.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. // // 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://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 // // 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 // atan2(+-0/+-0) sets single error tag to 38 #include "libm_support.h" // Assembly macros //============================================================== EXP_AD_P1 = r33 EXP_AD_P2 = r34 atan2_GR_sml_exp = 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_X = f9 atan2_Y = f8 atan2_u1_X = f32 atan2_u1_Y = f33 atan2_Umax = f34 atan2_Vmin = f35 atan2_two = f36 atan2_absX = f37 atan2_z1_X = f38 atan2_z1_Y = f39 atan2_B1X = f40 atan2_B1Y = f41 atan2_wp = f42 atan2_B1sq = 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_Pi_by_2 = f69 atan2_V13 = f70 atan2_W11 = f71 atan2_E = f72 atan2_gamma = 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_sml_norm = f103 atan2_FR_tmp = f103 atan2_W1 = f104 atan2_alpha_cub = f105 atan2_C = f106 atan2_P = 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 = f116 atan2_pi = f117 atan2_sgnX = f118 atan2_sgnXY = f119 atan2_3pi_by_4 = f120 atan2_pi_by_4 = f121 //atan2_sF = p7 //atan2_sT = p6 // 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. ///////////////////////////////////////////////////////////// #ifdef _LIBC .rodata #else .data #endif .align 16 atan2_tb1: ASM_TYPE_DIRECTIVE(atan2_tb1,@object) data8 0xB199DD6D2675C40F , 0x0000BFFA // P10 data8 0xA21922DC45605EA1 , 0x00003FFA // P11 data8 0xD78F28FC2A592781 , 0x0000BFFA // P8 data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9 data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5 data8 0xF0F03ADB3FC930D3 , 0x00003FFA // P7 data8 0xF396268151CFB11C , 0x00003FF7 // P17 data8 0x9D3436AABE218776 , 0x00003FF5 // P19 data8 0x80D601879218B53A , 0x00003FFA // P13 data8 0xA2270D30A90AA220 , 0x00003FF9 // P15 data8 0xCCCCCCCCCCC906CD , 0x00003FFC // P1 data8 0xE38E38E320A8A098 , 0x00003FFB // P3 data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22 data8 0xC90FDAA22168C235 , 0x00003FFE // pi/4 ASM_SIZE_DIRECTIVE(atan2_tb1) atan2_tb2: ASM_TYPE_DIRECTIVE(atan2_tb2,@object) data8 0x9F90FB984D8E39D0 , 0x0000BFF3 // P20 data8 0xCE585A259BD8374C , 0x00003FF0 // P21 data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4 data8 0x88887EBB209E3543 , 0x0000BFFB // P6 data8 0xD818B4BB43D84BF2 , 0x0000BFF8 // P16 data8 0xDEC343E068A6D2A8 , 0x0000BFF6 // P18 data8 0x9297B23CCFFB291F , 0x0000BFFA // P12 data8 0xD5F4F2182E7A8725 , 0x0000BFF9 // P14 data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0 data8 0x9249249247E37913 , 0x0000BFFC // P2 data8 0xC90FDAA22168C235 , 0x00003FFF // pi/2 data8 0xC90FDAA22168C235 , 0x00004000 // pi data8 0x96cbe3f9990e91a8 , 0x00004000 // 3pi/4 ASM_SIZE_DIRECTIVE(atan2_tb2) .align 32 .global atan2# #ifdef _LIBC .global __atan2# .global __ieee754_atan2# #endif //////////////////////////////////////////////////////// .section .text .align 32 .proc atan2# atan2: #ifdef _LIBC .proc __atan2# __atan2: .proc __ieee754_atan2# __ieee754_atan2: #endif // qnan snan inf norm unorm 0 -+ // 0 0 1 0 0 0 11 // Y NAN? p10 p11 // p10 ==> quiet Y and return // p11 X NAN? p12, p13 // p12 ==> quiet X and return { .mfi alloc r32 = ar.pfs,1,5,4,0 frcpa.s1 atan2_u1_X,p6 = f1,atan2_X addl EXP_AD_P2 = @ltoff(atan2_tb2), gp } { .mfi addl EXP_AD_P1 = @ltoff(atan2_tb1), gp fclass.m.unc p10,p11 = f8, 0xc3 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_two = f1,f1,f1 nop.i 999 ;; } { .mfi ld8 EXP_AD_P2 = [ EXP_AD_P2] famax.s1 atan2_Umax = f8,f9 nop.i 999 } ;; { .mfi nop.m 999 fmerge.s atan2_absX = f0,atan2_X nop.i 999 } ;; // p10 Y NAN, quiet and return { .mfi ldfe atan2_P10 = [EXP_AD_P1],16 fmerge.s atan2_sgnY = atan2_Y,f1 nop.i 999 } { .mfb nop.m 999 (p10) fma.d f8 = f8,f9,f0 (p10) br.ret.spnt b0 ;; } { .mmf ldfe atan2_P11 = [EXP_AD_P1],16 ldfe atan2_P20 = [EXP_AD_P2],16 fmerge.s atan2_sgnX = atan2_X,f1 ;; } { .mfi ldfe atan2_P8 = [EXP_AD_P1],16 fma.s1 atan2_z1_X = atan2_u1_X, atan2_Y, f0 nop.i 999 } { .mfi ldfe atan2_P21 = [EXP_AD_P2],16 fma.s1 atan2_z1_Y = atan2_u1_Y, atan2_X, f0 nop.i 999 ;; } { .mfi ldfe atan2_P9 = [EXP_AD_P1],16 fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two nop.i 999 } { .mfi ldfe atan2_P4 = [EXP_AD_P2],16 fnma.s1 atan2_B1Y = atan2_u1_Y, atan2_Y, atan2_two nop.i 999 ;; } // p6 (atan2_sT) true if swap // p7 (atan2_sF) true if no swap // p11 ==> Y !NAN; X NAN? { .mfi ldfe atan2_P5 = [EXP_AD_P1],16 // fcmp.eq.unc.s1 atan2_sF,atan2_sT = atan2_Umax, atan2_X fcmp.eq.unc.s1 p7,p6 = atan2_Umax, atan2_X nop.i 999 } { .mfi ldfe atan2_P6 = [EXP_AD_P2],16 (p11) fclass.m.unc p12,p13 = f9, 0xc3 nop.i 999 ;; } { .mmf ldfe atan2_P7 = [EXP_AD_P1],16 ldfe atan2_P16 = [EXP_AD_P2],16 famin.s1 atan2_Vmin = f8,f9 ;; } // p8 true if X positive // p9 true if X negative // both are false is swap is true { .mfi ldfe atan2_P17 = [EXP_AD_P1],16 //(atan2_sF) fcmp.eq.unc.s1 p8,p9 = atan2_sgnX,f1 (p7) fcmp.eq.unc.s1 p8,p9 = atan2_sgnX,f1 nop.i 999 } { .mfi ldfe atan2_P18 = [EXP_AD_P2],16 fma.s1 atan2_sgnXY = atan2_sgnX, atan2_sgnY, f0 nop.i 999 ;; } { .mfi ldfe atan2_P19 = [EXP_AD_P1],16 //(atan2_sF) fma.s1 atan2_wp = atan2_z1_X, atan2_z1_X, f0 (p7) fma.s1 atan2_wp = atan2_z1_X, atan2_z1_X, f0 nop.i 999 } { .mfi ldfe atan2_P12 = [EXP_AD_P2],16 //(atan2_sT) fma.s1 atan2_wp = atan2_z1_Y, atan2_z1_Y, f0 (p6) fma.s1 atan2_wp = atan2_z1_Y, atan2_z1_Y, f0 nop.i 999 ;; } { .mfi ldfe atan2_P13 = [EXP_AD_P1],16 //(atan2_sF) fma.s1 atan2_z = atan2_z1_X, atan2_B1X, f0 (p7) fma.s1 atan2_z = atan2_z1_X, atan2_B1X, f0 nop.i 999 } { .mfi ldfe atan2_P14 = [EXP_AD_P2],16 //(atan2_sT) fma.s1 atan2_z = atan2_z1_Y, atan2_B1Y, f0 (p6) fma.s1 atan2_z = atan2_z1_Y, atan2_B1Y, f0 nop.i 999 ;; } { .mfi ldfe atan2_P15 = [EXP_AD_P1],16 //(atan2_sF) fma.s1 atan2_B1sq = atan2_B1X, atan2_B1X, f0 (p7) fma.s1 atan2_B1sq = atan2_B1X, atan2_B1X, f0 nop.i 999 } { .mfi ldfe atan2_P0 = [EXP_AD_P2],16 //(atan2_sT) fma.s1 atan2_B1sq = atan2_B1Y, atan2_B1Y, f0 (p6) fma.s1 atan2_B1sq = atan2_B1Y, atan2_B1Y, f0 nop.i 999 ;; } // p12 ==> X NAN, quiet and return { .mfi ldfe atan2_P1 = [EXP_AD_P1],16 fmerge.s atan2_Umax = f0,atan2_Umax nop.i 999 } { .mfb ldfe atan2_P2 = [EXP_AD_P2],16 (p12) fma.d f8 = f9,f8,f0 (p12) br.ret.spnt b0 ;; } // p10 ==> x inf y ? // p11 ==> x !inf y ? { .mfi ldfe atan2_P3 = [EXP_AD_P1],16 fmerge.s atan2_Vmin = f0,atan2_Vmin nop.i 999 } { .mfi ldfe atan2_Pi_by_2 = [EXP_AD_P2],16 fclass.m.unc p10,p11 = f9, 0x23 nop.i 999 ;; } { .mmf ldfe atan2_P22 = [EXP_AD_P1],16 ldfe atan2_pi = [EXP_AD_P2],16 nop.f 999 ;; } { .mfi nop.m 999 fcmp.eq.s0 p12,p13=f9,f8 // Dummy to catch denormal and invalid nop.i 999 ;; } { .mfi ldfe atan2_pi_by_4 = [EXP_AD_P1],16 //(atan2_sT) fmerge.ns atan2_sgnXY = atan2_sgnXY, atan2_sgnXY (p6) fmerge.ns atan2_sgnXY = atan2_sgnXY, atan2_sgnXY nop.i 999 } { .mfi ldfe atan2_3pi_by_4 = [EXP_AD_P2],16 fma.s1 atan2_w = atan2_wp, atan2_B1sq,f0 nop.i 999 ;; } // p12 ==> x inf y inf // p13 ==> x inf y !inf { .mfi nop.m 999 fmerge.s atan2_z = f0, atan2_z nop.i 999 ;; } { .mfi nop.m 99 (p10) fclass.m.unc p12,p13 = f8, 0x23 nop.i 999 } { .mfi nop.m 99 (p11) fclass.m.unc p14,p15 = f8, 0x23 nop.i 999 ;; } { .mfi nop.m 999 (p12) fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 nop.i 99 ;; } { .mfb mov atan2_GR_sml_exp = 0x1 // Small exponent for making small norm (p14) fma.d f8 = atan2_sgnY, atan2_Pi_by_2, f0 (p14) br.ret.spnt b0 ;; } // Make a very small normal in case need to force inexact and underflow { .mfi setf.exp atan2_sml_norm = atan2_GR_sml_exp 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_E = atan2_Vmin, atan2_z, atan2_Umax nop.i 999 } { .mfi nop.m 999 fnma.s1 atan2_gamma = atan2_Umax, atan2_z, f1 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_V7 = atan2_w, atan2_P5 , atan2_P4 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_W7 = atan2_w, atan2_P17, atan2_P16 nop.i 999 } { .mfi nop.m 999 fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18 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_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_V4 = atan2_w, atan2_P3 , atan2_P2 nop.i 999 ;; } { .mfi nop.m 999 fma.s1 atan2_zcub = atan2_z, atan2_w, f0 nop.i 999 } { .mfi nop.m 999 fnma.s1 atan2_gV = atan2_Umax, atan2_z, atan2_Vmin nop.i 999 ;; } { .mfi nop.m 999 frcpa.s1 atan2_F,p15 = f1, atan2_E 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_V6 = atan2_V12, atan2_V8 , atan2_V7 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_W6 = atan2_V12, atan2_W8 , atan2_W7 nop.i 999 ;; } { .mfi nop.m 999 fma.s1 atan2_W2 = atan2_V12, atan2_W4 , atan2_W3 nop.i 999 } { .mfi nop.m 999 fma.s1 atan2_V2 = atan2_V12, atan2_V4 , atan2_V3 nop.i 999 ;; } // Both X and Y are INF // p10 ==> X + // p11 ==> X - .pred.rel "mutex",p10,p11 { .mfb nop.m 999 (p10) fma.d f8 = atan2_sgnY, atan2_pi_by_4, f0 (p10) br.ret.spnt b0 } { .mfb nop.m 999 (p11) fma.d f8 = atan2_sgnY, atan2_3pi_by_4, f0 (p11) br.ret.spnt b0 ;; } .pred.rel "mutex",p8,p9,p6 { .