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.file "asin.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.// 8/31/00 Avoided bank conflicts on loads, shortened |x|=1 path, // fixed mfb split issue stalls.
// Description//=========================================// The asin function computes the principle value of the arc sine of x.// asin(0) returns 0, asin(1) returns pi/2, asin(-1) returns -pi/2.// A doman error occurs for arguments not in the range [-1,+1].
// The asin function returns the arc sine in the range [-pi/2, +pi/2] radians.
//// Assembly macros//=========================================
// predicate registers//asin_pred_LEsqrt2by2 = p7//asin_pred_GTsqrt2by2 = p8
// integer registersASIN_Addr1 = r33ASIN_Addr2 = r34ASIN_FFFE = r35
GR_SAVE_B0 = r36GR_SAVE_PFS = r37GR_SAVE_GP = r38
GR_Parameter_X = r39GR_Parameter_Y = r40GR_Parameter_RESULT = r41GR_Parameter_Tag = r42
// floating point registersasin_coeff_P1 = f32asin_coeff_P2 = f33asin_coeff_P3 = f34asin_coeff_P4 = f35
asin_coeff_P5 = f36asin_coeff_P6 = f37asin_coeff_P7 = f38asin_coeff_P8 = f39asin_coeff_P9 = f40
asin_coeff_P10 = f41asin_coeff_P11 = f42asin_coeff_P12 = f43asin_coeff_P13 = f44asin_coeff_P14 = f45
asin_coeff_P15 = f46asin_coeff_P16 = f47asin_coeff_P17 = f48asin_coeff_P18 = f49asin_coeff_P19 = f50
asin_coeff_P20 = f51asin_coeff_P21 = f52asin_const_sqrt2by2 = f53asin_const_piby2 = f54asin_abs_x = f55
asin_tx = f56asin_tx2 = f57asin_tx3 = f58asin_tx4 = f59asin_tx8 = f60
asin_tx11 = f61asin_1poly_p8 = f62asin_1poly_p19 = f63asin_1poly_p4 = f64asin_1poly_p15 = f65
asin_1poly_p6 = f66asin_1poly_p17 = f67asin_1poly_p0 = f68asin_1poly_p11 = f69asin_1poly_p2 = f70
asin_1poly_p13 = f71asin_series_tx = f72asin_t = f73asin_t2 = f74asin_t3 = f75
asin_t4 = f76asin_t8 = f77asin_t11 = f78asin_poly_p8 = f79asin_poly_p19 = f80
asin_poly_p4 = f81asin_poly_p15 = f82asin_poly_p6 = f83asin_poly_p17 = f84asin_poly_p0 = f85
asin_poly_p11 = f86asin_poly_p2 = f87asin_poly_p13 = f88asin_series_t = f89asin_1by2 = f90
asin_3by2 = f91asin_5by2 = f92asin_11by4 = f93asin_35by8 = f94asin_63by8 = f95
asin_231by16 = f96 asin_y0 = f97 asin_H0 = f98 asin_S0 = f99 asin_d = f100
asin_l1 = f101asin_d2 = f102asin_T0 = f103asin_d1 = f104asin_e0 = f105
asin_l2 = f106asin_d3 = f107asin_T3 = f108asin_S1 = f109asin_e1 = f110
asin_z = f111answer2 = f112asin_sgn_x = f113asin_429by16 = f114asin_18by4 = f115
asin_3by4 = f116asin_l3 = f117asin_T6 = f118
// Data tables//==============================================================
.data
.align 16
asin_coeff_1_table:data8 0xE4E7E0A423A21249 , 0x00003FF8 //P7data8 0xC2F7EE0200FCE2A5 , 0x0000C003 //P18data8 0xB745D7F6C65C20E0 , 0x00003FF9 //P5data8 0xF75E381A323D4D94 , 0x0000C002 //P16data8 0x8959C2629C1024C0 , 0x0000C002 //P20data8 0xAFF68E7D241292C5 , 0x00003FF8 //P9data8 0xB6DB6DB7260AC30D , 0x00003FFA //P3data8 0xD0417CE2B41CB7BF , 0x0000C000 //P14data8 0x81D570FEA724E3E4 , 0x0000BFFD //P12data8 0xAAAAAAAAAAAAC277 , 0x00003FFC //P1data8 0xF534912FF3E7B76F , 0x00003FFF //P21data8 0xc90fdaa22168c235 , 0x00003fff // pi/2data8 0x0000000000000000 , 0x00000000 // pad to avoid data bank conflict
