diff options
Diffstat (limited to 'sysdeps/ia64/fpu/e_atan2.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_atan2.S | 738 |
1 files changed, 413 insertions, 325 deletions
diff --git a/sysdeps/ia64/fpu/e_atan2.S b/sysdeps/ia64/fpu/e_atan2.S index 7a17fbfed4..38dd2f749a 100644 --- a/sysdeps/ia64/fpu/e_atan2.S +++ b/sysdeps/ia64/fpu/e_atan2.S @@ -1,10 +1,10 @@ .file "atan2.s" - -// Copyright (c) 2000 - 2003, Intel Corporation +// Copyright (C) 2000, 2001, Intel Corporation // All rights reserved. -// -// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// +// 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 @@ -20,39 +20,33 @@ // * 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 +// +// 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 +// 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 +// 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. -// +// 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. +// problem reports or change requests be submitted to it directly at +// http://developer.intel.com/opensource. // // 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 +// 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 //============================================================== @@ -61,12 +55,10 @@ // 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| +// p6 swap True |Y| > |X| // p7 swap False |Y| <= |X| // p8 X+ (If swap=True p8=p9=0) // p9 X- @@ -74,21 +66,21 @@ // all the other predicates p10 thru p15 are false for the main path // // Simple trigonometric identities show -// Region 1 (-45 to +45 degrees): +// 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): +// 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): +// 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): +// 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 +// 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 // @@ -132,40 +124,30 @@ // +number -0 +pi/2 // -number -0 -pi/2 // -// +0 +number +0 -// -0 +number -0 +// +0 +number +0 +// -0 +number -0 // +0 -number +pi // -0 -number -pi // -// +0 +0 +0 -// -0 +0 -0 +// +0 +0 +0 +// -0 +0 -0 // +0 -0 +pi // -0 -0 -pi // // Nan anything quiet Y -// Not NaN NaN quiet X +// anything NaN quiet X // atan2(+-0/+-0) sets double error tag to 37 +// atan2(+-0/+-0) sets single error tag to 38 -// Registers used -//============================================================== - -// predicate registers used: -// p6 -> p15 - -// floating-point registers used: -// f8, f9 input -// f32 -> f119 - -// general registers used -// r32 -> r41 +#include "libm_support.h" // Assembly macros //============================================================== EXP_AD_P1 = r33 EXP_AD_P2 = r34 -rsig_near_one = r35 +atan2_GR_sml_exp = r35 GR_SAVE_B0 = r35 @@ -177,23 +159,22 @@ GR_Parameter_Y = r39 GR_Parameter_RESULT = r40 atan2_GR_tag = r41 -atan2_Y = f8 + atan2_X = f9 +atan2_Y = f8 atan2_u1_X = f32 atan2_u1_Y = f33 -atan2_z2_X = f34 -atan2_z2_Y = f35 - +atan2_Umax = f34 +atan2_Vmin = f35 atan2_two = f36 -atan2_B1sq_Y = f37 +atan2_absX = f37 atan2_z1_X = f38 atan2_z1_Y = f39 atan2_B1X = f40 - atan2_B1Y = f41 -atan2_wp_X = f42 -atan2_B1sq_X = f43 +atan2_wp = f42 +atan2_B1sq = f43 atan2_z = f44 atan2_w = f45 @@ -202,149 +183,178 @@ 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_Pi_by_2 = f69 +atan2_V13 = f70 atan2_W11 = f71 atan2_E = f72 -atan2_wp_Y = f73 +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_ysq = f103 + +atan2_sml_norm = f103 +atan2_FR_tmp = f103 + atan2_W1 = f104 atan2_alpha_cub = f105 - atan2_C = f106 -atan2_xsq = f107 +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 = f115 -atan2_sig_near_one = f116 -atan2_near_one = f116 +atan2_sgnY = f116 atan2_pi = f117 -atan2_sgn_pi = f117 -atan2_3pi_by_4 = f118 -atan2_pi_by_4 = f119 +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. ///////////////////////////////////////////////////////////// -RODATA +#ifdef _LIBC +.rodata +#else +.data +#endif .align 16 -LOCAL_OBJECT_START(atan2_tb1) -data8 0xA21922DC45605EA1 , 0x00003FFA // P11 +atan2_tb1: +ASM_TYPE_DIRECTIVE(atan2_tb1,@object) data8 0xB199DD6D2675C40F , 0x0000BFFA // P10 -data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9 +data8 0xA21922DC45605EA1 , 0x00003FFA // P11 data8 0xD78F28FC2A592781 , 0x0000BFFA // P8 -data8 0xF0F03ADB3FC930D3 , 0x00003FFA // P7 -data8 0x88887EBB209E3543 , 0x0000BFFB // P6 +data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9 data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5 -data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4 -data8 0xE38E38E320A8A098 , 0x00003FFB // P3 -data8 0x9249249247E37913 , 0x0000BFFC // P2 +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 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0 -data8 0xC90FDAA22168C235 , 0x00004000 // pi -LOCAL_OBJECT_END(atan2_tb1) +data8 0xE38E38E320A8A098 , 0x00003FFB // P3 +data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22 +data8 0xC90FDAA22168C235 , 0x00003FFE // pi/4 +ASM_SIZE_DIRECTIVE(atan2_tb1) -LOCAL_OBJECT_START(atan2_tb2) -data8 0xCE585A259BD8374C , 0x00003FF0 // P21 +atan2_tb2: +ASM_TYPE_DIRECTIVE(atan2_tb2,@object) data8 0x9F90FB984D8E39D0 , 0x0000BFF3 // P20 -data8 0x9D3436AABE218776 , 0x00003FF5 // P19 -data8 0xDEC343E068A6D2A8 , 0x0000BFF6 // P18 -data8 0xF396268151CFB11C , 0x00003FF7 // P17 +data8 0xCE585A259BD8374C , 0x00003FF0 // P21 +data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4 +data8 0x88887EBB209E3543 , 0x0000BFFB // P6 data8 0xD818B4BB43D84BF2 , 0x0000BFF8 // P16 -data8 0xA2270D30A90AA220 , 0x00003FF9 // P15 -data8 0xD5F4F2182E7A8725 , 0x0000BFF9 // P14 -data8 0x80D601879218B53A , 0x00003FFA // P13 +data8 0xDEC343E068A6D2A8 , 0x0000BFF6 // P18 data8 0x9297B23CCFFB291F , 0x0000BFFA // P12 -data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22 +data8 0xD5F4F2182E7A8725 , 0x0000BFF9 // P14 +data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0 +data8 0x9249249247E37913 , 0x0000BFFC // P2 data8 0xC90FDAA22168C235 , 0x00003FFF // pi/2 -data8 0xC90FDAA22168C235 , 0x00003FFE // pi/4 +data8 0xC90FDAA22168C235 , 0x00004000 // pi data8 0x96cbe3f9990e91a8 , 0x00004000 // 3pi/4 -LOCAL_OBJECT_END(atan2_tb2) +ASM_SIZE_DIRECTIVE(atan2_tb2) + + +.align 32 +.global atan2# +#ifdef _LIBC +.global __atan2# +.global __ieee754_atan2# +#endif +//////////////////////////////////////////////////////// .section .text -GLOBAL_IEEE754_ENTRY(atan2) +.