2001-02-19 09:09:18 +00:00
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.file "acosl.s"
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2002-07-06 06:36:39 +00:00
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// Copyright (C) 2000, 2001, Intel Corporation
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2001-02-19 09:09:18 +00:00
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// All rights reserved.
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//
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// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
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// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
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2002-07-06 06:36:39 +00:00
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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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//
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2001-02-19 09:09:18 +00:00
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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://developer.intel.com/opensource.
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//
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// History
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//==============================================================
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// 2/02/00 Initial version
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// 2/07/00 Modified calculation of acos_corr to correct acosl
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// 4/04/00 Unwind support added
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// 8/15/00 Bundle added after call to __libm_error_support to properly
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// set [the previously overwritten] GR_Parameter_RESULT.
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// 12/20/00 Set denormal flag properly.
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//
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// API
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//==============================================================
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// double-extended = acosl (double-extended)
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// input floating point f8
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// output floating point f8
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//
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// Registers used
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//==============================================================
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//
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// predicate registers used:
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// p6 -> p12
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//
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// floating-point registers used:
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// f8 has input, then output
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// f8 -> f15, f32 ->f99
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//
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// general registers used:
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// r32 -> r48
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//
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// Overview of operation
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//==============================================================
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// There are three paths
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// 1. |x| < 2^-25 ACOS_TINY
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// 2. 2^-25 <= |x| < 1/4 ACOS_POLY
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// 3. 1/4 <= |x| < 1 ACOS_ATAN
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#include "libm_support.h"
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// Assembly macros
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//==============================================================
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// f8 is input, but acos_V must be put in f8
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// when __libm_atan2_reg is called, f8 must get V
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// f9 gets U when __libm_atan2_reg is called
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// __libm_atan2_reg returns
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// f8 = Z_hi
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// f10 = Z_lo
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// f11 = s_lo
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acos_Z_hi = f8
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acos_Z_lo = f10
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acos_S_lo = f11
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// When we call __libm_atan2_reg, we must save
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// the following:
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acos_corr = f12
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acos_X = f13
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acos_pi_hi = f14
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acos_pi_lo = f15
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// The rest of the assembly macros
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acos_P79 = f32
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acos_P59 = f33
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acos_P39 = f34
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acos_P19 = f35
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acos_P810 = f36
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acos_P610 = f37
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acos_P410 = f38
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acos_P210 = f39
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acos_A1 = f41
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acos_A2 = f42
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acos_A3 = f43
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acos_A4 = f44
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acos_A5 = f45
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acos_A6 = f46
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acos_A7 = f47
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acos_A8 = f48
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acos_A9 = f49
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acos_A10 = f50
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acos_X2 = f51
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acos_X4 = f52
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acos_B = f53
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acos_Bb = f54
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acos_A = f55
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acos_Aa = f56
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acos_1mA = f57
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acos_W = f58
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acos_Ww = f59
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acos_y0 = f60
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acos_y1 = f61
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acos_y2 = f62
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acos_H = f63
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acos_Hh = f64
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acos_t1 = f65
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acos_t2 = f66
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acos_t3 = f67
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acos_t4 = f68
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acos_t5 = f69
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acos_Pseries = f70
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acos_NORM_f8 = f71
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acos_ABS_NORM_f8 = f72
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acos_2 = f73
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acos_P1P2 = f74
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acos_HALF = f75
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acos_U = f76
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acos_1mB = f77
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acos_V = f78
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acos_S = f79
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acos_BmUU = f80
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acos_BmUUpb = f81
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acos_2U = f82
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acos_1d2U = f83
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acos_Dd = f84
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acos_pi_by_2_hi = f85
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acos_pi_by_2_lo = f86
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acos_xmpi_by_2_lo = f87
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acos_xPmw = f88
