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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.
856 lines
23 KiB
ArmAsm
856 lines
23 KiB
ArmAsm
.file "asin.s"
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// Copyright (c) 2000 - 2003 Intel Corporation
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// All rights reserved.
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//
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// Contributed 2000 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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// History
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//==============================================================
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// 02/02/00 Initial version
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// 08/17/00 New and much faster algorithm.
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// 08/31/00 Avoided bank conflicts on loads, shortened |x|=1 path,
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// fixed mfb split issue stalls.
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// 12/19/00 Fixed small arg cases to force inexact, or inexact and underflow.
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// 08/02/02 New and much faster algorithm II
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// 02/06/03 Reordered header: .section, .global, .proc, .align
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// Description
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//=========================================
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// The asin function computes the principal value of the arc sine of x.
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// asin(0) returns 0, asin(1) returns pi/2, asin(-1) returns -pi/2.
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// A doman error occurs for arguments not in the range [-1,+1].
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//
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// The asin function returns the arc sine in the range [-pi/2, +pi/2] radians.
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//
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// There are 8 paths:
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// 1. x = +/-0.0
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// Return asin(x) = +/-0.0
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//
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// 2. 0.0 < |x| < 0.625
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// Return asin(x) = x + x^3 *PolA(x^2)
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// where PolA(x^2) = A3 + A5*x^2 + A7*x^4 +...+ A35*x^32
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//
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// 3. 0.625 <=|x| < 1.0
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// Return asin(x) = sign(x) * ( Pi/2 - sqrt(R) * PolB(R))
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// Where R = 1 - |x|,
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// PolB(R) = B0 + B1*R + B2*R^2 +...+B12*R^12
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//
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// sqrt(R) is approximated using the following sequence:
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// y0 = (1 + eps)/sqrt(R) - initial approximation by frsqrta,
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// |eps| < 2^(-8)
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// Then 3 iterations are used to refine the result:
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// H0 = 0.5*y0
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// S0 = R*y0
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//
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// d0 = 0.5 - H0*S0
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// H1 = H0 + d0*H0
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// S1 = S0 + d0*S0
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//
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// d1 = 0.5 - H1*S1
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// H2 = H1 + d0*H1
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// S2 = S1 + d0*S1
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//
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// d2 = 0.5 - H2*S2
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// S3 = S3 + d2*S3
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//
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// S3 approximates sqrt(R) with enough accuracy for this algorithm
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//
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// So, the result should be reconstracted as follows:
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// asin(x) = sign(x) * (Pi/2 - S3*PolB(R))
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//
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// But for optimization perposes the reconstruction step is slightly
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// changed:
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// asin(x) = sign(x)*(Pi/2 - PolB(R)*S2) + sign(x)*d2*S2*PolB(R)
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//
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// 4. |x| = 1.0
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// Return asin(x) = sign(x)*Pi/2
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//
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// 5. 1.0 < |x| <= +INF
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// A doman error occurs for arguments not in the range [-1,+1]
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//
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// 6. x = [S,Q]NaN
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// Return asin(x) = QNaN
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//
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// 7. x is denormal
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// Return asin(x) = x + x^3,
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//
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// 8. x is unnormal
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// Normalize input in f8 and return to the very beginning of the function
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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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// f6, f7, f9 -> f15, f32 -> f63
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// General registers used:
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// r3, r21 -> r31, r32 -> r38
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// Predicate registers used:
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// p0, p6 -> p14
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//
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// Assembly macros
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//=========================================
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// integer registers used
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// scratch
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rTblAddr = r3
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rPiBy2Ptr = r21
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rTmpPtr3 = r22
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rDenoBound = r23
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rOne = r24
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rAbsXBits = r25
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rHalf = r26
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r0625 = r27
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rSign = r28
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rXBits = r29
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rTmpPtr2 = r30
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rTmpPtr1 = r31
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// stacked
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GR_SAVE_PFS = r32
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GR_SAVE_B0 = r33
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GR_SAVE_GP = r34
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GR_Parameter_X = r35
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GR_Parameter_Y = r36
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GR_Parameter_RESULT = r37
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GR_Parameter_TAG = r38
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// floating point registers used
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FR_X = f10
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FR_Y = f1
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FR_RESULT = f8
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// scratch
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fXSqr = f6
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fXCube = f7
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fXQuadr = f9
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f1pX = f10
