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windows-nt/Source/XPSP1/NT/base/crts/fpw32/tran/ia64/asin.s

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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 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
asin_coeff_P1 = f32
asin_coeff_P2 = f33
asin_coeff_P3 = f34
asin_coeff_P4 = f35
asin_coeff_P5 = f36
asin_coeff_P6 = f37
asin_coeff_P7 = f38
asin_coeff_P8 = f39
asin_coeff_P9 = f40
asin_coeff_P10 = f41
asin_coeff_P11 = f42
asin_coeff_P12 = f43
asin_coeff_P13 = f44
asin_coeff_P14 = f45
asin_coeff_P15 = f46
asin_coeff_P16 = f47
asin_coeff_P17 = f48
asin_coeff_P18 = f49
asin_coeff_P19 = f50
asin_coeff_P20 = f51
asin_coeff_P21 = f52
asin_const_sqrt2by2 = f53
asin_const_piby2 = f54
asin_abs_x = f55
asin_tx = f56
asin_tx2 = f57
asin_tx3 = f58
asin_tx4 = f59
asin_tx8 = f60
asin_tx11 = f61
asin_1poly_p8 = f62
asin_1poly_p19 = f63
asin_1poly_p4 = f64
asin_1poly_p15 = f65
asin_1poly_p6 = f66
asin_1poly_p17 = f67
asin_1poly_p0 = f68
asin_1poly_p11 = f69
asin_1poly_p2 = f70
asin_1poly_p13 = f71
asin_series_tx = f72
asin_t = f73
asin_t2 = f74
asin_t3 = f75
asin_t4 = f76
asin_t8 = f77
asin_t11 = f78
asin_poly_p8 = f79
asin_poly_p19 = f80
asin_poly_p4 = f81
asin_poly_p15 = f82
asin_poly_p6 = f83
asin_poly_p17 = f84
asin_poly_p0 = f85
asin_poly_p11 = f86
asin_poly_p2 = f87
asin_poly_p13 = f88
asin_series_t = f89
asin_1by2 = f90
asin_3by2 = f91
asin_5by2 = f92
asin_11by4 = f93
asin_35by8 = f94
asin_63by8 = f95
asin_231by16 = f96
asin_y0 = f97
asin_H0 = f98
asin_S0 = f99
asin_d = f100
asin_l1 = f101
asin_d2 = f102
asin_T0 = f103
asin_d1 = f104
asin_e0 = f105
asin_l2 = f106
asin_d3 = f107
asin_T3 = f108
asin_S1 = f109
asin_e1 = f110
asin_z = f111
answer2 = f112
asin_sgn_x = f113
asin_429by16 = f114
asin_18by4 = f115
asin_3by4 = f116
asin_l3 = f117
asin_T6 = f118
// Data tables
//==============================================================
.data
.align 16
asin_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 data bank conflict
asin_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 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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