(very_large_skip2):
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andl %eax, %edx /* k&1 */
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lea L(DP_ZERONE)(%rip), %r9
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subsd %xmm4, %xmm3 /* tmp3 -= tmp4 */
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addsd (%r9,%rdx,8), %xmm3 /* t = DP_ZERONE[k&1] + tmp3 */
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addsd %xmm2, %xmm3 /* t += tmp2 */
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shrl $29, %ecx /* (sign of x) << 2 */
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addsd %xmm3, %xmm0 /* t += tmp0 */
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addl $1, %eax /* n=k+1 */
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addsd %xmm1, %xmm0 /* t += tmp1 */
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mulsd L(DP_PIO4)(%rip), %xmm0 /* t *= PI04 */
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jmp L(reconstruction) /* end of very_large_args peth */
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.p2align 4
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L(arg_less_pio4):
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/* Here if |x|<Pi/4 */
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cmpl $0x3d000000, %eax /* |x|<2^-5 ? */
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jl L(arg_less_2pn5)
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/* Here if 2^-5<=|x|<Pi/4 */
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movaps %xmm0, %xmm3 /* DP x */
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movhpd L(DP_ONES)(%rip), %xmm3 /* DP 1|x */
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mulsd %xmm0, %xmm0 /* DP y=x^2 */
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unpcklpd %xmm0, %xmm0 /* DP y|y */
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movaps %xmm0, %xmm1 /* y|y */
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mulpd %xmm0, %xmm0 /* z=x^4|z=x^4 */
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movapd L(DP_SC4)(%rip), %xmm4 /* S4 */
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mulpd %xmm0, %xmm4 /* z*S4 */
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movapd L(DP_SC3)(%rip), %xmm5 /* S3 */
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mulpd %xmm0, %xmm5 /* z*S3 */
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addpd L(DP_SC2)(%rip), %xmm4 /* S2+z*S4 */
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mulpd %xmm0, %xmm4 /* z*(S2+z*S4) */
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addpd L(DP_SC1)(%rip), %xmm5 /* S1+z*S3 */
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mulpd %xmm0, %xmm5 /* z*(S1+z*S3) */
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addpd L(DP_SC0)(%rip), %xmm4 /* S0+z*(S2+z*S4) */
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mulpd %xmm1, %xmm4 /* y*(S0+z*(S2+z*S4)) */
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mulpd %xmm3, %xmm5 /* x*z*(S1+z*S3) */
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mulpd %xmm3, %xmm4 /* x*y*(S0+z*(S2+z*S4)) */
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addpd %xmm5, %xmm4 /*x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
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addpd %xmm4, %xmm3 /*x+x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
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cvtpd2ps %xmm3, %xmm0 /* SP results */
