glibc/sysdeps/ia64/fpu/e_sqrtl.S

.file "sqrtl.s"

// Copyright (C) 2000, 2001, 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.
//
// 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://developer.intel.com/opensource.
//
// ********************************************************************
//
// History:
// 2/02/00 (hand-optimized)
// 4/04/00  Unwind support added
// 8/15/00  Bundle added after call to __libm_error_support to properly
//          set [the previously overwritten] GR_Parameter_RESULT.
//
// ********************************************************************
//
// 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
//
// ********************************************************************

#include "libm_support.h"

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
.proc sqrtl#
.global sqrtl#
.align 64

sqrtl:
#ifdef _LIBC
.global __sqrtl
.type __sqrtl,@function
__sqrtl:
.global __ieee754_sqrtl
.type __ieee754_sqrtl,@function
__ieee754_sqrtl:
#endif
{ .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
  (p0) 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
  (p0) mov GR_Parameter_TAG    = 48
  (p0) 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
.endp sqrtl#
ASM_SIZE_DIRECTIVE(sqrtl)
#ifdef _LIBC
ASM_SIZE_DIRECTIVE(__sqrtl)
ASM_SIZE_DIRECTIVE(__ieee754_sqrtl)
#endif

.proc __libm_error_region
__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
};;

.endp __libm_error_region
ASM_SIZE_DIRECTIVE(__libm_error_region)
.type   __libm_error_support#,@function
.global __libm_error_support#