diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_atan.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_atan.S | 1193 |
1 files changed, 490 insertions, 703 deletions
diff --git a/sysdeps/ia64/fpu/s_atan.S b/sysdeps/ia64/fpu/s_atan.S index c0daabd3d7..720ecad28a 100644 --- a/sysdeps/ia64/fpu/s_atan.S +++ b/sysdeps/ia64/fpu/s_atan.S @@ -1,10 +1,10 @@ .file "atan.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 @@ -20,947 +20,734 @@ // * 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 -// 4/13/00: Improved speed -// 4/19/00: Removed the qualifying predicate from the fmerge.s that -// takes the absolute value. -// 6/16/00: Reassigned FP registers to eliminate stalls on loads -// 8/30/00: Saved 5 cycles in main path by rearranging large argument logic -// and delaying use of result of fcmp in load by 1 group +// 02/02/00 Initial version +// 04/13/00 Improved speed +// 04/19/00 Removed the qualifying predicate from the fmerge.s that +// takes the absolute value. +// 06/16/00 Reassigned FP registers to eliminate stalls on loads +// 08/30/00 Saved 5 cycles in main path by rearranging large argument logic +// and delaying use of result of fcmp in load by 1 group +// 05/20/02 Cleaned up namespace and sf0 syntax +// 08/20/02 Use atan2 algorithm with x=1 for better accuracy +// 02/06/03 Reordered header: .section, .global, .proc, .align // // API //============================================================== -// double atan( double x); +// double atan(double Y) // // Overview of operation //============================================================== -// atan(x) = sign(X)pi/2 - atan(1/x) // -// We have two paths: |x| > 1 and |x| <= 1 +// The atan function returns values in the interval [-pi/2,+pi/2]. // -// |x| > 1 -// ========================================== +// The algorithm used is the atan2(Y,X) algorithm where we fix X=1.0. // -// c = frcpa(x) which is approximately 1/x +// 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. // -// xc = 1- B -// B = 1-xc +// p6 swap True |Y| > |X| +// p7 swap False |Y| <= |X| // -// Approximate 1/(1-B)^k by a polynomial in B, poly(B) -// k is 45. // -// poly(B) = 1 + r1 B + r2 B^2 + ...+ r10 B^10 +// Simple trigonometric identities show +// Region 1 +// |Y|<=1.0, V=Y, U=1.0 atan2(Y,X) = sgnY * (0 + atan(V/U)) // -// c^k = (1-B)^k/x^k -// c^k/(1-B)^k = 1/x^k -// c^k poly(B) = 1/x^k - -// poly(x) = series(atan(1/x)) = 1/x - 1/3x^3 + 1/5x^5 - 1/7x^7 .... + 1/45 x^45 -// = 1/x^45 ( x^44 - x^42/3 + x^40/5 - x^38/7 ... +1) -// = 1/x^45 ( y^22 - y^21/3 + y^20/5 - y^19/7 ... +1) -// -// = c^45 poly(B) poly(x) -// = c^45 r(B) q(y) - -// q(y) = q0 + q1 y + q2 y^2 + ... + q22 y^22 -// where q22 is 1.0 - -// atan(x) = sign(X)pi/2 - c^45 r(B) q(y) - -// |x| <= 1 -// ========================================== -// poly(x) = series(atan(x)) = x - x^3/3 + x^5/5 + ..... -// poly(x) = series(atan(x)) = x + x^3(- 1/3 + x^2/5 + ..... +x^47/47) -// poly(x) = series(atan(x)) = x + x^3(p0 + x^2/5 + ..... + x^44/47) -// poly(x) = series(atan(x)) = x + x^3(p0 + y/5 + ..... + y^22/47) - -// where p0 is about -1/3. - -// atan(x) = poly(x) - -#include "libm_support.h" +// Region 2 +// |Y|>1.0, V=1.0, U=Y atan2(Y,X) = sgnY * (pi/2 - 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 +// Special values //============================================================== // atan(QNAN) = QNAN // atan(SNAN) = quieted SNAN -// atan(+-inf) = +- pi/2 +// atan(+-inf) = +- pi/2 // atan(+-0) = +-0 - - // Registers used //============================================================== -// predicate registers used: -// p6 -> p11 +// predicate registers used: +// p6 -> p15 -// floating-point registers used: -// f32 -> f127 +// floating-point registers used: +// f8, input +// f32 -> f116 // general registers used -// r32 -> r37 +// r14 -> r16 // Assembly macros //============================================================== -atan_Pi_by_2 = f32 -atan_S_PI = f33 -atan_ABS_f8 = f34 - -atan_R0 = f35 -atan_R1 = f36 -atan_R2 = f37 -atan_R3 = f38 -atan_R4 = f39 -atan_R5 = f40 -atan_R6 = f41 -atan_R7 = f42 -atan_R8 = f43 -atan_R9 = f44 -atan_R10 = f45 - -atan_Q0 = f46 - -atan_Q1 = f47 -atan_Q2 = f48 -atan_Q3 = f49 -atan_Q4 = f50 -atan_Q5 = f51 -atan_Q6 = f52 -atan_Q7 = f53 -atan_Q8 = f54 -atan_Q9 = f55 -atan_Q10 = f56 - -atan_Q11 = f57 -atan_Q12 = f58 -atan_Q13 = f59 -atan_Q14 = f60 -atan_Q15 = f61 -atan_Q16 = f62 -atan_Q17 = f63 -atan_Q18 = f64 -atan_Q19 = f65 -atan_Q20 = f66 -atan_Q21 = f67 -atan_Q22 = f68 - -// P and Q constants are mutually exclusive -// so they can share macro definitions -atan_P0 = f46 - -atan_P1 = f47 -atan_P2 = f48 -atan_P3 = f49 -atan_P4 = f10 -atan_P5 = f11 -atan_P6 = f12 -atan_P7 = f13 -atan_P10 = f103 - -atan_P11 = f114 -atan_P12 = f58 -atan_P13 = f59 -atan_P14 = f60 -atan_P15 = f61 -atan_P16 = f62 -atan_P17 = f63 -atan_P18 = f64 -atan_P19 = f65 -atan_P20 = f14 -atan_P21 = f99 -atan_P22 = f68 -// end of P constant macros - -atan_C = f69 -atan_Y = f70 -atan_B = f71 -atan_Z = f72 -atan_V11 = f73 -atan_V12 = f74 - -atan_V7 = f75 -atan_V8 = f76 - -atan_W13 = f77 -atan_W11 = f78 - -atan_V3 = f79 -atan_V4 = f80 - -atan_G11 = f81 -atan_G12 = f82 -atan_G7 = f83 -atan_G8 = f84 - -atan_Z1 = f85 -atan_W7 = f86 - -atan_G3 = f87 -atan_W8 = f88 -atan_V9 = f89 -atan_V10 = f90 - -atan_G10 = f91 -atan_W3 = f92 -atan_G4 = f93 -atan_G9 = f94 - -atan_G6 = f95 -atan_W4 = f96 -atan_Z2 = f97 -atan_V6 = f98 - -atan_V2 = f99 -atan_W6 = f100 -atan_W10 = f101 -atan_Y3 = f102 - -atan_G2 = f103 - -atan_Y8 = f104 - -atan_G5 = f105 -atan_Z3 = f106 -atan_Z4 = f107 -atan_W2 = f108 -atan_V5 = f109 - -atan_W5 = f110 -atan_G1 = f111 -atan_Y11 = f112 - -atan_Z5 = f113 -atan_Z6 = f114 -atan_V1 = f115 -atan_W1 = f116 - -atan_Z7 = f117 -atan_Q = f118 -atan_Z = f119 -atan_abs_f8 = f120 - -atan_V13 = f121 -atan_Xcub = f122 -atan_Y12 = f123 -atan_P = f124 - -atan_NORM_f8 = f125 - -atan_P8 = f126 -atan_P9 = f127 - - - - -atan_GR_AD_R = r14 -atan_GR_AD_Q = r15 -atan_GR_AD_P = r16 -atan_GR_10172 = r17 -atan_GR_exp_f8 = r18 -atan_GR_signexp_f8 = r19 -atan_GR_exp_mask = r20 - - +EXP_AD_P1 = r14 +EXP_AD_P2 = r15 +rsig_near_one = r16 + +atan2_Y = f8 +atan2_X = f1 + +atan2_u1_X = f32 +atan2_u1_Y = f33 +atan2_z2_X = f34 + +atan2_two = f36 +atan2_B1sq_Y = f37 +atan2_z1_X = f38 +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_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_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 ///////////////////////////////////////////////////////////// -#ifdef _LIBC -.rodata -#else -.data -#endif +RODATA .align 16 -double_atan_constants_R: -ASM_TYPE_DIRECTIVE(double_atan_constants_R,@object) - data8 