mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-26 15:00:06 +00:00
30891f35fa
We stopped adding "Contributed by" or similar lines in sources in 2012 in favour of git logs and keeping the Contributors section of the glibc manual up to date. Removing these lines makes the license header a bit more consistent across files and also removes the possibility of error in attribution when license blocks or files are copied across since the contributed-by lines don't actually reflect reality in those cases. Move all "Contributed by" and similar lines (Written by, Test by, etc.) into a new file CONTRIBUTED-BY to retain record of these contributions. These contributors are also mentioned in manual/contrib.texi, so we just maintain this additional record as a courtesy to the earlier developers. The following scripts were used to filter a list of files to edit in place and to clean up the CONTRIBUTED-BY file respectively. These were not added to the glibc sources because they're not expected to be of any use in future given that this is a one time task: https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02 Reviewed-by: Carlos O'Donell <carlos@redhat.com>
879 lines
24 KiB
ArmAsm
879 lines
24 KiB
ArmAsm
.file "acos.s"
|
|
|
|
|
|
// Copyright (c) 2000 - 2003 Intel Corporation
|
|
// All rights reserved.
|
|
//
|
|
//
|
|
// 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
|
|
// 08/17/00 New and much faster algorithm.
|
|
// 08/30/00 Avoided bank conflicts on loads, shortened |x|=1 and x=0 paths,
|
|
// fixed mfb split issue stalls.
|
|
// 05/20/02 Cleaned up namespace and sf0 syntax
|
|
// 08/02/02 New and much faster algorithm II
|
|
// 02/06/03 Reordered header: .section, .global, .proc, .align
|
|
|
|
// Description
|
|
//=========================================
|
|
// The acos function computes the principal value of the arc cosine of x.
|
|
// acos(0) returns Pi/2, acos(1) returns 0, acos(-1) returns Pi.
|
|
// A doman error occurs for arguments not in the range [-1,+1].
|
|
//
|
|
// The acos function returns the arc cosine in the range [0, Pi] radians.
|
|
//
|
|
// There are 8 paths:
|
|
// 1. x = +/-0.0
|
|
// Return acos(x) = Pi/2 + x
|
|
//
|
|
// 2. 0.0 < |x| < 0.625
|
|
// Return acos(x) = Pi/2 - x - x^3 *PolA(x^2)
|
|
// where PolA(x^2) = A3 + A5*x^2 + A7*x^4 +...+ A35*x^32
|
|
//
|
|
// 3. 0.625 <=|x| < 1.0
|
|
// Return acos(x) = Pi/2 - asin(x) =
|
|
// = Pi/2 - sign(x) * ( Pi/2 - sqrt(R) * PolB(R))
|
|
// Where R = 1 - |x|,
|
|
// PolB(R) = B0 + B1*R + B2*R^2 +...+B12*R^12
|
|
//
|
|
// sqrt(R) is approximated using the following sequence:
|
|
// y0 = (1 + eps)/sqrt(R) - initial approximation by frsqrta,
|
|
// |eps| < 2^(-8)
|
|
// Then 3 iterations are used to refine the result:
|
|
// H0 = 0.5*y0
|
|
// S0 = R*y0
|
|
//
|
|
// d0 = 0.5 - H0*S0
|
|
// H1 = H0 + d0*H0
|
|
// S1 = S0 + d0*S0
|
|
//
|
|
// d1 = 0.5 - H1*S1
|
|
// H2 = H1 + d0*H1
|
|
// S2 = S1 + d0*S1
|
|
//
|
|
// d2 = 0.5 - H2*S2
|
|
// S3 = S3 + d2*S3
|
|
//
|
|
// S3 approximates sqrt(R) with enough accuracy for this algorithm
|
|
//
|
|
// So, the result should be reconstracted as follows:
