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.file "atan2.s"
// Copyright (c) 2000, 2001, Intel Corporation// All rights reserved.// // Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.// // WARRANTY DISCLAIMER// // 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
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// 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://developer.intel.com/opensource.//// History//==============================================================// 2/02/00 Initial version// 4/04/00 Unwind support added// 8/15/00 Bundle added after call to __libm_error_support to properly// set [the previously overwritten] GR_Parameter_RESULT.// 8/17/00 Changed predicate register macro-usage to direct predicate// names due to an assembler bug.// 9/28/00 Updated to set invalid on SNaN inputs// 1/19/01 Fixed flags for small results// 4/13/01 Rescheduled to make all paths faster//// API//==============================================================// double atan2(double Y, double X)//// Overview of operation//==============================================================//// 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// anything NaN quiet X
// atan2(+-0/+-0) sets double error tag to 37
// Assembly macros//==============================================================
EXP_AD_P1 = r33EXP_AD_P2 = r34atan2_GR_sml_exp = r35
GR_SAVE_B0 = r35GR_SAVE_GP = r36GR_SAVE_PFS = r37
GR_Parameter_X = r38GR_Parameter_Y = r39GR_Parameter_RESULT = r40atan2_GR_tag = r41
atan2_Y = f8atan2_X = f9
atan2_u1_X = f32atan2_u1_Y = f33atan2_z2_X = f34atan2_z2_Y = f35
atan2_two = f36atan2_B1sq_Y = f37atan2_z1_X = f38atan2_z1_Y = f39atan2_B1X = f40
atan2_B1Y = f41atan2_wp_X = f42atan2_B1sq_X = f43atan2_z = f44atan2_w = f45
atan2_P0 = f46atan2_P1 = f47atan2_P2 = f48atan2_P3 = f49atan2_P4 = f50
atan2_P5 = f51atan2_P6 = f52atan2_P7 = f53atan2_P8 = f54atan2_P9 = f55
atan2_P10 = f56atan2_P11 = f57atan2_P12 = f58atan2_P13 = f59atan2_P14 = f60
atan2_P15 = f61atan2_P16 = f62atan2_P17 = f63atan2_P18 = f64atan2_P19 = f65
atan2_P20 = f66atan2_P21 = f67atan2_P22 = f68atan2_pi_by_2 = f69atan2_V13 = f70
atan2_W11 = f71atan2_E = f72atan2_wp_Y = f73atan2_V11 = f74atan2_V12 = f75
atan2_V7 = f76atan2_V8 = f77atan2_W7 = f78atan2_W8 = f79atan2_W3 = f80
atan2_W4 = f81atan2_V3 = f82atan2_V4 = f83atan2_F = f84atan2_gV = f85
atan2_V10 = f86atan2_zcub = f87atan2_V6 = f88atan2_V9 = f89atan2_W10 = f90
atan2_W6 = f91atan2_W2 = f92atan2_V2 = f93atan2_alpha = f94atan2_alpha_1 = f95
atan2_gVF = f96atan2_V5 = f97atan2_W12 = f98atan2_W5 = f99atan2_alpha_sq = f100
atan2_Cp = f101atan2_V1 = f102atan2_ysq = f103atan2_W1 = f104atan2_alpha_cub = f105
atan2_C = f106atan2_xsq = f107atan2_d = f108atan2_A_hi = f109atan2_dsq = f110
atan2_pd = f111atan2_A_lo = f112atan2_A = f113atan2_Pp = f114atan2_sgnY = f115
atan2_pi = f116atan2_3pi_by_4 = f117atan2_pi_by_4 = f118
// These coefficients are for atan2. // You can also use this set to substitute those used in the |X| <= 1 case for atan;
// BUT NOT vice versa.
