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We stopped adding "Contributed by" or similar lines in sources in 2012 in favour of git logs and keeping the Contributors section of the glibc manual up to date. Removing these lines makes the license header a bit more consistent across files and also removes the possibility of error in attribution when license blocks or files are copied across since the contributed-by lines don't actually reflect reality in those cases. Move all "Contributed by" and similar lines (Written by, Test by, etc.) into a new file CONTRIBUTED-BY to retain record of these contributions. These contributors are also mentioned in manual/contrib.texi, so we just maintain this additional record as a courtesy to the earlier developers. The following scripts were used to filter a list of files to edit in place and to clean up the CONTRIBUTED-BY file respectively. These were not added to the glibc sources because they're not expected to be of any use in future given that this is a one time task: https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02 Reviewed-by: Carlos O'Donell <carlos@redhat.com>
676 lines
19 KiB
ArmAsm
676 lines
19 KiB
ArmAsm
.file "asinf.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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//
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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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// 06/28/00 Improved speed
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// 06/31/00 Changed register allocation because of some duplicate macros
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// moved nan exit bundle up to gain a cycle.
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// 08/08/00 Improved speed by avoiding SIR flush.
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// 08/15/00 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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// 08/17/00 Changed predicate register macro-usage to direct predicate
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// names due to an assembler bug.
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// 10/17/00 Improved speed of x=0 and x=1 paths, set D flag if x denormal.
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// 03/13/01 Corrected sign of imm1 value in dep instruction.
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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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// Description
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//=========================================
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// The asinf function computes the arc sine of x in the range [-pi,+pi].
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// A doman error occurs for arguments not in the range [-1,+1].
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// asinf(+-0) returns +-0
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// asinf(x) returns a Nan and raises the invalid exception for |x| >1
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// The acosf function returns the arc cosine in the range [0, +pi] radians.
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// A doman error occurs for arguments not in the range [-1,+1].
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// acosf(1) returns +0
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// acosf(x) returns a Nan and raises the invalid exception for |x| >1
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// |x| <= sqrt(2)/2. get Ax and Bx
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// poly_p1 = x p1
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// poly_p3 = x2 p4 + p3
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// poly_p1 = x2 (poly_p1) + x = x2(x p1) + x
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// poly_p2 = x2( poly_p3) + p2 = x2(x2 p4 + p3) + p2
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// poly_Ax = x5(x2( poly_p3) + p2) + x2(x p1) + x
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// = x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x
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// poly_p7 = x2 p8 + p7
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// poly_p5 = x2 p6 + p5
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// poly_p7 = x4 p9 + (poly_p7)
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// poly_p7 = x4 p9 + (x2 p8 + p7)
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// poly_Bx = x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5
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// answer1 = x11(x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5) + x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x
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// = x19 p9 + x17 p8 + x15 p7 x13 p6 + x11 p5 + x9 p4 + x7 p3 + x5 p2 + x3 p1 + x
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// |x| > sqrt(2)/2
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// Get z = sqrt(1-x2)
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// Get polynomial in t = 1-x2
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// t2 = t t
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// t4 = t2 t2
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// poly_p4 = t p5 + p4
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// poly_p1 = t p1 + 1
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// poly_p6 = t p7 + p6
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// poly_p2 = t p3 + p2
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// poly_p8 = t p9 + p8
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// poly_p4 = t2 poly_p6 + poly_p4
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// = t2 (t p7 + p6) + (t p5 + p4)
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// poly_p2 = t2 poly_p2 + poly_p1
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// = t2 (t p3 + p2) + (t p1 + 1)
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// poly_p4 = t4 poly_p8 + poly_p4
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// = t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4))
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// P(t) = poly_p2 + t4 poly_p8
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// = t2 (t p3 + p2) + (t p1 + 1) + t4 (t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4)))
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// = t3 p3 + t2 p2 + t p1 + 1 + t9 p9 + t8 p8 + t7 p7 + t6 p6 + t5 p5 + t4 p4
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// answer2 = - sign(x) z P(t) + (sign(x) pi/2)
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//
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// Assembly macros
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//=========================================
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// predicate registers
