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0609ec0a74
Continuing the preparation for additional _FloatN / _FloatNx function aliases, this patch makes ia64 libm function implementations use libm_alias_double to define function aliases. The same approach is followed as with the corresponding long double patch: the ia64-specific macros are left unchanged, with calls to libm_alias_double_other being added in most cases and libm_alias_double itself being used in only a few places. Tested with build-many-glibcs.py for ia64-linux-gnu that installed stripped shared libraries are unchanged by the patch. * sysdeps/ia64/fpu/libm-symbols.h: Include <libm-alias-double.h>. * sysdeps/ia64/fpu/e_acos.S (acos): Use libm_alias_double_other. * sysdeps/ia64/fpu/e_acosh.S (acosh): Likewise. * sysdeps/ia64/fpu/e_asin.S (asin): Likewise. * sysdeps/ia64/fpu/e_atan2.S (atan2): Likewise. * sysdeps/ia64/fpu/e_atanh.S (atanh): Likewise. * sysdeps/ia64/fpu/e_cosh.S (cosh): Likewise. * sysdeps/ia64/fpu/e_exp.S (exp): Likewise. * sysdeps/ia64/fpu/e_exp10.S (exp10): Likewise. * sysdeps/ia64/fpu/e_exp2.S (exp2): Likewise. * sysdeps/ia64/fpu/e_fmod.S (fmod): Likewise. * sysdeps/ia64/fpu/e_hypot.S (hypot): Likewise. * sysdeps/ia64/fpu/e_lgamma_r.c (lgamma_r): Define using libm_alias_double_r. * sysdeps/ia64/fpu/e_log.S (log10): Use libm_alias_double_other. (log): Likewise. * sysdeps/ia64/fpu/e_log2.S (log2): Likewise. * sysdeps/ia64/fpu/e_pow.S (pow): Likewise. * sysdeps/ia64/fpu/e_remainder.S (remainder): Likewise. * sysdeps/ia64/fpu/e_sinh.S (sinh): Likewise. * sysdeps/ia64/fpu/e_sqrt.S (sqrt): Likewise. * sysdeps/ia64/fpu/libm_sincos.S (sincos): Likewise. * sysdeps/ia64/fpu/s_asinh.S (asinh): Likewise. * sysdeps/ia64/fpu/s_atan.S (atan): Likewise. * sysdeps/ia64/fpu/s_cbrt.S (cbrt): Likewise. * sysdeps/ia64/fpu/s_ceil.S (ceil): Likewise. * sysdeps/ia64/fpu/s_copysign.S (copysign): Define using libm_alias_double. * sysdeps/ia64/fpu/s_cos.S (sin): Use libm_alias_double_other. (cos): Likewise. * sysdeps/ia64/fpu/s_erf.S (erf): Likewise. * sysdeps/ia64/fpu/s_erfc.S (erfc): Likewise. * sysdeps/ia64/fpu/s_expm1.S (expm1): Likewise. * sysdeps/ia64/fpu/s_fabs.S (fabs): Likewise. * sysdeps/ia64/fpu/s_fdim.S (fdim): Likewise. * sysdeps/ia64/fpu/s_floor.S (floor): Likewise. * sysdeps/ia64/fpu/s_fma.S (fma): Likewise. * sysdeps/ia64/fpu/s_fmax.S (fmax): Likewise. * sysdeps/ia64/fpu/s_frexp.c (frexp): Likewise. * sysdeps/ia64/fpu/s_ldexp.c (ldexp): Likewise. * sysdeps/ia64/fpu/s_log1p.S (log1p): Likewise. * sysdeps/ia64/fpu/s_logb.S (logb): Likewise. * sysdeps/ia64/fpu/s_modf.S (modf): Likewise. * sysdeps/ia64/fpu/s_nearbyint.S (nearbyint): Likewise. * sysdeps/ia64/fpu/s_nextafter.S (nextafter): Likewise. * sysdeps/ia64/fpu/s_rint.S (rint): Likewise. * sysdeps/ia64/fpu/s_round.S (round): Likewise. * sysdeps/ia64/fpu/s_scalbn.c (scalbn): Define using libm_alias_double. * sysdeps/ia64/fpu/s_tan.S (tan): Use libm_alias_double_other. * sysdeps/ia64/fpu/s_tanh.S (tanh): Likewise. * sysdeps/ia64/fpu/s_trunc.S (trunc): Likewise. * sysdeps/ia64/fpu/w_lgamma_main.c [BUILD_LGAMMA && !USE_AS_COMPAT] (lgamma): Likewise. * sysdeps/ia64/fpu/w_tgamma_compat.S (tgamma): Likewise.
