.file "atan2.s"
// Copyright (c) 2000 - 2003, Intel Corporation
// All rights reserved.
//
// Contributed 2000 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//==============================================================
// 02/02/00 Initial version
// 04/04/00 Unwind support added
// 08/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
// 08/17/00 Changed predicate register macro-usage to direct predicate
// names due to an assembler bug.
// 09/28/00 Updated to set invalid on SNaN inputs
// 01/19/01 Fixed flags for small results
// 04/13/01 Rescheduled to make all paths faster
// 05/20/02 Cleaned up namespace and sf0 syntax
// 08/20/02 Corrected inexact flag and directed rounding symmetry bugs
// 02/06/03 Reordered header: .section, .global, .proc, .align
// 04/17/03 Added missing mutex directive
// 12/23/03 atan2(NaN1,NaN2) now QNaN1, for consistency with atan2f, atan2l
//
// API
//==============================================================
// double atan2(double Y, double X)
//
// Overview of operation
//==============================================================
//
// The atan2 function returns values in the interval [-pi,+pi].
//
// There are two basic paths: swap true and swap false.
// atan2(Y,X) ==> atan2(V/U) where U >= V. If Y > X, we must swap.
//
// p6 swap True |Y| > |X|
// p7 swap False |Y| <= |X|
// p8 X+ (If swap=True p8=p9=0)
// p9 X-
//
// all the other predicates p10 thru p15 are false for the main path
//
// Simple trigonometric identities show
// Region 1 (-45 to +45 degrees):
// X>0, |Y|<=X, V=Y, U=X atan2(Y,X) = sgnY * (0 + atan(V/U))
//
// Region 2 (-90 to -45 degrees, and +45 to +90 degrees):
// X>0, |Y|>X, V=X, U=Y atan2(Y,X) = sgnY * (pi/2 - atan(V/U))
//
// Region 3 (-135 to -90 degrees, and +90 to +135 degrees):
// X<0, |Y|>X, V=X, U=Y atan2(Y,X) = sgnY * (pi/2 + atan(V/U))
//
// Region 4 (-180 to -135 degrees, and +135 to +180 degrees):
// X<0, |Y|<=X, V=Y, U=X atan2(Y,X) = sgnY * (pi - atan(V/U))
//
// So the result is always of the form atan2(Y,X) = P + sgnXY * atan(V/U)
//
// We compute atan(V/U) from the identity
// atan(z) + atan([(V/U)-z] / [1+(V/U)z])
// where z is a limited precision approximation (16 bits) to V/U
//
// z is calculated with the assistance of the frcpa instruction.
//
// atan(z) is calculated by a polynomial z + z^3 * p(w), w=z^2
// where p(w) = P0+P1*w+...+P22*w^22
//
// Let d = [(V/U)-z] / [1+(V/U)z]) = (V-U*z)/(U+V*z)
//
// Approximate atan(d) by d + P0*d^3
// Let F = 1/(U+V*z) * (1-a), where |a|< 2^-8.8.
// Compute q(a) = 1 + a + ... + a^5.
// Then F*q(a) approximates the reciprocal to more than 50 bits.
// Special values
//==============================================================
// Y x Result
// +number +inf +0
// -number +inf -0
// +number -inf +pi
// -number -inf -pi
//
// +inf +number +pi/2
// -inf +number -pi/2
// +inf -number +pi/2
// -inf -number -pi/2
//
// +inf +inf +pi/4
// -inf +inf -pi/4
// +inf -inf +3pi/4
// -inf -inf -3pi/4
//
// +1 +1 +pi/4
// -1 +1 -pi/4
// +1 -1 +3pi/4
// -1 -1 -3pi/4
//
// +number +0 +pi/2
// -number +0 -pi/2
// +number -0 +pi/2
// -number -0 -pi/2
//
// +0 +number +0
// -0 +number -0