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movss %xmm0, (ARG_SIN_PTR) /* store sin(x) from xmm0[0] */
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shufps $1, %xmm0, %xmm0 /* move cos(x) to xmm0[0] */
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movss %xmm0, (ARG_COS_PTR) /* store cos(x) */
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ret
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.p2align 4
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L(arg_less_2pn5):
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/* Here if |x|<2^-5 */
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cmpl $0x32000000, %eax /* |x|<2^-27 ? */
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jl L(arg_less_2pn27)
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/* Here if 2^-27<=|x|<2^-5 */
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movaps %xmm0, %xmm1 /* DP x */
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movhpd L(DP_ONES)(%rip), %xmm1 /* DP 1|x */
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mulsd %xmm0, %xmm0 /* DP x^2 */
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unpcklpd %xmm0, %xmm0 /* DP x^2|x^2 */
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movaps L(DP_SINCOS2_1)(%rip), %xmm3 /* DP DP_SIN2_1 */
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mulpd %xmm0, %xmm3 /* DP x^2*DP_SIN2_1 */
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addpd L(DP_SINCOS2_0)(%rip), %xmm3 /* DP DP_SIN2_0+x^2*DP_SIN2_1 */
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mulpd %xmm0, %xmm3 /* DP x^2*DP_SIN2_0+x^4*DP_SIN2_1 */
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mulpd %xmm1, %xmm3 /* DP x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
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addpd %xmm1, %xmm3 /* DP x+x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
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cvtpd2ps %xmm3, %xmm0 /* SP results */
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movss %xmm0, (ARG_SIN_PTR) /* store sin(x) from xmm0[0] */
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shufps $1, %xmm0, %xmm0 /* move cos(x) to xmm0[0] */
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movss %xmm0, (ARG_COS_PTR) /* store cos(x) */
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ret
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.p2align 4
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L(arg_less_2pn27):
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cmpl $0, %eax /* x=0 ? */
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je L(arg_zero) /* in case x=0 return sin(+-0)==+-0 */
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/* Here if |x|<2^-27 */
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/*
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* Special cases here:
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* sin(subnormal) raises inexact/underflow
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* sin(min_normalized) raises inexact/underflow
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* sin(normalized) raises inexact
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* cos(here)=1-|x| (raising inexact)
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*/
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movaps %xmm0, %xmm3 /* DP x */
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mulsd L(DP_SMALL)(%rip), %xmm0/* DP x*DP_SMALL */