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acos_Uu = f89
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acos_AmVV = f90
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acos_AmVVpa = f91
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acos_2V = f92
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acos_1d2V = f93
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acos_Vv = f94
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acos_Vu = f95
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acos_Uv = f96
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acos_2_Z_hi = f97
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acos_s_lo_Z_lo = f98
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acos_result_lo = f99
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acos_Z_hi = f8
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acos_Z_lo = f10
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acos_s_lo = f11
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acos_GR_17_ones = r33
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acos_GR_16_ones = r34
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acos_GR_signexp_f8 = r35
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acos_GR_exp = r36
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acos_GR_true_exp = r37
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acos_GR_fffe = r38
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GR_SAVE_PFS = r43
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GR_SAVE_B0 = r39
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GR_SAVE_GP = r41
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// r40 is address of table of coefficients
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// r42
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GR_Parameter_X = r44
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GR_Parameter_Y = r45
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GR_Parameter_RESULT = r46
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GR_Parameter_TAG = r47
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// 2^-40:
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// A true exponent of -40 is
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// : -40 + register_bias
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// : -28 + ffff = ffd7
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// A true exponent of 1 is
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// : 1 + register_bias
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// : 1 + ffff = 10000
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// Data tables
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//==============================================================
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#ifdef _LIBC
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.rodata
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#else
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.data
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#endif
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.align 16
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acos_coefficients:
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ASM_TYPE_DIRECTIVE(acos_coefficients,@object)
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data8 0xc90fdaa22168c234, 0x00003FFF // pi_by_2_hi
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data8 0xc4c6628b80dc1cd1, 0x00003FBF // pi_by_2_lo
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data8 0xc90fdaa22168c234, 0x00004000 // pi_hi
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data8 0xc4c6628b80dc1cd1, 0x00003FC0 // pi_lo
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data8 0xBB08911F2013961E, 0x00003FF8 // A10
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data8 0x981F1095A23A87D3, 0x00003FF8 // A9
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data8 0xBDF09C6C4177BCC6, 0x00003FF8 // A8
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data8 0xE4C3A60B049ACCEA, 0x00003FF8 // A7
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data8 0x8E2789F4E8A8F1AD, 0x00003FF9 // A6
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data8 0xB745D09B2B0E850B, 0x00003FF9 // A5
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data8 0xF8E38E3BC4C50920, 0x00003FF9 // A4
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data8 0xB6DB6DB6D89FCD81, 0x00003FFA // A3
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data8 0x99999999999AF376, 0x00003FFB // A2
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data8 0xAAAAAAAAAAAAAA71, 0x00003FFC // A1
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ASM_SIZE_DIRECTIVE(acos_coefficients)
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.align 32
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.global acosl#
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ASM_TYPE_DIRECTIVE(acosl#,@function)
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.section .text
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.proc acosl#
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.align 32
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acosl:
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// After normalizing f8, get its true exponent
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{ .mfi
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alloc r32 = ar.pfs,1,11,4,0
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(p0) fnorm.s1 acos_NORM_f8 = f8
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(p0) mov acos_GR_17_ones = 0x1ffff
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}
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{ .mmi
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(p0) mov acos_GR_16_ones = 0xffff
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(p0) addl r40 = @ltoff(acos_coefficients), gp
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nop.i 999
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}
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;;
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// Set denormal flag on denormal input with fcmp
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{ .mfi
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ld8 r40 = [r40]
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fcmp.eq p6,p0 = f8,f0
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nop.i 999
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}
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;;
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// Load the constants pi_by_2 and pi.
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// Each is stored as hi and lo values
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// Also load the coefficients for ACOS_POLY
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{ .mmi
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(p0) ldfe acos_pi_by_2_hi = [r40],16 ;;
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(p0) ldfe acos_pi_by_2_lo = [r40],16
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nop.i 999 ;;
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}
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{ .mmi
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(p0) ldfe acos_pi_hi = [r40],16 ;;
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(p0) ldfe acos_pi_lo = [r40],16
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nop.i 999 ;;
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}
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{ .mmi
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(p0) ldfe acos_A10 = [r40],16 ;;
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(p0) ldfe acos_A9 = [r40],16
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nop.i 999 ;;
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}
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// Take the absolute value of f8
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{ .mmf
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nop.m 999
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(p0) getf.exp acos_GR_signexp_f8 = acos_NORM_f8
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(p0) fmerge.s acos_ABS_NORM_f8 = f0, acos_NORM_f8
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}
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{ .mii
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(p0) ldfe acos_A8 = [r40],16
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nop.i 999 ;;
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(p0) and acos_GR_exp = acos_GR_signexp_f8, acos_GR_17_ones ;;
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}
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// case 1: |x| < 2^-25 ==> p6 ACOS_TINY
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// case 2: 2^-25 <= |x| < 2^-2 ==> p8 ACOS_POLY
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// case 3: 2^-2 <= |x| < 1 ==> p9 ACOS_ATAN
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// case 4: 1 <= |x| ==> p11 ACOS_ERROR_RETURN
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// Admittedly |x| = 1 is not an error but this is where that case is
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// handled.