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 - nop.i 999 + addl EXP_AD_P2 = @ltoff(atan2_tb2), gp } { .mfi addl EXP_AD_P1 = @ltoff(atan2_tb1), gp - fma.s1 atan2_two = f1,f1,f1 + fclass.m.unc p10,p11 = f8, 0xc3 nop.i 999 ;; } @@ -356,233 +366,256 @@ GLOBAL_IEEE754_ENTRY(atan2) } { .mfi nop.m 999 - fma.s1 atan2_xsq = atan2_X,atan2_X,f0 + fma.s1 atan2_two = f1,f1,f1 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 + ld8 EXP_AD_P2 = [ EXP_AD_P2] + famax.s1 atan2_Umax = f8,f9 nop.i 999 } ;; { .mfi - add EXP_AD_P2 = 0xd0,EXP_AD_P1 - fclass.m p12,p0 = atan2_X, 0xc3 // Test for x nan + nop.m 999 + fmerge.s atan2_absX = f0,atan2_X nop.i 999 } ;; - // p10 Y NAN, quiet and return { .mfi - ldfe atan2_P11 = [EXP_AD_P1],16 + ldfe atan2_P10 = [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 + nop.m 999 +(p10) fma.d f8 = f8,f9,f0 +(p10) br.ret.spnt b0 ;; } -{ .mfi - ldfe atan2_P10 = [EXP_AD_P1],16 +{ .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_P20 = [EXP_AD_P2],16 - fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two +{ .mfi + + ldfe atan2_P21 = [EXP_AD_P2],16 + fma.s1 atan2_z1_Y = atan2_u1_Y, atan2_X, f0 nop.i 999 ;; } -{ .mfi +{ .mfi ldfe atan2_P9 = [EXP_AD_P1],16 - fma.s1 atan2_z1_Y = atan2_u1_Y, atan2_X, f0 + fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two nop.i 999 } -{ .mfi - ldfe atan2_P19 = [EXP_AD_P2],16 +{ .mfi + + ldfe atan2_P4 = [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 } + +// p6 (atan2_sT) true if swap +// p7 (atan2_sF) true if no swap +// p11 ==> Y !NAN; X NAN? + { .mfi - ldfe atan2_P18 = [EXP_AD_P2],16 - fma.s1 atan2_z2_Y = atan2_u1_Y, atan2_xsq, f0 + 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 } -;; - -// 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 + ldfe atan2_P6 = [EXP_AD_P2],16 +(p11) fclass.m.unc p12,p13 = f9, 0xc3 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_P7 = [EXP_AD_P1],16 ldfe atan2_P16 = [EXP_AD_P2],16 - fcmp.ge.s1 p7,p6 = atan2_xsq, atan2_ysq + 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_P5 = [EXP_AD_P1],16 - fma.s1 atan2_wp_X = atan2_z1_X, atan2_z1_X, f0 + 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_P15 = [EXP_AD_P2],16 - fma.s1 atan2_B1sq_X = atan2_B1X, atan2_B1X, f0 + ldfe atan2_P18 = [EXP_AD_P2],16 + fma.s1 atan2_sgnXY = atan2_sgnX, atan2_sgnY, 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 + 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_P14 = [EXP_AD_P2],16 -(p6) fma.s1 atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0 + 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_P3 = [EXP_AD_P1],16 -(p6) fma.s1 atan2_E = atan2_z2_Y, atan2_B1Y, atan2_Y + 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_P13 = [EXP_AD_P2],16 -(p7) fma.s1 atan2_E = atan2_z2_X, atan2_B1X, atan2_X + 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_P2 = [EXP_AD_P1],16 -(p6) fma.s1 atan2_z = atan2_z1_Y, atan2_B1Y, f0 + 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_P12 = [EXP_AD_P2],16 -(p7) fma.s1 atan2_z = atan2_z1_X, atan2_B1X, f0 + 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 - fcmp.eq.s0 p14,p15=atan2_X,atan2_Y // Dummy for denorm and invalid + fmerge.s atan2_Umax = f0,atan2_Umax nop.i 999 } -{ .mlx - ldfe atan2_P22 = [EXP_AD_P2],16 - movl rsig_near_one = 0x8000000000000001 // signif near 1.0 +{ .mfb + ldfe atan2_P2 = [EXP_AD_P2],16 +(p12) fma.d f8 = f9,f8,f0 +(p12) br.ret.spnt b0 ;; } -// 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 -;; -} - +// p10 ==> x inf y ? +// p11 ==> x !inf y ? { .mfi - ldfe atan2_pi = [EXP_AD_P1],16 -(p6) fma.s1 atan2_w = atan2_wp_Y, atan2_B1sq_Y,f0 + ldfe atan2_P3 = [EXP_AD_P1],16 + fmerge.s atan2_Vmin = f0,atan2_Vmin 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 + 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 - 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.m 999 + fcmp.eq.s0 p12,p13=f9,f8 // Dummy to catch denormal and invalid 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 + 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 - nop.m 999 -(p6) fnma.s1 atan2_gV = atan2_Y, atan2_z, atan2_X + 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 - frcpa.s1 atan2_F,p0 = f1, atan2_E + 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 999 -(p7) fnma.s1 atan2_gV = atan2_X, atan2_z, atan2_Y + nop.m 99 +(p11) fclass.m.unc p14,p15 = f8, 0x23 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 +(p12) fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 + nop.i 99 +;; } + + { .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 + 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 - nop.m 999 + setf.exp atan2_sml_norm = atan2_GR_sml_exp fma.s1 atan2_V13 = atan2_w, atan2_P11, atan2_P10 nop.i 999 } @@ -593,58 +626,58 @@ GLOBAL_IEEE754_ENTRY(atan2) ;; } + { .mfi nop.m 999 - fma.s1 atan2_V11 = atan2_w, atan2_P9, atan2_P8 + fma.s1 atan2_E = atan2_Vmin, atan2_z, atan2_Umax nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_V12 = atan2_w, atan2_w, f0 + fnma.s1 atan2_gamma = atan2_Umax, atan2_z, f1 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_V8 = atan2_w, atan2_P7 , atan2_P6 + fma.s1 atan2_V11 = atan2_w, atan2_P9, atan2_P8 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18 + fma.s1 atan2_V12 = atan2_w, atan2_w, f0 nop.i 999 ;; } { .mfi nop.m 999 - fnma.s1 atan2_alpha = atan2_E, atan2_F, f1 + fma.s1 atan2_V7 = atan2_w, atan2_P5 , atan2_P4 nop.i 999 } { .mfi nop.m 999 - fnma.s1 atan2_alpha_1 = atan2_E, atan2_F, atan2_two + fma.s1 atan2_V8 = atan2_w, atan2_P7 , atan2_P6 nop.i 999 ;; } - { .mfi nop.m 999 - fma.s1 atan2_V7 = atan2_w, atan2_P5 , atan2_P4 + fma.s1 atan2_W7 = atan2_w, atan2_P17, atan2_P16 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_W7 = atan2_w, atan2_P17, atan2_P16 + fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_V4 = atan2_w, atan2_P3 , atan2_P2 + fma.s1 atan2_W3 = atan2_w, atan2_P13, atan2_P12 nop.i 999 } { .mfi @@ -656,55 +689,55 @@ GLOBAL_IEEE754_ENTRY(atan2) { .mfi nop.m 999 - fma.s1 atan2_V3 = atan2_w, atan2_P1 , atan2_P0 + 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 + fma.s1 atan2_V4 = atan2_w, atan2_P3 , atan2_P2 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_V10 = atan2_V12, atan2_V13, atan2_V11 + fma.s1 atan2_zcub = atan2_z, atan2_w, f0 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_gVF = atan2_gV, atan2_F, f0 + fnma.s1 atan2_gV = atan2_Umax, atan2_z, atan2_Vmin nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_alpha_sq = atan2_alpha, atan2_alpha, f0 + frcpa.s1 atan2_F,p15 = f1, atan2_E nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_Cp = atan2_alpha, atan2_alpha_1, f1 + fma.s1 atan2_V10 = atan2_V12, atan2_V13, atan2_V11 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_V9 = atan2_V12, atan2_V12, f0 + fma.s1 