diff options
Diffstat (limited to 'sysdeps/ia64/fpu/e_atan2.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_atan2.S | 736 |
1 files changed, 323 insertions, 413 deletions
diff --git a/sysdeps/ia64/fpu/e_atan2.S b/sysdeps/ia64/fpu/e_atan2.S index 38dd2f749a..8be7c6cec5 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, 2001, Intel Corporation + +// Copyright (c) 2000 - 2003, 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. +// +// 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 @@ -20,33 +20,38 @@ // * 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://developer.intel.com/opensource. +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. // // 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 +// 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 // // API //============================================================== @@ -55,10 +60,12 @@ // 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- @@ -66,21 +73,21 @@ // 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 // @@ -124,13 +131,13 @@ // +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 // @@ -138,16 +145,26 @@ // 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" +// 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 -atan2_GR_sml_exp = r35 +rsig_near_one = r35 GR_SAVE_B0 = r35 @@ -159,22 +176,23 @@ GR_Parameter_Y = r39 GR_Parameter_RESULT = r40 atan2_GR_tag = r41 - -atan2_X = f9 atan2_Y = f8 +atan2_X = f9 atan2_u1_X = f32 atan2_u1_Y = f33 -atan2_Umax = f34 -atan2_Vmin = f35 +atan2_z2_X = f34 +atan2_z2_Y = f35 + atan2_two = f36 -atan2_absX = f37 +atan2_B1sq_Y = f37 atan2_z1_X = f38 atan2_z1_Y = f39 atan2_B1X = f40 + atan2_B1Y = f41 -atan2_wp = f42 -atan2_B1sq = f43 +atan2_wp_X = f42 +atan2_B1sq_X = f43 atan2_z = f44 atan2_w = f45 @@ -183,178 +201,149 @@ 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_tmp = f68 +atan2_pi_by_2 = f69 +atan2_sgn_pi_by_2 = f69 atan2_V13 = f70 + atan2_W11 = f71 atan2_E = f72 -atan2_gamma = f73 +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_sml_norm = f103 -atan2_FR_tmp = f103 - +atan2_ysq = f103 atan2_W1 = f104 atan2_alpha_cub = f105 + atan2_C = f106 -atan2_P = f107 +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_sgnY = f116 +atan2_sig_near_one = f116 +atan2_near_one = 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 +atan2_sgn_pi = f117 +atan2_3pi_by_4 = f118 +atan2_pi_by_4 = f119 -// 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 +RODATA .align 16 -atan2_tb1: -ASM_TYPE_DIRECTIVE(atan2_tb1,@object) -data8 0xB199DD6D2675C40F , 0x0000BFFA // P10 +LOCAL_OBJECT_START(atan2_tb1) data8 0xA21922DC45605EA1 , 0x00003FFA // P11 -data8 0xD78F28FC2A592781 , 0x0000BFFA // P8 +data8 0xB199DD6D2675C40F , 0x0000BFFA // P10 data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9 -data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5 +data8 0xD78F28FC2A592781 , 0x0000BFFA // P8 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 0x88887EBB209E3543 , 0x0000BFFB // P6 +data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5 +data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4 