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.file "acos.s"
// Copyright (c) 2000, Intel Corporation // All rights reserved. // // Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, // and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. // // WARRANTY DISCLAIMER // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // // Intel Corporation is the author of this code, and requests that all // problem reports or change requests be submitted to it directly at // http://developer.intel.com/opensource.
// History //============================================================== // 2/02/00 Initial version // 8/17/00 New and much faster algorithm. // 8/30/00 Avoided bank conflicts on loads, shortened |x|=1 and x=0 paths, // fixed mfb split issue stalls.
// Description //========================================= // The acos function computes the principle value of the arc sine of x. // A doman error occurs for arguments not in the range [-1,+1].
// The acos function returns the arc cosine in the range [0, +pi] radians. // acos(1) returns +0, acos(-1) returns pi, acos(0) returns pi/2. // acos(x) returns a Nan and raises the invalid exception for |x| >1
// The acos function is just like asin except that pi/2 is added at the end.
// // Assembly macros //=========================================
// predicate registers //acos_pred_LEsqrt2by2 = p7 //acos_pred_GTsqrt2by2 = p8
// integer registers ASIN_Addr1 = r33 ASIN_Addr2 = r34 ASIN_FFFE = r35
GR_SAVE_B0 = r36 GR_SAVE_PFS = r37 GR_SAVE_GP = r38
GR_Parameter_X = r39 GR_Parameter_Y = r40 GR_Parameter_RESULT = r41 GR_Parameter_Tag = r42
// floating point registers acos_coeff_P1 = f32 acos_coeff_P2 = f33 acos_coeff_P3 = f34 acos_coeff_P4 = f35
acos_coeff_P5 = f36 acos_coeff_P6 = f37 acos_coeff_P7 = f38 acos_coeff_P8 = f39 acos_coeff_P9 = f40
acos_coeff_P10 = f41 acos_coeff_P11 = f42 acos_coeff_P12 = f43 acos_coeff_P13 = f44 acos_coeff_P14 = f45
acos_coeff_P15 = f46 acos_coeff_P16 = f47 acos_coeff_P17 = f48 acos_coeff_P18 = f49 acos_coeff_P19 = f50
acos_coeff_P20 = f51 acos_coeff_P21 = f52 acos_const_sqrt2by2 = f53 acos_const_piby2 = f54 acos_abs_x = f55
acos_tx = f56 acos_tx2 = f57 acos_tx3 = f58 acos_tx4 = f59 acos_tx8 = f60
acos_tx11 = f61 acos_1poly_p8 = f62 acos_1poly_p19 = f63 acos_1poly_p4 = f64 acos_1poly_p15 = f65
acos_1poly_p6 = f66 acos_1poly_p17 = f67 acos_1poly_p0 = f68 acos_1poly_p11 = f69 acos_1poly_p2 = f70
acos_1poly_p13 = f71 acos_series_tx = f72 acos_t = f73 acos_t2 = f74 acos_t3 = f75
acos_t4 = f76 acos_t8 = f77 acos_t11 = f78 acos_poly_p8 = f79 acos_poly_p19 = f80
acos_poly_p4 = f81 acos_poly_p15 = f82 acos_poly_p6 = f83 acos_poly_p17 = f84 acos_poly_p0 = f85
acos_poly_p11 = f86 acos_poly_p2 = f87 acos_poly_p13 = f88 acos_series_t = f89 acos_1by2 = f90
acos_3by2 = f91 acos_5by2 = f92 acos_11by4 = f93 acos_35by8 = f94 acos_63by8 = f95
acos_231by16 = f96 acos_y0 = f97 acos_H0 = f98 acos_S0 = f99 acos_d = f100
acos_l1 = f101 acos_d2 = f102 acos_T0 = f103 acos_d1 = f104 acos_e0 = f105
acos_l2 = f106 acos_d3 = f107 acos_T3 = f108 acos_S1 = f109 acos_e1 = f110
