1048 lines
28 KiB
ArmAsm
1048 lines
28 KiB
ArmAsm
.file "atan2.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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//
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// History
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//==============================================================
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// 02/02/00 Initial version
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// 04/04/00 Unwind support added
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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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// 09/28/00 Updated to set invalid on SNaN inputs
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// 01/19/01 Fixed flags for small results
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// 04/13/01 Rescheduled to make all paths faster
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 08/20/02 Corrected inexact flag and directed rounding symmetry bugs
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// 02/06/03 Reordered header: .section, .global, .proc, .align
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// 04/17/03 Added missing mutex directive
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//
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// API
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//==============================================================
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// double atan2(double Y, double X)
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//
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// Overview of operation
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//==============================================================
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//
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// The atan2 function returns values in the interval [-pi,+pi].
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//
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// There are two basic paths: swap true and swap false.
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// atan2(Y,X) ==> atan2(V/U) where U >= V. If Y > X, we must swap.
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//
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// p6 swap True |Y| > |X|
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// p7 swap False |Y| <= |X|
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// p8 X+ (If swap=True p8=p9=0)
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// p9 X-
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//
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// all the other predicates p10 thru p15 are false for the main path
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//
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// Simple trigonometric identities show
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// Region 1 (-45 to +45 degrees):
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// X>0, |Y|<=X, V=Y, U=X atan2(Y,X) = sgnY * (0 + atan(V/U))
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//
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// Region 2 (-90 to -45 degrees, and +45 to +90 degrees):
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// X>0, |Y|>X, V=X, U=Y atan2(Y,X) = sgnY * (pi/2 - atan(V/U))
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//
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// Region 3 (-135 to -90 degrees, and +90 to +135 degrees):
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// X<0, |Y|>X, V=X, U=Y atan2(Y,X) = sgnY * (pi/2 + atan(V/U))
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//
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// Region 4 (-180 to -135 degrees, and +135 to +180 degrees):
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// X<0, |Y|<=X, V=Y, U=X atan2(Y,X) = sgnY * (pi - atan(V/U))
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//
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// So the result is always of the form atan2(Y,X) = P + sgnXY * atan(V/U)
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//
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// We compute atan(V/U) from the identity
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// atan(z) + atan([(V/U)-z] / [1+(V/U)z])
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// where z is a limited precision approximation (16 bits) to V/U
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//
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// z is calculated with the assistance of the frcpa instruction.
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//
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// atan(z) is calculated by a polynomial z + z^3 * p(w), w=z^2
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// where p(w) = P0+P1*w+...+P22*w^22
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//
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// Let d = [(V/U)-z] / [1+(V/U)z]) = (V-U*z)/(U+V*z)
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//
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// Approximate atan(d) by d + P0*d^3
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// Let F = 1/(U+V*z) * (1-a), where |a|< 2^-8.8.
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// Compute q(a) = 1 + a + ... + a^5.
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// Then F*q(a) approximates the reciprocal to more than 50 bits.
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// Special values
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//==============================================================
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// Y x Result
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// +number +inf +0
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// -number +inf -0
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// +number -inf +pi
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// -number -inf -pi
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//
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// +inf +number +pi/2
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// -inf +number -pi/2
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// +inf -number +pi/2
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// -inf -number -pi/2
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//
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// +inf +inf +pi/4
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// -inf +inf -pi/4
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// +inf -inf +3pi/4
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// -inf -inf -3pi/4
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//
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// +1 +1 +pi/4
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// -1 +1 -pi/4
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// +1 -1 +3pi/4
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// -1 -1 -3pi/4
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//
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// +number +0 +pi/2
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// -number +0 -pi/2
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// +number -0 +pi/2
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// -number -0 -pi/2
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//
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// +0 +number +0
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// -0 +number -0
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// +0 -number +pi
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// -0 -number -pi
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//
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// +0 +0 +0
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// -0 +0 -0
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// +0 -0 +pi
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// -0 -0 -pi
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//
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// Nan anything quiet Y
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// anything NaN quiet X
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// atan2(+-0/+-0) sets double error tag to 37
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// Registers used
