You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
251 lines
6.8 KiB
251 lines
6.8 KiB
.file "sqrtf.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.
|
|
//
|
|
// WARRANTY DISCLAIMER
|
|
//
|
|
// 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 Initial version
|
|
// 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 sqrtf(x), where
|
|
// _
|
|
// sqrtf(x) = |x, for single 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.
|
|
// sqrtf(QNaN) = QNaN
|
|
// sqrtf(SNaN) = QNaN
|
|
// sqrtf(+/-0) = +/-0
|
|
// sqrtf(negative) = QNaN and error handling is called
|
|
//
|
|
//********************************************************************
|
|
//
|
|
// Implementation:
|
|
//
|
|
// Modified Newton-Raphson Algorithm
|
|
//
|
|
//********************************************************************
|
|
|
|
|
|
GR_SAVE_B0 = r34
|
|
GR_SAVE_PFS = r33
|
|
GR_SAVE_GP = r35
|
|
|
|
GR_Parameter_X = r37
|
|
GR_Parameter_Y = r38
|
|
GR_Parameter_RESULT = r39
|
|
GR_Parameter_TAG = r40
|
|
|
|
FR_X = f13
|
|
FR_Y = f0
|
|
FR_RESULT = f8
|
|
|
|
|
|
|
|
.section .text
|
|
.proc sqrtf#
|
|
.global sqrtf#
|
|
.align 64
|
|
|
|
sqrtf:
|
|
{ .mlx
|
|
// BEGIN SINGLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM
|
|
alloc r32= ar.pfs,0,5,4,0
|
|
// exponent of +1/2 in r2
|
|
movl r2 = 0x0fffe
|
|
} { .mfi
|
|
// +1/2 in f12
|
|
nop.m 0
|
|
frsqrta.s0 f7,p6=f8
|
|
nop.i 0;;
|
|
} { .mfi
|
|
setf.exp f12 = r2
|
|
// Step (1)
|
|
// y0 = 1/sqrt(a) in f7
|
|
fclass.m.unc p7,p8 = f8,0x3A
|
|
nop.i 0
|
|
} { .mfi
|
|
nop.m 0
|
|
// Make a copy of x just in case
|
|
mov f13 = 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
|
|
// Step (4)
|
|
// d = 1/2 - S0 * H0 in f10
|
|
(p6) fnma.s1 f10=f7,f9,f12
|
|
nop.i 0
|
|
} { .mfi
|
|
nop.m 0
|
|
// Step (0'')
|
|
// 3/2 = 1 + 1/2 in f12
|
|
(p6) fma.s1 f12=f12,f1,f1
|
|
nop.i 0;;
|
|
} { .mfi
|
|
nop.m 0
|
|
// Step (5)
|
|
// e = 1 + 3/2 * d in f12
|
|
(p6) fma.s1 f12=f12,f10,f1
|
|
nop.i 0
|
|
} { .mfi
|
|
nop.m 0
|
|
// Step (6)
|
|
// T0 = d * S0 in f11
|
|
(p6) fma.s1 f11=f10,f7,f0
|
|
nop.i 0;;
|
|
} { .mfi
|
|
nop.m 0
|
|
// Step (7)
|
|
// G0 = d * H0 in f10
|
|
(p6) fma.s1 f10=f10,f9,f0
|
|
nop.i 0;;
|
|
} { .mfi
|
|
nop.m 0
|
|
// Step (8)
|
|
// S1 = S0 + e * T0 in f7
|
|
(p6) fma.s.s1 f7=f12,f11,f7
|
|
nop.i 0;;
|
|
} { .mfi
|
|
nop.m 0
|
|
// Step (9)
|
|
// H1 = H0 + e * G0 in f12
|
|
(p6) fma.s1 f12=f12,f10,f9
|
|
nop.i 0;;
|
|
} { .mfi
|
|
nop.m 0
|
|
// Step (10)
|
|
// d1 = a - S1 * S1 in f9
|
|
(p6) fnma.s1 f9=f7,f7,f8
|
|
nop.i 0;;;
|
|
} { .mfb
|
|
nop.m 0
|
|
// Step (11)
|
|
// S = S1 + d1 * H1 in f7
|
|
(p6) fma.s.s0 f8=f9,f12,f7
|
|
(p6) br.ret.sptk b0 ;;
|
|
// END SINGLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM
|
|
} { .mfb
|
|
nop.m 0
|
|
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)
|
|
//
|
|
.endp sqrtf
|
|
|
|
|
|
.proc __libm_error_region
|
|
__libm_error_region:
|
|
.prologue
|
|
{ .mii
|
|
add GR_Parameter_Y=-32,sp // Parameter 2 value
|
|
mov GR_Parameter_TAG = 50
|
|
.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
|
|
stfs [GR_Parameter_Y] = FR_Y,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
|
|
{ .mib
|
|
stfs [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
|
|
stfs [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
|
|
ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
|
|
.restore
|
|
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
|
|
|
|
|
|
.type __libm_error_support#,@function
|
|
.global __libm_error_support#
|