acos_z = f111 answer2 = f112 acos_sgn_x = f113 acos_429by16 = f114 acos_18by4 = f115
acos_3by4 = f116 acos_l3 = f117 acos_T6 = f118 acos_const_add = f119
// Data tables //==============================================================
.data
.align 16
acos_coeff_1_table: data8 0xE4E7E0A423A21249 , 0x00003FF8 //P7 data8 0xC2F7EE0200FCE2A5 , 0x0000C003 //P18 data8 0xB745D7F6C65C20E0 , 0x00003FF9 //P5 data8 0xF75E381A323D4D94 , 0x0000C002 //P16 data8 0x8959C2629C1024C0 , 0x0000C002 //P20 data8 0xAFF68E7D241292C5 , 0x00003FF8 //P9 data8 0xB6DB6DB7260AC30D , 0x00003FFA //P3 data8 0xD0417CE2B41CB7BF , 0x0000C000 //P14 data8 0x81D570FEA724E3E4 , 0x0000BFFD //P12 data8 0xAAAAAAAAAAAAC277 , 0x00003FFC //P1 data8 0xF534912FF3E7B76F , 0x00003FFF //P21 data8 0xc90fdaa22168c235 , 0x00003fff // pi/2 data8 0x0000000000000000 , 0x00000000 // pad to avoid bank conflicts
acos_coeff_2_table: data8 0x8E26AF5F29B39A2A , 0x00003FF9 //P6 data8 0xB4F118A4B1015470 , 0x00004003 //P17 data8 0xF8E38E10C25990E0 , 0x00003FF9 //P4 data8 0x80F50489AEF1CAC6 , 0x00004002 //P15 data8 0x92728015172CFE1C , 0x00004003 //P19 data8 0xBBC3D831D4595971 , 0x00003FF8 //P8 data8 0x999999999952A5C3 , 0x00003FFB //P2 data8 0x855576BE6F0975EC , 0x00003FFF //P13 data8 0xF12420E778077D89 , 0x00003FFA //P11 data8 0xB6590FF4D23DE003 , 0x00003FF3 //P10 data8 0xb504f333f9de6484 , 0x00003ffe // sqrt(2)/2
.align 32 .global acos
.section .text .proc acos .align 32
acos: { .mfi alloc r32 = ar.pfs,1,6,4,0 fma.s1 acos_tx = f8,f8,f0 addl ASIN_Addr2 = @ltoff(acos_coeff_2_table),gp } { .mfi mov ASIN_FFFE = 0xFFFE fnma.s1 acos_t = f8,f8,f1 addl ASIN_Addr1 = @ltoff(acos_coeff_1_table),gp } ;;
{ .mfi setf.exp acos_1by2 = ASIN_FFFE fmerge.s acos_abs_x = f1,f8 nop.i 999 ;;
}
{ .mmf ld8 ASIN_Addr1 = [ASIN_Addr1] ld8 ASIN_Addr2 = [ASIN_Addr2] fmerge.s acos_sgn_x = f8,f1 } ;;
{ .mfi nop.m 999 fcmp.lt.s1 p11,p12 = f8, f0 nop.i 999 ;;
} { .mfi ldfe acos_coeff_P7 = [ASIN_Addr1],16 fma.s1 acos_tx2 = acos_tx,acos_tx,f0 nop.i 999 } { .mfi ldfe acos_coeff_P6 = [ASIN_Addr2],16 fma.s1 acos_t2 = acos_t,acos_t,f0 nop.i 999;;
}
{ .mmf ldfe acos_coeff_P18 = [ASIN_Addr1],16 ldfe acos_coeff_P17 = [ASIN_Addr2],16 fclass.m.unc p8,p0 = f8, 0xc3 //@qnan |@snan } ;;
{ .mmf ldfe acos_coeff_P5 = [ASIN_Addr1],16 ldfe acos_coeff_P4 = [ASIN_Addr2],16 frsqrta.s1 acos_y0,p0 = acos_t } ;;
{ .mfi ldfe acos_coeff_P16 = [ASIN_Addr1],16 fcmp.gt.s1 p9,p0 = acos_abs_x,f1 nop.i 999 } { .mfb ldfe acos_coeff_P15 = [ASIN_Addr2],16 (p8) fma.d f8 = f8,f1,f0 (p8) br.ret.spnt b0 } ;;
{ .mmf ldfe acos_coeff_P20 = [ASIN_Addr1],16 ldfe acos_coeff_P19 = [ASIN_Addr2],16 fclass.m.unc p10,p0 = f8, 0x07 //@zero } ;;
{ .mfi ldfe acos_coeff_P9 = [ASIN_Addr1],16 fma.s1 acos_t4 = acos_t2,acos_t2,f0 (p9) mov GR_Parameter_Tag = 58 } { .mfi ldfe acos_coeff_P8 = [ASIN_Addr2],16 fma.s1 acos_3by2 = acos_1by2,f1,f1 nop.i 999;;
}
{ .mfi ldfe acos_coeff_P2 = [ASIN_Addr2],16 fma.s1 acos_tx4 = acos_tx2,acos_tx2,f0 nop.i 999 } { .mfb ldfe acos_coeff_P3 = [ASIN_Addr1],16 fma.s1 acos_t3 = acos_t,acos_t2,f0 (p9) br.cond.spnt __libm_error_region } ;;