data8 0xE38E38E320A8A098 , 0x00003FFB // P3 -data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22 -data8 0xC90FDAA22168C235 , 0x00003FFE // pi/4 -ASM_SIZE_DIRECTIVE(atan2_tb1) +data8 0x9249249247E37913 , 0x0000BFFC // P2 +data8 0xCCCCCCCCCCC906CD , 0x00003FFC // P1 +data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0 +data8 0xC90FDAA22168C235 , 0x00004000 // pi +LOCAL_OBJECT_END(atan2_tb1) -atan2_tb2: -ASM_TYPE_DIRECTIVE(atan2_tb2,@object) -data8 0x9F90FB984D8E39D0 , 0x0000BFF3 // P20 +LOCAL_OBJECT_START(atan2_tb2) data8 0xCE585A259BD8374C , 0x00003FF0 // P21 -data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4 -data8 0x88887EBB209E3543 , 0x0000BFFB // P6 -data8 0xD818B4BB43D84BF2 , 0x0000BFF8 // P16 +data8 0x9F90FB984D8E39D0 , 0x0000BFF3 // P20 +data8 0x9D3436AABE218776 , 0x00003FF5 // P19 data8 0xDEC343E068A6D2A8 , 0x0000BFF6 // P18 -data8 0x9297B23CCFFB291F , 0x0000BFFA // P12 +data8 0xF396268151CFB11C , 0x00003FF7 // P17 +data8 0xD818B4BB43D84BF2 , 0x0000BFF8 // P16 +data8 0xA2270D30A90AA220 , 0x00003FF9 // P15 data8 0xD5F4F2182E7A8725 , 0x0000BFF9 // P14 -data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0 -data8 0x9249249247E37913 , 0x0000BFFC // P2 +data8 0x80D601879218B53A , 0x00003FFA // P13 +data8 0x9297B23CCFFB291F , 0x0000BFFA // P12 +data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22 data8 0xC90FDAA22168C235 , 0x00003FFF // pi/2 -data8 0xC90FDAA22168C235 , 0x00004000 // pi +data8 0xC90FDAA22168C235 , 0x00003FFE // pi/4 data8 0x96cbe3f9990e91a8 , 0x00004000 // 3pi/4 -ASM_SIZE_DIRECTIVE(atan2_tb2) - - +LOCAL_OBJECT_END(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 +GLOBAL_IEEE754_ENTRY(atan2) { .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 + nop.i 999 } { .mfi addl EXP_AD_P1 = @ltoff(atan2_tb1), gp - fclass.m.unc p10,p11 = f8, 0xc3 + fma.s1 atan2_two = f1,f1,f1 nop.i 999 ;; } @@ -366,256 +355,233 @@ __ieee754_atan2: } { .mfi nop.m 999 - fma.s1 atan2_two = f1,f1,f1 + fma.s1 atan2_xsq = atan2_X,atan2_X,f0 nop.i 999 ;; } - { .mfi - ld8 EXP_AD_P2 = [ EXP_AD_P2] - famax.s1 atan2_Umax = f8,f9 + nop.m 999 + fclass.m p10,p0 = atan2_Y, 0xc3 // Test for y=nan nop.i 999 } -;; - { .mfi nop.m 999 - fmerge.s atan2_absX = f0,atan2_X + fma.s1 atan2_ysq = atan2_Y,atan2_Y,f0 nop.i 999 } ;; -// p10 Y NAN, quiet and return { .mfi - ldfe atan2_P10 = [EXP_AD_P1],16 - fmerge.s atan2_sgnY = atan2_Y,f1 + add EXP_AD_P2 = 0xd0,EXP_AD_P1 + fclass.m p12,p0 = atan2_X, 0xc3 // Test for x nan nop.i 999 } -{ .mfb - nop.m 999 -(p10) fma.d f8 = f8,f9,f0 -(p10) br.ret.spnt b0 ;; -} -{ .mmf +// p10 Y NAN, quiet and return +{ .mfi ldfe atan2_P11 = [EXP_AD_P1],16 - ldfe atan2_P20 = [EXP_AD_P2],16 - fmerge.s atan2_sgnX = atan2_X,f1 + fmerge.s atan2_sgnY = atan2_Y,f1 + nop.i 999 +} +{ .mfb + ldfe atan2_P21 = [EXP_AD_P2],16 +(p10) fma.d.s0 f8 = atan2_Y,atan2_X,f0 // If y=nan, result quietized y +(p10) br.ret.spnt b0 // Exit if y=nan ;; } -{ .mfi - ldfe atan2_P8 = [EXP_AD_P1],16 +{ .