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//==============================================================
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// predicate registers used:
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// p6 -> p15
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// floating-point registers used:
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// f8, f9 input
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// f32 -> f119
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// general registers used
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// r32 -> r41
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// Assembly macros
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//==============================================================
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EXP_AD_P1 = r33
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EXP_AD_P2 = r34
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rsig_near_one = r35
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GR_SAVE_B0 = r35
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GR_SAVE_GP = r36
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GR_SAVE_PFS = r37
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GR_Parameter_X = r38
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GR_Parameter_Y = r39
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GR_Parameter_RESULT = r40
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atan2_GR_tag = r41
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atan2_Y = f8
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atan2_X = f9
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atan2_u1_X = f32
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atan2_u1_Y = f33
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atan2_z2_X = f34
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atan2_z2_Y = f35
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atan2_two = f36
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atan2_B1sq_Y = f37
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atan2_z1_X = f38
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atan2_z1_Y = f39
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atan2_B1X = f40
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atan2_B1Y = f41
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atan2_wp_X = f42
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atan2_B1sq_X = f43
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atan2_z = f44
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atan2_w = f45
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atan2_P0 = f46
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atan2_P1 = f47
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atan2_P2 = f48
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atan2_P3 = f49
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atan2_P4 = f50
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atan2_P5 = f51
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atan2_P6 = f52
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atan2_P7 = f53
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atan2_P8 = f54
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atan2_P9 = f55
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atan2_P10 = f56
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atan2_P11 = f57
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atan2_P12 = f58
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atan2_P13 = f59
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atan2_P14 = f60
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atan2_P15 = f61
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atan2_P16 = f62
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atan2_P17 = f63
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atan2_P18 = f64
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atan2_P19 = f65
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atan2_P20 = f66
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atan2_P21 = f67
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atan2_P22 = f68
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atan2_tmp = f68
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atan2_pi_by_2 = f69
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atan2_sgn_pi_by_2 = f69
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atan2_V13 = f70
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atan2_W11 = f71
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atan2_E = f72
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atan2_wp_Y = f73
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atan2_V11 = f74
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atan2_V12 = f75
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atan2_V7 = f76
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atan2_V8 = f77
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atan2_W7 = f78
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atan2_W8 = f79
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atan2_W3 = f80
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atan2_W4 = f81
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atan2_V3 = f82
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atan2_V4 = f83
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atan2_F = f84
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atan2_gV = f85
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atan2_V10 = f86
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atan2_zcub = f87
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atan2_V6 = f88
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atan2_V9 = f89
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atan2_W10 = f90
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atan2_W6 = f91
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atan2_W2 = f92
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atan2_V2 = f93
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atan2_alpha = f94
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atan2_alpha_1 = f95
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atan2_gVF = f96
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atan2_V5 = f97
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atan2_W12 = f98
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atan2_W5 = f99
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atan2_alpha_sq = f100
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atan2_Cp = f101
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atan2_V1 = f102
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atan2_ysq = f103
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atan2_W1 = f104
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atan2_alpha_cub = f105
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atan2_C = f106
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atan2_xsq = f107
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atan2_d = f108
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atan2_A_hi = f109
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atan2_dsq = f110
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atan2_pd = f111
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atan2_A_lo = f112
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atan2_A = f113
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atan2_Pp = f114
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atan2_sgnY = f115
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atan2_sig_near_one = f116
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atan2_near_one = f116
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atan2_pi = f117
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atan2_sgn_pi = f117
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atan2_3pi_by_4 = f118
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atan2_pi_by_4 = f119
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/////////////////////////////////////////////////////////////
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RODATA
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.align 16
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LOCAL_OBJECT_START(atan2_tb1)
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data8 0xA21922DC45605EA1 , 0x00003FFA // P11
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data8 0xB199DD6D2675C40F , 0x0000BFFA // P10