926 lines
24 KiB
ArmAsm
926 lines
24 KiB
ArmAsm
.file "erf.s"
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// Copyright (c) 2001 - 2005, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2001 by the Intel Numerics Group, Intel Corporation
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History
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//==============================================================
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// 08/15/01 Initial version
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 02/06/03 Reordered header: .section, .global, .proc, .align
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// 03/31/05 Reformatted delimiters between data tables
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//
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// API
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//==============================================================
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// double erf(double)
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//
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// Overview of operation
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//==============================================================
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// Background
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//
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//
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// There are 9 paths:
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// 1. x = +/-0.0
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// Return erf(x) = +/-0.0
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//
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// 2. 0.0 < |x| < 0.5
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// Return erf(x) = x *Pol9(x^2)
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//
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// 3. For several subranges of 0.5 <= |x| < 5.90625
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// Return erf(x) = sign(x)*Pol19(y),
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// where y = (|x|-b)/a, Pol19(y) = A0 + A1*y^1 + A2*y^2 + ... + A19*y^19
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//
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// For each subrange there is particular set of coefficients.
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// Below is the list of subranges:
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// 3.1 0.5 <= |x| < 1.0 b = a = 0.5
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// 3.2 1.0 <= |x| < 2.0, b = a = 1.0
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// 3.3 2.0 <= |x| < 3.25 b = a = 2.0
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// 3.4 4.0 <= |x| < 5.90625 b = 4.0, a = 2.0
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//
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// 4. 3.25 <= |x| < 4.0
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// Return erf(x) = sign(x)*Pol14(|x| - 3.25)
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//
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// 5. 5.90625 <= |x| < +INF
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// Return erf(x) = sign(x)*(1.0d - 2^(-63))
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//
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// 6. |x| = INF
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// Return erf(x) = sign(x) * 1.0
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//
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// 7. x = [S,Q]NaN
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// Return erf(x) = QNaN
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//
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// 8. x is positive denormal
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// Return erf(x) = A0*x - x^2,
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// where A0 = 2.0/sqrt(Pi)
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//
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// 9. x is negative denormal
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// Return erf(x) = A0*x + x^2,
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// where A0 = 2.0/sqrt(Pi)
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//
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// Registers used
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//==============================================================
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// Floating Point registers used:
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// f8, input, output
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// f32 -> f63
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// General registers used:
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// r32 -> r48, r2, r3
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// Predicate registers used:
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// p0, p6 -> p15
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// p6 to filter out case when x = denormal
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// p7 to filter out case when x = [Q,S]NaN or +/-0,
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// used also to process denormals
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// p8 to filter out case when 3.25 <= |x| < 4.0,
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// used also to process denormals
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// p9 to filter out case when |x| = inf
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// p10 to filter out case when |x| < 0.5
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// p11 set when |x| < 3.25 or |x| > 4.0
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// p12 to filter out case when |x| >= 5.90625
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// p13 set if 4.0 <=|x| < 5.90625
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// p14 set to 1 for positive x
