.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          = r33GR_SAVE_B0           = r34GR_SAVE_GP           = r35GR_Parameter_X       = r37GR_Parameter_Y       = r38GR_Parameter_RESULT  = r39.section .textGLOBAL_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 ALGORITHMGLOBAL_IEEE754_END(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.pfsLOCAL_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#