.file "sqrtl.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 (hand-optimized)

// 04/04/00 Unwind support added

// 08/15/00 Bundle added after call to __libm_error_support to properly

//          set [the previously overwritten] GR_Parameter_RESULT.

// 05/20/02 Cleaned up namespace and sf0 syntax

// 02/10/03 Reordered header: .section, .global, .proc, .align

//

//********************************************************************

//

// Function:   Combined sqrtl(x), where

//                         _

//             sqrtl(x) = |x, for double-extended precision x values

//

//********************************************************************

//

// Resources Used:

//

//    Floating-Point Registers: f8  (Input and Return Value)

//                              f7 -f14

//

//    General Purpose Registers:

//      r32-r36 (Locals)

//      r37-r40 (Used to pass arguments to error handling routine)

//

//    Predicate Registers:      p6, p7, p8

//

//********************************************************************

//

// IEEE Special Conditions:

//

//    All faults and exceptions should be raised correctly.

//    sqrtl(QNaN) = QNaN

//    sqrtl(SNaN) = QNaN

//    sqrtl(+/-0) = +/-0

//    sqrtl(negative) = QNaN and error handling is called

//

//********************************************************************

//

// Implementation:

//

//  Modified Newton-Raphson Algorithm

//

//********************************************************************

GR_SAVE_PFS         = r33

GR_SAVE_B0          = r34

GR_SAVE_GP          = r35

GR_Parameter_X      = r37

GR_Parameter_Y      = r38

GR_Parameter_RESULT = r39

GR_Parameter_TAG    = r40

FR_X                = f15

FR_Y                = f0

FR_RESULT           = f8

.section .text

GLOBAL_IEEE754_ENTRY(sqrtl)

{ .mlx

alloc r32= ar.pfs,0,5,4,0

  // exponent of +1/2 in r2

  movl r2 = 0x0fffe;;

} { .mfi

  // +1/2 in f10

  setf.exp f12 = r2

  // Step (1)

  // y0 = 1/sqrt(a) in f7

  frsqrta.s0 f7,p6=f8

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (2)

  // H0 = +1/2 * y0 in f9

  (p6) fma.s1 f9=f12,f7,f0

  nop.i 0

} { .mfi

  nop.m 0

  // Step (3)

  // S0 = a * y0 in f7

  (p6) fma.s1 f7=f8,f7,f0

  nop.i 0;;

} { .mfi

  nop.m 0

  // Make copy input x

  mov f13=f8

  nop.i 0

} { .mfi

  nop.m 0

  fclass.m.unc p7,p8 = f8,0x3A

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (4)

  // d0 = 1/2 - S0 * H0 in f10

  (p6) fnma.s1 f10=f7,f9,f12

  nop.i 0;;

}

{ .mfi

  nop.m 0

       mov f15=f8

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (5)

  // H1 = H0 + d0 * H0 in f9

  (p6) fma.s1 f9=f10,f9,f9

  nop.i 0

} { .mfi

  nop.m 0

  // Step (6)

  // S1 = S0 + d0 * S0 in f7

  (p6) fma.s1 f7=f10,f7,f7

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (7)

  // d1 = 1/2 - S1 * H1 in f10

  (p6) fnma.s1 f10=f7,f9,f12

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (8)

  // H2 = H1 + d1 * H1 in f9

  (p6) fma.s1 f9=f10,f9,f9

  nop.i 0

} { .mfi

  nop.m 0

  // Step (9)

  // S2 = S1 + d1 * S1 in f7

  (p6) fma.s1 f7=f10,f7,f7

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (10)

  // d2 = 1/2 - S2 * H2 in f10

  (p6) fnma.s1 f10=f7,f9,f12

  nop.i 0

} { .mfi

  nop.m 0

  // Step (11)

  // e2 = a - S2 * S2 in f12

  (p6) fnma.s1 f12=f7,f7,f8

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (12)

  // S3 = S2 + d2 * S2 in f7

  (p6) fma.s1 f7=f12,f9,f7

  nop.i 0

} { .mfi

  nop.m 0

  // Step (13)

  // H3 = H2 + d2 * H2 in f9

  (p6) fma.s1 f9=f10,f9,f9

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (14)

  // e3 = a - S3 * S3 in f12

  (p6) fnma.s1 f12=f7,f7,f8

  nop.i 0;;

} { .mfb

  nop.m 0

  // Step (15)

  // S = S3 + e3 * H3 in f7

  (p6) fma.s0 f8=f12,f9,f7

  (p6) br.ret.sptk b0 ;;

}

{ .mfb

       mov GR_Parameter_TAG    = 48

       mov   f8 = f7

  (p8) br.ret.sptk b0 ;;

}

//

// This branch includes all those special values that are not negative,

// with the result equal to frcpa(x)

//

// END DOUBLE EXTENDED PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM

GLOBAL_IEEE754_END(sqrtl)

libm_alias_ldouble_other (__sqrt, sqrt)

LOCAL_LIBM_ENTRY(__libm_error_region)

.prologue

{ .mfi

        add   GR_Parameter_Y=-32,sp             // Parameter 2 value

        nop.f 0

.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

        stfe [GR_Parameter_Y] = FR_Y,16         // Save 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

{ .mib

        stfe [GR_Parameter_X] = FR_X            // Store Parameter 1 on stack

        add   GR_Parameter_RESULT = 0,GR_Parameter_Y

        nop.b 0                                 // Parameter 3 address

}

{ .mib

        stfe [GR_Parameter_Y] = FR_RESULT      // 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

        ldfe  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#