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_P21 = [EXP_AD_P2],16 - fma.s1 atan2_z1_Y = atan2_u1_Y, atan2_X, f0 +{ .mfi + ldfe atan2_P20 = [EXP_AD_P2],16 + fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two nop.i 999 ;; } -{ .mfi +{ .mfi ldfe atan2_P9 = [EXP_AD_P1],16 - fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two + fma.s1 atan2_z1_Y = atan2_u1_Y, atan2_X, f0 nop.i 999 } -{ .mfi - - ldfe atan2_P4 = [EXP_AD_P2],16 +{ .mfi + ldfe atan2_P19 = [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 + ldfe atan2_P8 = [EXP_AD_P1],16 + fma.s1 atan2_z2_X = atan2_u1_X, atan2_ysq, f0 nop.i 999 } { .mfi - ldfe atan2_P6 = [EXP_AD_P2],16 -(p11) fclass.m.unc p12,p13 = f9, 0xc3 + ldfe atan2_P18 = [EXP_AD_P2],16 + fma.s1 atan2_z2_Y = atan2_u1_Y, atan2_xsq, f0 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 +// p10 ==> x inf y ? +// p11 ==> x !inf y ? { .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 + ldfe atan2_P7 = [EXP_AD_P1],16 + fclass.m p10,p11 = atan2_X, 0x23 // test for x inf nop.i 999 } -{ .mfi - ldfe atan2_P18 = [EXP_AD_P2],16 - fma.s1 atan2_sgnXY = atan2_sgnX, atan2_sgnY, f0 - 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_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 + 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_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 + ldfe atan2_P15 = [EXP_AD_P2],16 + fma.s1 atan2_B1sq_X = atan2_B1X, atan2_B1X, 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 + 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 -//(atan2_sT) fma.s1 atan2_z = atan2_z1_Y, atan2_B1Y, f0 -(p6) fma.s1 atan2_z = atan2_z1_Y, atan2_B1Y, f0 +(p6) fma.s1 atan2_B1sq_Y = atan2_B1Y, 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 + 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_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 + ldfe atan2_P13 = [EXP_AD_P2],16 +(p7) fma.s1 atan2_E = atan2_z2_X, atan2_B1X, atan2_X nop.i 999 ;; } -// p12 ==> X NAN, quiet and return { .mfi - ldfe atan2_P1 = [EXP_AD_P1],16 - fmerge.s atan2_Umax = f0,atan2_Umax + ldfe atan2_P2 = [EXP_AD_P1],16 +(p6) fma.s1 atan2_z = atan2_z1_Y, atan2_B1Y, f0 nop.i 999 } -{ .mfb - ldfe atan2_P2 = [EXP_AD_P2],16 -(p12) fma.d f8 = f9,f8,f0 -(p12) br.ret.spnt b0 +{ .mfi + ldfe atan2_P12 = [EXP_AD_P2],16 +(p7) fma.s1 atan2_z = atan2_z1_X, atan2_B1X, f0 + nop.i 999 ;; } -// p10 ==> x inf y ? -// p11 ==> x !inf y ? { .mfi - ldfe atan2_P3 = [EXP_AD_P1],16 - fmerge.s atan2_Vmin = f0,atan2_Vmin + ldfe atan2_P1 = [EXP_AD_P1],16 + fcmp.eq.s0 p14,p15=atan2_X,atan2_Y // Dummy for denorm and invalid nop.i 999 } -{ .mfi - ldfe atan2_Pi_by_2 = [EXP_AD_P2],16 - fclass.m.unc p10,p11 = f9, 0x23 - 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_P22 = [EXP_AD_P1],16 - ldfe atan2_pi = [EXP_AD_P2],16 - nop.f 999 + 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 - nop.m 999 - fcmp.eq.s0 p12,p13=f9,f8 // Dummy to catch denormal and invalid + 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_P1],16 -//(atan2_sT) fmerge.ns atan2_sgnXY = atan2_sgnXY, atan2_sgnXY -(p6) fmerge.ns atan2_sgnXY = atan2_sgnXY, atan2_sgnXY + 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 - fma.s1 atan2_w = atan2_wp, atan2_B1sq,f0 +(p11) fclass.m.unc p9,p0 = atan2_Y, 0x23 // x not inf, test if y inf nop.i 999 ;; } -// p12 ==> x inf y inf -// p13 ==> x inf y !inf +{ .