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Diffstat (limited to 'sysdeps/ia64/fpu/s_atan.S')
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diff --git a/sysdeps/ia64/fpu/s_atan.S b/sysdeps/ia64/fpu/s_atan.S new file mode 100644 index 0000000000..720ecad28a --- /dev/null +++ b/sysdeps/ia64/fpu/s_atan.S @@ -0,0 +1,753 @@ +.file "atan.s" + + +// Copyright (c) 2000 - 2003, Intel Corporation +// All rights reserved. +// +// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// +// * Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// +// * The name of Intel Corporation may not be used to endorse or promote +// products derived from this software without specific prior written +// permission. + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Intel Corporation is the author of this code, and requests that all +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. +// +// History +//============================================================== +// 02/02/00 Initial version +// 04/13/00 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 Y) +// +// Overview of operation +//============================================================== +// +// The atan function returns values in the interval [-pi/2,+pi/2]. +// +// The algorithm used is the atan2(Y,X) algorithm where we fix X=1.0. +// +// There are two basic paths: swap true and swap false. +// atan2(Y,X) ==> atan2(V/U) where U >= V. If Y > X, we must swap. +// +// p6 swap True |Y| > |X| +// p7 swap False |Y| <= |X| +// +// +// Simple trigonometric identities show +// Region 1 +// |Y|<=1.0, V=Y, U=1.0 atan2(Y,X) = sgnY * (0 + atan(V/U)) +// +// 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 +//============================================================== +// atan(QNAN) = QNAN +// atan(SNAN) = quieted SNAN +// atan(+-inf) = +- pi/2 +// atan(+-0) = +-0 + +// Registers used +//============================================================== + +// predicate registers used: +// p6 -> p15 + +// floating-point registers used: +// f8, input +// f32 -> f116 + +// general registers used +// r14 -> r16 + +// Assembly macros +//============================================================== + +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 + +///////////////////////////////////////////////////////////// + + +RODATA + +.align 16 + +LOCAL_OBJECT_START(atan2_tb1) +data8 0xA21922DC45605EA1 , 0x00003FFA // P11 +data8 0xB199DD6D2675C40F , 0x0000BFFA // P10 +data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9 +data8 0xD78F28FC2A592781 , 0x0000BFFA // P8 +data8 0xF0F03ADB3FC930D3 , 0x00003FFA // P7 +data8 0x88887EBB209E3543 , 0x0000BFFB // P6 +data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5 +data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4 +data8 0xE38E38E320A8A098 , 0x00003FFB // P3 +data8 0x9249249247E37913 , 0x0000BFFC // P2 +data8 0xCCCCCCCCCCC906CD , 0x00003FFC // P1 +data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0 +data8 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 +GLOBAL_LIBM_ENTRY(atan) + +{ .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 +;; +} + +{ .mfi + ld8 EXP_AD_P1 = [EXP_AD_P1] + frcpa.s1 atan2_u1_X,p6 = f1,atan2_X + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_ysq = atan2_Y,atan2_Y,f0 + nop.i 999 +} +;; + +{ .mfi + add EXP_AD_P2 = 0xd0,EXP_AD_P1 + fmerge.s atan2_sgnY = atan2_Y,f1 + nop.i 999 +} +;; + + +{ .mfi + ldfe atan2_P11 = [EXP_AD_P1],16 + fclass.m p10,p0 = atan2_Y, 0xc3 // Test for y=nan + nop.i 999 +} +{ .mfi + ldfe atan2_P21 = [EXP_AD_P2],16 + nop.f 999 + nop.i 999 +;; +} + + +{ .mfi + ldfe atan2_P10 = [EXP_AD_P1],16 + fnma.s1 atan2_B1Y = atan2_u1_Y, atan2_Y, atan2_two + nop.i 999 +} +{ .mfi + ldfe atan2_P20 = [EXP_AD_P2],16 + fma.s1 atan2_wp_Y = atan2_u1_Y, atan2_u1_Y, f0 + nop.i 999 +;; +} + +{ .mfi + ldfe atan2_P9 = [EXP_AD_P1],16 + fma.s1 atan2_z1_X = atan2_u1_X, atan2_Y, f0 + nop.i 999 +} +{ .mfi + ldfe atan2_P19 = [EXP_AD_P2],16 + fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, 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 +} +{ .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 + ldfe atan2_P7 = [EXP_AD_P1],16 + fcmp.ge.s1 p7,p6 = f1, atan2_ysq + nop.i 999 +} +{ .mmf + ldfe atan2_P17 = [EXP_AD_P2],16 + nop.m 999 + nop.f 999 +} +;; + +{ .mfi + ldfe atan2_P6 = [EXP_AD_P1],16 + fma.s1 atan2_E = atan2_u1_Y, atan2_B1Y, atan2_Y + nop.i 999 +} +{ .mfi + ldfe atan2_P16 = [EXP_AD_P2],16 + fma.s1 atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0 + nop.i 999 +;; +} + +{ .mfi + ldfe atan2_P5 = [EXP_AD_P1],16 +(p7) fma.s1 atan2_wp_X = atan2_z1_X, atan2_z1_X, f0 + nop.i 999 +} +{ .mfi + ldfe atan2_P15 = [EXP_AD_P2],16 +(p7) fma.s1 atan2_B1sq_X = atan2_B1X, atan2_B1X, f0 + nop.i 999 +;; +} + +{ .mfi + ldfe atan2_P4 = [EXP_AD_P1],16 +(p6) fma.s1 atan2_z = atan2_u1_Y, atan2_B1Y, f0 + nop.i 999 +} +{ .mfi + ldfe atan2_P14 = [EXP_AD_P2],16 +(p7) fma.s1 atan2_E = atan2_z2_X, atan2_B1X, atan2_X + nop.i 999 +;; +} + + +{ .mfi + ldfe atan2_P3 = [EXP_AD_P1],16 + fcmp.eq.s0 p14,p15=atan2_X,atan2_Y // Dummy for denorm and invalid + 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 + ldfe atan2_P2 = [EXP_AD_P1],16 +(p6) fma.s1 atan2_w = atan2_wp_Y, atan2_B1sq_Y,f0 + nop.i 999 +} +{ .mlx + ldfe atan2_P12 = [EXP_AD_P2],16 + movl rsig_near_one = 0x8000000000000001 // signif near 1.0 +;; +} + +{ .mfi + ldfe atan2_P1 = [EXP_AD_P1],16 + fclass.m p9,p0 = atan2_Y, 0x23 // test if y inf + nop.i 999 +} +{ .mfi + ldfe atan2_P22 = [EXP_AD_P2],16 +(p7) fma.s1 atan2_w = atan2_wp_X, atan2_B1sq_X,f0 + nop.i 999 +;; +} + +{ .mfi + ldfe atan2_P0 = [EXP_AD_P1],16 + frcpa.s1 atan2_F,p0 = f1, atan2_E + nop.i 999 +} +{ .mfi + ldfe atan2_pi_by_2 = [EXP_AD_P2],16 +(p6) fnma.s1 atan2_gV = atan2_Y, atan2_z, atan2_X + nop.i 999 +;; +} + +{ .mfi + setf.sig atan2_sig_near_one = rsig_near_one +(p7) fnma.s1 atan2_gV = atan2_X, atan2_z, atan2_Y + 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 + nop.m 999 + fma.s1 atan2_V13 = atan2_w, atan2_P11, atan2_P10 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W11 = atan2_w, atan2_P21, atan2_P20 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_V11 = atan2_w, atan2_P9, atan2_P8 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_V12 = atan2_w, atan2_w, f0 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_V8 = atan2_w, atan2_P7 , atan2_P6 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fnma.s1 atan2_alpha = atan2_E, atan2_F, f1 + nop.i 999 +} +{ .mfi + nop.m 999 + fnma.s1 atan2_alpha_1 = atan2_E, atan2_F, atan2_two + nop.i 999 +;; +} + + +{ .mfi + nop.m 999 + fma.s1 atan2_V7 = atan2_w, atan2_P5 , atan2_P4 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W7 = atan2_w, atan2_P17, atan2_P16 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_V4 = atan2_w, atan2_P3 , atan2_P2 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W4 = atan2_w, atan2_P15, atan2_P14 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_V3 = atan2_w, atan2_P1 , atan2_P0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W3 = atan2_w, atan2_P13, atan2_P12 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_V10 = atan2_V12, atan2_V13, atan2_V11 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_gVF = atan2_gV, atan2_F, f0 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_alpha_sq = atan2_alpha, atan2_alpha, f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_Cp = atan2_alpha, atan2_alpha_1, f1 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_V9 = atan2_V12, atan2_V12, f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W10 = atan2_V12, atan2_P22 , atan2_W11 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_V6 = atan2_V12, atan2_V8 , atan2_V7 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W6 = atan2_V12, atan2_W8 , atan2_W7 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_V2 = atan2_V12, atan2_V4 , atan2_V3 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W2 = atan2_V12, atan2_W4 , atan2_W3 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_C = atan2_gVF, atan2_Cp, f0 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_W12 = atan2_V9, atan2_V9, f0 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_V5 = atan2_V9, atan2_V10, atan2_V6 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W5 = atan2_V9, atan2_W10, atan2_W6 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fclass.m p8,p0 = atan2_Y, 0x07 // Test for y=0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_d = atan2_alpha_cub, atan2_C, atan2_C + nop.i 999 +} +;; + +{ .mfi + nop.m 999 + fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0 + nop.i 999 +} +;; + +{ .mfi + nop.m 999 + fma.s1 atan2_V1 = atan2_V9, atan2_V5, atan2_V2 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_W1 = atan2_V9, atan2_W5, atan2_W2 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 +(p8) fmerge.s f8 = atan2_sgnY, f0 // +-0 if y=0 + 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 + fma.s1 atan2_pd = atan2_P0, atan2_d, f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_dsq = atan2_d, atan2_d, f0 + nop.i 999 +;; +} + + +{ .mfi + nop.m 999 + fmerge.se atan2_near_one = f1, atan2_sig_near_one // Const ~1.0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fma.s1 atan2_sgn_pi_by_2 = atan2_pi_by_2, atan2_sgnY, f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 atan2_A_lo = atan2_pd, atan2_dsq, atan2_d + nop.i 999 +;; +} + + +{ .mfi + nop.m 999 + fma.s1 atan2_A_hi = atan2_zcub, atan2_Pp, atan2_z + nop.i 999 +;; +} + + +{ .mfi + 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.d.s0 f8 = atan2_A_hi, f1, atan2_A_lo + 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 +(p6) fnma.d.s0 f8 = atan2_A, atan2_near_one, atan2_sgn_pi_by_2 + br.ret.sptk b0 +;; +} + +GLOBAL_LIBM_END(atan) |