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+.file "asinf.s"
+
+
+// Copyright (c) 2000 - 2003, Intel Corporation
+// All rights reserved.
+//
+// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+// * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//
+// * Redistributions in binary form must reproduce the above copyright
+// notice, this list of conditions and the following disclaimer in the
+// documentation and/or other materials provided with the distribution.
+//
+// * The name of Intel Corporation may not be used to endorse or promote
+// products derived from this software without specific prior written
+// permission.
+
+// 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://www.intel.com/software/products/opensource/libraries/num.htm.
+
+// History
+//==============================================================
+// 02/02/00 Initial version
+// 06/28/00 Improved speed
+// 06/31/00 Changed register allocation because of some duplicate macros
+// moved nan exit bundle up to gain a cycle.
+// 08/08/00 Improved speed by avoiding SIR flush.
+// 08/15/00 Bundle added after call to __libm_error_support to properly
+// set [the previously overwritten] GR_Parameter_RESULT.
+// 08/17/00 Changed predicate register macro-usage to direct predicate
+// names due to an assembler bug.
+// 10/17/00 Improved speed of x=0 and x=1 paths, set D flag if x denormal.
+// 03/13/01 Corrected sign of imm1 value in dep instruction.
+// 05/20/02 Cleaned up namespace and sf0 syntax
+// 02/06/03 Reordered header: .section, .global, .proc, .align
+
+
+// Description
+//=========================================
+// The asinf function computes the arc sine of x in the range [-pi,+pi].
+// A doman error occurs for arguments not in the range [-1,+1].
+// asinf(+-0) returns +-0
+// asinf(x) returns a Nan and raises the invalid exception for |x| >1
+
+// The acosf function returns the arc cosine in the range [0, +pi] radians.
+// A doman error occurs for arguments not in the range [-1,+1].
+// acosf(1) returns +0
+// acosf(x) returns a Nan and raises the invalid exception for |x| >1
+
+
+// |x| <= sqrt(2)/2. get Ax and Bx
+
+// poly_p1 = x p1
+// poly_p3 = x2 p4 + p3
+// poly_p1 = x2 (poly_p1) + x = x2(x p1) + x
+// poly_p2 = x2( poly_p3) + p2 = x2(x2 p4 + p3) + p2
+
+// poly_Ax = x5(x2( poly_p3) + p2) + x2(x p1) + x
+// = x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x
+
+// poly_p7 = x2 p8 + p7
+// poly_p5 = x2 p6 + p5
+
+// poly_p7 = x4 p9 + (poly_p7)
+// poly_p7 = x4 p9 + (x2 p8 + p7)
+// poly_Bx = x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5
+
+// answer1 = x11(x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5) + x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x
+// = x19 p9 + x17 p8 + x15 p7 x13 p6 + x11 p5 + x9 p4 + x7 p3 + x5 p2 + x3 p1 + x
+
+
+
+// |x| > sqrt(2)/2
+
+// Get z = sqrt(1-x2)
+
+// Get polynomial in t = 1-x2
+
+// t2 = t t
+// t4 = t2 t2
+
+// poly_p4 = t p5 + p4
+// poly_p1 = t p1 + 1
+
+// poly_p6 = t p7 + p6
+// poly_p2 = t p3 + p2
+
+// poly_p8 = t p9 + p8
+
+// poly_p4 = t2 poly_p6 + poly_p4
+// = t2 (t p7 + p6) + (t p5 + p4)
+
+// poly_p2 = t2 poly_p2 + poly_p1
+// = t2 (t p3 + p2) + (t p1 + 1)
+
+// poly_p4 = t4 poly_p8 + poly_p4
+// = t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4))
+
+// P(t) = poly_p2 + t4 poly_p8