atan2_V6 = atan2_V12, atan2_V8 , atan2_V7 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_W10 = atan2_V12, atan2_P22 , atan2_W11 + fma.s1 atan2_V9 = atan2_V12, atan2_V12, f0 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_V6 = atan2_V12, atan2_V8 , atan2_V7 + fma.s1 atan2_W10 = atan2_V12, atan2_P22 , atan2_W11 nop.i 999 } { .mfi @@ -716,47 +749,65 @@ GLOBAL_IEEE754_ENTRY(atan2) { .mfi nop.m 999 - fma.s1 atan2_V2 = atan2_V12, atan2_V4 , atan2_V3 + fma.s1 atan2_W2 = atan2_V12, atan2_W4 , atan2_W3 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_W2 = atan2_V12, atan2_W4 , atan2_W3 + fma.s1 atan2_V2 = atan2_V12, atan2_V4 , atan2_V3 nop.i 999 ;; } -// p8 ==> y 0 x? -// p9 ==> y !0 x? + +// 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 - fclass.m p8,p9 = atan2_Y, 0x07 // Test for y=0 + fnma.s1 atan2_alpha = atan2_E, atan2_F, f1 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_zcub = atan2_z, atan2_w, f0 + fnma.s1 atan2_alpha_1 = atan2_E, atan2_F, atan2_two nop.i 999 ;; } + { .mfi nop.m 999 - fma.s1 atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0 +//(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_C = atan2_gVF, atan2_Cp, f0 + fma.s1 atan2_gVF = atan2_gV, atan2_F, 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 + fma.s1 atan2_V5 = atan2_V9, atan2_V10, atan2_V6 nop.i 999 } { .mfi @@ -766,9 +817,11 @@ GLOBAL_IEEE754_ENTRY(atan2) ;; } + + { .mfi nop.m 999 - fma.s1 atan2_V5 = atan2_V9, atan2_V10, atan2_V6 +(p8) fmerge.s atan2_P = atan2_sgnY, f0 nop.i 999 } { .mfi @@ -779,215 +832,249 @@ GLOBAL_IEEE754_ENTRY(atan2) } -// 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 +(p9) fmerge.s atan2_P = atan2_sgnY, atan2_pi 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 + fma.s1 atan2_alpha_sq = atan2_alpha, atan2_alpha, f0 nop.i 999 } -// p11 ==> X -INF, Y +-INF -{ .mfb +{ .mfi 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 + fma.s1 atan2_Cp = atan2_alpha, atan2_alpha_1, f1 + nop.i 999 ;; } + { .mfi nop.m 999 -(p13) fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x not 0, y=0, test if x>0 + fma.s1 atan2_V1 = atan2_V9, atan2_V5, atan2_V2 nop.i 999 } -{ .mfb +{ .mfi 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 + fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0 + nop.i 999 ;; } + +// p13 ==> x inf y !inf { .mfi nop.m 999 - fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0 + fma.s1 atan2_W1 = atan2_V9, atan2_W5, atan2_W2 nop.i 999 } -{ .mfb +{ .mfi 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 +(p13) fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 + nop.i 999 ;; } + { .mfi nop.m 999 - fma.s1 atan2_V1 = atan2_V9, atan2_V5, atan2_V2 + fma.s1 atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0 nop.i 999 } -{ .mfb +{ .mfi 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 + fma.s1 atan2_C = atan2_gVF, atan2_Cp, f0 + nop.i 999 ;; } -{ .mfi +.pred.rel "mutex",p10,p11 +// x inf y !inf +{ .mfb nop.m 999 -(p10) fmerge.s f8 = atan2_sgnY, f0 // +-0 if x>0, y=0 - nop.i 999 +(p10) fmerge.s f8 = atan2_sgnY, f0 +(p10) br.ret.spnt b0 } { .