.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#