+// = t2 (t p3 + p2) + (t p1 + 1) + t4 (t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4)))
+// = t3 p3 + t2 p2 + t p1 + 1 + t9 p9 + t8 p8 + t7 p7 + t6 p6 + t5 p5 + t4 p4
+
+
+// answer2 = - sign(x) z P(t) + (sign(x) pi/2)
+//
+
+
+// Assembly macros
+//=========================================
+
+// predicate registers
+//asinf_pred_LEsqrt2by2 = p7
+//asinf_pred_GTsqrt2by2 = p8
+
+// integer registers
+ASINF_Addr1 = r33
+ASINF_Addr2 = r34
+ASINF_GR_1by2 = r35
+
+ASINF_GR_3by2 = r36
+ASINF_GR_5by2 = r37
+
+GR_SAVE_B0 = r38
+GR_SAVE_PFS = r39
+GR_SAVE_GP = r40
+
+GR_Parameter_X = r41
+GR_Parameter_Y = r42
+GR_Parameter_RESULT = r43
+GR_Parameter_TAG = r44
+
+// floating point registers
+
+asinf_y = f32
+asinf_abs_x = f33
+asinf_x2 = f34
+asinf_sgn_x = f35
+
+asinf_1by2 = f36
+asinf_3by2 = f37
+asinf_5by2 = f38
+asinf_coeff_P3 = f39
+asinf_coeff_P8 = f40
+
+asinf_coeff_P1 = f41
+asinf_coeff_P4 = f42
+asinf_coeff_P5 = f43
+asinf_coeff_P2 = f44
+asinf_coeff_P7 = f45
+
+asinf_coeff_P6 = f46
+asinf_coeff_P9 = f47
+asinf_x2 = f48
+asinf_x3 = f49
+asinf_x4 = f50
+
+asinf_x8 = f51
+asinf_x5 = f52
+asinf_const_piby2 = f53
+asinf_const_sqrt2by2 = f54
+asinf_x11 = f55
+
+asinf_poly_p1 = f56
+asinf_poly_p3 = f57
+asinf_sinf1 = f58
+asinf_poly_p2 = f59
+asinf_poly_Ax = f60
+
+asinf_poly_p7 = f61
+asinf_poly_p5 = f62
+asinf_sgnx_t4 = f63
+asinf_poly_Bx = f64
+asinf_t = f65
+
+asinf_yby2 = f66
+asinf_B = f67
+asinf_B2 = f68
+asinf_Az = f69
+asinf_dz = f70
+
+asinf_Sz = f71
+asinf_d2z = f72
+asinf_Fz = f73
+asinf_z = f74
+asinf_sgnx_z = f75
+
+asinf_t2 = f76
+asinf_2poly_p4 = f77
+asinf_2poly_p6 = f78
+asinf_2poly_p1 = f79
+asinf_2poly_p2 = f80
+
+asinf_2poly_p8 = f81
+asinf_t4 = f82
+asinf_Pt = f83
+asinf_sgnx_2poly_p2 = f84
+asinf_sgn_x_piby2 = f85
+
+asinf_poly_p7a = f86
+asinf_2poly_p4a = f87
+asinf_2poly_p4b = f88
+asinf_2poly_p2a = f89
+asinf_poly_p1a = f90
+
+
+
+
+
+// Data tables
+//==============================================================
+
+RODATA
+
+.align 16
+
+LOCAL_OBJECT_START(asinf_coeff_1_table)
+data8 0x3FC5555607DCF816 // P1
+data8 0x3F9CF81AD9BAB2C6 // P4
+data8 0x3FC59E0975074DF3 // P7
+data8 0xBFA6F4CC2780AA1D // P6
+data8 0x3FC2DD45292E93CB // P9
+data8 0x3fe6a09e667f3bcd // sqrt(2)/2
+LOCAL_OBJECT_END(asinf_coeff_1_table)
+
+LOCAL_OBJECT_START(asinf_coeff_2_table)
+data8 0x3FA6F108E31EFBA6 // P3
+data8 0xBFCA31BF175D82A0 // P8
+data8 0x3FA30C0337F6418B // P5
+data8 0x3FB332C9266CB1F9 // P2
+data8 0x3ff921fb54442d18 // pi_by_2
+LOCAL_OBJECT_END(asinf_coeff_2_table)
+
+
+.section .text
+GLOBAL_LIBM_ENTRY(asinf)
+
+// Load the addresses of the two tables.
+// Then, load the coefficients and other constants.
+
+{ .mfi
+ alloc r32 = ar.pfs,1,8,4,0
+ fnma.s1 asinf_t = f8,f8,f1
+ dep.z ASINF_GR_1by2 = 0x3f,24,8 // 0x3f000000
+}
+{ .mfi
+ addl ASINF_Addr1 = @ltoff(asinf_coeff_1_table),gp
+ fma.s1 asinf_x2 = f8,f8,f0
+ addl ASINF_Addr2 = @ltoff(asinf_coeff_2_table),gp ;;
+}
+
+
+{ .mfi
+ ld8 ASINF_Addr1 = [ASINF_Addr1]
+ fmerge.s asinf_abs_x = f1,f8
+ dep ASINF_GR_3by2 = -1,r0,22,8 // 0x3fc00000
+}
+{ .mlx
+ nop.m 999
+ movl ASINF_GR_5by2 = 0x40200000;;
+}
+
+
+
+{ .mfi
+ setf.s asinf_1by2 = ASINF_GR_1by2
+ fmerge.s asinf_sgn_x = f8,f1
+ nop.i 999
+}
+{ .mfi
+ ld8 ASINF_Addr2 = [ASINF_Addr2]
+ nop.f 0
+ nop.i 999;;
+}
+
+
+{ .mfi