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{ .mii
|
|
|
|
|
(p0) ldfe acos_A7 = [r40],16
|
|
|
|
|
(p0) sub acos_GR_true_exp = acos_GR_exp, acos_GR_16_ones ;;
|
|
|
|
|
(p0) cmp.ge.unc p6, p7 = -26, acos_GR_true_exp ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mii
|
|
|
|
|
(p0) ldfe acos_A6 = [r40],16
|
|
|
|
|
(p7) cmp.ge.unc p8, p9 = -3, acos_GR_true_exp ;;
|
|
|
|
|
(p9) cmp.ge.unc p10, p11 = -1, acos_GR_true_exp
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mmi
|
|
|
|
|
(p0) ldfe acos_A5 = [r40],16 ;;
|
|
|
|
|
(p0) ldfe acos_A4 = [r40],16
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mmi
|
|
|
|
|
(p0) ldfe acos_A3 = [r40],16 ;;
|
|
|
|
|
(p0) ldfe acos_A2 = [r40],16
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// ACOS_ERROR_RETURN ==> p11 is true
|
|
|
|
|
// case 4: |x| >= 1
|
|
|
|
|
{ .mib
|
|
|
|
|
(p0) ldfe acos_A1 = [r40],16
|
|
|
|
|
nop.i 999
|
|
|
|
|
(p11) br.spnt L(ACOS_ERROR_RETURN) ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// ACOS_TINY ==> p6 is true
|
|
|
|
|
// case 1: |x| < 2^-25
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fms.s1 acos_xmpi_by_2_lo = acos_NORM_f8,f1, acos_pi_by_2_lo
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfb
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fms.s0 f8 = acos_pi_by_2_hi,f1, acos_xmpi_by_2_lo
|
|
|
|
|
(p6) br.ret.spnt b0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// ACOS_POLY ==> p8 is true
|
|
|
|
|
// case 2: 2^-25 <= |x| < 2^-2
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fms.s1 acos_W = acos_pi_by_2_hi, f1, acos_NORM_f8
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_X2 = f8,f8, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fms.s1 acos_Ww = acos_pi_by_2_hi, f1, acos_W
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_X4 = acos_X2,acos_X2, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fms.s1 acos_Ww = acos_Ww, f1, acos_NORM_f8
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P810 = acos_X4, acos_A10, acos_A8
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_P79 = X4*A9 + A7
|
|
|
|
|
// acos_P810 = X4*A10 + A8
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P79 = acos_X4, acos_A9, acos_A7
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_Ww = acos_Ww, f1, acos_pi_by_2_lo
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P610 = acos_X4, acos_P810, acos_A6
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// acos_P59 = X4*(X4*A9 + A7) + A5
|
|
|
|
|
// acos_P610 = X4*(X4*A10 + A8) + A6
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P59 = acos_X4, acos_P79, acos_A5
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P410 = acos_X4, acos_P610, acos_A4
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_P39 = X4*(X4*(X4*A9 + A7) + A5) + A3
|
|
|
|
|
// acos_P410 = X4*(X4*(X4*A10 + A8) + A6) + A4
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P39 = acos_X4, acos_P59, acos_A3
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P210 = acos_X4, acos_P410, acos_A2
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_P19 = X4*(X4*(X4*(X4*A9 + A7) + A5) + A3) + A1 = P1
|
|
|
|
|
// acos_P210 = X4*(X4*(X4*(X4*A10 + A8) + A6) + A4) + A2 = P2
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P19 = acos_X4, acos_P39, acos_A1
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_P1P2 = Xsq*P2 + P1
|
|
|
|
|
// acos_P1P2 = Xsq*(Xsq*P2 + P1)
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P1P2 = acos_X2, acos_P210, acos_P19
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s1 acos_P1P2 = acos_X2, acos_P1P2, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fms.s1 acos_xPmw = acos_NORM_f8, acos_P1P2, acos_Ww
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfb
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fms.s0 f8 = acos_W, f1, acos_xPmw
|
|
|
|
|
(p8) br.ret.spnt b0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// ACOS_ATAN
|
|
|
|
|
// case 3: 2^-2 <= |x| < 1
|
|
|
|
|
// case 3: 2^-2 <= |x| < 1 ==> p9 ACOS_ATAN
|
|
|
|
|
|
|
|
|
|
// Step 1.1: Get A,B and a,b
|
|
|
|
|
// A + a = 1- |X|
|
|
|
|
|
// B + b = 1+ |X|
|
|
|
|
|
// Note also that we will use acos_corr (f13)
|
|
|
|
|
// and acos_W
|
|
|
|
|
|
|
|
|
|
// Step 2
|
|
|
|
|
// Call __libm_atan2_reg
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
(p0) mov acos_GR_fffe = 0xfffe
|
|
|
|
|
(p0) fma.s1 acos_B = f1,f1, acos_ABS_NORM_f8
|
|
|
|
|
(p0) mov GR_SAVE_B0 = b0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mmf
|
|
|
|
|
(p0) mov GR_SAVE_GP = gp
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fms.s1 acos_A = f1,f1, acos_ABS_NORM_f8