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subsd %xmm0, %xmm3 /* DP sin result is x-x*DP_SMALL */
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andps L(SP_ABS_MASK)(%rip), %xmm7/* SP |x| */
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cvtsd2ss %xmm3, %xmm0 /* sin(x) */
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movss L(SP_ONE)(%rip), %xmm1 /* SP 1.0 */
|
|
movss %xmm0, (ARG_SIN_PTR) /* sin(x) store */
|
|
subss %xmm7, %xmm1 /* cos(x) */
|
|
movss %xmm1, (ARG_COS_PTR) /* cos(x) store */
|
|
ret
|
|
|
|
.p2align 4
|
|
L(arg_zero):
|
|
movss L(SP_ONE)(%rip), %xmm0 /* 1.0 */
|
|
movss %xmm7, (ARG_SIN_PTR) /* sin(+-0)==x */
|
|
movss %xmm0, (ARG_COS_PTR) /* cos(+-0)==1 */
|
|
ret
|
|
|
|
.p2align 4
|
|
L(arg_inf_or_nan):
|
|
/* Here if |x| is Inf or NAN */
|
|
jne L(skip_errno_setting) /* in case of x is NaN */
|
|
|
|
/* Align stack to 16 bytes. */
|
|
subq $8, %rsp
|
|
cfi_adjust_cfa_offset (8)
|
|
/* Here if x is Inf. Set errno to EDOM. */
|
|
call JUMPTARGET(__errno_location)
|
|
addq $8, %rsp
|
|
cfi_adjust_cfa_offset (-8)
|
|
|
|
movl $EDOM, (%rax)
|
|
|
|
.p2align 4
|
|
L(skip_errno_setting):
|
|
/* Here if |x| is Inf or NAN. Continued. */
|
|
subss %xmm7, %xmm7 /* x-x, result is NaN */
|
|
movss %xmm7, (ARG_SIN_PTR)
|
|
movss %xmm7, (ARG_COS_PTR)
|
|
ret
|
|
END(__sincosf)
|
|
|
|
.section .rodata, "a"
|
|
.p2align 3
|
|
L(PIO4J): /* Table of j*Pi/4, for j=0,1,..,10 */
|
|
.long 0x00000000,0x00000000
|
|
.long 0x54442d18,0x3fe921fb
|
|
.long 0x54442d18,0x3ff921fb
|
|
.long 0x7f3321d2,0x4002d97c
|
|
.long 0x54442d18,0x400921fb
|
|
.long 0x2955385e,0x400f6a7a
|
|
.long 0x7f3321d2,0x4012d97c
|
|
.long 0xe9bba775,0x4015fdbb
|
|
.long 0x54442d18,0x401921fb
|
|
.long 0xbeccb2bb,0x401c463a
|
|
.long 0x2955385e,0x401f6a7a
|
|
.type L(PIO4J), @object
|
|
ASM_SIZE_DIRECTIVE(L(PIO4J))
|
|
|
|
.p2align 3
|
|
L(_FPI): /* 4/Pi broken into sum of positive DP values */
|
|
.long 0x00000000,0x00000000
|
|
.long 0x6c000000,0x3ff45f30
|
|
.long 0x2a000000,0x3e3c9c88
|
|
.long 0xa8000000,0x3c54fe13
|
|
.long 0xd0000000,0x3aaf47d4
|
|
.long 0x6c000000,0x38fbb81b
|
|
.long 0xe0000000,0x3714acc9
|
|
.long 0x7c000000,0x3560e410
|
|
.long 0x56000000,0x33bca2c7
|
|
.long 0xac000000,0x31fbd778
|
|
.long 0xe0000000,0x300b7246
|
|
.long 0xe8000000,0x2e5d2126
|
|
.long 0x48000000,0x2c970032
|
|
.long 0xe8000000,0x2ad77504
|
|
.long 0xe0000000,0x290921cf
|
|
.long 0xb0000000,0x274deb1c
|
|
.long 0xe0000000,0x25829a73
|
|
.long 0xbe000000,0x23fd1046
|
|
.long 0x10000000,0x2224baed
|
|
.long 0x8e000000,0x20709d33
|
|
.long 0x80000000,0x1e535a2f
|
|
.long 0x64000000,0x1cef904e
|
|
.long 0x30000000,0x1b0d6398
|
|
.long 0x24000000,0x1964ce7d
|
|
.long 0x16000000,0x17b908bf
|
|
.type L(_FPI), @object
|
|
ASM_SIZE_DIRECTIVE(L(_FPI))
|
|
|
|
/* Coefficients of polynomials for */
|
|
/* sin(x)~=x+x*x^2*(DP_SIN2_0+x^2*DP_SIN2_1) in low DP part, */
|
|
/* cos(x)~=1+1*x^2*(DP_COS2_0+x^2*DP_COS2_1) in high DP part, */
|
|
/* for |x|<2^-5. */
|
|
.p2align 4
|
|
L(DP_SINCOS2_0):
|
|
.long 0x5543d49d,0xbfc55555
|
|
.long 0xff5cc6fd,0xbfdfffff
|
|
.type L(DP_SINCOS2_0), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_0))
|
|
|
|
.p2align 4
|
|
L(DP_SINCOS2_1):
|
|
.long 0x75cec8c5,0x3f8110f4
|
|
.long 0xb178dac5,0x3fa55514
|
|
.type L(DP_SINCOS2_1), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_1))
|
|
|
|
|
|
.p2align 3
|
|
L(DP_ZERONE):
|
|
.long 0x00000000,0x00000000 /* 0.0 */
|
|
.long 0x00000000,0xbff00000 /* 1.0 */
|