+ setf.s asinf_5by2 = ASINF_GR_5by2
+ fcmp.lt.s1 p11,p12 = f8,f0
+ nop.i 999;;
+}
+
+{ .mmf
+ ldfpd asinf_coeff_P1,asinf_coeff_P4 = [ASINF_Addr1],16
+ setf.s asinf_3by2 = ASINF_GR_3by2
+ fclass.m.unc p8,p0 = f8, 0xc3 ;; //@qnan | @snan
+}
+
+
+{ .mfi
+ ldfpd asinf_coeff_P7,asinf_coeff_P6 = [ASINF_Addr1],16
+ fma.s1 asinf_t2 = asinf_t,asinf_t,f0
+ nop.i 999
+}
+{ .mfi
+ ldfpd asinf_coeff_P3,asinf_coeff_P8 = [ASINF_Addr2],16
+ fma.s1 asinf_x4 = asinf_x2,asinf_x2,f0
+ nop.i 999;;
+}
+
+
+{ .mfi
+ ldfpd asinf_coeff_P9,asinf_const_sqrt2by2 = [ASINF_Addr1]
+ fclass.m.unc p10,p0 = f8, 0x07 //@zero
+ nop.i 999
+}
+{ .mfi
+ ldfpd asinf_coeff_P5,asinf_coeff_P2 = [ASINF_Addr2],16
+ fma.s1 asinf_x3 = f8,asinf_x2,f0
+ nop.i 999;;
+}
+
+
+{ .mfi
+ ldfd asinf_const_piby2 = [ASINF_Addr2]
+ frsqrta.s1 asinf_B,p0 = asinf_t
+ nop.i 999
+}
+{ .mfb
+ nop.m 999
+(p8) fma.s.s0 f8 = f8,f1,f0
+(p8) br.ret.spnt b0 ;; // Exit if x=nan
+}
+
+
+{ .mfb
+ nop.m 999
+ fcmp.eq.s1 p6,p0 = asinf_abs_x,f1
+(p10) br.ret.spnt b0 ;; // Exit if x=0
+}
+
+{ .mfi
+ nop.m 999
+ fcmp.gt.s1 p9,p0 = asinf_abs_x,f1
+ nop.i 999;;
+}
+
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_x8 = asinf_x4,asinf_x4,f0
+ nop.i 999
+}
+{ .mfb
+ nop.m 999
+ fma.s1 asinf_t4 = asinf_t2,asinf_t2,f0
+(p6) br.cond.spnt ASINF_ABS_ONE ;; // Branch if |x|=1
+}
+
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_x5 = asinf_x2,asinf_x3,f0
+ nop.i 999
+}
+{ .mfb
+(p9) mov GR_Parameter_TAG = 62
+ fma.s1 asinf_yby2 = asinf_t,asinf_1by2,f0
+(p9) br.cond.spnt __libm_error_region ;; // Branch if |x|>1
+}
+
+
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_Az = asinf_t,asinf_B,f0
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_B2 = asinf_B,asinf_B,f0
+ nop.i 999;;
+}
+
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_poly_p1 = f8,asinf_coeff_P1,f0
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_2poly_p1 = asinf_coeff_P1,asinf_t,f1
+ nop.i 999;;
+}
+
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_poly_p3 = asinf_coeff_P4,asinf_x2,asinf_coeff_P3
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_2poly_p6 = asinf_coeff_P7,asinf_t,asinf_coeff_P6
+ nop.i 999;;
+}
+
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_poly_p7 = asinf_x2,asinf_coeff_P8,asinf_coeff_P7
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_2poly_p2 = asinf_coeff_P3,asinf_t,asinf_coeff_P2
+ nop.i 999;;
+}
+
+
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_poly_p5 = asinf_x2,asinf_coeff_P6,asinf_coeff_P5
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_2poly_p4 = asinf_coeff_P5,asinf_t,asinf_coeff_P4
+ nop.i 999;;
+}
+
+
+{ .mfi
+ nop.m 999
+ fma.d.s1 asinf_x11 = asinf_x8,asinf_x3,f0
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+ fnma.s1 asinf_dz = asinf_B2,asinf_yby2,asinf_1by2
+ nop.i 999;;
+}
+
+
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_poly_p1a = asinf_x2,asinf_poly_p1,f8
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_2poly_p8 = asinf_coeff_P9,asinf_t,asinf_coeff_P8
+ nop.i 999;;
+}
+
+
+// Get the absolute value of x and determine the region in which x lies
+
+{ .mfi
+ nop.m 999
+ fcmp.le.s1 p7,p8 = asinf_abs_x,asinf_const_sqrt2by2
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_poly_p2 = asinf_x2,asinf_poly_p3,asinf_coeff_P2
+ nop.i 999;;
+}
+
+
