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.file "acosf.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 revision// 6/28/00 Improved speed// 6/31/00 Changed register allocation because of some duplicate macros// moved nan exit bundle up to gain a cycle.// 8/15/00 Bundle added after call to __libm_error_support to properly// set [the previously overwritten] GR_Parameter_RESULT.// 8/17/00 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.
// Description//=========================================// The acosf function computes the principle value of the arc sine of x.// A doman error occurs for arguments not in the range [-1,+1].
// The acosf function returns the arc cosine in the range [0, +pi] radians.// acos(1) returns +0// acos(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 + (x2 p8 + p7)// poly_Bx = x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5
// sinf1 = 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// answer1 = pi/2 - sinf1
// |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) if x>0// = sign(x) z P(t) + pi if x<0
//// Assembly macros//=========================================
// predicate registers//acosf_pred_LEsqrt2by2 = p7//acosf_pred_GTsqrt2by2 = p8
// integer registersACOSF_Addr1 = r33ACOSF_Addr2 = r34ACOSF_GR_1by2 = r35
ACOSF_GR_3by2 = r36ACOSF_GR_5by2 = r37
GR_SAVE_B0 = r38GR_SAVE_PFS = r39GR_SAVE_GP = r40
GR_Parameter_X = r41GR_Parameter_Y = r42GR_Parameter_RESULT = r43GR_Parameter_TAG = r44
// floating point registers
acosf_y = f32acosf_abs_x = f33acosf_x2 = f34acosf_sgn_x = f35
acosf_1by2 = f36acosf_3by2 = f37acosf_5by2 = f38acosf_coeff_P3 = f39acosf_coeff_P8 = f40
acosf_coeff_P1 = f41acosf_coeff_P4 = f42acosf_coeff_P5 = f43acosf_coeff_P2 = f44acosf_coeff_P7 = f45
acosf_coeff_P6 = f46acosf_coeff_P9 = f47acosf_x2 = f48acosf_x3 = f49acosf_x4 = f50
acosf_x8 = f51acosf_x5 = f52acosf_const_piby2 = f53acosf_const_sqrt2by2 = f54acosf_x11 = f55
acosf_poly_p1 = f56acosf_poly_p3 = f57acosf_sinf1 = f58acosf_poly_p2 = f59acosf_poly_Ax = f60
acosf_poly_p7 = f61acosf_poly_p5 = f62acosf_sgnx_t4 = f63acosf_poly_Bx = f64acosf_t = f65
acosf_yby2 = f66acosf_B = f67acosf_B2 = f68acosf_Az = f69acosf_dz = f70
acosf_Sz = f71acosf_d2z = f72acosf_Fz = f73acosf_z = f74acosf_sgnx_z = f75
acosf_t2 = f76acosf_2poly_p4 = f77acosf_2poly_p6 = f78acosf_2poly_p1 = f79acosf_2poly_p2 = f80
acosf_2poly_p8 = f81acosf_t4 = f82acosf_Pt = f83acosf_sgnx_2poly_p2 = f84acosf_sgn_x_piby2 = f85
acosf_poly_p7a = f86acosf_2poly_p4a = f87acosf_2poly_p4b = f88acosf_2poly_p2a = f89acosf_poly_p1a = f90
// Data tables//==============================================================
.data
.align 16
acosf_coeff_1_table:data8 0x3FC5555607DCF816 // P1data8 0x3F9CF81AD9BAB2C6 // P4data8 0x3FC59E0975074DF3 // P7data8 0xBFA6F4CC2780AA1D // P6data8 0x3FC2DD45292E93CB // P9data8 0x3fe6a09e667f3bcd // sqrt(2)/2
