.file "sqrt.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

// 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.

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

//

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

//

// Function:   Combined sqrt(x), where

//                        _

//             sqrt(x) = |x, for double precision x values

//

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

//

// Accuracy:       Correctly Rounded

//

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

//

// 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.

//    sqrt(QNaN) = QNaN

//    sqrt(SNaN) = QNaN

//    sqrt(+/-0) = +/-0

//    sqrt(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

.section .text

GLOBAL_IEEE754_ENTRY(sqrt)

{ .mfi

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

  frsqrta.s0 f7,p6=f8

  nop.i 0

} { .mlx

  // BEGIN DOUBLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM

  nop.m 0

  // exponent of +1/2 in r2

  movl r2 = 0x0fffe;;

} { .mmi

  // +1/2 in f9

  setf.exp f9 = r2

  nop.m 0

  nop.i 0

} { .mlx

  nop.m 0

  // 3/2 in r3

  movl r3=0x3fc00000;;

} { .mfi

  setf.s f10=r3

  // Step (1)

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

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

  nop.i 0;;

} { .mlx

  nop.m 0

  // 5/2 in r2

  movl r2 = 0x40200000

} { .mlx

  nop.m 0

  // 63/8 in r3

  movl r3 = 0x40fc0000;;

} { .mfi

  setf.s f11=r2

  // Step (2)

  // h = +1/2 * y0 in f6

  (p6) fma.s1 f6=f9,f7,f0

  nop.i 0

} { .mfi

  setf.s f12=r3

  // Step (3)

  // g = a * y0 in f7

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

  nop.i 0

} { .mfi

  nop.m 0

  mov   f15 = f8

  nop.i 0;;

} { .mlx

  nop.m 0

  // 231/16 in r2

  movl r2 = 0x41670000;;

} { .mfi

  setf.s f13=r2

  // Step (4)

  // e = 1/2 - g * h in f9

  (p6) fnma.s1 f9=f7,f6,f9

  nop.i 0

} { .mlx

  nop.m 0

  // 35/8 in r3

  movl r3 = 0x408c0000;;

} { .mfi

  setf.s f14=r3

  // Step (5)

  // S = 3/2 + 5/2 * e in f10

  (p6) fma.s1 f10=f11,f9,f10

  nop.i 0

} { .mfi

  nop.m 0

  // Step (6)

  // e2 = e * e in f11

  (p6) fma.s1 f11=f9,f9,f0

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (7)

  // t = 63/8 + 231/16 * e in f12

  (p6) fma.s1 f12=f13,f9,f12

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (8)

  // S1 = e + e2 * S in f10

  (p6) fma.s1 f10=f11,f10,f9

  nop.i 0

} { .mfi

  nop.m 0

  // Step (9)

  // e4 = e2 * e2 in f11

  (p6) fma.s1 f11=f11,f11,f0

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (10)

  // t1 = 35/8 + e * t in f9

  (p6) fma.s1 f9=f9,f12,f14

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (11)

  // G = g + S1 * g in f12

  (p6) fma.s1 f12=f10,f7,f7

  nop.i 0

} { .mfi

  nop.m 0

  // Step (12)

  // E = g * e4 in f7

  (p6) fma.s1 f7=f7,f11,f0

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (13)

  // u = S1 + e4 * t1 in f10

  (p6) fma.s1 f10=f11,f9,f10

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (14)

  // g1 = G + t1 * E in f7

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

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (15)

  // h1 = h + u * h in f6

  (p6) fma.s1 f6=f10,f6,f6

  nop.i 0;;

} { .mfi

  nop.m 0

  // Step (16)

  // d = a - g1 * g1 in f9

  (p6) fnma.s1 f9=f7,f7,f8

  nop.i 0;;

} { .mfb

  nop.m 0

  // Step (17)

  // g2 = g1 + d * h1 in f7

  (p6) fma.d.s0 f8=f9,f6,f7

  (p6) br.ret.sptk b0 ;;

}

{ .mfb

  nop.m 0

       mov   f8 = f7

  (p8) br.ret.sptk b0 ;;

}

{ .mfb

  (p7) mov   r40 = 49

  nop.f 0

  (p7) br.cond.sptk __libm_error_region ;;

}

// END DOUBLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM

GLOBAL_IEEE754_END(sqrt)

libm_alias_double_other (__sqrt, sqrt)

// Stack operations when calling error support.

//       (1)               (2)                          (3) (call)              (4)

//   sp   -> +          psp -> +                     psp -> +                   sp -> +

//           |                 |                            |                         |

//           |                 | <- GR_Y               R3 ->| <- GR_RESULT            | -> f8

//           |                 |                            |                         |

//           | <-GR_Y      Y2->|                       Y2 ->| <- GR_Y                 |

//           |                 |                            |                         |

//           |                 | <- GR_X               X1 ->|                         |

//           |                 |                            |                         |

//  sp-64 -> +          sp ->  +                     sp ->  +                         +

//    save ar.pfs          save b0                                               restore gp

//    save gp                                                                    restore ar.pfs

LOCAL_LIBM_ENTRY(__libm_error_region)

//

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

// with the result equal to frcpa(x)

//

.prologue

// We are distinguishing between over(under)flow and letting

// __libm_error_support set ERANGE or do anything else needed.

// (1)

{ .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

};;

// (2)

{ .mmi

        stfd [GR_Parameter_Y] = f0,16         // 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

// (3)

{ .mib

        stfd [GR_Parameter_X] = f15                    // STORE Parameter 1 on stack

        add   GR_Parameter_RESULT = 0,GR_Parameter_Y   // Parameter 3 address

        nop.b 0

}

{ .mib

        stfd [GR_Parameter_Y] = f8                     // 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

};;

// (4)

{ .mmi

        ldfd  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#