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data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9
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data8 0xD78F28FC2A592781 , 0x0000BFFA // P8
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data8 0xF0F03ADB3FC930D3 , 0x00003FFA // P7
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data8 0x88887EBB209E3543 , 0x0000BFFB // P6
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data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5
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data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4
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data8 0xE38E38E320A8A098 , 0x00003FFB // P3
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data8 0x9249249247E37913 , 0x0000BFFC // P2
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data8 0xCCCCCCCCCCC906CD , 0x00003FFC // P1
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data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0
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data8 0xC90FDAA22168C235 , 0x00004000 // pi
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LOCAL_OBJECT_END(atan2_tb1)
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LOCAL_OBJECT_START(atan2_tb2)
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data8 0xCE585A259BD8374C , 0x00003FF0 // P21
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data8 0x9F90FB984D8E39D0 , 0x0000BFF3 // P20
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data8 0x9D3436AABE218776 , 0x00003FF5 // P19
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data8 0xDEC343E068A6D2A8 , 0x0000BFF6 // P18
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data8 0xF396268151CFB11C , 0x00003FF7 // P17
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data8 0xD818B4BB43D84BF2 , 0x0000BFF8 // P16
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data8 0xA2270D30A90AA220 , 0x00003FF9 // P15
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data8 0xD5F4F2182E7A8725 , 0x0000BFF9 // P14
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data8 0x80D601879218B53A , 0x00003FFA // P13
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data8 0x9297B23CCFFB291F , 0x0000BFFA // P12
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data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22
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data8 0xC90FDAA22168C235 , 0x00003FFF // pi/2
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data8 0xC90FDAA22168C235 , 0x00003FFE // pi/4
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data8 0x96cbe3f9990e91a8 , 0x00004000 // 3pi/4
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LOCAL_OBJECT_END(atan2_tb2)
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.section .text
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GLOBAL_IEEE754_ENTRY(atan2)
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{ .mfi
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alloc r32 = ar.pfs,1,5,4,0
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frcpa.s1 atan2_u1_X,p6 = f1,atan2_X
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nop.i 999
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}
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{ .mfi
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addl EXP_AD_P1 = @ltoff(atan2_tb1), gp
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fma.s1 atan2_two = f1,f1,f1
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nop.i 999
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;;
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}
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{ .mfi
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ld8 EXP_AD_P1 = [EXP_AD_P1]
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frcpa.s1 atan2_u1_Y,p7 = f1,atan2_Y
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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 atan2_xsq = atan2_X,atan2_X,f0
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nop.i 999
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;;
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}
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{ .mfi
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nop.m 999
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fclass.m p10,p0 = atan2_Y, 0xc3 // Test for y=nan
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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 atan2_ysq = atan2_Y,atan2_Y,f0
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nop.i 999
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}
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;;
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{ .mfi
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add EXP_AD_P2 = 0xd0,EXP_AD_P1
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fclass.m p12,p0 = atan2_X, 0xc3 // Test for x nan
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nop.i 999
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}
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;;
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// p10 Y NAN, quiet and return
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{ .mfi
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ldfe atan2_P11 = [EXP_AD_P1],16
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fmerge.s atan2_sgnY = atan2_Y,f1
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nop.i 999
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}
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{ .mfb
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ldfe atan2_P21 = [EXP_AD_P2],16
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(p10) fma.d.s0 f8 = atan2_Y,atan2_X,f0 // If y=nan, result quietized y
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(p10) br.ret.spnt b0 // Exit if y=nan
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;;
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}
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{ .mfi
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ldfe atan2_P10 = [EXP_AD_P1],16
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fma.s1 atan2_z1_X = atan2_u1_X, atan2_Y, f0
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nop.i 999
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}
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{ .mfi
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ldfe atan2_P20 = [EXP_AD_P2],16
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fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two
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nop.i 999
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;;
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}
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{ .mfi
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ldfe atan2_P9 = [EXP_AD_P1],16
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fma.s1 atan2_z1_Y = atan2_u1_Y, atan2_X, f0
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nop.i 999
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}
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{ .mfi
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ldfe atan2_P19 = [EXP_AD_P2],16
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fnma.s1 atan2_B1Y = atan2_u1_Y, atan2_Y, atan2_two
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nop.i 999
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}
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;;
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{ .mfi
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ldfe atan2_P8 = [EXP_AD_P1],16
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fma.s1 atan2_z2_X = atan2_u1_X, atan2_ysq, f0
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nop.i 999
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}
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{ .mfi
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ldfe atan2_P18 = [EXP_AD_P2],16
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fma.s1 atan2_z2_Y = atan2_u1_Y, atan2_xsq, f0
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nop.i 999
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}
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;;
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// p10 ==> x inf y ?
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// p11 ==> x !inf y ?