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//asinf_pred_LEsqrt2by2 = p7
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//asinf_pred_GTsqrt2by2 = p8
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// integer registers
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ASINF_Addr1 = r33
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ASINF_Addr2 = r34
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ASINF_GR_1by2 = r35
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ASINF_GR_3by2 = r36
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ASINF_GR_5by2 = r37
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GR_SAVE_B0 = r38
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GR_SAVE_PFS = r39
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GR_SAVE_GP = r40
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GR_Parameter_X = r41
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GR_Parameter_Y = r42
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GR_Parameter_RESULT = r43
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GR_Parameter_TAG = r44
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// floating point registers
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asinf_y = f32
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asinf_abs_x = f33
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asinf_x2 = f34
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asinf_sgn_x = f35
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asinf_1by2 = f36
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asinf_3by2 = f37
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asinf_5by2 = f38
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asinf_coeff_P3 = f39
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asinf_coeff_P8 = f40
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asinf_coeff_P1 = f41
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asinf_coeff_P4 = f42
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asinf_coeff_P5 = f43
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asinf_coeff_P2 = f44
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asinf_coeff_P7 = f45
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asinf_coeff_P6 = f46
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asinf_coeff_P9 = f47
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asinf_x2 = f48
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asinf_x3 = f49
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asinf_x4 = f50
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asinf_x8 = f51
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asinf_x5 = f52
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asinf_const_piby2 = f53
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asinf_const_sqrt2by2 = f54
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asinf_x11 = f55
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asinf_poly_p1 = f56
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asinf_poly_p3 = f57
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asinf_sinf1 = f58
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asinf_poly_p2 = f59
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asinf_poly_Ax = f60
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asinf_poly_p7 = f61
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asinf_poly_p5 = f62
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asinf_sgnx_t4 = f63
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asinf_poly_Bx = f64
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asinf_t = f65
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asinf_yby2 = f66
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asinf_B = f67
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asinf_B2 = f68
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asinf_Az = f69
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asinf_dz = f70
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asinf_Sz = f71
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asinf_d2z = f72
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asinf_Fz = f73
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asinf_z = f74
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asinf_sgnx_z = f75
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asinf_t2 = f76
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asinf_2poly_p4 = f77
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asinf_2poly_p6 = f78
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asinf_2poly_p1 = f79
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asinf_2poly_p2 = f80
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asinf_2poly_p8 = f81
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asinf_t4 = f82
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asinf_Pt = f83
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asinf_sgnx_2poly_p2 = f84
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asinf_sgn_x_piby2 = f85
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asinf_poly_p7a = f86
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asinf_2poly_p4a = f87
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asinf_2poly_p4b = f88
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asinf_2poly_p2a = f89
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asinf_poly_p1a = f90
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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(asinf_coeff_1_table)
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data8 0x3FC5555607DCF816 // P1
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data8 0x3F9CF81AD9BAB2C6 // P4
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data8 0x3FC59E0975074DF3 // P7
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data8 0xBFA6F4CC2780AA1D // P6
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data8 0x3FC2DD45292E93CB // P9
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data8 0x3fe6a09e667f3bcd // sqrt(2)/2
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LOCAL_OBJECT_END(asinf_coeff_1_table)
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LOCAL_OBJECT_START(asinf_coeff_2_table)
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data8 0x3FA6F108E31EFBA6 // P3
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data8 0xBFCA31BF175D82A0 // P8
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data8 0x3FA30C0337F6418B // P5
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data8 0x3FB332C9266CB1F9 // P2
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data8 0x3ff921fb54442d18 // pi_by_2
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LOCAL_OBJECT_END(asinf_coeff_2_table)
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.section .text
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GLOBAL_LIBM_ENTRY(asinf)
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// Load the addresses of the two tables.
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// Then, load the coefficients and other constants.