asin_coeff_2_table:data8 0x8E26AF5F29B39A2A , 0x00003FF9 //P6data8 0xB4F118A4B1015470 , 0x00004003 //P17data8 0xF8E38E10C25990E0 , 0x00003FF9 //P4data8 0x80F50489AEF1CAC6 , 0x00004002 //P15data8 0x92728015172CFE1C , 0x00004003 //P19data8 0xBBC3D831D4595971 , 0x00003FF8 //P8data8 0x999999999952A5C3 , 0x00003FFB //P2data8 0x855576BE6F0975EC , 0x00003FFF //P13data8 0xF12420E778077D89 , 0x00003FFA //P11data8 0xB6590FF4D23DE003 , 0x00003FF3 //P10data8 0xb504f333f9de6484 , 0x00003ffe // sqrt(2)/2
.align 32.global asin
.section .text.proc asin.align 32
asin: { .mfi alloc r32 = ar.pfs,1,6,4,0 fma.s1 asin_tx = f8,f8,f0 addl ASIN_Addr2 = @ltoff(asin_coeff_2_table),gp} { .mfi mov ASIN_FFFE = 0xFFFE fnma.s1 asin_t = f8,f8,f1 addl ASIN_Addr1 = @ltoff(asin_coeff_1_table),gp};;
{ .mfi setf.exp asin_1by2 = ASIN_FFFE fmerge.s asin_abs_x = f1,f8 nop.i 999 ;;
} { .mmf ld8 ASIN_Addr1 = [ASIN_Addr1] ld8 ASIN_Addr2 = [ASIN_Addr2] fmerge.s asin_sgn_x = f8,f1 ;;
}
{ .mfi ldfe asin_coeff_P7 = [ASIN_Addr1],16 fma.s1 asin_tx2 = asin_tx,asin_tx,f0 nop.i 999} { .mfi ldfe asin_coeff_P6 = [ASIN_Addr2],16 fma.s1 asin_t2 = asin_t,asin_t,f0 nop.i 999;;
}
{ .mmf ldfe asin_coeff_P18 = [ASIN_Addr1],16 ldfe asin_coeff_P17 = [ASIN_Addr2],16 fclass.m.unc p8,p0 = f8, 0xc3 //@qnan |@snan} ;;
{ .mmf ldfe asin_coeff_P5 = [ASIN_Addr1],16 ldfe asin_coeff_P4 = [ASIN_Addr2],16 frsqrta.s1 asin_y0,p0 = asin_t} ;;
{ .mfi ldfe asin_coeff_P16 = [ASIN_Addr1],16 fcmp.gt.s1 p9,p0 = asin_abs_x,f1 nop.i 999} { .mfb ldfe asin_coeff_P15 = [ASIN_Addr2],16(p8) fma.d f8 = f8,f1,f0(p8) br.ret.spnt b0};;
{ .mmf ldfe asin_coeff_P20 = [ASIN_Addr1],16 ldfe asin_coeff_P19 = [ASIN_Addr2],16 fclass.m.unc p8,p0 = f8, 0x07 //@zero} ;;
{ .mfi ldfe asin_coeff_P9 = [ASIN_Addr1],16 fma.s1 asin_t4 = asin_t2,asin_t2,f0(p9) mov GR_Parameter_Tag = 61 } { .mfi ldfe asin_coeff_P8 = [ASIN_Addr2],16 fma.s1 asin_3by2 = asin_1by2,f1,f1 nop.i 999;;
}
{ .mfi ldfe asin_coeff_P2 = [ASIN_Addr2],16 fma.s1 asin_tx4 = asin_tx2,asin_tx2,f0 nop.i 999} { .mfb ldfe asin_coeff_P3 = [ASIN_Addr1],16 fma.s1 asin_t3 = asin_t,asin_t2,f0(p8) br.ret.spnt b0};;
{ .mfi ldfe asin_coeff_P13 = [ASIN_Addr2],16 fma.s1 asin_H0 = asin_y0,asin_1by2,f0 nop.i 999} { .mfb ldfe asin_coeff_P14 = [ASIN_Addr1],16 fma.s1 asin_S0 = asin_y0,asin_t,f0(p9) br.cond.spnt __libm_error_region};;
{ .mfi ldfe asin_coeff_P11 = [ASIN_Addr2],16 fcmp.eq.s1 p6,p0 = asin_abs_x,f1 nop.i 999} { .mfi ldfe asin_coeff_P12 = [ASIN_Addr1],16 fma.s1 asin_tx3 = asin_tx,asin_tx2,f0 nop.i 999;;
}
{ .mfi ldfe asin_coeff_P10 = [ASIN_Addr2],16 fma.s1 asin_1poly_p6 = asin_tx,asin_coeff_P7,asin_coeff_P6 nop.i 999} { .mfi ldfe asin_coeff_P1 = [ASIN_Addr1],16 fma.s1 asin_poly_p6 = asin_t,asin_coeff_P7,asin_coeff_P6 nop.i 999;;
}
{ .mfi ldfe asin_const_sqrt2by2 = [ASIN_Addr2],16 fma.s1 asin_5by2 = asin_3by2,f1,f1 nop.i 999} { .mfi ldfe asin_coeff_P21 = [ASIN_Addr1],16 fma.s1 asin_11by4 = asin_3by2,asin_3by2,asin_1by2 nop.i 999;;
}
{ .mfi ldfe asin_const_piby2 = [ASIN_Addr1],16 fma.s1 asin_poly_p17 = asin_t,asin_coeff_P18,asin_coeff_P17 nop.i 999} { .mfb nop.m 999 fma.s1 asin_3by4 = asin_3by2,asin_1by2,f0(p6) br.cond.spnt ASIN_ABS_1 // Branch to short exit if |x|=1};;