acosf_coeff_2_table:data8 0x3FA6F108E31EFBA6 // P3data8 0xBFCA31BF175D82A0 // P8data8 0x3FA30C0337F6418B // P5data8 0x3FB332C9266CB1F9 // P2data8 0x3ff921fb54442d18 // pi_by_2
.align 32.global acosf
.section .text.proc acosf.align 32
acosf: // 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 acosf_t = f8,f8,f1 dep.z ACOSF_GR_1by2 = 0x3f,24,8 // 0x3f000000} { .mfi addl ACOSF_Addr1 = @ltoff(acosf_coeff_1_table),gp fma.s1 acosf_x2 = f8,f8,f0 addl ACOSF_Addr2 = @ltoff(acosf_coeff_2_table),gp ;;
}
{ .mfi ld8 ACOSF_Addr1 = [ACOSF_Addr1] fmerge.s acosf_abs_x = f1,f8 dep ACOSF_GR_3by2 = 1,r0,22,8 // 0x3fc00000} { .mlx nop.m 999 movl ACOSF_GR_5by2 = 0x40200000;;
}
{ .mfi setf.s acosf_1by2 = ACOSF_GR_1by2 fmerge.s acosf_sgn_x = f8,f1 nop.i 999} { .mfi ld8 ACOSF_Addr2 = [ACOSF_Addr2] nop.f 0 nop.i 999;;
}
{ .mfi setf.s acosf_5by2 = ACOSF_GR_5by2 fcmp.lt.s1 p11,p12 = f8,f0 nop.i 999;;
}
{ .mmf ldfpd acosf_coeff_P1,acosf_coeff_P4 = [ACOSF_Addr1],16 setf.s acosf_3by2 = ACOSF_GR_3by2 fclass.m.unc p8,p0 = f8, 0xc3 ;; //@qnan | @snan
}
{ .mfi ldfpd acosf_coeff_P7,acosf_coeff_P6 = [ACOSF_Addr1],16 fma.s1 acosf_t2 = acosf_t,acosf_t,f0 nop.i 999} { .mfi ldfpd acosf_coeff_P3,acosf_coeff_P8 = [ACOSF_Addr2],16 fma.s1 acosf_x4 = acosf_x2,acosf_x2,f0 nop.i 999;;
}
{ .mfi ldfpd acosf_coeff_P9,acosf_const_sqrt2by2 = [ACOSF_Addr1] fclass.m.unc p10,p0 = f8, 0x07 //@zero nop.i 999} { .mfi ldfpd acosf_coeff_P5,acosf_coeff_P2 = [ACOSF_Addr2],16 fma.s1 acosf_x3 = f8,acosf_x2,f0 nop.i 999;;
}
{ .mfi ldfd acosf_const_piby2 = [ACOSF_Addr2] frsqrta.s1 acosf_B,p0 = acosf_t nop.i 999} { .mfb nop.m 999(p8) fma.s f8 = f8,f1,f0(p8) br.ret.spnt b0 ;; // Exit if x=nan
}
{ .mfb nop.m 999 fcmp.eq.s1 p6,p0 = acosf_abs_x,f1(p10) br.cond.spnt ACOSF_ZERO ;; // Branch if x=0
} { .mfi nop.m 999 fcmp.gt.s1 p9,p0 = acosf_abs_x,f1 nop.i 999;;
} { .mfi nop.m 999 fma.s1 acosf_x8 = acosf_x4,acosf_x4,f0 nop.i 999} { .mfb nop.m 999 fma.s1 acosf_t4 = acosf_t2,acosf_t2,f0(p6) br.cond.spnt ACOSF_ABS_ONE ;; // Branch if |x|=1
}
{ .mfi nop.m 999 fma.s1 acosf_x5 = acosf_x2,acosf_x3,f0 nop.i 999}{ .mfb (p9) mov GR_Parameter_TAG = 59 fma.s1 acosf_yby2 = acosf_t,acosf_1by2,f0(p9) br.cond.spnt __libm_error_region ;; // Branch if |x|>1
}
{ .mfi nop.m 999 fma.s1 acosf_Az = acosf_t,acosf_B,f0 nop.i 999} { .mfi nop.m 999 fma.s1 acosf_B2 = acosf_B,acosf_B,f0 nop.i 999;;
} { .mfi nop.m 999 fma.s1 acosf_poly_p1 = f8,acosf_coeff_P1,f0 nop.i 999} { .mfi nop.m 999 fma.s1 acosf_2poly_p1 = acosf_coeff_P1,acosf_t,f1 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acosf_poly_p3 = acosf_coeff_P4,acosf_x2,acosf_coeff_P3 nop.i 999} { .mfi nop.m 999 fma.s1 acosf_2poly_p6 = acosf_coeff_P7,acosf_t,acosf_coeff_P6 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acosf_poly_p7 = acosf_x2,acosf_coeff_P8,acosf_coeff_P7 nop.i 999} { .mfi nop.m 999 fma.s1 acosf_2poly_p2 = acosf_coeff_P3,acosf_t,acosf_coeff_P2 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acosf_poly_p5 = acosf_x2,acosf_coeff_P6,acosf_coeff_P5 nop.i 999} { .mfi nop.m 999 fma.s1 acosf_2poly_p4 = acosf_coeff_P5,acosf_t,acosf_coeff_P4 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acosf_x11 = acosf_x8,acosf_x3,f0 nop.i 999} { .mfi nop.m 999 fnma.s1 acosf_dz = acosf_B2,acosf_yby2,acosf_1by2 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acosf_poly_p1a = acosf_x2,acosf_poly_p1,f8 nop.i 999}{ .mfi nop.m 999 fma.s1 acosf_2poly_p8 = acosf_coeff_P9,acosf_t,acosf_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 = acosf_abs_x,acosf_const_sqrt2by2 nop.i 999} { .mfi nop.m 999 fma.s1 acosf_poly_p2 = acosf_x2,acosf_poly_p3,acosf_coeff_P2 nop.i 999;;
}
{ .mfi nop.m 999 fma.s1 acosf_poly_p7a = acosf_x4,acosf_coeff_P9,acosf_poly_p7 nop.i 999} { .mfi nop.m 999 fma.s1 acosf_2poly_p2a = acosf_2poly_p2,acosf_t2,acosf_2poly_p1 nop.i 999;;
}
{ .mfi nop.m 999(p8) fma.s1 acosf_sgnx_t4 = acosf_sgn_x,acosf_t4,f0 nop.i 999} { .mfi nop.m 999(p8) fma.s1 acosf_2poly_p4a = acosf_2poly_p6,acosf_t2,acosf_2poly_p4 nop.i 999;;
}
{ .mfi nop.m 999(p8) fma.s1 acosf_Sz = acosf_5by2,acosf_dz,acosf_3by2 nop.i 999} { .mfi nop.m 999(p8) fma.s1 acosf_d2z = acosf_dz,acosf_dz,f0 nop.i 999;;
}
{ .mfi nop.m 999(p8) fnma.d.s1 acosf_sgn_x_piby2 = acosf_sgn_x,acosf_const_piby2,acosf_const_piby2 nop.i 999} { .mfi nop.m 999(p7) fma.s1 acosf_poly_Ax = acosf_x5,acosf_poly_p2,acosf_poly_p1a nop.i 999;;
} { .mfi nop.m 999(p7) fma.s1 acosf_poly_Bx = acosf_x4,acosf_poly_p7a,acosf_poly_p5 nop.i 999} { .mfi nop.m 999(p8) fma.s1 acosf_sgnx_2poly_p2 = acosf_sgn_x,acosf_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 acosf_2poly_p4b = acosf_2poly_p8,acosf_t4,acosf_2poly_p4a nop.i 999;;
}
{ .mfi nop.m 999(p8) fma.s1 acosf_Fz = acosf_d2z,acosf_Sz,acosf_dz nop.i 999;;
}
{ .mfi nop.m 999(p8) fma.d.s1 acosf_Pt = acosf_2poly_p4b,acosf_sgnx_t4,acosf_sgnx_2poly_p2 nop.i 999;;
} { .mfi nop.m 999(p8) fma.d.s1 acosf_z = acosf_Az,acosf_Fz,acosf_Az nop.i 999 ;;
} { .mfi nop.m 999(p7) fma.d.s1 acosf_sinf1 = acosf_x11,acosf_poly_Bx,acosf_poly_Ax nop.i 999;;
} .pred.rel "mutex",p8,p7 //acosf_pred_GTsqrt2by2,acosf_pred_LEsqrt2by2{ .mfi nop.m 999(p8) fma.s f8 = acosf_z,acosf_Pt,acosf_sgn_x_piby2 nop.i 999} { .mfb nop.m 999(p7) fms.s f8 = acosf_const_piby2,f1,acosf_sinf1 br.ret.sptk b0 ;;
}
ACOSF_ZERO:// Here if x=0{ .mfb nop.m 999 fma.s f8 = acosf_const_piby2,f1,f0 // acosf(0)=pi/2 br.ret.sptk b0 ;;
}
.pred.rel "mutex",p11,p12ACOSF_ABS_ONE:// Here if |x|=1{ .mfi nop.m 999(p11) fma.s f8 = acosf_const_piby2,f1,acosf_const_piby2 // acosf(-1)=pi nop.i 999} { .mfb nop.m 999(p12) fma.s f8 = f1,f0,f0 // acosf(1)=0 br.ret.sptk b0 ;;
}
.endp acosf
// 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
.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{ .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 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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