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 - fmerge.s atan2_z = f0, atan2_z +(p6) fnma.s1 atan2_gV = atan2_Y, atan2_z, atan2_X nop.i 999 ;; } { .mfi - nop.m 99 -(p10) fclass.m.unc p12,p13 = f8, 0x23 + nop.m 999 + frcpa.s1 atan2_F,p0 = f1, atan2_E nop.i 999 } { .mfi - nop.m 99 -(p11) fclass.m.unc p14,p15 = f8, 0x23 + 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 -(p12) fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 - nop.i 99 -;; +(p13) fcmp.gt.unc.s1 p14,p15 = atan2_X,f0 // x inf, y !inf, test if x +inf + nop.i 999 } - - { .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 + 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 ;; } -// Make a very small normal in case need to force inexact and underflow { .mfi - setf.exp atan2_sml_norm = atan2_GR_sml_exp + nop.m 999 fma.s1 atan2_V13 = atan2_w, atan2_P11, atan2_P10 nop.i 999 } @@ -626,58 +592,58 @@ __ieee754_atan2: ;; } - { .mfi nop.m 999 - fma.s1 atan2_E = atan2_Vmin, atan2_z, atan2_Umax + fma.s1 atan2_V11 = atan2_w, atan2_P9, atan2_P8 nop.i 999 } { .mfi nop.m 999 - fnma.s1 atan2_gamma = atan2_Umax, atan2_z, f1 + fma.s1 atan2_V12 = atan2_w, atan2_w, f0 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_V11 = atan2_w, atan2_P9, atan2_P8 + fma.s1 atan2_V8 = atan2_w, atan2_P7 , atan2_P6 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_V12 = atan2_w, atan2_w, f0 + fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_V7 = atan2_w, atan2_P5 , atan2_P4 + fnma.s1 atan2_alpha = atan2_E, atan2_F, f1 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_V8 = atan2_w, atan2_P7 , atan2_P6 + fnma.s1 atan2_alpha_1 = atan2_E, atan2_F, atan2_two nop.i 999 ;; } + { .mfi nop.m 999 - fma.s1 atan2_W7 = atan2_w, atan2_P17, atan2_P16 + fma.s1 atan2_V7 = atan2_w, atan2_P5 , atan2_P4 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18 + fma.s1 atan2_W7 = atan2_w, atan2_P17, atan2_P16 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 @@ -689,55 +655,55 @@ __ieee754_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_V4 = atan2_w, atan2_P3 , atan2_P2 + fma.s1 atan2_W3 = atan2_w, atan2_P13, atan2_P12 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_zcub = atan2_z, atan2_w, f0 + fma.s1 atan2_V10 = atan2_V12, atan2_V13, atan2_V11 nop.i 999 } { .mfi nop.m 999 - fnma.s1 atan2_gV = atan2_Umax, atan2_z, atan2_Vmin + fma.s1 atan2_gVF = atan2_gV, atan2_F, f0 nop.i 999 ;; } { .mfi nop.m 999 - frcpa.s1 atan2_F,p15 = f1, atan2_E + fma.s1 atan2_alpha_sq = atan2_alpha, atan2_alpha, f0 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_V10 = atan2_V12, atan2_V13, atan2_V11 + fma.s1 atan2_Cp = atan2_alpha, atan2_alpha_1, f1 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_V6 = atan2_V12, atan2_V8 , atan2_V7 + fma.s1 atan2_V9 = atan2_V12, atan2_V12, f0 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_V9 = atan2_V12, atan2_V12, f0 + fma.s1 atan2_W10 = atan2_V12, atan2_P22 , atan2_W11 nop.i 999 ;; } { .mfi nop.m 999 - fma.s1 atan2_W10 = atan2_V12, atan2_P22 , atan2_W11 + fma.s1 atan2_V6 = atan2_V12, atan2_V8 , atan2_V7 nop.i 999 } { .mfi @@ -749,65 +715,47 @@ __ieee754_atan2: { .