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// p15 set to 1 for negative x
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// Assembly macros
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//==============================================================
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rDataPtr = r2
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rDataPtr1 = r3
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rBias = r33
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rCoeffAddr3 = r34
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rThreeAndQ = r35
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rCoeffAddr2 = r36
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rMask = r37
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rArg = r38
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rSignBit = r39
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rAbsArg = r40
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rSaturation = r41
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rIndex = r42
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rCoeffAddr1 = r43
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rCoeffAddr4 = r44
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rShiftedArg = r45
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rShiftedArgMasked = r46
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rBiasedExpOf4 = r47
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rShiftedAbsArg = r48
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//==============================================================
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fA0 = f32
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fA1 = f33
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fA2 = f34
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fA3 = f35
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fA4 = f36
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fA5 = f37
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fA6 = f38
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fA7 = f39
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fA8 = f40
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fA9 = f41
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fA10 = f42
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fA11 = f43
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fA12 = f44
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fA13 = f45
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fA14 = f46
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fA15 = f47
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fA16 = f48
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fA17 = f49
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fA18 = f50
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fA19 = f51
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fArgSqr = f52
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fArgAbsNorm = f53
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fSignumX = f54
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fRes = f55
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fThreeAndQ = f56
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fArgAbs = f57
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fTSqr = f58
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fTQuadr = f59
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fTDeg3 = f60
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fTDeg7 = f61
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fArgAbsNormSgn = f62
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fTQuadrSgn = f63
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// Data tables
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//==============================================================
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RODATA
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.align 64
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LOCAL_OBJECT_START(erf_data)
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// Coefficients ##0..15
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// Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0
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data8 0xB69AC40646D1F6C1, 0x00003FD2 //A19
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data8 0x90AD48C0118FA10C, 0x00003FD7 //A18
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data8 0x826FBAD055EA4AB8, 0x0000BFDB //A17
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data8 0x8DAB171246CC2B89, 0x00003FDC //A16
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data8 0xC0B1D6662F8A7564, 0x00003FDF //A15
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data8 0xA46374AC35099BAF, 0x0000BFE1 //A14
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data8 0xB2F230996346EF27, 0x0000BFE4 //A13
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data8 0xCDEC50950FACE04A, 0x00003FE6 //A12
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data8 0x826014649396E9D2, 0x00003FE9 //A11
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data8 0xCDB787DC718B13F9, 0x0000BFEB //A10
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data8 0x8E0B23C24EE0C8EE, 0x0000BFED //A9
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data8 0xA49EA40A4E5A3F76, 0x00003FF0 //A8
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data8 0xB11E30BE912617D3, 0x00003FF0 //A7
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data8 0xCCF89D9351CE26E3, 0x0000BFF4 //A6
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data8 0xEFF75AD1F0F22809, 0x00003FF2 //A5
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data8 0xBB793EF404C09A22, 0x00003FF8 //A4
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// Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0
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data8 0xBAE93FF4174EA59B, 0x00003FE6 //A19
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data8 0x8A0FD46092F95D44, 0x0000BFEA //A18
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data8 0xA37B3242B7809E12, 0x00003FEC //A17