// +0 -number +pi
// -0 -number -pi
//
// +0 +0 +0
// -0 +0 -0
// +0 -0 +pi
// -0 -0 -pi
//
// Nan anything quiet Y
// Not NaN NaN quiet X
// atan2(+-0/+-0) sets double error tag to 37
// Registers used
//==============================================================
// predicate registers used:
// p6 -> p15
// floating-point registers used:
// f8, f9 input
// f32 -> f119
// general registers used
// r32 -> r41
// Assembly macros
//==============================================================
EXP_AD_P1 = r33
EXP_AD_P2 = r34
rsig_near_one = r35
GR_SAVE_B0 = r35
GR_SAVE_GP = r36
GR_SAVE_PFS = r37
GR_Parameter_X = r38
GR_Parameter_Y = r39
GR_Parameter_RESULT = r40
atan2_GR_tag = r41
atan2_Y = f8
atan2_X = f9
atan2_u1_X = f32
atan2_u1_Y = f33
atan2_z2_X = f34
atan2_z2_Y = f35
atan2_two = f36
atan2_B1sq_Y = f37
atan2_z1_X = f38
atan2_z1_Y = f39
atan2_B1X = f40
atan2_B1Y = f41
atan2_wp_X = f42
atan2_B1sq_X = f43
atan2_z = f44
atan2_w = f45
atan2_P0 = f46
atan2_P1 = f47
atan2_P2 = f48
atan2_P3 = f49
atan2_P4 = f50
atan2_P5 = f51
atan2_P6 = f52
atan2_P7 = f53
atan2_P8 = f54
atan2_P9 = f55
atan2_P10 = f56
atan2_P11 = f57
atan2_P12 = f58
atan2_P13 = f59
atan2_P14 = f60
atan2_P15 = f61
atan2_P16 = f62
atan2_P17 = f63
atan2_P18 = f64
atan2_P19 = f65
atan2_P20 = f66
atan2_P21 = f67
atan2_P22 = f68
atan2_tmp = f68
atan2_pi_by_2 = f69
atan2_sgn_pi_by_2 = f69
atan2_V13 = f70
atan2_W11 = f71
atan2_E = f72
atan2_wp_Y = f73
atan2_V11 = f74
atan2_V12 = f75
atan2_V7 = f76
atan2_V8 = f77
atan2_W7 = f78
atan2_W8 = f79
atan2_W3 = f80
atan2_W4 = f81
atan2_V3 = f82
atan2_V4 = f83
atan2_F = f84
atan2_gV = f85
atan2_V10 = f86
atan2_zcub = f87
atan2_V6 = f88
atan2_V9 = f89
atan2_W10 = f90
atan2_W6 = f91
atan2_W2 = f92
atan2_V2 = f93
atan2_alpha = f94
atan2_alpha_1 = f95
atan2_gVF = f96
atan2_V5 = f97
atan2_W12 = f98
atan2_W5 = f99
atan2_alpha_sq = f100
atan2_Cp = f101
atan2_V1 = f102
atan2_ysq = f103
atan2_W1 = f104
atan2_alpha_cub = f105
atan2_C = f106
atan2_xsq = f107
atan2_d = f108
atan2_A_hi = f109
atan2_dsq = f110
atan2_pd = f111
atan2_A_lo = f112
atan2_A = f113
atan2_Pp = f114
atan2_sgnY = f115
atan2_sig_near_one = f116
atan2_near_one = f116
atan2_pi = f117
atan2_sgn_pi = f117
atan2_3pi_by_4 = f118
atan2_pi_by_4 = f119
/////////////////////////////////////////////////////////////
RODATA
.align 16
LOCAL_OBJECT_START(atan2_tb1)
data8 0xA21922DC45605EA1 , 0x00003FFA // P11
data8 0xB199DD6D2675C40F , 0x0000BFFA // P10
data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9
data8 0xD78F28FC2A592781 , 0x0000BFFA // P8
data8 0xF0F03ADB3FC930D3 , 0x00003FFA // P7
data8 0x88887EBB209E3543 , 0x0000BFFB // P6
data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5
data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4
data8 0xE38E38E320A8A098 , 0x00003FFB // P3
data8 0x9249249247E37913 , 0x0000BFFC // P2
data8 0xCCCCCCCCCCC906CD , 0x00003FFC // P1
data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0
data8 0xC90FDAA22168C235 , 0x00004000 // pi
LOCAL_OBJECT_END(atan2_tb1)
LOCAL_OBJECT_START(atan2_tb2)
data8 0xCE585A259BD8374C , 0x00003FF0 // P21
data8 0x9F90FB984D8E39D0 , 0x0000BFF3 // P20
data8 0x9D3436AABE218776 , 0x00003FF5 // P19