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f1mX = f11
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f1pXRcp = f12
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f1mXRcp = f13
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fH = f14
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fS = f15
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// stacked
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fA3 = f32
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fB1 = f32
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fA5 = f33
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fB2 = f33
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fA7 = f34
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fPiBy2 = f34
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fA9 = f35
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fA11 = f36
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fB10 = f35
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fB11 = f36
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fA13 = f37
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fA15 = f38
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fB4 = f37
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fB5 = f38
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fA17 = f39
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fA19 = f40
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fB6 = f39
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fB7 = f40
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fA21 = f41
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fA23 = f42
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fB3 = f41
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fB8 = f42
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fA25 = f43
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fA27 = f44
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fB9 = f43
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fB12 = f44
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fA29 = f45
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fA31 = f46
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fA33 = f47
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fA35 = f48
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fBaseP = f49
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fB0 = f50
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fSignedS = f51
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fD = f52
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fHalf = f53
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fR = f54
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fCloseTo1Pol = f55
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fSignX = f56
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fDenoBound = f57
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fNormX = f58
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fX8 = f59
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fRSqr = f60
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fRQuadr = f61
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fR8 = f62
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fX16 = f63
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// Data tables
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//==============================================================
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RODATA
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.align 16
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LOCAL_OBJECT_START(asin_base_range_table)
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// Ai: Polynomial coefficients for the asin(x), |x| < .625000
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// Bi: Polynomial coefficients for the asin(x), |x| > .625000
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data8 0xBFDAAB56C01AE468 //A29
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data8 0x3FE1C470B76A5B2B //A31
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data8 0xBFDC5FF82A0C4205 //A33
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data8 0x3FC71FD88BFE93F0 //A35
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data8 0xB504F333F9DE6487, 0x00003FFF //B0
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data8 0xAAAAAAAAAAAAFC18, 0x00003FFC //A3
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data8 0x3F9F1C71BC4A7823 //A9
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data8 0x3F96E8BBAAB216B2 //A11
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data8 0x3F91C4CA1F9F8A98 //A13
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data8 0x3F8C9DDCEDEBE7A6 //A15
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data8 0x3F877784442B1516 //A17
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data8 0x3F859C0491802BA2 //A19
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data8 0x9999999998C88B8F, 0x00003FFB //A5
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data8 0x3F6BD7A9A660BF5E //A21
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data8 0x3F9FC1659340419D //A23
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data8 0xB6DB6DB798149BDF, 0x00003FFA //A7
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data8 0xBFB3EF18964D3ED3 //A25
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data8 0x3FCD285315542CF2 //A27
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data8 0xF15BEEEFF7D2966A, 0x00003FFB //B1
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data8 0x3EF0DDA376D10FB3 //B10
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data8 0xBEB83CAFE05EBAC9 //B11
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data8 0x3F65FFB67B513644 //B4
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data8 0x3F5032FBB86A4501 //B5
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data8 0x3F392162276C7CBA //B6
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data8 0x3F2435949FD98BDF //B7
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data8 0xD93923D7FA08341C, 0x00003FF9 //B2
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data8 0x3F802995B6D90BDB //B3
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data8 0x3F10DF86B341A63F //B8
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data8 0xC90FDAA22168C235, 0x00003FFF // Pi/2
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data8 0x3EFA3EBD6B0ECB9D //B9
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data8 0x3EDE18BA080E9098 //B12
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LOCAL_OBJECT_END(asin_base_range_table)
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.section .text
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GLOBAL_LIBM_ENTRY(asin)
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asin_unnormal_back:
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{ .mfi
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getf.d rXBits = f8 // grab bits of input value
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// set p12 = 1 if x is a NaN, denormal, or zero
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fclass.m p12, p0 = f8, 0xcf
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adds rSign = 1, r0
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}
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{ .mfi
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addl rTblAddr = @ltoff(asin_base_range_table),gp
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// 1 - x = 1 - |x| for positive x
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fms.s1 f1mX = f1, f1, f8
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addl rHalf = 0xFFFE, r0 // exponent of 1/2
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}
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;;
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{ .mfi
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addl r0625 = 0x3FE4, r0 // high 16 bits of 0.625
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// set p8 = 1 if x < 0
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fcmp.lt.s1 p8, p9 = f8, f0
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shl rSign = rSign, 63 // sign bit
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}
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{ .mfi
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// point to the beginning of the table
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ld8 rTblAddr = [rTblAddr]
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// 1 + x = 1 - |x| for negative x
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fma.s1 f1pX = f1, f1, f8
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adds rOne = 0x3FF, r0
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}
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;;
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{ .mfi
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andcm rAbsXBits = rXBits, rSign // bits of |x|
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fmerge.s fSignX = f8, f1 // signum(x)
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shl r0625 = r0625, 48 // bits of DP representation of 0.625
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}