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 } { .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 ;; } - -// 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 +// p8 ==> y 0 x? +// p9 ==> y !0 x? { .mfi nop.m 999 - fnma.s1 atan2_alpha = atan2_E, atan2_F, f1 + fclass.m p8,p9 = atan2_Y, 0x07 // Test for y=0 nop.i 999 } { .mfi nop.m 999 - fnma.s1 atan2_alpha_1 = atan2_E, atan2_F, atan2_two + fma.s1 atan2_zcub = atan2_z, atan2_w, f0 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 + fma.s1 atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_gVF = atan2_gV, atan2_F, f0 + fma.s1 atan2_C = atan2_gVF, atan2_Cp, f0 nop.i 999 ;; } - +// p12 ==> y0 x0 +// p13 ==> y0 x!0 { .mfi nop.m 999 - fma.s1 atan2_V5 = atan2_V9, atan2_V10, atan2_V6 +(p8) fclass.m.unc p12,p13 = atan2_X, 0x07 // y=0, test if x is 0 nop.i 999 } { .mfi @@ -817,11 +765,9 @@ __ieee754_atan2: ;; } - - { .mfi nop.m 999 -(p8) fmerge.s atan2_P = atan2_sgnY, f0 + fma.s1 atan2_V5 = atan2_V9, atan2_V10, atan2_V6 nop.i 999 } { .mfi @@ -832,249 +778,214 @@ __ieee754_atan2: } - - +// p9 ==> y!0 x0 { .mfi nop.m 999 -(p9) fmerge.s atan2_P = atan2_sgnY, atan2_pi +(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 - fma.s1 atan2_alpha_sq = atan2_alpha, atan2_alpha, f0 +(p14) fmerge.s f8 = atan2_sgnY, f0 // x=+inf, y !inf, result +-0 nop.i 999 } -{ .mfi +// p11 ==> X -INF, Y +-INF +{ .mfb nop.m 999 - fma.s1 atan2_Cp = atan2_alpha, atan2_alpha_1, f1 - nop.i 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 - fma.s1 atan2_V1 = atan2_V9, atan2_V5, atan2_V2 +(p13) fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x not 0, y=0, test if x>0 nop.i 999 } -{ .mfi +{ .mfb nop.m 999 - fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0 - nop.i 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 ;; } - -// p13 ==> x inf y !inf { .mfi nop.m 999 - fma.s1 atan2_W1 = atan2_V9, atan2_W5, atan2_W2 + fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0 nop.i 999 } -{ .mfi +{ .mfb nop.m 999 -(p13) fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 - nop.i 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_alpha_cub = atan2_alpha, atan2_alpha_sq, f0 + fma.s1 atan2_V1 = atan2_V9, atan2_V5, atan2_V2 nop.i 999 } -{ .mfi +{ .mfb nop.m 999 - fma.s1 atan2_C = atan2_gVF, atan2_Cp, f0 - nop.i 999 + fma.s1 atan2_W1 = atan2_V9, atan2_W5, atan2_W2 +(p12) br.spnt ATAN2_ERROR // Branch if x=0 and y=0 ;; } -.pred.rel "mutex",p10,p11 -// x inf y !inf -{ .mfb +{ .mfi nop.m 999 -(p10) fmerge.s f8 = atan2_sgnY, f0 -(p10) br.ret.spnt b0 +(p10) fmerge.s f8 = atan2_sgnY, f0 // +-0 if x>0, y=0 + nop.i 999 } { .mfb nop.m 999 -(p11) fma.d f8 = atan2_sgnY, atan2_pi, f0 -(p11) br.ret.spnt b0 +(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 ;; } - -// p10 ==> y 0 x? -// p11 ==> y !0 x? { .mfi nop.m 999 - fclass.m.unc p10,p11 = f8, 0x07 + fma.s1 atan2_pd = atan2_P0, atan2_d, f0 nop.i 999 -;; } - { .mfi nop.m 999 -(p8) fmerge.s