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{ .mfi
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ldfe atan2_P7 = [EXP_AD_P1],16
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fclass.m p10,p11 = atan2_X, 0x23 // test for x inf
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nop.i 999
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}
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{ .mfb
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ldfe atan2_P17 = [EXP_AD_P2],16
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(p12) fma.d.s0 f8 = atan2_X,atan2_Y,f0 // If x nan, result quiet x
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(p12) br.ret.spnt b0 // Exit for x nan
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;;
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}
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// p6 true if swap, means |y| > |x| or ysq > xsq
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// p7 true if no swap, means |x| >= |y| or xsq >= ysq
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{ .mmf
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ldfe atan2_P6 = [EXP_AD_P1],16
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ldfe atan2_P16 = [EXP_AD_P2],16
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fcmp.ge.s1 p7,p6 = atan2_xsq, atan2_ysq
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;;
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}
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{ .mfi
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ldfe atan2_P5 = [EXP_AD_P1],16
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fma.s1 atan2_wp_X = atan2_z1_X, atan2_z1_X, f0
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nop.i 999
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}
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{ .mfi
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ldfe atan2_P15 = [EXP_AD_P2],16
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fma.s1 atan2_B1sq_X = atan2_B1X, atan2_B1X, f0
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nop.i 999
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;;
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}
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{ .mfi
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ldfe atan2_P4 = [EXP_AD_P1],16
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(p6) fma.s1 atan2_wp_Y = atan2_z1_Y, atan2_z1_Y, f0
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nop.i 999
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}
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{ .mfi
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ldfe atan2_P14 = [EXP_AD_P2],16
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(p6) fma.s1 atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0
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nop.i 999
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;;
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}
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|
|
{ .mfi
|
|
ldfe atan2_P3 = [EXP_AD_P1],16
|
|
(p6) fma.s1 atan2_E = atan2_z2_Y, atan2_B1Y, atan2_Y
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
ldfe atan2_P13 = [EXP_AD_P2],16
|
|
(p7) fma.s1 atan2_E = atan2_z2_X, atan2_B1X, atan2_X
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
ldfe atan2_P2 = [EXP_AD_P1],16
|
|
(p6) fma.s1 atan2_z = atan2_z1_Y, atan2_B1Y, f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
ldfe atan2_P12 = [EXP_AD_P2],16
|
|
(p7) fma.s1 atan2_z = atan2_z1_X, atan2_B1X, f0
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
ldfe atan2_P1 = [EXP_AD_P1],16
|
|
fcmp.eq.s0 p14,p15=atan2_X,atan2_Y // Dummy for denorm and invalid
|
|
nop.i 999
|
|
}
|
|
{ .mlx
|
|
ldfe atan2_P22 = [EXP_AD_P2],16
|
|
movl rsig_near_one = 0x8000000000000001 // signif near 1.0
|
|
;;
|
|
}
|
|
|
|
|
|
// p12 ==> x inf y inf
|
|
// p13 ==> x inf y !inf
|
|
{ .mmf
|
|
ldfe atan2_P0 = [EXP_AD_P1],16
|
|
ldfe atan2_pi_by_2 = [EXP_AD_P2],16
|
|
(p10) fclass.m.unc p12,p13 = atan2_Y, 0x23 // x inf, test if y inf
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
ldfe atan2_pi = [EXP_AD_P1],16
|
|
(p6) fma.s1 atan2_w = atan2_wp_Y, atan2_B1sq_Y,f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
ldfe atan2_pi_by_4 = [EXP_AD_P2],16
|
|
(p7) fma.s1 atan2_w = atan2_wp_X, atan2_B1sq_X,f0
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
ldfe atan2_3pi_by_4 = [EXP_AD_P2],16
|
|