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data8 0xA0330A5CD2E91689, 0x0000BFED //A16
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data8 0x8E34A678F3497D17, 0x0000BFEC //A15
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data8 0xAC185D45A2772384, 0x00003FEF //A14
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data8 0xB0C11347CE7EEDE8, 0x00003FEF //A13
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data8 0xD3330DC14EA0E4EB, 0x0000BFF2 //A12
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data8 0xB4A6DFDE578A428F, 0x00003FF1 //A11
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data8 0xA0B4034310D2D9CB, 0x00003FF5 //A10
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data8 0xF71662D3132B7759, 0x0000BFF5 //A9
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data8 0x9C88BF157695E9EC, 0x0000BFF7 //A8
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data8 0xF84B80EFCA43895D, 0x00003FF8 //A7
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data8 0x9722D22DA628A17B, 0x00003FF7 //A6
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data8 0x8DB0A586F8F3381F, 0x0000BFFB //A5
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data8 0x8DB0A5879F87E5BE, 0x00003FFB //A4
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// Polynomial coefficients for the erf(x), 2.0 <= |x| < 3.25
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data8 0x9C4AF1F3A4B21AFC, 0x00003FF6 //A19
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data8 0x8D40D5D5DB741AB8, 0x0000BFF9 //A18
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data8 0xDEBE7099E0A75BA4, 0x00003FFA //A17
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data8 0xB99A33294D32429D, 0x0000BFFB //A16
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data8 0x8109D9C7197BC7C9, 0x00003FFB //A15
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data8 0xC30DE8E2EFC2D760, 0x00003FFA //A14
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data8 0x80DDA28C5B35DC73, 0x0000BFFC //A13
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data8 0x9BE4DE5095BACE0D, 0x00003FF9 //A12
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data8 0xDA4092509EE7D111, 0x00003FFC //A11
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data8 0x89D98C561B0C9040, 0x0000BFFD //A10
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data8 0xD20B26EB2F0881D4, 0x0000BFF9 //A9
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data8 0xD089C56948731561, 0x00003FFD //A8
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data8 0xDD704DEFFB21B7E7, 0x0000BFFD //A7
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data8 0xF0C9A6BBDE469115, 0x00003FF9 //A6
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data8 0xD673A02CB5766633, 0x00003FFD //A5
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data8 0x8D162CBAD8A12649, 0x0000BFFE //A4
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// Polynomial coefficients for the erf(x), 4.0 <= |x| < 6.0
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data8 0xD4428B75C6FE8FD1, 0x0000BFFC //A19
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data8 0xF76BE1935675D5C8, 0x00003FFE //A18
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data8 0xFD6BB3B14AA7A8E6, 0x0000BFFF //A17
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data8 0x8BE8F573D348DDA4, 0x00004000 //A16
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data8 0x81E91923A1030502, 0x0000BFFF //A15
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data8 0xCE7FE87B26CFD286, 0x0000BFFE //A14
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data8 0x84EF6B4E17404384, 0x00004000 //A13
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data8 0x91FEF33015404991, 0x0000C000 //A12
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data8 0xDEDF6A9370747E56, 0x00003FFF //A11
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data8 0x8397E6FF56CDFD9D, 0x0000BFFF //A10
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data8 0xFAD1CE912473937B, 0x00003FFD //A9
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data8 0xC48C1EA8AAA624EA, 0x0000BFFC //A8
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data8 0xFECAF0097ACF981B, 0x00003FFA //A7
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data8 0x8829A394065E4B95, 0x0000BFF9 //A6
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data8 0xED3003E477A53EE7, 0x00003FF6 //A5
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data8 0xA4C07E9BB3FCB0F3, 0x0000BFF4 //A4
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//
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// Coefficients ##16..19
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// Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0
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data8 0x95FA98C337005D13, 0x0000BFF9 //A3
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data8 0xE0F7E524D2808A97, 0x0000BFFB //A2
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data8 0xE0F7E524D2808A98, 0x00003FFD //A1
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data8 0x853F7AE0C76E915F, 0x00003FFE //A0
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// Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0
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data8 0x8DB0A587A96ABCF0, 0x00003FFC //A3
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data8 0xD488F84B7DE18DA8, 0x0000BFFD //A2
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data8 0xD488F84B7DE12E9C, 0x00003FFD //A1
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data8 0xD7BB3D3A08445636, 0x00003FFE //A0
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// Polynomial coefficients for the erf(x), 2.0 <= |x| < 3.25
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data8 0xC58571D23D5C4B3A, 0x00003FFD //A3
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data8 0xA94DCF467CD6AFF3, 0x0000BFFC //A2
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data8 0xA94DCF467CD10A16, 0x00003FFA //A1
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data8 0xFECD70A13CAF1997, 0x00003FFE //A0
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// Polynomial coefficients for the erf(x), 4.0 <= |x| < 6.0