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{ .mfi
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alloc r32 = ar.pfs,1,8,4,0
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fnma.s1 asinf_t = f8,f8,f1
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dep.z ASINF_GR_1by2 = 0x3f,24,8 // 0x3f000000
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}
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{ .mfi
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addl ASINF_Addr1 = @ltoff(asinf_coeff_1_table),gp
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fma.s1 asinf_x2 = f8,f8,f0
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addl ASINF_Addr2 = @ltoff(asinf_coeff_2_table),gp ;;
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}
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{ .mfi
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ld8 ASINF_Addr1 = [ASINF_Addr1]
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fmerge.s asinf_abs_x = f1,f8
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dep ASINF_GR_3by2 = -1,r0,22,8 // 0x3fc00000
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}
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{ .mlx
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nop.m 999
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movl ASINF_GR_5by2 = 0x40200000;;
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}
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{ .mfi
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setf.s asinf_1by2 = ASINF_GR_1by2
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fmerge.s asinf_sgn_x = f8,f1
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nop.i 999
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}
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{ .mfi
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ld8 ASINF_Addr2 = [ASINF_Addr2]
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nop.f 0
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nop.i 999;;
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}
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{ .mfi
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setf.s asinf_5by2 = ASINF_GR_5by2
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fcmp.lt.s1 p11,p12 = f8,f0
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nop.i 999;;
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}
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{ .mmf
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ldfpd asinf_coeff_P1,asinf_coeff_P4 = [ASINF_Addr1],16
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setf.s asinf_3by2 = ASINF_GR_3by2
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fclass.m.unc p8,p0 = f8, 0xc3 ;; //@qnan | @snan
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}
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{ .mfi
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ldfpd asinf_coeff_P7,asinf_coeff_P6 = [ASINF_Addr1],16
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fma.s1 asinf_t2 = asinf_t,asinf_t,f0
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nop.i 999
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}
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{ .mfi
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ldfpd asinf_coeff_P3,asinf_coeff_P8 = [ASINF_Addr2],16
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fma.s1 asinf_x4 = asinf_x2,asinf_x2,f0
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nop.i 999;;
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}
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{ .mfi
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ldfpd asinf_coeff_P9,asinf_const_sqrt2by2 = [ASINF_Addr1]
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fclass.m.unc p10,p0 = f8, 0x07 //@zero
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nop.i 999
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}
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{ .mfi
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ldfpd asinf_coeff_P5,asinf_coeff_P2 = [ASINF_Addr2],16
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fma.s1 asinf_x3 = f8,asinf_x2,f0
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nop.i 999;;
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}
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{ .mfi
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ldfd asinf_const_piby2 = [ASINF_Addr2]
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frsqrta.s1 asinf_B,p0 = asinf_t
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nop.i 999
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}
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{ .mfb
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nop.m 999
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(p8) fma.s.s0 f8 = f8,f1,f0
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(p8) br.ret.spnt b0 ;; // Exit if x=nan
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}
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{ .mfb
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nop.m 999
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fcmp.eq.s1 p6,p0 = asinf_abs_x,f1
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(p10) br.ret.spnt b0 ;; // Exit if x=0
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}
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{ .mfi
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nop.m 999
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fcmp.gt.s1 p9,p0 = asinf_abs_x,f1
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_x8 = asinf_x4,asinf_x4,f0
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nop.i 999
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}
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{ .mfb
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nop.m 999
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fma.s1 asinf_t4 = asinf_t2,asinf_t2,f0
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(p6) br.cond.spnt ASINF_ABS_ONE ;; // Branch if |x|=1
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_x5 = asinf_x2,asinf_x3,f0
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nop.i 999
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}