|
|
// acos(x) = Pi/2 - sign(x) * (Pi/2 - S3*PolB(R))
|
|
//
|
|
// But for optimization purposes the reconstruction step is slightly
|
|
// changed:
|
|
// acos(x) = Cpi + sign(x)*PolB(R)*S2 - sign(x)*d2*S2*PolB(R)
|
|
// where Cpi = 0 if x > 0 and Cpi = Pi if x < 0
|
|
//
|
|
// 4. |x| = 1.0
|
|
// Return acos(1.0) = 0.0, acos(-1.0) = Pi
|
|
//
|
|
// 5. 1.0 < |x| <= +INF
|
|
// A doman error occurs for arguments not in the range [-1,+1]
|
|
//
|
|
// 6. x = [S,Q]NaN
|
|
// Return acos(x) = QNaN
|
|
//
|
|
// 7. x is denormal
|
|
// Return acos(x) = Pi/2 - x,
|
|
//
|
|
// 8. x is unnormal
|
|
// Normalize input in f8 and return to the very beginning of the function
|
|
//
|
|
// Registers used
|
|
//==============================================================
|
|
// Floating Point registers used:
|
|
// f8, input, output
|
|
// f6, f7, f9 -> f15, f32 -> f64
|
|
|
|
// General registers used:
|
|
// r3, r21 -> r31, r32 -> r38
|
|
|
|
// Predicate registers used:
|
|
// p0, p6 -> p14
|
|
|
|
//
|
|
// Assembly macros
|
|
//=========================================
|
|
// integer registers used
|
|
// scratch
|
|
rTblAddr = r3
|
|
|
|
rPiBy2Ptr = r21
|
|
rTmpPtr3 = r22
|
|
rDenoBound = r23
|
|
rOne = r24
|
|
rAbsXBits = r25
|
|
rHalf = r26
|
|
r0625 = r27
|
|
rSign = r28
|
|
rXBits = r29
|
|
rTmpPtr2 = r30
|
|
rTmpPtr1 = r31
|
|
|
|
// stacked
|
|
GR_SAVE_PFS = r32
|
|
GR_SAVE_B0 = r33
|
|
GR_SAVE_GP = r34
|
|
GR_Parameter_X = r35
|
|
GR_Parameter_Y = r36
|
|
GR_Parameter_RESULT = r37
|
|
GR_Parameter_TAG = r38
|
|
|
|
// floating point registers used
|
|
FR_X = f10
|
|
FR_Y = f1
|
|
FR_RESULT = f8
|
|
|
|
|
|
// scratch
|
|
fXSqr = f6
|
|
fXCube = f7
|
|
fXQuadr = f9
|
|
f1pX = f10
|
|
f1mX = f11
|
|
f1pXRcp = f12
|
|
f1mXRcp = f13
|
|
fH = f14
|
|
fS = f15
|
|
// stacked
|
|
fA3 = f32
|
|
fB1 = f32
|
|
fA5 = f33
|
|
fB2 = f33
|
|
fA7 = f34
|
|
fPiBy2 = f34
|
|
fA9 = f35
|
|
fA11 = f36
|
|
fB10 = f35
|
|
fB11 = f36
|
|
fA13 = f37
|
|
fA15 = f38
|
|
fB4 = f37
|
|
fB5 = f38
|
|
fA17 = f39
|
|
fA19 = f40
|
|
fB6 = f39
|
|
fB7 = f40
|
|
fA21 = f41
|
|
fA23 = f42
|
|
fB3 = f41
|
|
fB8 = f42
|
|
fA25 = f43
|
|
fA27 = f44
|
|
fB9 = f43
|
|
fB12 = f44
|
|
fA29 = f45
|
|
fA31 = f46
|
|
fA33 = f47
|
|
fA35 = f48
|
|
fBaseP = f49
|
|
fB0 = f50
|
|
fSignedS = f51
|
|
fD = f52
|
|
fHalf = f53
|
|
fR = f54
|
|
fCloseTo1Pol = f55
|
|
fSignX = f56
|
|
fDenoBound = f57
|
|
fNormX = f58
|
|
fX8 = f59
|
|
fRSqr = f60
|
|
fRQuadr = f61
|
|
fR8 = f62
|
|
fX16 = f63
|
|
fCpi = f64
|
|
|
|
// Data tables
|
|
//==============================================================
|
|
RODATA
|
|
.align 16
|
|
LOCAL_OBJECT_START(acos_base_range_table)
|
|
// Ai: Polynomial coefficients for the acos(x), |x| < .625000
|
|
// Bi: Polynomial coefficients for the acos(x), |x| > .625000
|
|
data8 0xBFDAAB56C01AE468 //A29
|
|
data8 0x3FE1C470B76A5B2B //A31
|
|
data8 0xBFDC5FF82A0C4205 //A33
|
|
data8 0x3FC71FD88BFE93F0 //A35
|
|
data8 0xB504F333F9DE6487, 0x00003FFF //B0
|
|
data8 0xAAAAAAAAAAAAFC18, 0x00003FFC //A3
|
|
data8 0x3F9F1C71BC4A7823 //A9
|
|
data8 0x3F96E8BBAAB216B2 //A11
|
|