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 +(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 - fma.s1 atan2_pd = atan2_P0, atan2_d, f0 + fclass.m.unc p10,p11 = f8, 0x07 nop.i 999 +;; } + { .mfi nop.m 999 - fma.s1 atan2_dsq = atan2_d, atan2_d, f0 +(p8) fmerge.s atan2_sml_norm = atan2_sgnY, atan2_sml_norm nop.i 999 ;; } - { .mfi nop.m 999 - fmerge.se atan2_near_one = f1, atan2_sig_near_one // Const ~1.0 + fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1 + fma.s1 atan2_d = atan2_alpha_cub, atan2_C, atan2_C 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 +// 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 -(p7) fcmp.ge.unc.s1 p8,p9 = atan2_X,f0 +(p11) fclass.m.unc p14,p15 = f9, 0x07 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 +(p13) fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 +(p12) br.spnt ATAN2_ERROR ;; } + + { .mfi nop.m 999 - fma.s1 atan2_sgn_pi_by_2 = atan2_pi_by_2, atan2_sgnY, f0 + fma.s1 atan2_pd = atan2_P0, atan2_d, f0 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_A_lo = atan2_pd, atan2_dsq, atan2_d + fma.s1 atan2_dsq = atan2_d, atan2_d, f0 nop.i 999 ;; } - { .mfi nop.m 999 - fma.s1 atan2_sgn_pi = atan2_pi, atan2_sgnY, f0 + fma.s1 atan2_A_hi = atan2_zcub, atan2_Pp, atan2_z nop.i 999 } -{ .mfi +{ .mfb nop.m 999 - fma.s1 atan2_A_hi = atan2_zcub, atan2_Pp, atan2_z - nop.i 999 +(p14) fma.d f8 = atan2_sgnY, atan2_Pi_by_2, f0 +(p14) br.ret.spnt b0 ;; } -// For |Y| <= |X| and X > 0, force inexact in case A_lo is zero -{ .mfi + +{ .mfb nop.m 999 -(p8) fmpy.s0 atan2_tmp = atan2_P22, atan2_P22 - nop.i 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 = atan2_A_hi, f1, atan2_A_lo + fma.s1 atan2_A_lo = atan2_pd, atan2_dsq, atan2_d 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 + fma.s1 atan2_A = 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) +// Force inexact and possibly underflow if very small results { .mfi nop.m 999 -(p6) fnma.d.s0 f8 = atan2_A, atan2_near_one, atan2_sgn_pi_by_2 +(p8) fma.d atan2_FR_tmp = atan2_sgnXY, atan2_A, atan2_sml_norm 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 + fma.d f8 = atan2_sgnXY, atan2_A, atan2_P + 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 + 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 // x=+0, y=0 - nop.i 999 + mov atan2_GR_tag = 37 +(p10) fmerge.s f10 = atan2_sgnY, f0 + nop.i 999 } { .mfi nop.m 999 -(p11) fma.d.s0 f10 = atan2_sgnY, atan2_pi, f0 // x=-0, y=0 +(p11) fma.d f10 = atan2_sgnY, atan2_pi, f0 nop.i 999 ;; } -GLOBAL_IEEE754_END(atan2) +.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 -LOCAL_LIBM_ENTRY(__libm_error_region) + +.proc __libm_error_region +__libm_error_region: .prologue // (1) { .mfi @@ -1015,19 +1102,19 @@ LOCAL_LIBM_ENTRY(__libm_error_region) .body // (3) { .mib - stfd [GR_Parameter_X] = f9 // STORE Parameter 1 on stack + stfd [GR_Parameter_X] = f9 // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address - nop.b 0 + nop.b 0 } { .mib - stfd [GR_Parameter_Y] = f10 // STORE Parameter 3 on stack + 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 + br.call.sptk b0=__libm_error_support# // Call error handling function };; { .mmi - add GR_Parameter_RESULT = 48,sp nop.m 0 - nop.i 0 + nop.m 0 + add GR_Parameter_RESULT = 48,sp };; // (4) @@ -1043,7 +1130,8 @@ LOCAL_LIBM_ENTRY(__libm_error_region) br.ret.sptk b0 // Return };; -LOCAL_LIBM_END(__libm_error_region) +.endp __libm_error_region +ASM_SIZE_DIRECTIVE(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support# |