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
(p0) setf.exp acos_HALF = acos_GR_fffe
|
|
|
|
|
nop.f 999
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fms.s1 acos_1mB = f1,f1, acos_B
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// We want atan2(V,U)
|
|
|
|
|
// so put V in f8 and U in f9
|
|
|
|
|
// but save X in acos_X
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fmerge.se acos_X = f8, f8
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// Step 1.2:
|
|
|
|
|
/////////////////////////
|
|
|
|
|
// Get U = sqrt(B)
|
|
|
|
|
/////////////////////////
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) frsqrta.s1 acos_y0,p8 = acos_B
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fms.s1 acos_1mA = f1,f1, acos_A
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_Bb = acos_1mB,f1, acos_ABS_NORM_f8
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_Hh = acos_HALF, acos_B, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_t1 = acos_y0, acos_y0, f0
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fms.s1 acos_Aa = acos_1mA,f1, acos_ABS_NORM_f8
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fnma.s1 acos_t2 = acos_t1, acos_Hh, acos_HALF
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_y1 = acos_t2, acos_y0, acos_y0
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// Step 1.2:
|
|
|
|
|
/////////////////////////
|
|
|
|
|
// Get V = sqrt(A)
|
|
|
|
|
/////////////////////////
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) frsqrta.s1 acos_y0,p8 = acos_A
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_t3 = acos_y1, acos_Hh, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_t1 = acos_y0, acos_y0, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fnma.s1 acos_t4 = acos_t3, acos_y1, acos_HALF
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_y2 = acos_t4, acos_y1, acos_y1
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_S = acos_B, acos_y2, f0
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_H = acos_y2, acos_HALF, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_t5 = acos_Hh, acos_y2, f0
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_Hh = acos_HALF, acos_A, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fnma.s1 acos_Dd = acos_S, acos_S, acos_B
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fnma.s1 acos_t2 = acos_t1, acos_Hh, acos_HALF
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_U = acos_Dd, acos_H, acos_S
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_y1 = acos_t2, acos_y0, acos_y0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_2U = acos_U, f1, acos_U
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_t3 = acos_y1, acos_Hh, f0
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// Step 1.3:
|
|
|
|
|
// sqrt(A + a) = V + v
|
|
|
|
|
// sqrt(B + b) = U + u
|
|
|
|
|
|
|
|
|
|
/////////////////////////
|
|
|
|
|
// Get u
|
|
|
|
|
/////////////////////////
|
|
|
|
|
|
|
|
|
|
// acos_BmUU = B - UU
|
|
|
|
|
// acos_BmUUpb = (B - UU) + b
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fnma.s1 acos_BmUU = acos_U, acos_U, acos_B
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fmerge.se f9 = acos_U, acos_U
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fnma.s1 acos_t4 = acos_t3, acos_y1, acos_HALF
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_1d2U = frcpa(2U)
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) frcpa.s1 acos_1d2U,p9 = f1, acos_2U
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_BmUUpb = acos_BmUU, f1, acos_Bb
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_y2 = acos_t4, acos_y1, acos_y1
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
// acos_Uu = ((B - UU) + b) * frcpa(2U)
|
|
|
|
|
(p0) fma.s1 acos_Uu = acos_BmUUpb, acos_1d2U, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_S = acos_A, acos_y2, f0
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_H = acos_y2, acos_HALF, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_t5 = acos_Hh, acos_y2, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fnma.s1 acos_Dd = acos_S, acos_S, acos_A
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_V = acos_Dd, acos_H, acos_S
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_2V = acos_V, f1, acos_V
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// Step 3
|
|
|
|
|
/////////////////////////
|
|
|
|
|
// Calculate the correction, acos_corr
|
|
|
|
|
/////////////////////////
|
|
|
|
|
// acos_corr = U*v - (V*u)
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_Vu = acos_V,acos_Uu, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/////////////////////////