data8 0x3F91C4CA1F9F8A98 //A13
|
|
data8 0x3F8C9DDCEDEBE7A6 //A15
|
|
data8 0x3F877784442B1516 //A17
|
|
data8 0x3F859C0491802BA2 //A19
|
|
data8 0x9999999998C88B8F, 0x00003FFB //A5
|
|
data8 0x3F6BD7A9A660BF5E //A21
|
|
data8 0x3F9FC1659340419D //A23
|
|
data8 0xB6DB6DB798149BDF, 0x00003FFA //A7
|
|
data8 0xBFB3EF18964D3ED3 //A25
|
|
data8 0x3FCD285315542CF2 //A27
|
|
data8 0xF15BEEEFF7D2966A, 0x00003FFB //B1
|
|
data8 0x3EF0DDA376D10FB3 //B10
|
|
data8 0xBEB83CAFE05EBAC9 //B11
|
|
data8 0x3F65FFB67B513644 //B4
|
|
data8 0x3F5032FBB86A4501 //B5
|
|
data8 0x3F392162276C7CBA //B6
|
|
data8 0x3F2435949FD98BDF //B7
|
|
data8 0xD93923D7FA08341C, 0x00003FF9 //B2
|
|
data8 0x3F802995B6D90BDB //B3
|
|
data8 0x3F10DF86B341A63F //B8
|
|
data8 0xC90FDAA22168C235, 0x00003FFF // Pi/2
|
|
data8 0x3EFA3EBD6B0ECB9D //B9
|
|
data8 0x3EDE18BA080E9098 //B12
|
|
LOCAL_OBJECT_END(acos_base_range_table)
|
|
|
|
.section .text
|
|
GLOBAL_LIBM_ENTRY(acos)
|
|
acos_unnormal_back:
|
|
{ .mfi
|
|
getf.d rXBits = f8 // grab bits of input value
|
|
// set p12 = 1 if x is a NaN, denormal, or zero
|
|
fclass.m p12, p0 = f8, 0xcf
|
|
adds rSign = 1, r0
|
|
}
|
|
{ .mfi
|
|
addl rTblAddr = @ltoff(acos_base_range_table),gp
|
|
// 1 - x = 1 - |x| for positive x
|
|
fms.s1 f1mX = f1, f1, f8
|
|
addl rHalf = 0xFFFE, r0 // exponent of 1/2
|
|
}
|
|
;;
|
|
{ .mfi
|
|
addl r0625 = 0x3FE4, r0 // high 16 bits of 0.625
|
|
// set p8 = 1 if x < 0
|
|
fcmp.lt.s1 p8, p9 = f8, f0
|
|
shl rSign = rSign, 63 // sign bit
|
|
}
|
|
{ .mfi
|
|
// point to the beginning of the table
|
|
ld8 rTblAddr = [rTblAddr]
|
|
// 1 + x = 1 - |x| for negative x
|
|
fma.s1 f1pX = f1, f1, f8
|
|
adds rOne = 0x3FF, r0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
andcm rAbsXBits = rXBits, rSign // bits of |x|
|
|
fmerge.s fSignX = f8, f1 // signum(x)
|
|
shl r0625 = r0625, 48 // bits of DP representation of 0.625
|
|
}
|
|
{ .mfb
|
|
setf.exp fHalf = rHalf // load A2 to FP reg
|
|
fma.s1 fXSqr = f8, f8, f0 // x^2
|
|
// branch on special path if x is a NaN, denormal, or zero
|
|
(p12) br.cond.spnt acos_special
|
|
}
|
|
;;
|
|
{ .mfi
|
|
adds rPiBy2Ptr = 272, rTblAddr
|
|
nop.f 0
|
|
shl rOne = rOne, 52 // bits of 1.0
|
|
}
|
|
{ .mfi
|
|
adds rTmpPtr1 = 16, rTblAddr
|
|
nop.f 0
|
|
// set p6 = 1 if |x| < 0.625
|
|
cmp.lt p6, p7 = rAbsXBits, r0625
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA29, fA31 = [rTblAddr] // A29, fA31
|
|
// 1 - x = 1 - |x| for positive x
|
|
(p9) fms.s1 fR = f1, f1, f8
|
|
// point to coefficient of "near 1" polynomial
|
|
(p7) adds rTmpPtr2 = 176, rTblAddr
|
|
}
|
|
{ .mfi
|
|
ldfpd fA33, fA35 = [rTmpPtr1], 16 // A33, fA35
|
|
// 1 + x = 1 - |x| for negative x
|
|
(p8) fma.s1 fR = f1, f1, f8
|
|
(p6) adds rTmpPtr2 = 48, rTblAddr
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fB0 = [rTmpPtr1], 16 // B0
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mib
|
|
adds rTmpPtr3 = 16, rTmpPtr2
|
|
// set p10 = 1 if |x| = 1.0
|
|
cmp.eq p10, p0 = rAbsXBits, rOne
|
|
// branch on special path for |x| = 1.0
|
|
(p10) br.cond.spnt acos_abs_1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA3 = [rTmpPtr2], 48 // A3 or B1