{ .mfi ldfe acos_coeff_P13 = [ASIN_Addr2],16 fma.s1 acos_H0 = acos_y0,acos_1by2,f0 nop.i 999 } { .mfi ldfe acos_coeff_P14 = [ASIN_Addr1],16 fma.s1 acos_S0 = acos_y0,acos_t,f0 nop.i 999;;
}
{ .mfi ldfe acos_coeff_P11 = [ASIN_Addr2],16 fcmp.eq.s1 p6,p0 = acos_abs_x, f1 nop.i 999 } { .mfi ldfe acos_coeff_P12 = [ASIN_Addr1],16 fma.s1 acos_tx3 = acos_tx,acos_tx2,f0 nop.i 999 } ;;
{ .mfi ldfe acos_coeff_P10 = [ASIN_Addr2],16 fma.s1 acos_1poly_p6 = acos_tx,acos_coeff_P7,acos_coeff_P6 nop.i 999 } { .mfi ldfe acos_coeff_P1 = [ASIN_Addr1],16 fma.s1 acos_poly_p6 = acos_t,acos_coeff_P7,acos_coeff_P6 nop.i 999;;
}
{ .mfi ldfe acos_const_sqrt2by2 = [ASIN_Addr2],16 fma.s1 acos_5by2 = acos_3by2,f1,f1 nop.i 999 } { .mfi ldfe acos_coeff_P21 = [ASIN_Addr1],16 fma.s1 acos_11by4 = acos_3by2,acos_3by2,acos_1by2 nop.i 999;;
}
{ .mfi ldfe acos_const_piby2 = [ASIN_Addr1],16 fma.s1 acos_poly_p17 = acos_t,acos_coeff_P18,acos_coeff_P17 nop.i 999 } { .mfb nop.m 999 fma.s1 acos_3by4 = acos_3by2,acos_1by2,f0 (p10) br.cond.spnt ACOS_ZERO // Branch to short path if x=0 } ;;
{ .mfi nop.m 999 fma.s1 acos_poly_p15 = acos_t,acos_coeff_P16,acos_coeff_P15 nop.i 999 } { .mfb nop.m 999 fnma.s1 acos_d = acos_S0,acos_H0,acos_1by2 (p6) br.cond.spnt ACOS_ABS_ONE // Branch to short path if |x|=1 } ;;
{ .mfi nop.m 999 fma.s1 acos_poly_p19 = acos_t,acos_coeff_P20,acos_coeff_P19 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_poly_p4 = acos_t,acos_coeff_P5,acos_coeff_P4 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p17 = acos_tx,acos_coeff_P18,acos_coeff_P17 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_poly_p8 = acos_t,acos_coeff_P9,acos_coeff_P8 nop.i 999;;
}
{ .mfi nop.m 999 fms.s1 acos_35by8 = acos_5by2,acos_11by4,acos_5by2 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_63by8 = acos_5by2,acos_11by4,f1 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_poly_p13 = acos_t,acos_coeff_P14,acos_coeff_P13 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_18by4 = acos_3by2,acos_5by2,acos_3by4 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_l1 = acos_5by2,acos_d,acos_3by2 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_d2 = acos_d,acos_d,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_poly_p15 = acos_t2,acos_poly_p17,acos_poly_p15 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_T0 = acos_d,acos_S0,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_poly_p19 = acos_t2,acos_coeff_P21,acos_poly_p19 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_poly_p4 = acos_t2,acos_poly_p6,acos_poly_p4 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_d1 = acos_35by8,acos_d,f0 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_231by16 = acos_3by2,acos_35by8,acos_63by8 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_poly_p2 = acos_t,acos_coeff_P3,acos_coeff_P2 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_poly_p8 = acos_t2,acos_coeff_P10,acos_poly_p8 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_poly_p11 = acos_t,acos_coeff_P12,acos_coeff_P11 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_e0 = acos_d2,acos_l1,acos_d nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p15 = acos_tx,acos_coeff_P16,acos_coeff_P15 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_poly_p0 = acos_t,acos_coeff_P1,f1 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p19 = acos_tx,acos_coeff_P20,acos_coeff_P19 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_1poly_p4 = acos_tx,acos_coeff_P5,acos_coeff_P4 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p8 = acos_tx,acos_coeff_P9,acos_coeff_P8 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_l2 = acos_231by16,acos_d,acos_63by8 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_d3 = acos_d2,acos_d,f0 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_T3 = acos_d2,acos_T0,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_429by16 = acos_18by4,acos_11by4,acos_231by16 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_S1 = acos_e0,acos_S0,acos_S0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_poly_p4 = acos_t4,acos_poly_p8,acos_poly_p4 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_poly_p15 = acos_t4,acos_poly_p19,acos_poly_p15 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_poly_p0 = acos_t2,acos_poly_p2,acos_poly_p0 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_poly_p11 = acos_t2,acos_poly_p13,acos_poly_p11 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_t8 = acos_t4,acos_t4,f0 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_e1 = acos_d2,acos_l2,acos_d1 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p4 = acos_tx2,acos_1poly_p6,acos_1poly_p4 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_1poly_p15 = acos_tx2,acos_1poly_p17,acos_1poly_p15 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p8 = acos_tx2,acos_coeff_P10,acos_1poly_p8 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_1poly_p19 = acos_tx2,acos_coeff_P21,acos_1poly_p19 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p2 = acos_tx,acos_coeff_P3,acos_coeff_P2 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_1poly_p13 = acos_tx,acos_coeff_P14,acos_coeff_P13 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p0 = acos_tx,acos_coeff_P1,f1 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_1poly_p11 = acos_tx,acos_coeff_P12,acos_coeff_P11 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_l3 = acos_429by16,acos_d,f0 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_z = acos_e1,acos_T3,acos_S1 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_poly_p11 = acos_t4,acos_poly_p15,acos_poly_p11 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_T6 = acos_T3,acos_d3,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_t11 = acos_t8,acos_t3,f0 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_poly_p0 = acos_t4,acos_poly_p4,acos_poly_p0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p4 = acos_tx4,acos_1poly_p8,acos_1poly_p4 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_1poly_p15 = acos_tx4,acos_1poly_p19,acos_1poly_p15 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_1poly_p0 = acos_tx2,acos_1poly_p2,acos_1poly_p0 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_1poly_p11 = acos_tx2,acos_1poly_p13,acos_1poly_p11 nop.i 999;;
