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