|
|
nop.f 0
|
|
adds rTmpPtr1 = 64, rTmpPtr3
|
|
}
|
|
{ .mib
|
|
ldfpd fA9, fA11 = [rTmpPtr3], 16 // A9, A11 or B10, B11
|
|
// set p11 = 1 if |x| > 1.0
|
|
cmp.gt p11, p0 = rAbsXBits, rOne
|
|
// branch on special path for |x| > 1.0
|
|
(p11) br.cond.spnt acos_abs_gt_1
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA17, fA19 = [rTmpPtr2], 16 // A17, A19 or B6, B7
|
|
// initial approximation of 1 / sqrt(1 - x)
|
|
frsqrta.s1 f1mXRcp, p0 = f1mX
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA13, fA15 = [rTmpPtr3] // A13, A15 or B4, B5
|
|
fma.s1 fXCube = fXSqr, f8, f0 // x^3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA5 = [rTmpPtr2], 48 // A5 or B2
|
|
// initial approximation of 1 / sqrt(1 + x)
|
|
frsqrta.s1 f1pXRcp, p0 = f1pX
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA21, fA23 = [rTmpPtr1], 16 // A21, A23 or B3, B8
|
|
fma.s1 fXQuadr = fXSqr, fXSqr, f0 // x^4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA7 = [rTmpPtr1] // A7 or Pi/2
|
|
fma.s1 fRSqr = fR, fR, f0 // R^2
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
ldfpd fA25, fA27 = [rTmpPtr2] // A25, A27 or B9, B12
|
|
nop.f 0
|
|
(p6) br.cond.spnt acos_base_range;
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p9) fma.s1 fH = fHalf, f1mXRcp, f0 // H0 for x > 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p9) fma.s1 fS = f1mX, f1mXRcp, f0 // S0 for x > 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
(p8) fma.s1 fH = fHalf, f1pXRcp, f0 // H0 for x < 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p8) fma.s1 fS = f1pX, f1pXRcp, f0 // S0 for x > 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRQuadr = fRSqr, fRSqr, f0 // R^4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB11 = fB11, fR, fB10
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB1 = fB1, fR, fB0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB5 = fB5, fR, fB4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB7 = fB7, fR, fB6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB3 = fB3, fR, fB2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 fD = fH, fS, fHalf // d0 = 1/2 - H0*S0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fR8 = fRQuadr, fRQuadr, f0 // R^4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB9 = fB9, fR, fB8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fB12 = fB12, fRSqr, fB11
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fB7 = fB7, fRSqr, fB5
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 fB3 = fB3, fRSqr, fB1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fH = fH, fD, fH // H1 = H0 + H0*d0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fS = fS, fD, fS // S1 = S0 + S0*d0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
(p9) fma.s1 fCpi = f1, f0, f0 // Cpi = 0 if x > 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p8) fma.s1 fCpi = fPiBy2, f1, fPiBy2 // Cpi = Pi if x < 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB12 = fB12, fRSqr, fB9