|
|
|
|
|
// Get v
|
|
|
|
|
/////////////////////////
|
|
|
|
|
// acos_AmVV = A - VV
|
|
|
|
|
// acos_AmVVpa = (A - VV) + a
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fnma.s1 acos_AmVV = acos_V, acos_V, acos_A
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fmerge.se f8 = acos_V, acos_V
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_AmVVpa = acos_AmVV, f1, acos_Aa
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_1d2V = frcpa(2V)
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) frcpa.s1 acos_1d2V,p9 = f1, acos_2V
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_Vv = ((A - VV) + a) * frcpa(2V)
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_Vv = acos_AmVVpa, acos_1d2V, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_Uv = acos_U,acos_Vv, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.endp acosl#
|
|
|
|
|
ASM_SIZE_DIRECTIVE(acosl#)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.proc __libm_callout
|
|
|
|
|
__libm_callout:
|
|
|
|
|
.prologue
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 0
|
|
|
|
|
nop.f 0
|
|
|
|
|
.save ar.pfs,GR_SAVE_PFS
|
|
|
|
|
mov GR_SAVE_PFS=ar.pfs
|
|
|
|
|
}
|
|
|
|
|
;;
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
mov GR_SAVE_GP=gp
|
|
|
|
|
nop.f 0
|
|
|
|
|
.save b0, GR_SAVE_B0
|
|
|
|
|
mov GR_SAVE_B0=b0
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
.body
|
|
|
|
|
{ .mfb
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fms.s1 acos_corr = acos_Uv,f1, acos_Vu
|
|
|
|
|
(p0) br.call.sptk.many b0=__libm_atan2_reg# ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// p6 ==> X is negative
|
|
|
|
|
// p7 ==> x is positive
|
|
|
|
|
// We know that |X| >= 1/4
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
(p0) mov gp = GR_SAVE_GP
|
|
|
|
|
(p0) fcmp.lt.unc p6,p7 = acos_X , f0
|
|
|
|
|
(p0) mov b0 = GR_SAVE_B0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_2_Z_hi = 2 * acos_Z_hi
|
|
|
|
|
// acos_s_lo_Z_lo = s_lo * Z_lo
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_2_Z_hi = acos_Z_hi, f1, acos_Z_hi
|
|
|
|
|
(p0) mov ar.pfs = GR_SAVE_PFS
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_s_lo_Z_lo = acos_s_lo, acos_Z_lo, f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 2 is a constant needed later
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s1 acos_2 = f1,f1,f1
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// X >= 1/4
|
|
|
|
|
// acos_result_lo = 2(s_lo * Z_lo) - corr
|
|
|
|
|
// f8 = (2*Z_hi) + (2(s_lo * Z_lo) - corr)
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p7) fma.s1 acos_result_lo = acos_s_lo_Z_lo, acos_2, acos_corr
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p7) fma.s0 f8 = acos_2_Z_hi, f1, acos_result_lo
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_result_lo = (pi_lo - corr)
|
|
|
|
|
// acos_result_lo = (pi_lo - corr) + acos_Ww
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fms.s1 acos_result_lo = acos_pi_lo, f1, acos_corr
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// X <= -1/4
|
|
|
|
|
// acos_W = pi_hi - 2 * Z_hi
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fnma.s1 acos_W = acos_2, acos_Z_hi, acos_pi_hi
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_Ww = pi_hi - W
|
|
|
|
|
// acos_Ww = (pi_hi - W) + (2 * Z_hi)
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fms.s1 acos_Ww = acos_pi_hi, f1, acos_W
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fms.s1 acos_Ww = acos_Ww, f1, acos_2_Z_hi
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fma.s1 acos_result_lo = acos_result_lo, f1, acos_Ww
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// acos_Z_lo = ((pi_lo - corr) + acos_Ww) - 2 * (s_lo * Z_lo)
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fnma.s1 acos_Z_lo = acos_s_lo_Z_lo, acos_2, acos_result_lo
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfb
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fma.s0 f8 = acos_W, f1, acos_Z_lo
|
|
|
|
|
(p0) br.ret.sptk b0 ;;
|
|
|
|
|
}
|
|
|
|
|
.endp __libm_callout
|
|
|
|
|
ASM_SIZE_DIRECTIVE(__libm_callout)
|
|
|
|
|
|
|
|
|
|
.proc SPECIAL
|
|
|
|
|
SPECIAL:
|
|
|
|
|
L(ACOS_NAN):
|
|
|
|
|
{ .mfb
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fma.s0 f8 = f8,f1,f0
|
|
|
|
|
(p0) br.ret.sptk b0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
L(ACOS_ERROR_RETURN):
|
|
|
|
|
// Save ar.pfs, b0, and gp; restore on exit
|
|
|
|
|
|
|
|
|
|
// qnan snan inf norm unorm 0 -+
|
|
|
|
|
// 1 1 0 0 0 0 11 = 0xc3
|
|
|
|
|
|
|
|
|
|
// Coming in as X = +- 1
|
|
|
|
|
// What should we return?