(p11) fclass.m.unc p9,p0 = atan2_Y, 0x23 // x not inf, test if y inf
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
setf.sig atan2_sig_near_one = rsig_near_one
|
|
(p12) fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x inf, y inf, test if x +inf
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p6) fnma.s1 atan2_gV = atan2_Y, atan2_z, atan2_X
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
frcpa.s1 atan2_F,p0 = f1, atan2_E
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fnma.s1 atan2_gV = atan2_X, atan2_z, atan2_Y
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
// p13 ==> x inf y !inf
|
|
{ .mfi
|
|
nop.m 999
|
|
(p13) fcmp.gt.unc.s1 p14,p15 = atan2_X,f0 // x inf, y !inf, test if x +inf
|
|
nop.i 999
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p9) fma.d.s0 f8 = atan2_sgnY, atan2_pi_by_2, f0 // +-pi/2 if x !inf, y inf
|
|
(p9) br.ret.spnt b0 // exit if x not inf, y inf, result is +-pi/2
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V13 = atan2_w, atan2_P11, atan2_P10
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W11 = atan2_w, atan2_P21, atan2_P20
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V11 = atan2_w, atan2_P9, atan2_P8
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V12 = atan2_w, atan2_w, f0
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V8 = atan2_w, atan2_P7 , atan2_P6
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fnma.s1 atan2_alpha = atan2_E, atan2_F, f1
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fnma.s1 atan2_alpha_1 = atan2_E, atan2_F, atan2_two
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V7 = atan2_w, atan2_P5 , atan2_P4
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W7 = atan2_w, atan2_P17, atan2_P16
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V4 = atan2_w, atan2_P3 , atan2_P2
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W4 = atan2_w, atan2_P15, atan2_P14
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V3 = atan2_w, atan2_P1 , atan2_P0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W3 = atan2_w, atan2_P13, atan2_P12
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V10 = atan2_V12, atan2_V13, atan2_V11
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_gVF = atan2_gV, atan2_F, f0
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_alpha_sq = atan2_alpha, atan2_alpha, f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_Cp = atan2_alpha, atan2_alpha_1, f1
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V9 = atan2_V12, atan2_V12, f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W10 = atan2_V12, atan2_P22 , atan2_W11
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V6 = atan2_V12, atan2_V8 , atan2_V7
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W6 = atan2_V12, atan2_W8 , atan2_W7
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V2 = atan2_V12, atan2_V4 , atan2_V3
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W2 = atan2_V12, atan2_W4 , atan2_W3
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
// p8 ==> y 0 x?
|
|
// p9 ==> y !0 x?
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.m p8,p9 = atan2_Y, 0x07 // Test for y=0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_zcub = atan2_z, atan2_w, f0
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_C = atan2_gVF, atan2_Cp, f0
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
// p12 ==> y0 x0
|
|
// p13 ==> y0 x!0
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fclass.m.unc p12,p13 = atan2_X, 0x07 // y=0, test if x is 0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W12 = atan2_V9, atan2_V9, f0
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V5 = atan2_V9, atan2_V10, atan2_V6
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W5 = atan2_V9, atan2_W10, atan2_W6
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
|
|
// p9 ==> y!0 x0
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fclass.m.unc p9,p0 = atan2_X, 0x07 // y not 0, test if x is 0
|
|
nop.i 999
|
|
}
|
|
// p10 ==> X +INF, Y +-INF
|
|
{ .mfb
|
|
nop.m 999
|
|
(p10) fma.d.s0 f8 = atan2_sgnY, atan2_pi_by_4, f0 // x=+inf, y=inf
|
|
(p10) br.ret.spnt b0 // Exit for x=+inf, y=inf, result is +-pi/4
|
|
;;
|
|
}
|
|
|
|
.pred.rel "mutex",p11,p14
|
|
{ .mfi
|
|
nop.m 999
|
|
(p14) fmerge.s f8 = atan2_sgnY, f0 // x=+inf, y !inf, result +-0
|
|
nop.i 999
|
|
}
|
|
// p11 ==> X -INF, Y +-INF
|
|
{ .mfb
|
|
nop.m 999
|
|
(p11) fma.d.s0 f8 = atan2_sgnY, atan2_3pi_by_4, f0 // x=-inf, y=inf
|
|
(p11) br.ret.spnt b0 // Exit for x=-inf, y=inf, result is +-3pi/4