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data8 0xB01D2B4F0D5AB8B0, 0x00003FF1 //A3
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data8 0x8858A465CE594BD1, 0x0000BFEE //A2
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data8 0x8858A447456DE61D, 0x00003FEA //A1
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data8 0xFFFFFFBDC88BB107, 0x00003FFE //A0
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// Polynomial coefficients for the erf(x), 0.0 <= |x| < 0.5
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data8 0xBE839EDBB36C7FCE //A9
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data8 0x3EBB7745A18DD242 //A8
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data8 0xBF4C02DB238F2AFC //A5
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data8 0x3F7565BCD0A9A3EA //A4
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data8 0xC093A3581BCF3333, 0x0000BFFD //A1
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data8 0xBEEF4BB82AD8AE22 //A7
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data8 0x3F1F9A2A57A218CD //A6
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data8 0xBF9B82CE3127F4E4 //A3
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data8 0x3FBCE2F21A042B25 //A2
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data8 0x906EBA8214DB688D, 0x00003FFF //A0
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// 1.0 - 2^(-63)
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data8 0xFFFFFFFFFFFFFFFF, 0x00003FFE
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// Polynomial coefficients for the erf(x), 3.25 <= |x| < 4.0
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data8 0x95E91576C7A12250, 0x00003FE7 //A14
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data8 0x8E5E0D0E1F5D3CB5, 0x0000BFEA //A13
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data8 0xED761DAFAF814DE9, 0x00003FEB //A12
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data8 0xB3A77D921D0ACFC7, 0x0000BFEC //A11
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data8 0xA662D27096B08D7C, 0x0000BFEC //A10
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data8 0xDA0F410AE6233EA5, 0x00003FEF //A9
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data8 0xAB4A8B16B3124327, 0x0000BFF1 //A8
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data8 0xB241E236A5EDCED3, 0x00003FF2 //A7
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data8 0x8A2A65BA1F551F77, 0x0000BFF3 //A6
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data8 0xA4852D0B1D87000A, 0x00003FF3 //A5
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data8 0x963EB00039489476, 0x0000BFF3 //A4
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data8 0xCD5244FF4F7313A5, 0x00003FF2 //A3
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data8 0xC6F1E695363BCB26, 0x0000BFF1 //A2
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data8 0xF4DAF4680DA54C02, 0x00003FEF //A1
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data8 0xFFFFB7CFB3F2ABBE, 0x00003FFE //A0
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// A = 2.0/sqrt(Pi)
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data8 0x906EBA8214DB688D, 0x00003FFF
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LOCAL_OBJECT_END(erf_data)
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.section .text
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GLOBAL_LIBM_ENTRY(erf)
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{ .mfi
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alloc r32 = ar.pfs, 0, 17, 0, 0
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fmerge.se fArgAbsNorm = f1, f8 // normalized x
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adds rSignBit = 0x1, r0
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}
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{ .mfi
|
|
addl rDataPtr = @ltoff(erf_data), gp
|
|
fma.s1 fArgSqr = f8, f8, f0 // x^2
|
|
addl rThreeAndQ = 0x400A0, r0 // shifted bits of 3.25
|
|
}
|
|
;;
|
|
{ .mfi
|
|
getf.d rArg = f8 // x in GR
|
|
fclass.m p6,p0 = f8, 0x0b // is x denormal ?
|
|
shl rThreeAndQ = rThreeAndQ, 44 // bits of 3.25
|
|
}
|
|
{ .mfi
|
|
ld8 rDataPtr = [rDataPtr]
|
|
nop.f 0
|
|
addl rBiasedExpOf4 = 0x40100, r0 // shifted bits of 4.0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
addl rSaturation = 0x4017A, r0 // shifted bits of 5.90625
|
|
fclass.m p7,p0 = f8, 0xc7 // is x [S,Q]NaN or +/-0 ?
|
|
shl rSignBit = rSignBit, 63 // mask for sign bit
|
|
}
|
|
{ .mfi
|
|
addl rMask = 0x7FF00, r0 // Mask for index bits
|
|
nop.f 0
|
|
addl rBias = 0x3FE00, r0 // bias of 0.5 << 8
|
|
}
|
|
;;
|
|
{ .mfi
|
|
setf.d fThreeAndQ = rThreeAndQ // 3.25 if FP register
|
|
fclass.m p9,p0 = f8, 0x23 // is x +/- inf?
|
|
shr.u rShiftedArg = rArg, 44
|
|
}
|
|
{ .mfb
|
|
andcm rAbsArg = rArg, rSignBit // |x| in GR
|
|
nop.f 0
|
|
(p6) br.cond.spnt erf_denormal // branch out if x is denormal
|
|
}
|
|
;;
|
|
{ .mfi
|
|
and rShiftedArgMasked = rShiftedArg, rMask // bias of x << 8
|
|
fmerge.s fArgAbs = f1, f8 // |x|
|
|
shr rShiftedAbsArg = rAbsArg, 44
|
|
}
|
|
{ .mfb
|
|
cmp.lt p8, p11 = rThreeAndQ, rAbsArg // p8 = 1 if |x| >= 3.25
|
|
(p7) fma.d.s0 f8 = f8,f1,f8 // NaN or +/-0
|
|
(p7) br.ret.spnt b0 // exit for x = NaN or +/-0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
sub rIndex = rShiftedArgMasked, rBias // index << 8
|
|
nop.f 0
|
|
cmp.lt p10, p0 = rShiftedArgMasked, rBias // p10 = 1 if |x| < 0.5
|
|
}
|
|
{ .mfb
|
|
// p8 = 1 if 3.25 <= |x| < 4.0
|
|
(p8) cmp.lt p8, p11 = rShiftedAbsArg, rBiasedExpOf4
|
|
fms.s1 fArgAbsNorm = fArgAbsNorm, f1, f1
|
|
(p10) br.cond.spnt erf_near_zero // branch out if |x| < 0.5
|
|
}
|
|
;;
|
|
.pred.rel "mutex", p8, p11
|
|
{ .mfi
|
|
(p8) adds rCoeffAddr1 = 1392, rDataPtr // coeff. for 3.25 <=|x|<4.0
|
|
(p9) fmerge.s f8 = f8,f1 // +/- inf
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
(p11) add rCoeffAddr1 = rDataPtr, rIndex// coeff. ##0,2,..14
|
|
nop.f 0
|
|
(p9) br.ret.spnt b0 // exit for x = +/- inf
|
|
}
|
|
;;
|
|
{ .mfi
|
|
adds rCoeffAddr2 = 16, rCoeffAddr1
|
|
fmerge.s fSignumX = f8, f1 // signum(x)
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
cmp.lt p12, p0 = rSaturation, rShiftedAbsArg // |x| > 5.90625?