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{ .mfb
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setf.exp fHalf = rHalf // load A2 to FP reg
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fma.s1 fXSqr = f8, f8, f0 // x^2
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// branch on special path if x is a NaN, denormal, or zero
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(p12) br.cond.spnt asin_special
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}
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;;
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{ .mfi
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adds rPiBy2Ptr = 272, rTblAddr
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nop.f 0
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shl rOne = rOne, 52 // bits of 1.0
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}
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{ .mfi
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adds rTmpPtr1 = 16, rTblAddr
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nop.f 0
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// set p6 = 1 if |x| < 0.625
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cmp.lt p6, p7 = rAbsXBits, r0625
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}
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;;
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{ .mfi
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ldfpd fA29, fA31 = [rTblAddr] // A29, fA31
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// 1 - x = 1 - |x| for positive x
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(p9) fms.s1 fR = f1, f1, f8
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// point to coefficient of "near 1" polynomial
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(p7) adds rTmpPtr2 = 176, rTblAddr
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}
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{ .mfi
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ldfpd fA33, fA35 = [rTmpPtr1], 16 // A33, fA35
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// 1 + x = 1 - |x| for negative x
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(p8) fma.s1 fR = f1, f1, f8
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(p6) adds rTmpPtr2 = 48, rTblAddr
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}
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;;
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{ .mfi
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ldfe fB0 = [rTmpPtr1], 16 // B0
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nop.f 0
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nop.i 0
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}
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{ .mib
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adds rTmpPtr3 = 16, rTmpPtr2
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// set p10 = 1 if |x| = 1.0
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cmp.eq p10, p0 = rAbsXBits, rOne
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// branch on special path for |x| = 1.0
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(p10) br.cond.spnt asin_abs_1
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}
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;;
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{ .mfi
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ldfe fA3 = [rTmpPtr2], 48 // A3 or B1
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nop.f 0
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adds rTmpPtr1 = 64, rTmpPtr3
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}
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{ .mib
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ldfpd fA9, fA11 = [rTmpPtr3], 16 // A9, A11 or B10, B11
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// set p11 = 1 if |x| > 1.0
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cmp.gt p11, p0 = rAbsXBits, rOne
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// branch on special path for |x| > 1.0
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(p11) br.cond.spnt asin_abs_gt_1
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}
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;;
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{ .mfi
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ldfpd fA17, fA19 = [rTmpPtr2], 16 // A17, A19 or B6, B7
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// initial approximation of 1 / sqrt(1 - x)
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frsqrta.s1 f1mXRcp, p0 = f1mX
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nop.i 0
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}
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{ .mfi
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ldfpd fA13, fA15 = [rTmpPtr3] // A13, A15 or B4, B5
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fma.s1 fXCube = fXSqr, f8, f0 // x^3
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nop.i 0
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}
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;;
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{ .mfi
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ldfe fA5 = [rTmpPtr2], 48 // A5 or B2
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// initial approximation of 1 / sqrt(1 + x)
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frsqrta.s1 f1pXRcp, p0 = f1pX
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nop.i 0
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}
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{ .mfi
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ldfpd fA21, fA23 = [rTmpPtr1], 16 // A21, A23 or B3, B8
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fma.s1 fXQuadr = fXSqr, fXSqr, f0 // x^4
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nop.i 0
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}
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;;
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{ .mfi
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ldfe fA7 = [rTmpPtr1] // A7 or Pi/2
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fma.s1 fRSqr = fR, fR, f0 // R^2
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nop.i 0
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}
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{ .mfb
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ldfpd fA25, fA27 = [rTmpPtr2] // A25, A27 or B9, B12
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nop.f 0
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(p6) br.cond.spnt asin_base_range;
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}
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;;
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{ .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
|
|
fma.s1 fPiBy2 = fPiBy2, fSignX, f0 // signum(x)*Pi/2
|
|
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
|
|
// signum(x)*(Pi/2 - PolB*S2)
|
|
fma.s1 fPiBy2 = fSignedS, fCloseTo1Pol, fPiBy2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// -signum(x)*PolB * S2
|
|
fma.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, fPiBy2
|
|
// exit here for 0.625 <= |x| < 1
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
|
|
// here if |x| < 0.625
|
|
.align 32
|
|
asin_base_range:
|
|
{ .mfi
|
|
nop.m 0
|
|
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
|
|
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
|
|
fma.d.s0 f8 = fBaseP, fXCube, f8
|
|
// exit here for |x| < 0.625 path
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if |x| = 1
|
|
// asin(x) = sign(x) * Pi/2
|
|
.align 32
|
|
asin_abs_1:
|
|
{ .mfi
|
|
ldfe fPiBy2 = [rPiBy2Ptr] // Pi/2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{.mfb
|
|
nop.m 0
|
|
// result for |x| = 1.0
|
|
fma.d.s0 f8 = fPiBy2, fSignX, f0
|
|
// exit here for |x| = 1.0
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if x is a NaN, denormal, or zero
|
|
.align 32
|
|
asin_special:
|
|
{ .mfi
|
|
nop.m 0
|
|
// 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
|
|
nop.m 0
|
|
// 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
|
|
}
|
|
;;
|
|
{ .mfb
|
|
nop.m 0
|
|
nop.f 0
|
|
// 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
|
|
// absolute value of normalized x
|
|
fmerge.s fNormX = f1, fNormX
|
|
nop.i 0
|
|
}
|
|
;;
|
|
{ .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 asin_unnormal_back
|
|
}
|
|
;;
|
|
// if we still here it means that input is "true" denormal
|
|
{ .mfb
|
|
nop.m 0
|
|
// final result if x is denormal
|
|
fma.d.s0 f8 = f8, fXSqr, f8
|
|
// exit here if x is denormal
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// here if |x| > 1.0
|
|
// error handler should be called
|
|
.align 32
|
|
asin_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 = 61 // error code
|
|
frcpa.s0 FR_RESULT, p0 = f0,f0
|
|
// call error handler routine
|
|
br.cond.sptk __libm_error_region
|
|
}
|
|
;;
|
|
GLOBAL_LIBM_END(asin)
|
|
libm_alias_double_other (asin, asin)
|
|
|
|
|
|
|
|
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#
|