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p13) fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x not 0, y=0, test if x>0
|
|
nop.i 999
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
fma.s1 atan2_d = atan2_alpha_cub, atan2_C, atan2_C
|
|
(p14) br.ret.spnt b0 // Exit if x=+inf, y !inf, result +-0
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0
|
|
nop.i 999
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p9) fma.d.s0 f8 = atan2_sgnY, atan2_pi_by_2, f0 // x=0, y not 0
|
|
(p9) br.ret.spnt b0 // Exit if x=0 and y not 0, result is +-pi/2
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_V1 = atan2_V9, atan2_V5, atan2_V2
|
|
nop.i 999
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
fma.s1 atan2_W1 = atan2_V9, atan2_W5, atan2_W2
|
|
(p12) br.spnt ATAN2_ERROR // Branch if x=0 and y=0
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fmerge.s f8 = atan2_sgnY, f0 // +-0 if x>0, y=0
|
|
nop.i 999
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p11) fma.d.s0 f8 = atan2_sgnY, atan2_pi, f0 // +-pi if x<0, y=0
|
|
(p13) br.ret.spnt b0 // Exit if x!0 and y=0
|
|
;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_pd = atan2_P0, atan2_d, f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_dsq = atan2_d, atan2_d, f0
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fmerge.se atan2_near_one = f1, atan2_sig_near_one // Const ~1.0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
// p8 true if no swap and X positive
|
|
// p9 true if no swap and X negative
|
|
// both are false is swap is true
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fcmp.ge.unc.s1 p8,p9 = atan2_X,f0
|
|
nop.i 999
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p15) fma.d.s0 f8 = atan2_sgnY, atan2_pi, f0
|
|
(p15) br.ret.spnt b0 // Exit if x=-inf, y !inf, result +-pi
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_sgn_pi_by_2 = atan2_pi_by_2, atan2_sgnY, f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_A_lo = atan2_pd, atan2_dsq, atan2_d
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_sgn_pi = atan2_pi, atan2_sgnY, f0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_A_hi = atan2_zcub, atan2_Pp, atan2_z
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
|
|
// For |Y| <= |X| and X > 0, force inexact in case A_lo is zero
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fmpy.s0 atan2_tmp = atan2_P22, atan2_P22
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 atan2_A = atan2_A_hi, f1, atan2_A_lo
|
|
nop.i 999
|
|
}
|
|
// For |Y| <= |X| and X > 0, result is A_hi + A_lo
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.d.s0 f8 = atan2_A_hi, f1, atan2_A_lo
|
|
nop.i 999
|
|
;;
|
|
}
|
|
|
|
.pred.rel "mutex",p6,p9
|
|
// We perturb A by multiplying by 1.0+1ulp as we produce the result
|
|
// in order to get symmetrically rounded results in directed rounding modes.
|
|
// If we don't do this, there are a few cases where the trailing 11 bits of
|
|
// the significand of the result, before converting to double, are zero. These
|
|
// cases do not round symmetrically in round to +infinity or round to -infinity.
|
|
// The perturbation also insures that the inexact flag is set.
|
|
// For |Y| > |X|, result is +- pi/2 - (A_hi + A_lo)
|
|
{ .mfi
|
|
nop.m 999
|
|
(p6) fnma.d.s0 f8 = atan2_A, atan2_near_one, atan2_sgn_pi_by_2
|
|
nop.i 999
|
|
}
|
|
// For |Y| <= |X|, and X < 0, result is +- pi + (A_hi + A_lo)
|
|
{ .mfb
|
|
nop.m 999
|
|
(p9) fma.d.s0 f8 = atan2_A, atan2_near_one, atan2_sgn_pi
|
|
br.ret.sptk b0
|
|
;;
|
|
}
|
|
|
|
ATAN2_ERROR:
|
|
// Here if x=0 and y=0
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.m p10,p11 = atan2_X,0x05 // Test if x=+0
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
mov atan2_GR_tag = 37
|
|
(p10) fmerge.s f10 = atan2_sgnY, f0 // x=+0, y=0
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p11) fma.d.s0 f10 = atan2_sgnY, atan2_pi, f0 // x=-0, y=0
|
|
nop.i 999
|
|
;;
|
|
}
|
|
GLOBAL_IEEE754_END(atan2)
|
|
|
|
LOCAL_LIBM_ENTRY(__libm_error_region)
|
|
.prologue
|
|
// (1)
|
|
{ .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
|
|
};;
|
|
|
|
|
|
// (2)
|
|
{ .mmi
|
|
stfd [GR_Parameter_Y] = f8,16 // 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
|
|
stfd [GR_Parameter_X] = f9 // STORE Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
|
|
nop.b 0
|
|
}
|
|
{ .mib
|
|
stfd [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
|
|
add GR_Parameter_RESULT = 48,sp
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
// (4)
|
|
{ .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#
|