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{ .mfb
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(p9) mov GR_Parameter_TAG = 62
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fma.s1 asinf_yby2 = asinf_t,asinf_1by2,f0
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(p9) br.cond.spnt __libm_error_region ;; // Branch if |x|>1
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_Az = asinf_t,asinf_B,f0
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_B2 = asinf_B,asinf_B,f0
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_poly_p1 = f8,asinf_coeff_P1,f0
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_2poly_p1 = asinf_coeff_P1,asinf_t,f1
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_poly_p3 = asinf_coeff_P4,asinf_x2,asinf_coeff_P3
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_2poly_p6 = asinf_coeff_P7,asinf_t,asinf_coeff_P6
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_poly_p7 = asinf_x2,asinf_coeff_P8,asinf_coeff_P7
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_2poly_p2 = asinf_coeff_P3,asinf_t,asinf_coeff_P2
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_poly_p5 = asinf_x2,asinf_coeff_P6,asinf_coeff_P5
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_2poly_p4 = asinf_coeff_P5,asinf_t,asinf_coeff_P4
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.d.s1 asinf_x11 = asinf_x8,asinf_x3,f0
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fnma.s1 asinf_dz = asinf_B2,asinf_yby2,asinf_1by2
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_poly_p1a = asinf_x2,asinf_poly_p1,f8
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_2poly_p8 = asinf_coeff_P9,asinf_t,asinf_coeff_P8
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nop.i 999;;
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}
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// Get the absolute value of x and determine the region in which x lies
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{ .mfi
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nop.m 999
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fcmp.le.s1 p7,p8 = asinf_abs_x,asinf_const_sqrt2by2
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 asinf_poly_p2 = asinf_x2,asinf_poly_p3,asinf_coeff_P2
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nop.i 999;;
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}
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|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 asinf_poly_p7a = asinf_x4,asinf_coeff_P9,asinf_poly_p7
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 asinf_2poly_p2a = asinf_2poly_p2,asinf_t2,asinf_2poly_p1
|
|
nop.i 999;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 asinf_sgnx_t4 = asinf_sgn_x,asinf_t4,f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 asinf_2poly_p4a = asinf_2poly_p6,asinf_t2,asinf_2poly_p4
|
|
nop.i 999;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 asinf_Sz = asinf_5by2,asinf_dz,asinf_3by2
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 asinf_d2z = asinf_dz,asinf_dz,f0
|
|
nop.i 999;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 asinf_sgn_x_piby2 = asinf_sgn_x,asinf_const_piby2,f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.d.s1 asinf_poly_Ax = asinf_x5,asinf_poly_p2,asinf_poly_p1a
|
|
nop.i 999;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.d.s1 asinf_poly_Bx = asinf_x4,asinf_poly_p7a,asinf_poly_p5
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 asinf_sgnx_2poly_p2 = asinf_sgn_x,asinf_2poly_p2a,f0
|
|
nop.i 999;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fcmp.eq.s0 p6,p0 = f8,f0 // Only purpose is to set D if x denormal
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 asinf_2poly_p4b = asinf_2poly_p8,asinf_t4,asinf_2poly_p4a
|
|
nop.i 999;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 asinf_Fz = asinf_d2z,asinf_Sz,asinf_dz
|
|
nop.i 999;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.d.s1 asinf_Pt = asinf_2poly_p4b,asinf_sgnx_t4,asinf_sgnx_2poly_p2
|
|
nop.i 999;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.d.s1 asinf_z = asinf_Az,asinf_Fz,asinf_Az
|
|
nop.i 999;;
|
|
}
|
|
|
|
.pred.rel "mutex",p8,p7 //asinf_pred_GTsqrt2by2,asinf_pred_LEsqrt2by2
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fnma.s.s0 f8 = asinf_z,asinf_Pt,asinf_sgn_x_piby2
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
(p7) fma.s.s0 f8 = asinf_x11,asinf_poly_Bx,asinf_poly_Ax
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
|
|
ASINF_ABS_ONE:
|
|
// Here for short exit if |x|=1
|
|
{ .mfb
|
|
nop.m 999
|
|
fma.s.s0 f8 = asinf_sgn_x,asinf_const_piby2,f0
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
GLOBAL_LIBM_END(asinf)
|
|
libm_alias_float_other (asin, asin)
|
|
|
|
// Stack operations when calling error support.
|
|
// (1) (2)
|
|
// sp -> + psp -> +
|
|
// | |
|
|
// | | <- GR_Y
|
|
// | |
|
|
// | <-GR_Y Y2->|
|
|
// | |
|
|
// | | <- GR_X
|
|
// | |
|
|
// sp-64 -> + sp -> +
|
|
// save ar.pfs save b0
|
|
// save gp
|
|
|
|
|
|
// Stack operations when calling error support.
|
|
// (3) (call) (4)
|
|
// psp -> + sp -> +
|
|
// | |
|
|
// R3 ->| <- GR_RESULT | -> f8
|
|
// | |
|
|
// Y2 ->| <- GR_Y |
|
|
// | |
|
|
// X1 ->| |
|
|
// | |
|
|
// sp -> + +
|
|
// restore gp
|
|
// restore ar.pfs
|
|
|
|
LOCAL_LIBM_ENTRY(__libm_error_region)
|
|
.prologue
|
|
{ .mfi
|
|
add GR_Parameter_Y=-32,sp // Parameter 2 value
|
|
nop.f 999
|
|
.save ar.pfs,GR_SAVE_PFS
|
|
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
|
|
}
|
|
{ .mfi
|
|
.fframe 64
|
|
add sp=-64,sp // Create new stack
|
|
nop.f 0
|
|
mov GR_SAVE_GP=gp // Save gp
|
|
};;
|
|
{ .mmi
|
|
stfs [GR_Parameter_Y] = 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
|
|
{ .mfi
|
|
nop.m 0
|
|
frcpa.s0 f9,p0 = f0,f0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mib
|
|
stfs [GR_Parameter_X] = f8 // Store Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y
|
|
nop.b 0 // Parameter 3 address
|
|
}
|
|
{ .mib
|
|
stfs [GR_Parameter_Y] = f9 // Store Parameter 3 on stack
|
|
add GR_Parameter_Y = -16,GR_Parameter_Y
|
|
br.call.sptk b0=__libm_error_support# // Call error handling function
|
|
};;
|
|
{ .mmi
|
|
nop.m 0
|
|
nop.m 0
|
|
add GR_Parameter_RESULT = 48,sp
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
|
|
.restore 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#
|