| .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# |