atan2_sml_norm = atan2_sgnY, atan2_sml_norm + fma.s1 atan2_dsq = atan2_d, atan2_d, f0 nop.i 999 ;; } + { .mfi nop.m 999 - fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1 + fmerge.se atan2_near_one = f1, atan2_sig_near_one // Const ~1.0 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_d = atan2_alpha_cub, atan2_C, atan2_C + fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1 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 -} +// 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 -(p11) fclass.m.unc p14,p15 = f9, 0x07 +(p7) fcmp.ge.unc.s1 p8,p9 = atan2_X,f0 nop.i 999 -;; } - - - - { .mfb nop.m 999 -(p13) fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 -(p12) br.spnt ATAN2_ERROR +(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_pd = atan2_P0, atan2_d, f0 + fma.s1 atan2_sgn_pi_by_2 = atan2_pi_by_2, atan2_sgnY, f0 nop.i 999 } { .mfi nop.m 999 - fma.s1 atan2_dsq = atan2_d, atan2_d, f0 + fma.s1 atan2_A_lo = atan2_pd, atan2_dsq, atan2_d nop.i 999 ;; } + { .mfi nop.m 999 - fma.s1 atan2_A_hi = atan2_zcub, atan2_Pp, atan2_z + fma.s1 atan2_sgn_pi = atan2_pi, atan2_sgnY, f0 nop.i 999 } -{ .mfb +{ .mfi nop.m 999 -(p14) fma.d f8 = atan2_sgnY, atan2_Pi_by_2, f0 -(p14) br.ret.spnt b0 + fma.s1 atan2_A_hi = atan2_zcub, atan2_Pp, atan2_z + nop.i 999 ;; } - -{ .mfb - nop.m 999 -(p10) fmerge.s f8 = atan2_sgnY, f0 -(p10) br.ret.spnt b0 -} -{ .mfb +// For |Y| <= |X| and X > 0, force inexact in case A_lo is zero +{ .mfi nop.m 999 -(p11) fma.d f8 = atan2_sgnY, atan2_pi, f0 -(p11) br.ret.spnt b0 +(p8) fmpy.s0 atan2_tmp = atan2_P22, atan2_P22 + nop.i 999 ;; } - - { .mfi nop.m 999 - fma.s1 atan2_A_lo = atan2_pd, atan2_dsq, atan2_d + 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 - fma.s1 atan2_A = atan2_A_hi, f1, atan2_A_lo +(p8) fma.d.s0 f8 = atan2_A_hi, f1, atan2_A_lo nop.i 999 ;; } -// Force inexact and possibly underflow if very small results +.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 -(p8) fma.d atan2_FR_tmp = atan2_sgnXY, atan2_A, atan2_sml_norm +(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 - fma.d f8 = atan2_sgnXY, atan2_A, atan2_P - br.ret.sptk b0 +(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 - fcmp.eq.unc.s1 p10,p11 = atan2_sgnX,f1 + 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 - nop.i 999 + mov atan2_GR_tag = 37 +(p10) fmerge.s f10 = atan2_sgnY, f0 // x=+0, y=0 + nop.i 999 } { .mfi nop.m 999 -(p11) fma.d f10 = atan2_sgnY, atan2_pi, f0 +(p11) fma.d.s0 f10 = atan2_sgnY, atan2_pi, f0 // x=-0, y=0 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 +GLOBAL_IEEE754_END(atan2) - -.proc __libm_error_region -__libm_error_region: +LOCAL_LIBM_ENTRY(__libm_error_region) .prologue // (1) { .mfi @@ -1102,19 +1013,19 @@ __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 - nop.m 0 - nop.m 0 add GR_Parameter_RESULT = 48,sp + nop.m 0 + nop.i 0 };; // (4) @@ -1130,8 +1041,7 @@ __libm_error_region: br.ret.sptk b0 // Return };; -.endp __libm_error_region -ASM_SIZE_DIRECTIVE(__libm_error_region) +LOCAL_LIBM_END(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support# |