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 //(atan2_sT) fmerge.s atan2_P = atan2_Y, atan2_Pi_by_2 (p6) fmerge.s atan2_P = atan2_Y, atan2_Pi_by_2 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_V5 = atan2_V9, atan2_V10, atan2_V6 nop.i 999 } { .mfi nop.m 999 fma.s1 atan2_W12 = atan2_V9, atan2_V9, f0 nop.i 999 ;; } { .mfi nop.m 999 (p8) fmerge.s atan2_P = atan2_sgnY, f0 nop.i 999 } { .mfi nop.m 999 fma.s1 atan2_W5 = atan2_V9, atan2_W10, atan2_W6 nop.i 999 ;; } { .mfi nop.m 999 (p9) fmerge.s atan2_P = atan2_sgnY, atan2_pi 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_V1 = atan2_V9, atan2_V5, atan2_V2 nop.i 999 } { .mfi nop.m 999 fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0 nop.i 999 ;; } // p13 ==> x inf y !inf { .mfi nop.m 999 fma.s1 atan2_W1 = atan2_V9, atan2_W5, atan2_W2 nop.i 999 } { .mfi nop.m 999 (p13) fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 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 ;; } .pred.rel "mutex",p10,p11 // x inf y !inf { .mfb nop.m 999 (p10) fmerge.s f8 = atan2_sgnY, f0 (p10) br.ret.spnt b0 } { .mfb nop.m 999 (p11) fma.d f8 = atan2_sgnY, atan2_pi, f0 (p11) br.ret.spnt b0 ;; } // p10 ==> y 0 x? // p11 ==> y !0 x? { .mfi nop.m 999 fclass.m.unc p10,p11 = f8, 0x07 nop.i 999 ;; } { .mfi nop.m 999 (p8) fmerge.s atan2_sml_norm = atan2_sgnY, atan2_sml_norm nop.i 999 ;; } { .mfi nop.m 999 fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1 nop.i 999 } { .mfi nop.m 999 fma.s1 atan2_d = atan2_alpha_cub, atan2_C, atan2_C nop.i 999 ;; } // p12 ==> y0 x0 // p13 ==> y0 x!0 // p14 ==> y!0 x0 // p15 ==> y!0 x!0 { .mfi nop.m 999 (p10) fclass.m.unc p12,p13 = f9, 0x07 nop.i 999 } { .mfi nop.m 999 (p11) fclass.m.unc p14,p15 = f9, 0x07 nop.i 999 ;; } { .mfb nop.m 999 (p13) fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 (p12) br.spnt ATAN2_ERROR ;; } { .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_A_hi = atan2_zcub, atan2_Pp, atan2_z nop.i 999 } { .mfb nop.m 999 (p14) fma.d f8 = atan2_sgnY, atan2_Pi_by_2, f0 (p14) br.ret.spnt b0 ;; } { .mfb nop.m 999 (p10) fmerge.s f8 = atan2_sgnY, f0 (p10) br.ret.spnt b0 } { .mfb nop.m 999 (p11) fma.d f8 = atan2_sgnY, atan2_pi, f0 (p11) br.ret.spnt b0 ;; } { .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 = atan2_A_hi, f1, atan2_A_lo nop.i 999 ;; } // Force inexact and possibly underflow if very small results { .mfi nop.m 999 (p8) fma.d atan2_FR_tmp = atan2_sgnXY, atan2_A, atan2_sml_norm nop.i 999 } { .mfb nop.m 999 fma.d f8 = atan2_sgnXY, atan2_A, atan2_P br.ret.sptk b0 ;; } ATAN2_ERROR: { .mfi nop.m 999 fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 nop.i 999 } ;; { .mfi mov atan2_GR_tag = 37 (p10) fmerge.s f10 = atan2_sgnY, f0 nop.i 999 } { .mfi nop.m 999 (p11) fma.d f10 = atan2_sgnY, atan2_pi, f0 nop.i 999 ;; } .endp atan2# ASM_SIZE_DIRECTIVE(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 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 };; .endp __libm_error_region ASM_SIZE_DIRECTIVE(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support#