data8 0xDEC343E068A6D2A8 , 0x0000BFF6 // P18
data8 0xF396268151CFB11C , 0x00003FF7 // P17
data8 0xD818B4BB43D84BF2 , 0x0000BFF8 // P16
data8 0xA2270D30A90AA220 , 0x00003FF9 // P15
data8 0xD5F4F2182E7A8725 , 0x0000BFF9 // P14
data8 0x80D601879218B53A , 0x00003FFA // P13
data8 0x9297B23CCFFB291F , 0x0000BFFA // P12
data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22
data8 0xC90FDAA22168C235 , 0x00003FFF // pi/2
data8 0xC90FDAA22168C235 , 0x00003FFE // pi/4
data8 0x96cbe3f9990e91a8 , 0x00004000 // 3pi/4
LOCAL_OBJECT_END(atan2_tb2)
.section .text
GLOBAL_IEEE754_ENTRY(atan2)
{ .mfi
alloc r32 = ar.pfs,1,5,4,0
frcpa.s1 atan2_u1_X,p6 = f1,atan2_X
nop.i 999
}
{ .mfi
addl EXP_AD_P1 = @ltoff(atan2_tb1), gp
fma.s1 atan2_two = f1,f1,f1
nop.i 999
;;
}
{ .mfi
ld8 EXP_AD_P1 = [EXP_AD_P1]
frcpa.s1 atan2_u1_Y,p7 = f1,atan2_Y
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_xsq = atan2_X,atan2_X,f0
nop.i 999
;;
}
{ .mfi
nop.m 999
fclass.m p10,p0 = atan2_Y, 0xc3 // Test for y=nan
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 atan2_ysq = atan2_Y,atan2_Y,f0
nop.i 999
}
;;
{ .mfi
add EXP_AD_P2 = 0xd0,EXP_AD_P1
fclass.m p12,p0 = atan2_X, 0xc3 // Test for x nan
nop.i 999
}
;;
// p10 Y NAN, quiet and return
{ .mfi
ldfe atan2_P11 = [EXP_AD_P1],16
fmerge.s atan2_sgnY = atan2_Y,f1
nop.i 999
}
{ .mfb
ldfe atan2_P21 = [EXP_AD_P2],16
(p10) fma.d.s0 f8 = atan2_X,atan2_Y,f0 // If y=nan, result quietized y
(p10) br.ret.spnt b0 // Exit if y=nan
;;
}
{ .mfi
ldfe atan2_P10 = [EXP_AD_P1],16
fma.s1 atan2_z1_X = atan2_u1_X, atan2_Y, f0
nop.i 999
}
{ .mfi
ldfe atan2_P20 = [EXP_AD_P2],16
fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two
nop.i 999
;;
}
{ .mfi
ldfe atan2_P9 = [EXP_AD_P1],16
fma.s1 atan2_z1_Y = atan2_u1_Y, atan2_X, f0
nop.i 999
}
{ .mfi
ldfe atan2_P19 = [EXP_AD_P2],16
fnma.s1 atan2_B1Y = atan2_u1_Y, atan2_Y, atan2_two
nop.i 999
}
;;
{ .mfi
ldfe atan2_P8 = [EXP_AD_P1],16
fma.s1 atan2_z2_X = atan2_u1_X, atan2_ysq, f0
nop.i 999
}
{ .mfi
ldfe atan2_P18 = [EXP_AD_P2],16
fma.s1 atan2_z2_Y = atan2_u1_Y, atan2_xsq, f0
nop.i 999
}
;;
// p10 ==> x inf y ?
// p11 ==> x !inf y ?
{ .mfi
ldfe atan2_P7 = [EXP_AD_P1],16
fclass.m p10,p11 = atan2_X, 0x23 // test for x inf
nop.i 999
}
{ .mfb
ldfe atan2_P17 = [EXP_AD_P2],16
(p12) fma.d.s0 f8 = atan2_X,atan2_Y,f0 // If x nan, result quiet x
(p12) br.ret.spnt b0 // Exit for x nan
;;
}
// p6 true if swap, means |y| > |x| or ysq > xsq
// p7 true if no swap, means |x| >= |y| or xsq >= ysq
{ .mmf
ldfe atan2_P6 = [EXP_AD_P1],16
ldfe atan2_P16 = [EXP_AD_P2],16
fcmp.ge.s1 p7,p6 = atan2_xsq, atan2_ysq
;;
}
{ .mfi
ldfe atan2_P5 = [EXP_AD_P1],16
fma.s1 atan2_wp_X = atan2_z1_X, atan2_z1_X, f0
nop.i 999
}
{ .mfi
ldfe atan2_P15 = [EXP_AD_P2],16
fma.s1 atan2_B1sq_X = atan2_B1X, atan2_B1X, f0
nop.i 999
;;
}
{ .mfi
ldfe atan2_P4 = [EXP_AD_P1],16
(p6) fma.s1 atan2_wp_Y = atan2_z1_Y, atan2_z1_Y, f0
nop.i 999
}
{ .mfi
ldfe atan2_P14 = [EXP_AD_P2],16
(p6) fma.s1 atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0
nop.i 999
;;
}
{ .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)
libm_alias_double_other (__atan2, 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#