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Diffstat (limited to 'sysdeps/ia64/fpu/e_atan2.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_atan2.S | 1049 |
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diff --git a/sysdeps/ia64/fpu/e_atan2.S b/sysdeps/ia64/fpu/e_atan2.S new file mode 100644 index 0000000..7a17fbf --- /dev/null +++ b/sysdeps/ia64/fpu/e_atan2.S @@ -0,0 +1,1049 @@ +.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 +// 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://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) + + +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# |