|
|
.file "asinf.s"
// Copyright (c) 2000, Intel Corporation// All rights reserved.//// Contributed 2/02/2000 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. // 8/08/00 Improved speed by avoiding SIR flush.// 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 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 registersASINF_Addr1 = r33ASINF_Addr2 = r34ASINF_GR_1by2 = r35
ASINF_GR_3by2 = r36ASINF_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
asinf_y = f32asinf_abs_x = f33asinf_x2 = f34asinf_sgn_x = f35
asinf_1by2 = f36asinf_3by2 = f37asinf_5by2 = f38asinf_coeff_P3 = f39asinf_coeff_P8 = f40
asinf_coeff_P1 = f41asinf_coeff_P4 = f42asinf_coeff_P5 = f43asinf_coeff_P2 = f44asinf_coeff_P7 = f45
asinf_coeff_P6 = f46asinf_coeff_P9 = f47asinf_x2 = f48asinf_x3 = f49asinf_x4 = f50
asinf_x8 = f51asinf_x5 = f52asinf_const_piby2 = f53asinf_const_sqrt2by2 = f54asinf_x11 = f55
asinf_poly_p1 = f56asinf_poly_p3 = f57asinf_sinf1 = f58asinf_poly_p2 = f59asinf_poly_Ax = f60
asinf_poly_p7 = f61asinf_poly_p5 = f62asinf_sgnx_t4 = f63asinf_poly_Bx = f64asinf_t = f65
asinf_yby2 = f66asinf_B = f67asinf_B2 = f68asinf_Az = f69asinf_dz = f70
asinf_Sz = f71asinf_d2z = f72asinf_Fz = f73asinf_z = f74asinf_sgnx_z = f75
asinf_t2 = f76asinf_2poly_p4 = f77asinf_2poly_p6 = f78asinf_2poly_p1 = f79asinf_2poly_p2 = f80
asinf_2poly_p8 = f81asinf_t4 = f82asinf_Pt = f83asinf_sgnx_2poly_p2 = f84asinf_sgn_x_piby2 = f85
asinf_poly_p7a = f86asinf_2poly_p4a = f87asinf_2poly_p4b = f88asinf_2poly_p2a = f89asinf_poly_p1a = f90
// Data tables//==============================================================
.data
.align 16
asinf_coeff_1_table:data8 0x3FC5555607DCF816 // P1data8 0x3F9CF81AD9BAB2C6 // P4data8 0x3FC59E0975074DF3 // P7data8 0xBFA6F4CC2780AA1D // P6data8 0x3FC2DD45292E93CB // P9data8 0x3fe6a09e667f3bcd // sqrt(2)/2
asinf_coeff_2_table:data8 0x3FA6F108E31EFBA6 // P3data8 0xBFCA31BF175D82A0 // P8data8 0x3FA30C0337F6418B // P5data8 0x3FB332C9266CB1F9 // P2data8 0x3ff921fb54442d18 // pi_by_2
.align 32.global asinf
.section .text.proc asinf.align 32
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 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 f8 = asinf_z,asinf_Pt,asinf_sgn_x_piby2 nop.i 999} { .mfb nop.m 999(p7) fma.s 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 f8 = asinf_sgn_x,asinf_const_piby2,f0 br.ret.sptk b0} ;;
.endp 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
.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#
|