{ .mfi nop.m 999 fma.s1 asin_poly_p15 = asin_t,asin_coeff_P16,asin_coeff_P15 nop.i 999} { .mfi nop.m 999 fnma.s1 asin_d = asin_S0,asin_H0,asin_1by2 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_poly_p19 = asin_t,asin_coeff_P20,asin_coeff_P19 nop.i 999} { .mfi nop.m 999 fma.s1 asin_poly_p4 = asin_t,asin_coeff_P5,asin_coeff_P4 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p17 = asin_tx,asin_coeff_P18,asin_coeff_P17 nop.i 999} { .mfi nop.m 999 fma.s1 asin_poly_p8 = asin_t,asin_coeff_P9,asin_coeff_P8 nop.i 999;;
}
{ .mfi nop.m 999 fms.s1 asin_35by8 = asin_5by2,asin_11by4,asin_5by2 nop.i 999} { .mfi nop.m 999 fma.s1 asin_63by8 = asin_5by2,asin_11by4,f1 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_poly_p13 = asin_t,asin_coeff_P14,asin_coeff_P13 nop.i 999} { .mfi nop.m 999 fma.s1 asin_18by4 = asin_3by2,asin_5by2,asin_3by4 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_l1 = asin_5by2,asin_d,asin_3by2 nop.i 999} { .mfi nop.m 999 fma.s1 asin_d2 = asin_d,asin_d,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_poly_p15 = asin_t2,asin_poly_p17,asin_poly_p15 nop.i 999} { .mfi nop.m 999 fma.s1 asin_T0 = asin_d,asin_S0,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_poly_p19 = asin_t2,asin_coeff_P21,asin_poly_p19 nop.i 999} { .mfi nop.m 999 fma.s1 asin_poly_p4 = asin_t2,asin_poly_p6,asin_poly_p4 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_d1 = asin_35by8,asin_d,f0 nop.i 999} { .mfi nop.m 999 fma.s1 asin_231by16 = asin_3by2,asin_35by8,asin_63by8 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_poly_p2 = asin_t,asin_coeff_P3,asin_coeff_P2 nop.i 999} { .mfi nop.m 999 fma.s1 asin_poly_p8 = asin_t2,asin_coeff_P10,asin_poly_p8 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_poly_p11 = asin_t,asin_coeff_P12,asin_coeff_P11 nop.i 999} { .mfi nop.m 999 fma.s1 asin_e0 = asin_d2,asin_l1,asin_d nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p15 = asin_tx,asin_coeff_P16,asin_coeff_P15 nop.i 999} { .mfi nop.m 999 fma.s1 asin_poly_p0 = asin_t,asin_coeff_P1,f1 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p19 = asin_tx,asin_coeff_P20,asin_coeff_P19 nop.i 999} { .mfi nop.m 999 fma.s1 asin_1poly_p4 = asin_tx,asin_coeff_P5,asin_coeff_P4 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p8 = asin_tx,asin_coeff_P9,asin_coeff_P8 nop.i 999} { .mfi nop.m 999 fma.s1 asin_l2 = asin_231by16,asin_d,asin_63by8 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_d3 = asin_d2,asin_d,f0 nop.i 999} { .mfi nop.m 999 fma.s1 asin_T3 = asin_d2,asin_T0,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_429by16 = asin_18by4,asin_11by4,asin_231by16 nop.i 999} { .mfi nop.m 999 fma.s1 asin_S1 = asin_e0,asin_S0,asin_S0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_poly_p4 = asin_t4,asin_poly_p8,asin_poly_p4 nop.i 999} { .mfi nop.m 999 fma.s1 asin_poly_p15 = asin_t4,asin_poly_p19,asin_poly_p15 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_poly_p0 = asin_t2,asin_poly_p2,asin_poly_p0 nop.i 999} { .mfi nop.m 999 fma.s1 asin_poly_p11 = asin_t2,asin_poly_p13,asin_poly_p11 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_t8 = asin_t4,asin_t4,f0 nop.i 999} { .mfi nop.m 999 fma.s1 asin_e1 = asin_d2,asin_l2,asin_d1 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p4 = asin_tx2,asin_1poly_p6,asin_1poly_p4 nop.i 999} { .mfi nop.m 999 fma.s1 asin_1poly_p15 = asin_tx2,asin_1poly_p17,asin_1poly_p15 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p8 = asin_tx2,asin_coeff_P10,asin_1poly_p8 nop.i 999} { .mfi nop.m 999 fma.s1 asin_1poly_p19 = asin_tx2,asin_coeff_P21,asin_1poly_p19 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p2 = asin_tx,asin_coeff_P3,asin_coeff_P2 nop.i 999} { .mfi nop.m 999 fma.s1 asin_1poly_p13 = asin_tx,asin_coeff_P14,asin_coeff_P13 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p0 = asin_tx,asin_coeff_P1,f1 nop.i 999} { .mfi nop.m 999 fma.s1 asin_1poly_p11 = asin_tx,asin_coeff_P12,asin_coeff_P11 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_l3 = asin_429by16,asin_d,f0 nop.i 999} { .mfi nop.m 999 fma.s1 asin_z = asin_e1,asin_T3,asin_S1 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_poly_p11 = asin_t4,asin_poly_p15,asin_poly_p11 nop.i 999} { .mfi nop.m 999 fma.s1 asin_T6 = asin_T3,asin_d3,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_t11 = asin_t8,asin_t3,f0 nop.i 999} { .mfi nop.m 999 fma.s1 asin_poly_p0 = asin_t4,asin_poly_p4,asin_poly_p0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p4 = asin_tx4,asin_1poly_p8,asin_1poly_p4 nop.i 999} { .mfi nop.m 999 fma.s1 asin_1poly_p15 = asin_tx4,asin_1poly_p19,asin_1poly_p15 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_1poly_p0 = asin_tx2,asin_1poly_p2,asin_1poly_p0 nop.i 999} { .mfi nop.m 999 fma.s1 asin_1poly_p11 = asin_tx2,asin_1poly_p13,asin_1poly_p11 nop.i 999;;
}
{ .mfi nop.m 999// fcmp.le.s1 asin_pred_LEsqrt2by2,asin_pred_GTsqrt2by2 = asin_abs_x,asin_const_sqrt2by2 fcmp.le.s1 p7,p8 = asin_abs_x,asin_const_sqrt2by2 nop.i 999} { .mfi nop.m 999 fma.s1 asin_tx8 = asin_tx4,asin_tx4,f0 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_z = asin_l3,asin_T6,asin_z nop.i 999;;
} { .mfi nop.m 999 fma.s1 asin_series_t = asin_t11,asin_poly_p11,asin_poly_p0 nop.i 999;;
} { .mfi nop.m 999 fma.s1 asin_1poly_p0 = asin_tx4,asin_1poly_p4,asin_1poly_p0 nop.i 999} { .mfi nop.m 999 fma.s1 asin_1poly_p11 = asin_tx4,asin_1poly_p15,asin_1poly_p11 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 asin_tx11 = asin_tx8,asin_tx3,f0 nop.i 999;;
} { .mfi nop.m 999//(asin_pred_GTsqrt2by2) fnma.s1 answer2 = asin_z,asin_series_t,asin_const_piby2(p8) fnma.s1 answer2 = asin_z,asin_series_t,asin_const_piby2 nop.i 999;;
} { .mfi nop.m 999 fma.s1 asin_series_tx = asin_tx11,asin_1poly_p11,asin_1poly_p0 nop.i 999;;
} { .mfi nop.m 999//(asin_pred_GTsqrt2by2) fma.d f8 = asin_sgn_x,answer2,f0(p8) fma.d f8 = asin_sgn_x,answer2,f0 nop.i 999;;
} { .mfb nop.m 999//(asin_pred_LEsqrt2by2) fma.d f8 = f8,asin_series_tx,f0(p7) fma.d f8 = f8,asin_series_tx,f0 br.ret.sptk b0} ;;
ASIN_ABS_1:// Here for short exit if |x|=1{ .mfb nop.m 999 fma.d f8 = asin_sgn_x,asin_const_piby2,f0 br.ret.sptk b0} ;;
.endp asin
.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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