.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#