/////////////////////////////////////////////////////////////
.data
.align 16
atan2_tb1:data8 0xA21922DC45605EA1 , 0x00003FFA // P11data8 0xB199DD6D2675C40F , 0x0000BFFA // P10data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9data8 0xD78F28FC2A592781 , 0x0000BFFA // P8data8 0xF0F03ADB3FC930D3 , 0x00003FFA // P7data8 0x88887EBB209E3543 , 0x0000BFFB // P6data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4data8 0xE38E38E320A8A098 , 0x00003FFB // P3data8 0x9249249247E37913 , 0x0000BFFC // P2data8 0xCCCCCCCCCCC906CD , 0x00003FFC // P1data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0data8 0xC90FDAA22168C235 , 0x00004000 // pi
atan2_tb2:data8 0xCE585A259BD8374C , 0x00003FF0 // P21data8 0x9F90FB984D8E39D0 , 0x0000BFF3 // P20data8 0x9D3436AABE218776 , 0x00003FF5 // P19data8 0xDEC343E068A6D2A8 , 0x0000BFF6 // P18data8 0xF396268151CFB11C , 0x00003FF7 // P17 data8 0xD818B4BB43D84BF2 , 0x0000BFF8 // P16data8 0xA2270D30A90AA220 , 0x00003FF9 // P15data8 0xD5F4F2182E7A8725 , 0x0000BFF9 // P14data8 0x80D601879218B53A , 0x00003FFA // P13data8 0x9297B23CCFFB291F , 0x0000BFFA // P12data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22data8 0xC90FDAA22168C235 , 0x00003FFF // pi/2data8 0xC90FDAA22168C235 , 0x00003FFE // pi/4data8 0x96cbe3f9990e91a8 , 0x00004000 // 3pi/4
.align 32.global atan2#
////////////////////////////////////////////////////////
.section .text.proc atan2#
.align 32atan2:
{ .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 f8 = atan2_Y,atan2_X,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 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;;
}
{ .mmf ldfe atan2_P1 = [EXP_AD_P1],16 ldfe atan2_P22 = [EXP_AD_P2],16 fcmp.eq.s0 p14,p15=atan2_X,atan2_Y // Dummy for denorm and invalid;;
}
// 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 nop.m 999(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 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 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 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 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 f8 = atan2_sgnY, atan2_pi, f0 // +-pi if x<0, y=0(p13) br.ret.spnt b0 // Exit if x!0 and y=0;;
}
{ .mfb nop.m 999(p15) fma.d 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_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 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}{ .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_A_hi = atan2_zcub, atan2_Pp, atan2_z 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 f8 = atan2_A_hi, f1, atan2_A_lo nop.i 999;;
}
// For |Y| > |X|, result is +- pi/2 - (A_hi + A_lo){ .mfi nop.m 999(p6) fms.d f8 = atan2_sgnY, atan2_pi_by_2, atan2_A nop.i 999}// For |Y| <= |X|, and X < 0, result is +- pi + (A_hi + A_lo){ .mfb nop.m 999(p9) fma.d f8 = atan2_sgnY, atan2_pi, atan2_A 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 f10 = atan2_sgnY, atan2_pi, f0 // x=-0, y=0 nop.i 999;;
}.endp atan2#
// Stack operations when calling error support.// (1) (2) (3) (call) (4)// sp -> + psp -> + psp -> + sp -> +// | | | |// | | <- GR_Y R3 ->| <- GR_RESULT | -> f8// | | | |// | <-GR_Y Y2->| Y2 ->| <- GR_Y |// | | | |// | | <- GR_X X1 ->| |// | | | |// sp-64 -> + sp -> + sp -> + +// save ar.pfs save b0 restore gp// save gp restore ar.pfs
.proc __libm_error_region__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 nop.m 0 nop.m 0 add GR_Parameter_RESULT = 48,sp};;
// (4){ .mmi ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack.restore add sp = 64,sp // Restore stack pointer mov b0 = GR_SAVE_B0 // Restore return address};;
{ .mib mov gp = GR_SAVE_GP // Restore gp mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs br.ret.sptk b0 // Return};;
.endp __libm_error_region
.type __libm_error_support#,@function
.global __libm_error_support#
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