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fB7 = fB7, fRQuadr, fB3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fnma.s1 fD = fH, fS, fHalf // d1 = 1/2 - H1*S1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 fSignedS = fSignX, fS, f0 // -signum(x)*S1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fCloseTo1Pol = fB12, fR8, fB7
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fH = fH, fD, fH // H2 = H1 + H1*d1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fS = fS, fD, fS // S2 = S1 + S1*d1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// -signum(x)* S2 = -signum(x)*(S1 + S1*d1)
|
|
fma.s1 fSignedS = fSignedS, fD, fSignedS
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
nop.m 0
|
|
fnma.s1 fD = fH, fS, fHalf // d2 = 1/2 - H2*S2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Cpi + signum(x)*PolB*S2
|
|
fnma.s1 fCpi = fSignedS, fCloseTo1Pol, fCpi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// signum(x)*PolB * S2
|
|
fnma.s1 fCloseTo1Pol = fSignedS, fCloseTo1Pol, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result for 0.625 <= |x| < 1
|
|
fma.d.s0 f8 = fCloseTo1Pol, fD, fCpi
|
|
// exit here for 0.625 <= |x| < 1
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
|
|
// here if |x| < 0.625
|
|
.align 32
|
|
acos_base_range:
|
|
{ .mfi
|
|
ldfe fCpi = [rPiBy2Ptr] // Pi/2
|
|
fma.s1 fA33 = fA33, fXSqr, fA31
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, fXSqr, fA13
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA29 = fA29, fXSqr, fA27
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA25 = fA25, fXSqr, fA23
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA21 = fA21, fXSqr, fA19
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, fXSqr, fA7
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA5 = fA5, fXSqr, fA3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA35 = fA35, fXQuadr, fA33
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA17 = fA17, fXQuadr, fA15
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fX8 = fXQuadr, fXQuadr, f0 // x^8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA25 = fA25, fXQuadr, fA21
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, fXQuadr, fA5
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 fCpi = fCpi, f1, f8 // Pi/2 - x
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA35 = fA35, fXQuadr, fA29
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA17 = fA17, fXSqr, fA11
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fX16 = fX8, fX8, f0 // x^16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA35 = fA35, fX8, fA25
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA17 = fA17, fX8, fA9
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fBaseP = fA35, fX16, fA17
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result for |x| < 0.625
|
|
fnma.d.s0 f8 = fBaseP, fXCube, fCpi
|
|
// exit here for |x| < 0.625 path
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if |x| = 1
|
|
// acos(1) = 0
|
|
// acos(-1) = Pi
|
|
.align 32
|
|
acos_abs_1:
|
|
{ .mfi
|
|
ldfe fPiBy2 = [rPiBy2Ptr] // Pi/2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
.pred.rel "mutex", p8, p9
|
|
{ .mfi
|
|
nop.m 0
|
|
// result for x = 1.0
|
|