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_poly_p7a = asinf_x4,asinf_coeff_P9,asinf_poly_p7
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+ fma.s1 asinf_2poly_p2a = asinf_2poly_p2,asinf_t2,asinf_2poly_p1
+ nop.i 999;;
+}
+
+
+{ .mfi
+ nop.m 999
+(p8) fma.s1 asinf_sgnx_t4 = asinf_sgn_x,asinf_t4,f0
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p8) fma.s1 asinf_2poly_p4a = asinf_2poly_p6,asinf_t2,asinf_2poly_p4
+ nop.i 999;;
+}
+
+
+{ .mfi
+ nop.m 999
+(p8) fma.s1 asinf_Sz = asinf_5by2,asinf_dz,asinf_3by2
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p8) fma.s1 asinf_d2z = asinf_dz,asinf_dz,f0
+ nop.i 999;;
+}
+
+
+{ .mfi
+ nop.m 999
+(p8) fma.s1 asinf_sgn_x_piby2 = asinf_sgn_x,asinf_const_piby2,f0
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p7) fma.d.s1 asinf_poly_Ax = asinf_x5,asinf_poly_p2,asinf_poly_p1a
+ nop.i 999;;
+}
+
+{ .mfi
+ nop.m 999
+(p7) fma.d.s1 asinf_poly_Bx = asinf_x4,asinf_poly_p7a,asinf_poly_p5
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p8) fma.s1 asinf_sgnx_2poly_p2 = asinf_sgn_x,asinf_2poly_p2a,f0
+ nop.i 999;;
+}
+
+{ .mfi
+ nop.m 999
+ fcmp.eq.s0 p6,p0 = f8,f0 // Only purpose is to set D if x denormal
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p8) fma.s1 asinf_2poly_p4b = asinf_2poly_p8,asinf_t4,asinf_2poly_p4a
+ nop.i 999;;
+}
+
+
+{ .mfi
+ nop.m 999
+(p8) fma.s1 asinf_Fz = asinf_d2z,asinf_Sz,asinf_dz
+ nop.i 999;;
+}
+
+
+{ .mfi
+ nop.m 999
+(p8) fma.d.s1 asinf_Pt = asinf_2poly_p4b,asinf_sgnx_t4,asinf_sgnx_2poly_p2
+ nop.i 999;;
+}
+
+{ .mfi
+ nop.m 999
+(p8) fma.d.s1 asinf_z = asinf_Az,asinf_Fz,asinf_Az
+ nop.i 999;;
+}
+
+.pred.rel "mutex",p8,p7 //asinf_pred_GTsqrt2by2,asinf_pred_LEsqrt2by2
+{ .mfi
+ nop.m 999
+(p8) fnma.s.s0 f8 = asinf_z,asinf_Pt,asinf_sgn_x_piby2
+ nop.i 999
+}
+
+{ .mfb
+ nop.m 999
+(p7) fma.s.s0 f8 = asinf_x11,asinf_poly_Bx,asinf_poly_Ax
+ br.ret.sptk b0 ;;
+}
+
+ASINF_ABS_ONE:
+// Here for short exit if |x|=1
+{ .mfb
+ nop.m 999
+ fma.s.s0 f8 = asinf_sgn_x,asinf_const_piby2,f0
+ br.ret.sptk b0
+}
+;;
+
+GLOBAL_LIBM_END(asinf)
+
+// Stack operations when calling error support.
+// (1) (2)
+// sp -> + psp -> +
+// | |
+// | | <- GR_Y
+// | |
+// | <-GR_Y Y2->|
+// | |
+// | | <- GR_X
+// | |
+// sp-64 -> + sp -> +
+// save ar.pfs save b0
+// save gp
+
+
+// Stack operations when calling error support.
+// (3) (call) (4)
+// psp -> + sp -> +
+// | |
+// R3 ->| <- GR_RESULT | -> f8
+// | |
+// Y2 ->| <- GR_Y |
+// | |
+// X1 ->| |
+// | |
+// sp -> + +
+// restore gp
+// restore ar.pfs
+
+LOCAL_LIBM_ENTRY(__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
+{ .mfi
+ nop.m 0
+ frcpa.s0 f9,p0 = f0,f0
+ nop.i 0
+};;
+
+{ .mib
+ stfs [GR_Parameter_X] = f8 // Store Parameter 1 on stack
+ add GR_Parameter_RESULT = 0,GR_Parameter_Y
+ nop.b 0 // Parameter 3 address
+}
+{ .mib
+ stfs [GR_Parameter_Y] = f9 // Store Parameter 3 on stack
+ add GR_Parameter_Y = -16,GR_Parameter_Y
+ br.call.sptk b0=__libm_error_support# // Call error handling function
+};;
+{ .mmi
+ nop.m 0
+ nop.m 0
+ add GR_Parameter_RESULT = 48,sp
+};;
+
+{ .mmi
+ ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
+.restore sp
+ 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
+};;
+
+LOCAL_LIBM_END(__libm_error_region)
+
+.type __libm_error_support#,@function
+.global __libm_error_support#
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