0xB36B46B9C5443CED, 0x0000401C //R8 - data8 0x842633E0D126261F, 0x0000401F //R9 - data8 0xBE04FFFFFFFF46E0, 0x00004010 //R4 - data8 0xE8C62000244D66E2, 0x00004013 //R5 - data8 0xF2790C001E3789B3, 0x00004016 //R6 - data8 0xDCD2CCF97D7C764F, 0x00004019 //R7 - data8 0xB40000000000000B, 0x00004004 //R1 - data8 0xB265F3D38F5EE28F, 0x00004021 //R10 - data8 0x8160000000000001, 0x00004009 //R2 - data8 0xFD5BFFFFFFFE55CD, 0x0000400C //R3 - data8 0xC90FDAA22168C235, 0x00003FFF // pi/2 -ASM_SIZE_DIRECTIVE(double_atan_constants_R) - -double_atan_constants_Q: -ASM_TYPE_DIRECTIVE(double_atan_constants_Q,@object) - data8 0xEBD602FA7761BC33, 0x00003FF9 //Q8 - data8 0x8CB1CABD6A91913C, 0x0000BFFA //Q9 - data8 0x84C665C37D623CD2, 0x00003FF7 //Q4 - data8 0x8DE0D1673DAEA9BC, 0x0000BFF8 //Q5 - data8 0xF658ADBE2C6E6FCC, 0x00003FF8 //Q6 - - data8 0xB56307BE1DD3FFB6, 0x0000BFF9 //Q7 - data8 0xAAAAAAAAAAAA8000, 0x0000BFFD //Q21 - data8 0x8000000000000000, 0x00003FFF //Q22 - data8 0x924924923A9D710C, 0x0000BFFC //Q19 - data8 0xCCCCCCCCCC9380E7, 0x00003FFC //Q20 - - data8 0xA644DC250EFA2800, 0x00003FED //Q0 - data8 0x83DEAE24EEBF5E44, 0x0000BFF1 //Q1 - data8 0xC758CCC64793D4EC, 0x00003FF3 //Q2 - data8 0xBFDC0B54E7C89DCE, 0x0000BFF5 //Q3 - data8 0x888855199D1290AF, 0x0000BFFB //Q15 - - data8 0x9D89D3BE514B0178, 0x00003FFB //Q16 - data8 0xBA2E8B4DEC70282A, 0x0000BFFB //Q17 - data8 0xE38E38DF9E9FC83B, 0x00003FFB //Q18 - data8 0x9F8781CC990029D9, 0x00003FFA //Q10 - data8 0xB0B39472DEBA3C79, 0x0000BFFA //Q11 - - data8 0xC2AFAEF8C85B0BC6, 0x00003FFA //Q12 - data8 0xD780E539797525DD, 0x0000BFFA //Q13 - data8 0xF0EDC449AC786DF9, 0x00003FFA //Q14 -ASM_SIZE_DIRECTIVE(double_atan_constants_Q) - - - -double_atan_constants_P: -ASM_TYPE_DIRECTIVE(double_atan_constants_P,@object) - data8 0xB1899EC590CDB8DF, 0x0000BFFA //P10 - data8 0xA1E79850A67D59B0, 0x00003FFA //P11 - data8 0x911D8B30C2A96E6D, 0x0000BFF3 //P20 - data8 0xB87233C68A640706, 0x00003FF0 //P21 - data8 0xD78E4B82F3C29D7A, 0x0000BFFA //P8 - - data8 0xC2EBE37AF932C14F, 0x00003FFA //P9 - data8 0xBA2E8B94AA104DD6, 0x0000BFFB //P4 - data8 0x9D89D7A640B71D38, 0x00003FFB //P5 - data8 0x88887CA2CE9B2A40, 0x0000BFFB //P6 - data8 0xF0F017D57A919C1E, 0x00003FFA //P7 - - data8 0xD0D635F230C80E06, 0x0000BFF8 //P16 - data8 0xE847BECA7209B479, 0x00003FF7 //P17 - data8 0xD14C6A2AAE0D5B07, 0x0000BFF6 //P18 - data8 0x915F612A5C469117, 0x00003FF5 //P19 - data8 0x921EDE5FD0DBBBE2, 0x0000BFFA //P12 - - data8 0xFFD303C2C8535445, 0x00003FF9 //P13 - data8 0xD30DF50E295386F7, 0x0000BFF9 //P14 - data8 0x9E81F2B1BBD210A8, 0x00003FF9 //P15 - data8 0xAAAAAAAAAAAAA800, 0x0000BFFD //P0 - data8 0xCCCCCCCCCCC7D476, 0x00003FFC //P1 - - data8 0x9249249247838066, 0x0000BFFC //P2 - data8 0xE38E38E302290D68, 0x00003FFB //P3 - data8 0xDF7F0A816F7E5025, 0x0000BFEC //P22 -ASM_SIZE_DIRECTIVE(double_atan_constants_P) - - -.align 32 -.global atan# - -//////////////////////////////////////////////////////// - +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 0x0000000000000000 , 0x00000000 // pad to avoid bank conflict +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 +LOCAL_OBJECT_END(atan2_tb2) -.section .text -.proc atan# -.align 32 -atan: - -{ .mmf -(p0) addl atan_GR_AD_P = @ltoff(double_atan_constants_P), gp -(p0) addl atan_GR_AD_Q = @ltoff(double_atan_constants_Q), gp -(p0) fmerge.s atan_ABS_f8 = f0,f8 -} -;; -{ .mmf - ld8 atan_GR_AD_P = [atan_GR_AD_P] - ld8 atan_GR_AD_Q = [atan_GR_AD_Q] -(p0) frcpa.s1 atan_C,p8 = f1,f8 -} -;; +.section .text +GLOBAL_LIBM_ENTRY(atan) -{ .mmf -(p0) addl atan_GR_AD_R = @ltoff(double_atan_constants_R), gp -(p0) addl atan_GR_exp_mask = 0x1ffff, r0 -(p0) fma.s1 atan_Y = f8,f8,f0 +{ .mfi + nop.m 999 + frcpa.s1 atan2_u1_Y,p7 = f1,atan2_Y + nop.i 999 } +{ .mfi + addl EXP_AD_P1 = @ltoff(atan2_tb1), gp + fma.s1 atan2_two = f1,f1,f1 + nop.i 999 ;; - -// This fnorm takes faults or sets fault flags -{ .mmf -(p0) mov atan_GR_10172 = 0x10172 - ld8 atan_GR_AD_R = [atan_GR_AD_R] -(p0) fnorm atan_NORM_f8 = f8 } -;; - - -// qnan snan inf norm unorm 0 -+ -// 1 1 0 0 0 1 11 -// c 7 - -// p9 set if we have a NAN or +-0 -{ .mmf -(p0) ldfe atan_Q8 = [atan_GR_AD_Q],16 -(p0) ldfe atan_P10 = [atan_GR_AD_P],16 -(p0) fclass.m.unc p9, p0 = f8, 0xc7 +{ .mfi + ld8 EXP_AD_P1 = [EXP_AD_P1] + frcpa.s1 atan2_u1_X,p6 = f1,atan2_X + nop.i 999 } -;; - - -{ .mmi -(p0) ldfe atan_Q9 = [atan_GR_AD_Q],16 -(p0) ldfe atan_P11 = [atan_GR_AD_P],16 - nop.i 999 +{ .mfi + nop.m 999 + fma.s1 atan2_ysq = atan2_Y,atan2_Y,f0 + nop.i 999 } ;; - -{ .mmf -(p0) ldfe atan_Q4 = [atan_GR_AD_Q],16 -(p0) ldfe atan_P20 = [atan_GR_AD_P],16 -(p9) fma.d.s0 f8 = f8,f1,f0 -;; -} - -// Exit if we have a NAN or +-0 -{ .mmb -(p0) ldfe atan_Q5 = [atan_GR_AD_Q],16 -(p0) ldfe atan_P21 = [atan_GR_AD_P],16 -(p9) br.ret.spnt b0 -;; +{ .mfi + add EXP_AD_P2 = 0xd0,EXP_AD_P1 + fmerge.s atan2_sgnY = atan2_Y,f1 + nop.i 999 } - - -// p6 is TRUE if |x| <= 1 -// p7 is TRUE if |x| > 1 -{ .mmf -(p0) ldfe atan_Q6 = [atan_GR_AD_Q],16 -(p0) ldfe atan_P8 = [atan_GR_AD_P],16 -(p0) fcmp.le.unc p6,p7 = atan_ABS_f8, f1 ;; -} { .mfi -(p0) ldfe atan_Q7 = [atan_GR_AD_Q],16 -(p0) fma.s1 atan_Z = atan_C, atan_C, f0 - nop.i 999 + ldfe atan2_P11 = [EXP_AD_P1],16 + fclass.m p10,p0 = atan2_Y, 0xc3 // Test for y=nan + nop.i 999 } { .mfi -(p0) ldfe atan_P9 = [atan_GR_AD_P],16 -(p0) fnma.s1 atan_B = atan_C,f8, f1 - nop.i 999 ;; + ldfe atan2_P21 = [EXP_AD_P2],16 + nop.f 999 + nop.i 999 +;; } { .mfi -(p0) ldfe atan_Q21 = [atan_GR_AD_Q],16 -(p0) fma.s1 atan_V12 = atan_Y, atan_Y, f0 - nop.i 999 + ldfe atan2_P10 = [EXP_AD_P1],16 + fnma.s1 atan2_B1Y = atan2_u1_Y, atan2_Y, atan2_two + nop.i 999 } { .mfi -(p0) ldfe atan_P4 = [atan_GR_AD_P],16 -(p0) fma.s1 atan_Xcub = f8, atan_Y , f0 - nop.i 999 -;; -} - - -{ .mmi -(p7) ldfe atan_Q22 = [atan_GR_AD_Q],16 -(p6) ldfe atan_P5 = [atan_GR_AD_P],16 -(p6) cmp.eq.unc p8,p0 = r0,r0 -;; -} - - -{ .mmi -(p7) ldfe atan_Q19 = [atan_GR_AD_Q],16 -(p6) ldfe atan_P6 = [atan_GR_AD_P],16 -(p7) cmp.eq.unc p9,p0 = r0,r0 -;; -} - - -{ .mmi -(p7) ldfe atan_Q20 = [atan_GR_AD_Q],16 -(p6) ldfe atan_P7 = [atan_GR_AD_P],16 - nop.i 999 + ldfe atan2_P20 = [EXP_AD_P2],16 + fma.s1 atan2_wp_Y = atan2_u1_Y, atan2_u1_Y, f0 + nop.i 999 ;; } { .mfi -(p7) ldfe atan_Q0 = [atan_GR_AD_Q],16 -(p6) fma.s1 atan_V13 = atan_Y, atan_P11, atan_P10 - nop.i 999 + ldfe atan2_P9 = [EXP_AD_P1],16 + fma.s1 atan2_z1_X = atan2_u1_X, atan2_Y, f0 + nop.i 999 } { .mfi -(p6) ldfe atan_P16 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_V11 = atan_Y, atan_Q9, atan_Q8 - nop.i 999 ;; + ldfe atan2_P19 = [EXP_AD_P2],16 + fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two + nop.i 999 } - +;; { .mfi -(p7) ldfe atan_Q1 = [atan_GR_AD_Q],16 -(p7) fma.s1 atan_G12 = atan_B, atan_B, f0 - nop.i 999 + ldfe atan2_P8 = [EXP_AD_P1],16 + fma.s1 atan2_z2_X = atan2_u1_X, atan2_ysq, f0 + nop.i 999 } -{ .mfi -(p6) ldfe atan_P17 = [atan_GR_AD_P],16 -(p0) fma.s1 atan_V9 = atan_V12, atan_V12, f0 - nop.i 999 ;; +{ .mfb + ldfe atan2_P18 = [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 } +;; - +// p6 true if swap, means |y| > 1.0 or ysq > 1.0 +// p7 true if no swap, means 1.0 >= |y| or 1.0 >= ysq { .mfi -(p7) ldfe atan_Q2 = [atan_GR_AD_Q],16 -(p6) fma.s1 atan_W11 = atan_Y, atan_P21, atan_P20 - nop.i 999 + ldfe atan2_P7 = [EXP_AD_P1],16 + fcmp.ge.s1 p7,p6 = f1, atan2_ysq + nop.i 999 } -{ .mfi -(p6) ldfe atan_P18 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_V7 = atan_Y, atan_Q5, atan_Q4 - nop.i 999 ;; +{ .mmf + ldfe atan2_P17 = [EXP_AD_P2],16 + nop.m 999 + nop.f 999 } +;; { .mfi -(p7) ldfe atan_Q3 = [atan_GR_AD_Q],16 -(p7) fma.s1 atan_Z1 = atan_Z, atan_Z, f0 - nop.i 999 + ldfe atan2_P6 = [EXP_AD_P1],16 + fma.s1 atan2_E = atan2_u1_Y, atan2_B1Y, atan2_Y + nop.i 999 } { .mfi -(p6) ldfe atan_P19 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_Y3 = atan_Y , atan_V12, f0 - nop.i 999 ;; + ldfe atan2_P16 = [EXP_AD_P2],16 + fma.s1 atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0 + nop.i 999 +;; } { .mfi -(p7) ldfe atan_R8 = [atan_GR_AD_R],16 -(p6) fma.s1 atan_V11 = atan_Y, atan_P9, atan_P8 - nop.i 999 + ldfe atan2_P5 = [EXP_AD_P1],16 +(p7) fma.s1 atan2_wp_X = atan2_z1_X, atan2_z1_X, f0 + nop.i 999 } { .mfi -(p6) ldfe atan_P12 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_V8 = atan_Y, atan_Q7, atan_Q6 - nop.i 999 ;; -} - -{ .mmi -(p7) ldfe atan_R9 = [atan_GR_AD_R],16 -(p6) ldfe atan_P13 = [atan_GR_AD_P],16 - nop.i 999 + ldfe atan2_P15 = [EXP_AD_P2],16 +(p7) fma.s1 atan2_B1sq_X = atan2_B1X, atan2_B1X, f0 + nop.i 999 ;; } { .mfi -(p7) ldfe atan_R4 = [atan_GR_AD_R],16 -(p6) fma.s1 atan_V7 = atan_Y, atan_P5, atan_P4 - nop.i 999 + ldfe atan2_P4 = [EXP_AD_P1],16 +(p6) fma.s1 atan2_z = atan2_u1_Y, atan2_B1Y, f0 + nop.i 999 } { .mfi -(p6) ldfe atan_P14 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_W13 = atan_Y, atan_Q22, atan_Q21 - nop.i 999 ;; + ldfe atan2_P14 = [EXP_AD_P2],16 +(p7) fma.s1 atan2_E = atan2_z2_X, atan2_B1X, atan2_X + nop.i 999 +;; } { .mfi -(p7) ldfe atan_R5 = [atan_GR_AD_R],16 -(p6) fma.s1 atan_Y12 = atan_V9 , atan_V9 , f0 - nop.i 999 + ldfe atan2_P3 = [EXP_AD_P1],16 + fcmp.eq.s0 p14,p15=atan2_X,atan2_Y // Dummy for denorm and invalid + nop.i 999 } -{ .mfi -(p6) ldfe atan_P15 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_Y8 = atan_V9 , atan_V9 , f0 - nop.i 999 ;; +{ .mmf + ldfe atan2_P13 = [EXP_AD_P2],16 + nop.m 999 +(p7) fma.s1 atan2_z = atan2_z1_X, atan2_B1X, f0 +;; } - { .mfi -(p7) ldfe atan_R6 = [atan_GR_AD_R],16 -(p6) fma.s1 atan_V8 = atan_Y, atan_P7, atan_P6 - nop.i 999 + ldfe atan2_P2 = [EXP_AD_P1],16 +(p6) fma.s1 atan2_w = atan2_wp_Y, atan2_B1sq_Y,f0 + nop.i 999 } -{ .mfi -(p6) ldfe atan_P0 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_W11 = atan_Y, atan_Q20, atan_Q19 - nop.i 999 ;; +{ .mlx + ldfe atan2_P12 = [EXP_AD_P2],16 + movl rsig_near_one = 0x8000000000000001 // signif near 1.0 +;; } - { .mfi -(p7) ldfe atan_R7 = [atan_GR_AD_R],16 -(p7) fma.s1 atan_Z2 = atan_Z1 , atan_Z1, f0 - nop.i 999 + ldfe atan2_P1 = [EXP_AD_P1],16 + fclass.m p9,p0 = atan2_Y, 0x23 // test if y inf + nop.i 999 } { .mfi -(p6) ldfe atan_P1 = [atan_GR_AD_P],16 -(p6) fma.s1 atan_V10 = atan_V12, atan_V13, atan_V11 - nop.i 999 ;; + ldfe atan2_P22 = [EXP_AD_P2],16 +(p7) fma.s1 atan2_w = atan2_wp_X, atan2_B1sq_X,f0 + nop.i 999 +;; } { .mfi -(p7) ldfe atan_Q15 = [atan_GR_AD_Q],16 -(p6) fma.s1 atan_W7 = atan_Y, atan_P17, atan_P16 - nop.i 999 + ldfe atan2_P0 = [EXP_AD_P1],16 + frcpa.s1 atan2_F,p0 = f1, atan2_E + nop.i 999 } { .mfi -(p6) ldfe atan_P2 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_V3 = atan_Y, atan_Q1 , atan_Q0 - nop.i 999 ;; + ldfe atan2_pi_by_2 = [EXP_AD_P2],16 +(p6) fnma.s1 atan2_gV = atan2_Y, atan2_z, atan2_X + nop.i 999 +;; } { .mfi -(p7) ldfe atan_Q16 = [atan_GR_AD_Q],16 -(p7) fma.s1 atan_G9 = atan_G12, atan_G12, f0 - nop.i 999 + setf.sig atan2_sig_near_one = rsig_near_one +(p7) fnma.s1 atan2_gV = atan2_X, atan2_z, atan2_Y + nop.i 999 } -{ .mfi -(p6) ldfe atan_P3 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_V6 = atan_V12, atan_V8, atan_V7 - nop.i 999 ;; +{ .mfb + nop.m 999 +(p9) fma.d.s0 f8 = atan2_sgnY, atan2_pi_by_2, f0 // +-pi/2 if y inf +(p9) br.ret.spnt b0 // exit if y inf, result is +-pi/2 +;; } - { .mfi -(p7) ldfe atan_R1 = [atan_GR_AD_R],16 -(p6) fma.s1 atan_W8 = atan_Y, atan_P19, atan_P18 - nop.i 999 + nop.m 999 + fma.s1 atan2_V13 = atan2_w, atan2_P11, atan2_P10 + nop.i 999 } { .mfi -(p6) ldfe atan_P22 = [atan_GR_AD_P],16 -(p7) fma.s1 atan_V4 = atan_Y, atan_Q3 , atan_Q2 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W11 = atan2_w, atan2_P21, atan2_P20 + nop.i 999 +;; } - { .mfi - getf.exp atan_GR_signexp_f8 = atan_NORM_f8 -(p7) fma.s1 atan_Y11 = atan_Y3 , atan_Y8 , f0 - nop.i 999 + nop.m 999 + fma.s1 atan2_V11 = atan2_w, atan2_P9, atan2_P8 + nop.i 999 } { .mfi -(p7) ldfe atan_Q17 = [atan_GR_AD_Q],16 -(p6) fma.s1 atan_V6 = atan_V12, atan_V8, atan_V7 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_V12 = atan2_w, atan2_w, f0 + nop.i 999 +;; } - { .mfi -(p7) ldfe atan_Q18 = [atan_GR_AD_Q],16 -(p6) fma.s1 atan_W3 = atan_Y, atan_P13, atan_P12 - nop.i 999 + nop.m 999 + fma.s1 atan2_V8 = atan2_w, atan2_P7 , atan2_P6 + nop.i 999 } { .mfi -(p7) ldfe atan_R10 = [atan_GR_AD_R],16 -(p7) fma.s1 atan_G11 = atan_B, atan_R9 , atan_R8 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18 + nop.i 999 +;; } - { .mfi -(p7) ldfe atan_Q10 = [atan_GR_AD_Q],16 -(p7) fma.s1 atan_Z3 = atan_Z1 , atan_Z2 , f0 -(p0) and atan_GR_exp_f8 = atan_GR_signexp_f8,atan_GR_exp_mask + nop.m 999 + fnma.s1 atan2_alpha = atan2_E, atan2_F, f1 + nop.i 999 } { .mfi -(p7) ldfe atan_R2 = [atan_GR_AD_R],16 -(p7) fma.s1 atan_Z4 = atan_Z2 , atan_Z2 , f0 - nop.i 999 ;; + nop.m 999 + fnma.s1 atan2_alpha_1 = atan2_E, atan2_F, atan2_two + nop.i 999 +;; } { .mfi -(p7) ldfe atan_Q11 = [atan_GR_AD_Q],16 -(p6) fma.s1 atan_W4 = atan_Y, atan_P15, atan_P14 - nop.i 999 + nop.m 999 + fma.s1 atan2_V7 = atan2_w, atan2_P5 , atan2_P4 + nop.i 999 } { .mfi -(p7) ldfe atan_R3 = [atan_GR_AD_R],16 -(p7) fma.s1 atan_G7 = atan_B, atan_R5 , atan_R4 -(p0) cmp.le.unc p11,p0 = atan_GR_10172,atan_GR_exp_f8 -;; -} - - -{ .mmf -(p9) ldfe atan_Q12 = [atan_GR_AD_Q],16 -(p0) ldfe atan_S_PI = [atan_GR_AD_R],16 -(p8) fma.s1 atan_W6 = atan_V12, atan_W8, atan_W7 + nop.m 999 + fma.s1 atan2_W7 = atan2_w, atan2_P17, atan2_P16 + nop.i 999 ;; } - - { .mfi -(p9) ldfe atan_Q13 = [atan_GR_AD_Q],16 -(p8) fma.s1 atan_V3 = atan_Y, atan_P1 , atan_P0 -(p11) cmp.ne.and p6,p7 = r0,r0 + nop.m 999 + fma.s1 atan2_V4 = atan2_w, atan2_P3 , atan2_P2 + nop.i 999 } { .mfi - nop.m 999 -(p8) fma.s1 atan_V5 = atan_V9 , atan_V10, atan_V6 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W4 = atan2_w, atan2_P15, atan2_P14 + nop.i 999 +;; } - -.pred.rel "mutex",p6,p7,p11 { .mfi -(p7) ldfe atan_Q14 = [atan_GR_AD_Q],16 -(p6) fma.s1 atan_Y12 = atan_V9 , atan_Y12, f0 - nop.i 999 + nop.m 999 + fma.s1 atan2_V3 = atan2_w, atan2_P1 , atan2_P0 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_G8 = atan_B, atan_R7 , atan_R6 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W3 = atan2_w, atan2_P13, atan2_P12 + nop.i 999 +;; } - { .mfi - nop.m 999 -(p6) fma.s1 atan_V4 = atan_Y, atan_P3 , atan_P2 - nop.i 999 + nop.m 999 + fma.s1 atan2_V10 = atan2_V12, atan2_V13, atan2_V11 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_W7 = atan_Y, atan_Q16, atan_Q15 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_gVF = atan2_gV, atan2_F, f0 + nop.i 999 +;; } - { .mfi - nop.m 999 -(p6) fma.s1 atan_W10 = atan_V12, atan_P22, atan_W11 - nop.i 999 + nop.m 999 + fma.s1 atan2_alpha_sq = atan2_alpha, atan2_alpha, f0 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_G3 = atan_B, atan_R1 , f1 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_Cp = atan2_alpha, atan2_alpha_1, f1 + nop.i 999 +;; } - { .mfi - nop.m 999 -(p6) fma.s1 atan_W2 = atan_V12, atan_W4 , atan_W3 - nop.i 999 + nop.m 999 + fma.s1 atan2_V9 = atan2_V12, atan2_V12, f0 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_V2 = atan_V12, atan_V4 , atan_V3 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W10 = atan2_V12, atan2_P22 , atan2_W11 + nop.i 999 +;; } { .mfi - nop.m 999 -(p7) fma.s1 atan_W8 = atan_Y, atan_Q18, atan_Q17 - nop.i 999 + nop.m 999 + fma.s1 atan2_V6 = atan2_V12, atan2_V8 , atan2_V7 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_G10 = atan_G12, atan_R10, atan_G11 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W6 = atan2_V12, atan2_W8 , atan2_W7 + nop.i 999 +;; } { .mfi - nop.m 999 -(p7) fma.s1 atan_V10 = atan_V12, atan_Q10, atan_V11 - nop.i 999 + nop.m 999 + fma.s1 atan2_V2 = atan2_V12, atan2_V4 , atan2_V3 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_G6 = atan_G12, atan_G8 , atan_G7 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W2 = atan2_V12, atan2_W4 , atan2_W3 + nop.i 999 +;; } - { .mfi - nop.m 999 -(p6) fma.s1 atan_V2 = atan_V12, atan_V4, atan_V3 - nop.i 999 + nop.m 999 + fma.s1 atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_G4 = atan_B , atan_R3 , atan_R2 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_C = atan2_gVF, atan2_Cp, f0 + nop.i 999 +;; } - { .mfi - nop.m 999 -(p6) fma.s1 atan_W5 = atan_V9 , atan_W10, atan_W6 - nop.i 999 -} -{ .mfi - nop.m 999 -(p7) fma.s1 atan_W3 = atan_Y , atan_Q12, atan_Q11 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W12 = atan2_V9, atan2_V9, f0 + nop.i 999 +;; } - { .mfi - nop.m 999 -(p7) fma.s1 atan_Z5 = atan_Z3 , atan_Z4 , f0 - nop.i 999 + nop.m 999 + fma.s1 atan2_V5 = atan2_V9, atan2_V10, atan2_V6 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_W10 = atan_V12, atan_W13, atan_W11 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W5 = atan2_V9, atan2_W10, atan2_W6 + nop.i 999 +;; } - { .mfi - nop.m 999 -(p7) fma.s1 atan_W4 = atan_Y , atan_Q14, atan_Q13 - nop.i 999 + nop.m 999 + fclass.m p8,p0 = atan2_Y, 0x07 // Test for y=0 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_W6 = atan_V12, atan_W8, atan_W7 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_d = atan2_alpha_cub, atan2_C, atan2_C + nop.i 999 } +;; { .mfi - nop.m 999 -(p7) fma.s1 atan_V5 = atan_V9 , atan_V10, atan_V6 - nop.i 999 + nop.m 999 + fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0 + nop.i 999 } -{ .mfi - nop.m 999 -(p7) fma.s1 atan_G5 = atan_G9 , atan_G10, atan_G6 - nop.i 999 ;; -} - +;; { .mfi - nop.m 999 -(p6) fma.s1 atan_V1 = atan_V9 , atan_V5 , atan_V2 - nop.i 999 + nop.m 999 + fma.s1 atan2_V1 = atan2_V9, atan2_V5, atan2_V2 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_G2 = atan_G12, atan_G4 , atan_G3 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_W1 = atan2_V9, atan2_W5, atan2_W2 + nop.i 999 +;; } - -{ .mfi - nop.m 999 -(p6) fma.s1 atan_W1 = atan_V9 , atan_W5 , atan_W2 - nop.i 999 -} { .mfi - nop.m 999 -(p7) fma.s1 atan_Z6 = atan_Z4 , atan_C , f0 - nop.i 999 ;; + nop.m 999 +(p8) fmerge.s f8 = atan2_sgnY, f0 // +-0 if y=0 + nop.i 999 } - -{ .mfi - nop.m 999 -(p0) fmerge.s atan_S_PI = f8, atan_S_PI - nop.i 999 ;; +{ .mfb + nop.m 999 + fma.s1 atan2_zcub = atan2_z, atan2_w, f0 +(p8) br.ret.spnt b0 // Exit if y=0 +;; } - { .mfi - nop.m 999 -(p7) fma.s1 atan_W5 = atan_V9 , atan_W10, atan_W6 - nop.i 999 + nop.m 999 + fma.s1 atan2_pd = atan2_P0, atan2_d, f0 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_W2 = atan_V12, atan_W4 , atan_W3 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_dsq = atan2_d, atan2_d, f0 + nop.i 999 +;; } { .mfi - nop.m 999 -(p7) fma.s1 atan_G1 = atan_G9 , atan_G5 , atan_G2 - nop.i 999 + nop.m 999 + fmerge.se atan2_near_one = f1, atan2_sig_near_one // Const ~1.0 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_V1 = atan_V9 , atan_V5 , atan_V2 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1 + nop.i 999 +;; } - { .mfi - nop.m 999 -(p6) fma.s1 atan_P = atan_Y12, atan_W1 , atan_V1 - nop.i 999 + nop.m 999 + fma.s1 atan2_sgn_pi_by_2 = atan2_pi_by_2, atan2_sgnY, f0 + nop.i 999 } { .mfi - nop.m 999 -(p7) fma.s1 atan_Z7 = atan_Z5 , atan_Z6 , f0 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_A_lo = atan2_pd, atan2_dsq, atan2_d + nop.i 999 +;; } { .mfi - nop.m 999 -(p7) fma.s1 atan_W1 = atan_V9 , atan_W5 , atan_W2 - nop.i 999 ;; + nop.m 999 + fma.s1 atan2_A_hi = atan2_zcub, atan2_Pp, atan2_z + nop.i 999 +;; } { .mfi - nop.m 999 -(p11) fma.d.s0 f8 = atan_S_PI,f1,f0 - nop.i 999 + nop.m 999 +(p6) 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 -(p7) fma.s1 atan_Z = atan_G1 , atan_Z7 , f0 - nop.i 999 ;; -} - - -{ .mfi - nop.m 999 -(p7) fma.s1 atan_Q = atan_Y11, atan_W1 , atan_V1 - nop.i 999 ;; + nop.m 999 +(p7) fma.d.s0 f8 = atan2_A_hi, f1, atan2_A_lo + nop.i 999 +;; } - -{ .mfi - nop.m 999 -(p6) fma.d.s0 f8 = atan_P , atan_Xcub , f8 - nop.i 999 -} +// For |Y| > |X|, result is +- pi/2 - (A_hi + A_lo) +// 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. { .mfb - nop.m 999 -(p7) fnma.d.s0 f8 = atan_Z , atan_Q , atan_S_PI -(p0) br.ret.sptk b0 ;; + nop.m 999 +(p6) fnma.d.s0 f8 = atan2_A, atan2_near_one, atan2_sgn_pi_by_2 + br.ret.sptk b0 +;; } -.endp atan -ASM_SIZE_DIRECTIVE(atan) +GLOBAL_LIBM_END(atan) |