(p9) fma.d.s0 f8 = f1, f0, f0 // 0.0
|
|
nop.i 0
|
|
}
|
|
{.mfb
|
|
nop.m 0
|
|
// result for x = -1.0
|
|
(p8) fma.d.s0 f8 = fPiBy2, f1, fPiBy2 // Pi
|
|
// exit here for |x| = 1.0
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if x is a NaN, denormal, or zero
|
|
.align 32
|
|
acos_special:
|
|
{ .mfi
|
|
// point to Pi/2
|
|
adds rPiBy2Ptr = 272, rTblAddr
|
|
// set p12 = 1 if x is a NaN
|
|
fclass.m p12, p0 = f8, 0xc3
|
|
nop.i 0
|
|
}
|
|
{ .mlx
|
|
nop.m 0
|
|
// smallest positive DP normalized number
|
|
movl rDenoBound = 0x0010000000000000
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fPiBy2 = [rPiBy2Ptr] // Pi/2
|
|
// set p13 = 1 if x = 0.0
|
|
fclass.m p13, p0 = f8, 0x07
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnorm.s1 fNormX = f8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
// load smallest normal to FP reg
|
|
setf.d fDenoBound = rDenoBound
|
|
// answer if x is a NaN
|
|
(p12) fma.d.s0 f8 = f8,f1,f0
|
|
// exit here if x is a NaN
|
|
(p12) br.ret.spnt b0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// absolute value of normalized x
|
|
fmerge.s fNormX = f1, fNormX
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result for x = 0
|
|
(p13) fma.d.s0 f8 = fPiBy2, f1, f8
|
|
// exit here if x = 0.0
|
|
(p13) br.ret.spnt b0
|
|
}
|
|
;;
|
|
// if we still here then x is denormal or unnormal
|
|
{ .mfi
|
|
nop.m 0
|
|
// set p14 = 1 if normalized x is greater than or
|
|
// equal to the smallest denormalized value
|
|
// So, if p14 is set to 1 it means that we deal with
|
|
// unnormal rather than with "true" denormal
|
|
fcmp.ge.s1 p14, p0 = fNormX, fDenoBound
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
(p14) fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag if x unnormal
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
// normalize unnormal input
|
|
(p14) fnorm.s1 f8 = f8
|
|
// return to the main path
|
|
(p14) br.cond.sptk acos_unnormal_back
|
|
}
|
|
;;
|
|
// if we still here it means that input is "true" denormal
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result if x is denormal
|
|
fms.d.s0 f8 = fPiBy2, f1, f8 // Pi/2 - x
|
|
// exit here if x is denormal
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if |x| > 1.0
|
|
// error handler should be called
|
|
.align 32
|
|
acos_abs_gt_1:
|
|
{ .mfi
|
|
alloc r32 = ar.pfs, 0, 3, 4, 0 // get some registers
|
|
fmerge.s FR_X = f8,f8
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
mov GR_Parameter_TAG = 58 // error code
|
|
frcpa.s0 FR_RESULT, p0 = f0,f0
|
|
// call error handler routine
|
|
br.cond.sptk __libm_error_region
|
|
}
|
|
;;
|
|
GLOBAL_LIBM_END(acos)
|
|
libm_alias_double_other (acos, acos)
|
|
|
|
|
|
|
|
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
|
|
stfd [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
|
|
stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
|
|
nop.b 0
|
|
}
|
|
{ .mib
|
|
stfd [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
|
|
add GR_Parameter_RESULT = 48,sp
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
{ .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#
|