|
|
nop.f 0
|
|
(p12) br.cond.spnt erf_saturation // branch out if x |x| >= 6.0
|
|
}
|
|
;;
|
|
// Here if paths #3,4
|
|
// if path #4 we'll branch out after loading of 14 necessary coefficients
|
|
{.mfi
|
|
ldfe fA19 = [rCoeffAddr1], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
ldfe fA18 = [rCoeffAddr2], 32
|
|
nop.f 0
|
|
adds rCoeffAddr3 = 1024, rDataPtr
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fA17 = [rCoeffAddr1], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
ldfe fA16 = [rCoeffAddr2], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fA15 = [rCoeffAddr1], 32
|
|
fma.s1 fTSqr = fArgAbsNorm, fArgAbsNorm, f0
|
|
shr.u rIndex = rIndex, 2
|
|
}
|
|
{.mfi
|
|
ldfe fA14 = [rCoeffAddr2], 32
|
|
nop.f 0
|
|
adds rCoeffAddr4 = 16, r0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fA13 = [rCoeffAddr1], 32
|
|
nop.f 0
|
|
// address of coefficients ##16..23
|
|
add rCoeffAddr3 = rCoeffAddr3, rIndex
|
|
}
|
|
{.mfi
|
|
ldfe fA12 = [rCoeffAddr2], 32
|
|
nop.f 0
|
|
cmp.lt p15, p14 = rArg, r0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fA11 = [rCoeffAddr1], 32
|
|
nop.f 0
|
|
add rCoeffAddr4 = rCoeffAddr3, rCoeffAddr4
|
|
}
|
|
{.mfi
|
|
ldfe fA10 = [rCoeffAddr2], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fA9 = [rCoeffAddr1], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
ldfe fA8 = [rCoeffAddr2], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fA7 = [rCoeffAddr1], 32
|
|
fms.s1 fArgAbs = fArgAbs, f1, fThreeAndQ
|
|
nop.i 0
|
|
}
|
|
{.mfb
|
|
ldfe fA6 = [rCoeffAddr2], 32
|
|
nop.f 0
|
|
(p8) br.cond.spnt erf_3q_4 // branch out if 3.25 < |x| < 4.0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fA5 = [rCoeffAddr1], 32
|
|
fma.s1 fTDeg3 = fArgAbsNorm, fTSqr, f0
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
ldfe fA4 = [rCoeffAddr2], 32
|
|
fma.s1 fTQuadr = fTSqr, fTSqr, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
// Path #3 Polynomial Pol19(y) computation; y = fArgAbsNorm
|
|
{.mfi
|
|
ldfe fA3 = [rCoeffAddr3], 32
|
|
fma.s1 fArgAbsNormSgn = fArgAbsNorm, fSignumX, f0
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
ldfe fA2 = [rCoeffAddr4], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfi
|
|
ldfe fA1 = [rCoeffAddr3], 32
|
|
fma.s1 fRes = fA19, fArgAbsNorm, fA18
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
ldfe fA0 = [rCoeffAddr4], 32
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA17 = fA17, fArgAbsNorm, fA16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, fArgAbsNorm, fA14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fTDeg7 = fTDeg3, fTQuadr, f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA13 = fA13, fArgAbsNorm, fA12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, fArgAbsNorm, fA10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, fArgAbsNorm, fA8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fRes, fTSqr, fA17
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA7 = fA7, fArgAbsNorm, fA6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA5 = fA5, fArgAbsNorm, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, fTSqr, fA13
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA4 = fA4, fArgAbsNorm, fA3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA2 = fA2, fArgAbsNorm, fA1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, fTSqr, fA9
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA7 = fA7, fTSqr, fA5
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fRes, fTQuadr, fA15
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA4 = fA4, fTSqr, fA2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fRes, fTQuadr, fA11
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA4 = fA7, fTDeg3, fA4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fRes, fTDeg7, fA4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// result for negative argument
|
|
(p15) fms.d.s0 f8 = fRes, fArgAbsNormSgn, fA0
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
// result for positive argument
|
|
(p14) fma.d.s0 f8 = fRes, fArgAbsNormSgn, fA0
|
|
br.ret.sptk b0
|
|
}
|
|
|
|
// Here if 3.25 < |x| < 4.0
|
|
.align 32
|
|
erf_3q_4:
|
|
.pred.rel "mutex", p14, p15
|
|
{ .mfi
|
|
ldfe fA5 = [rCoeffAddr1], 32
|
|