|
.type L(DP_ZERONE), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_ZERONE))
|
|
|
|
.p2align 3
|
|
L(DP_ONES):
|
|
.long 0x00000000,0x3ff00000 /* +1.0 */
|
|
.long 0x00000000,0xbff00000 /* -1.0 */
|
|
.type L(DP_ONES), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_ONES))
|
|
|
|
/* Coefficients of polynomials for */
|
|
/* sin(t)~=t+t*t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4)))) in low DP part, */
|
|
/* cos(t)~=1+1*t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4)))) in high DP part, */
|
|
/* for |t|<Pi/4. */
|
|
.p2align 4
|
|
L(DP_SC4):
|
|
.long 0x1674b58a,0xbe5a947e
|
|
.long 0xdd8844d7,0xbe923c97
|
|
.type L(DP_SC4), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_SC4))
|
|
|
|
.p2align 4
|
|
L(DP_SC3):
|
|
.long 0x64e6b5b4,0x3ec71d72
|
|
.long 0x9ac43cc0,0x3efa00eb
|
|
.type L(DP_SC3), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_SC3))
|
|
|
|
.p2align 4
|
|
L(DP_SC2):
|
|
.long 0x8b4bd1f9,0xbf2a019f
|
|
.long 0x348b6874,0xbf56c16b
|
|
.type L(DP_SC2), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_SC2))
|
|
|
|
.p2align 4
|
|
L(DP_SC1):
|
|
.long 0x10c2688b,0x3f811111
|
|
.long 0x545c50c7,0x3fa55555
|
|
.type L(DP_SC1), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_SC1))
|
|
|
|
.p2align 4
|
|
L(DP_SC0):
|
|
.long 0x55551cd9,0xbfc55555
|
|
.long 0xfffe98ae,0xbfdfffff
|
|
.type L(DP_SC0), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_SC0))
|
|
|
|
.p2align 3
|
|
L(DP_SMALL):
|
|
.long 0x00000000,0x3cd00000 /* 2^(-50) */
|
|
.type L(DP_SMALL), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_SMALL))
|
|
|
|
.p2align 3
|
|
L(DP_PIO4):
|
|
.long 0x54442d18,0x3fe921fb /* Pi/4 */
|
|
.type L(DP_PIO4), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_PIO4))
|
|
|
|
.p2align 3
|
|
L(DP_2POW52):
|
|
.long 0x00000000,0x43300000 /* +2^52 */
|
|
.long 0x00000000,0xc3300000 /* -2^52 */
|
|
.type L(DP_2POW52), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_2POW52))
|
|
|
|
.p2align 3
|
|
L(DP_INVPIO4):
|
|
.long 0x6dc9c883,0x3ff45f30 /* 4/Pi */
|
|
.type L(DP_INVPIO4), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_INVPIO4))
|
|
|
|
.p2align 3
|
|
L(DP_PIO4HI):
|
|
.long 0x54000000,0xbfe921fb /* High part of Pi/4 */
|
|
.type L(DP_PIO4HI), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_PIO4HI))
|
|
|
|
.p2align 3
|
|
L(DP_PIO4LO):
|
|
.long 0x11A62633,0xbe010b46 /* Low part of Pi/4 */
|
|
.type L(DP_PIO4LO), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_PIO4LO))
|
|
|
|
.p2align 2
|
|
L(SP_INVPIO4):
|
|
.long 0x3fa2f983 /* 4/Pi */
|
|
.type L(SP_INVPIO4), @object
|
|
ASM_SIZE_DIRECTIVE(L(SP_INVPIO4))
|
|
|
|
.p2align 4
|
|
L(DP_ABS_MASK): /* Mask for getting DP absolute value */
|
|
.long 0xffffffff,0x7fffffff
|
|
.long 0xffffffff,0x7fffffff
|
|
.type L(DP_ABS_MASK), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_ABS_MASK))
|
|
|
|
.p2align 3
|
|
L(DP_HI_MASK): /* Mask for getting high 21 bits of DP value */
|
|
.long 0x00000000,0xffffffff
|
|
.type L(DP_HI_MASK), @object
|
|
ASM_SIZE_DIRECTIVE(L(DP_HI_MASK))
|
|
|
|
.p2align 4
|
|
L(SP_ABS_MASK): /* Mask for getting SP absolute value */
|
|
.long 0x7fffffff,0x7fffffff
|
|
.long 0x7fffffff,0x7fffffff
|
|
.type L(SP_ABS_MASK), @object
|
|
ASM_SIZE_DIRECTIVE(L(SP_ABS_MASK))
|
|
|
|
.p2align 2
|
|
L(SP_ONE):
|
|
.long 0x3f800000 /* 1.0 */
|
|
.type L(SP_ONE), @object
|
|
ASM_SIZE_DIRECTIVE(L(SP_ONE))
|
|
|
|
#ifndef __sincosf
|
|
libm_alias_float (__sincos, sincos)
|
|
#endif
|