}
{ .mfi nop.m 999 // fcmp.le.s1 acos_pred_LEsqrt2by2,acos_pred_GTsqrt2by2 = acos_abs_x,acos_const_sqrt2by2 fcmp.le.s1 p7,p8 = acos_abs_x,acos_const_sqrt2by2 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_tx8 = acos_tx4,acos_tx4,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_z = acos_l3,acos_T6,acos_z nop.i 999;;
} { .mfi nop.m 999 fma.s1 acos_series_t = acos_t11,acos_poly_p11,acos_poly_p0 nop.i 999 } { .mfi nop.m 999 (p11) fma.s1 acos_const_add = acos_const_piby2, f1, acos_const_piby2 nop.i 999 } ;;
{ .mfi nop.m 999 (p12) fma.s1 acos_const_add = f1,f0,f0 nop.i 999 } ;;
{ .mfi nop.m 999 fma.s1 acos_1poly_p0 = acos_tx4,acos_1poly_p4,acos_1poly_p0 nop.i 999 } { .mfi nop.m 999 fma.s1 acos_1poly_p11 = acos_tx4,acos_1poly_p15,acos_1poly_p11 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acos_tx11 = acos_tx8,acos_tx3,f0 nop.i 999;;
} { .mfi nop.m 999 //(acos_pred_GTsqrt2by2) fnma.s1 answer2 = acos_z,acos_series_t,acos_const_piby2 (p8) fnma.s1 answer2 = acos_z,acos_series_t,f0 nop.i 999;;
} { .mfi nop.m 999 fma.s1 acos_series_tx = acos_tx11,acos_1poly_p11,acos_1poly_p0 nop.i 999;;
} { .mfi nop.m 999 //(acos_pred_GTsqrt2by2) fnma.d f8 = acos_sgn_x,answer2,acos_const_piby2 (p8) fnma.d f8 = acos_sgn_x,answer2,acos_const_add nop.i 999;;
} { .mfb nop.m 999 //(acos_pred_LEsqrt2by2) fnma.d f8 = f8,acos_series_tx,acos_const_piby2 (p7) fnma.d f8 = f8,acos_series_tx,acos_const_piby2 br.ret.sptk b0 ;;
}
ACOS_ZERO: // Here if x=0 { .mfb nop.m 999 fma.d f8 = acos_const_piby2,f1,f0 br.ret.sptk b0 ;;
}
.pred.rel "mutex",p11,p12 ACOS_ABS_ONE: // Here if |x|=1 { .mfi nop.m 999 (p11) fma.d f8 = acos_const_piby2,f1,acos_const_piby2 // acos(-1)=pi nop.i 999 } { .mfb nop.m 999 (p12) fma.d f8 = f1,f0,f0 // acos(1)=0 br.ret.sptk b0 ;;
}
.endp acos
.proc __libm_error_region __libm_error_region: .prologue { .mfi add GR_Parameter_Y=-32,sp // Parameter 2 value nop.f 999 .save ar.pfs,GR_SAVE_PFS mov GR_SAVE_PFS=ar.pfs // Save ar.pfs } { .mfi .fframe 64 add sp=-64,sp // Create new stack nop.f 0 mov GR_SAVE_GP=gp // Save gp };;
{ .mmi stfs [GR_Parameter_Y] = f1,16 // Store Parameter 2 on stack add GR_Parameter_X = 16,sp // Parameter 1 address .save b0, GR_SAVE_B0 mov GR_SAVE_B0=b0 // Save b0 };;
.body frcpa.s0 f9,p0 = f0,f0 ;;
{ .mib stfd [GR_Parameter_X] = f8 // Store Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y nop.b 0 // Parameter 3 address } { .mib stfd [GR_Parameter_Y] = f9,-16 // Store Parameter 3 on stack adds r32 = 48,sp br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi ldfd f8 = [r32] // Get return result off stack .restore add sp = 64,sp // Restore stack pointer mov b0 = GR_SAVE_B0 // Restore return address };;
{ .mib mov gp = GR_SAVE_GP // Restore gp mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs br.ret.sptk b0 // Return
};;
.endp __libm_error_region
.type __libm_error_support,@function .global __libm_error_support
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