fma.s1 fTSqr = fArgAbs, fArgAbs, f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fA19, fArgAbs, fA18
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA17 = fA17, fArgAbs, fA16
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, fArgAbs, fA14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA13 = fA13, fArgAbs, fA12
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, fArgAbs, fA10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA9 = fA9, fArgAbs, fA8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fArgAbsNormSgn = fArgAbs, fSignumX, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fTQuadr = fTSqr, fTSqr, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fRes, fTSqr, fA17
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA15 = fA15, fTSqr, fA13
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, fTSqr, fA9
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA7 = fA7, fArgAbs, fA6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fTDeg7 = fTQuadr, fTSqr, f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fRes, fTQuadr, fA15
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA11 = fA11, fTSqr, fA7
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fRes, fTDeg7, fA11
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
// result for negative argument
|
|
(p15) fms.d.s0 f8 = fRes, fArgAbsNormSgn, fA5
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
// result for positive argument
|
|
(p14) fma.d.s0 f8 = fRes, fArgAbsNormSgn, fA5
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// Here if |x| < 0.5
|
|
.align 32
|
|
erf_near_zero:
|
|
{ .mfi
|
|
adds rCoeffAddr1 = 1280, rDataPtr // address of A9
|
|
fma.s1 fTSqr = fArgSqr, fArgSqr, f0 // x^4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
adds rCoeffAddr2 = 1328, rDataPtr // address of A7
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA9, fA8 = [rCoeffAddr1], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA7, fA6 = [rCoeffAddr2], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfpd fA5, fA4 = [rCoeffAddr1], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd fA3, fA2 = [rCoeffAddr2], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA1 = [rCoeffAddr1]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe fA0 = [rCoeffAddr2]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fTQuadr = fTSqr, fTSqr, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fA9, fArgSqr, fA8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA7 = fA7, fArgSqr, fA6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA3 = fA3, fArgSqr, fA2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA5 = fA5, fArgSqr, fA4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA1 = fA1, fArgSqr, fA0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fTQuadrSgn = fTQuadr, f8, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fRes, fTSqr, fA7
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA1 = fA3, fTSqr, fA1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fRes = fRes, fTSqr, fA5
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA1 = fA1, f8, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.d.s0 f8 = fRes, fTQuadrSgn, fA1 // x*Pol9(x^2)
|
|
br.ret.sptk b0 // Exit for |x| < 0.5
|
|
};;
|
|
|
|
// Here if 5.90625 <= |x| < +inf
|
|
.align 32
|
|
erf_saturation:
|
|
{ .mfi
|
|
adds rDataPtr = 1376, rDataPtr // address of A0
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA0 = [rDataPtr]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.d.s0 f8 = fA0, fSignumX, f0 // sign(x)*(1.0 - 2^(-63))
|
|
// Exit for 5.90625 <= |x| < +inf
|
|
br.ret.sptk b0 // Exit for 5.90625 <=|x|< +inf
|
|
}
|
|
;;
|
|
|
|
// Here if x is double precision denormal
|
|
.align 32
|
|
erf_denormal:
|
|
{ .mfi
|
|
adds rDataPtr = 1632, rDataPtr // address of A0
|
|
fclass.m p7,p8 = f8, 0x0a // is x -denormal ?
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
ldfe fA0 = [rDataPtr] // A0
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 fA0 = fA0,f8,f0 // A0*x
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.d.s0 f8 = f8,f8,fA0 // -denormal
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p8) fnma.d.s0 f8 = f8,f8,fA0 // +denormal
|
|
br.ret.sptk b0 // Exit for denormal
|
|
}
|
|
;;
|
|
|
|
GLOBAL_LIBM_END(erf)
|
|
libm_alias_double_other (erf, erf)
|