|
|
|
|
|
|
|
|
|
|
// If X is 1, return (sign of X)pi/2
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fcmp.eq.unc p6,p7 = acos_ABS_NORM_f8,f1
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p6) fcmp.lt.unc p8,p9 = f8,f0
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p8) fma.s0 f8 = acos_pi_hi, f1, acos_pi_lo
|
|
|
|
|
nop.i 999
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfb
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p9) fmerge.s f8 = f8,f0
|
|
|
|
|
(p6) br.ret.spnt b0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// If X is a NAN, leave
|
|
|
|
|
{ .mfi
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p0) fclass.m.unc p12,p0 = f8, 0xc3
|
|
|
|
|
nop.i 999 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfb
|
|
|
|
|
nop.m 999
|
|
|
|
|
(p12) fma.s0 f8 = f8,f1,f0
|
|
|
|
|
(p12) br.ret.spnt b0 ;;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
{ .mfi
|
|
|
|
|
(p0) mov GR_Parameter_TAG = 57
|
|
|
|
|
(p0) frcpa f10, p6 = f0, f0
|
|
|
|
|
nop.i 999
|
|
|
|
|
};;
|
|
|
|
|
|
|
|
|
|
.endp SPECIAL
|
|
|
|
|
ASM_SIZE_DIRECTIVE(SPECIAL)
|
|
|
|
|
|
|
|
|
|
.proc __libm_error_region
|
|
|
|
|
__libm_error_region:
|
|
|
|
|
.prologue
|
|
|
|
|
// (1)
|
|
|
|
|
{ .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
|
|
|
|
|
};;
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// (2)
|
|
|
|
|
{ .mmi
|
|
|
|
|
stfe [GR_Parameter_Y] = f1,16 // 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
|
|
|
|
|
// (3)
|
|
|
|
|
{ .mib
|
|
|
|
|
stfe [GR_Parameter_X] = f8 // Store Parameter 1 on stack
|
|
|
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y
|
|
|
|
|
nop.b 0 // Parameter 3 address
|
|
|
|
|
}
|
|
|
|
|
{ .mib
|
|
|
|
|
stfe [GR_Parameter_Y] = f10 // Store Parameter 3 on stack
|
|
|
|
|
add GR_Parameter_Y = -16,GR_Parameter_Y
|
|
|
|
|
br.call.sptk b0=__libm_error_support# // Call error handling function
|
|
|
|
|
};;
|
|
|
|
|
{ .mmi
|
|
|
|
|
nop.m 0
|
|
|
|
|
nop.m 0
|
|
|
|
|
add GR_Parameter_RESULT = 48,sp
|
|
|
|
|
};;
|
|
|
|
|
|
|
|
|
|
// (4)
|
|
|
|
|
{ .mmi
|
|
|
|
|
ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
|
|
|
|
|
.restore sp
|
|
|
|
|
add sp = 64,sp // Restore stack pointer
|
|
|
|
|
mov b0 = GR_SAVE_B0 // Restore return address
|
|
|
|
|
};;
|
|
|
|
|
|
|
|
|
|
{ .mib
|
|
|
|
|
mov gp = GR_SAVE_GP // Restore gp
|
|
|
|
|
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
|
|
|
|
|
br.ret.sptk b0 // Return
|
|
|
|
|
};;
|
|
|
|
|
|
|
|
|
|
.endp __libm_error_region
|
|
|
|
|
ASM_SIZE_DIRECTIVE(__libm_error_region)
|
|
|
|
|
|
|
|
|
|
.type __libm_error_support#,@function
|
|
|
|
|
.global __libm_error_support#
|
|
|
|
|
|
|
|
|
|
.type __libm_atan2_reg#,@function
|
|
|
|
|
.global __libm_atan2_reg#
|
