From 5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 Mon Sep 17 00:00:00 2001 From: Zack Weinberg Date: Thu, 8 Jun 2017 15:39:03 -0400 Subject: Prepare for radical source tree reorganization. All top-level files and directories are moved into a temporary storage directory, REORG.TODO, except for files that will certainly still exist in their current form at top level when we're done (COPYING, COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which are moved to the new directory OldChangeLogs, instead), and the generated file INSTALL (which is just deleted; in the new order, there will be no generated files checked into version control). --- REORG.TODO/sysdeps/ia64/fpu/s_cosf.S | 716 +++++++++++++++++++++++++++++++++++ 1 file changed, 716 insertions(+) create mode 100644 REORG.TODO/sysdeps/ia64/fpu/s_cosf.S (limited to 'REORG.TODO/sysdeps/ia64/fpu/s_cosf.S') diff --git a/REORG.TODO/sysdeps/ia64/fpu/s_cosf.S b/REORG.TODO/sysdeps/ia64/fpu/s_cosf.S new file mode 100644 index 0000000000..2dcdaa8879 --- /dev/null +++ b/REORG.TODO/sysdeps/ia64/fpu/s_cosf.S @@ -0,0 +1,716 @@ +.file "sincosf.s" + + +// Copyright (c) 2000 - 2005, 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 +// 04/02/00 Unwind support added. +// 06/16/00 Updated tables to enforce symmetry +// 08/31/00 Saved 2 cycles in main path, and 9 in other paths. +// 09/20/00 The updated tables regressed to an old version, so reinstated them +// 10/18/00 Changed one table entry to ensure symmetry +// 01/03/01 Improved speed, fixed flag settings for small arguments. +// 02/18/02 Large arguments processing routine excluded +// 05/20/02 Cleaned up namespace and sf0 syntax +// 06/03/02 Insure inexact flag set for large arg result +// 09/05/02 Single precision version is made using double precision one as base +// 02/10/03 Reordered header: .section, .global, .proc, .align +// 03/31/05 Reformatted delimiters between data tables +// +// API +//============================================================== +// float sinf( float x); +// float cosf( float x); +// +// Overview of operation +//============================================================== +// +// Step 1 +// ====== +// Reduce x to region -1/2*pi/2^k ===== 0 ===== +1/2*pi/2^k where k=4 +// divide x by pi/2^k. +// Multiply by 2^k/pi. +// nfloat = Round result to integer (round-to-nearest) +// +// r = x - nfloat * pi/2^k +// Do this as (x - nfloat * HIGH(pi/2^k)) - nfloat * LOW(pi/2^k) + +// for increased accuracy. +// pi/2^k is stored as two numbers that when added make pi/2^k. +// pi/2^k = HIGH(pi/2^k) + LOW(pi/2^k) +// HIGH part is rounded to zero, LOW - to nearest +// +// x = (nfloat * pi/2^k) + r +// r is small enough that we can use a polynomial approximation +// and is referred to as the reduced argument. +// +// Step 3 +// ====== +// Take the unreduced part and remove the multiples of 2pi. +// So nfloat = nfloat (with lower k+1 bits cleared) + lower k+1 bits +// +// nfloat (with lower k+1 bits cleared) is a multiple of 2^(k+1) +// N * 2^(k+1) +// nfloat * pi/2^k = N * 2^(k+1) * pi/2^k + (lower k+1 bits) * pi/2^k +// nfloat * pi/2^k = N * 2 * pi + (lower k+1 bits) * pi/2^k +// nfloat * pi/2^k = N2pi + M * pi/2^k +// +// +// Sin(x) = Sin((nfloat * pi/2^k) + r) +// = Sin(nfloat * pi/2^k) * Cos(r) + Cos(nfloat * pi/2^k) * Sin(r) +// +// Sin(nfloat * pi/2^k) = Sin(N2pi + Mpi/2^k) +// = Sin(N2pi)Cos(Mpi/2^k) + Cos(N2pi)Sin(Mpi/2^k) +// = Sin(Mpi/2^k) +// +// Cos(nfloat * pi/2^k) = Cos(N2pi + Mpi/2^k) +// = Cos(N2pi)Cos(Mpi/2^k) + Sin(N2pi)Sin(Mpi/2^k) +// = Cos(Mpi/2^k) +// +// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) +// +// +// Step 4 +// ====== +// 0 <= M < 2^(k+1) +// There are 2^(k+1) Sin entries in a table. +// There are 2^(k+1) Cos entries in a table. +// +// Get Sin(Mpi/2^k) and Cos(Mpi/2^k) by table lookup. +// +// +// Step 5 +// ====== +// Calculate Cos(r) and Sin(r) by polynomial approximation. +// +// Cos(r) = 1 + r^2 q1 + r^4 q2 = Series for Cos +// Sin(r) = r + r^3 p1 + r^5 p2 = Series for Sin +// +// and the coefficients q1, q2 and p1, p2 are stored in a table +// +// +// Calculate +// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) +// +// as follows +// +// S[m] = Sin(Mpi/2^k) and C[m] = Cos(Mpi/2^k) +// rsq = r*r +// +// +// P = P1 + r^2*P2 +// Q = Q1 + r^2*Q2 +// +// rcub = r * rsq +// Sin(r) = r + rcub * P +// = r + r^3p1 + r^5p2 = Sin(r) +// +// The coefficients are not exactly these values, but almost. +// +// p1 = -1/6 = -1/3! +// p2 = 1/120 = 1/5! +// p3 = -1/5040 = -1/7! +// p4 = 1/362889 = 1/9! +// +// P = r + r^3 * P +// +// Answer = S[m] Cos(r) + C[m] P +// +// Cos(r) = 1 + rsq Q +// Cos(r) = 1 + r^2 Q +// Cos(r) = 1 + r^2 (q1 + r^2q2) +// Cos(r) = 1 + r^2q1 + r^4q2 +// +// S[m] Cos(r) = S[m](1 + rsq Q) +// S[m] Cos(r) = S[m] + S[m] rsq Q +// S[m] Cos(r) = S[m] + s_rsq Q +// Q = S[m] + s_rsq Q +// +// Then, +// +// Answer = Q + C[m] P + + +// Registers used +//============================================================== +// general input registers: +// r14 -> r19 +// r32 -> r45 + +// predicate registers used: +// p6 -> p14 + +// floating-point registers used +// f9 -> f15 +// f32 -> f61 + +// Assembly macros +//============================================================== +sincosf_NORM_f8 = f9 +sincosf_W = f10 +sincosf_int_Nfloat = f11 +sincosf_Nfloat = f12 + +sincosf_r = f13 +sincosf_rsq = f14 +sincosf_rcub = f15 +sincosf_save_tmp = f15 + +sincosf_Inv_Pi_by_16 = f32 +sincosf_Pi_by_16_1 = f33 +sincosf_Pi_by_16_2 = f34 + +sincosf_Inv_Pi_by_64 = f35 + +sincosf_Pi_by_16_3 = f36 + +sincosf_r_exact = f37 + +sincosf_Sm = f38 +sincosf_Cm = f39 + +sincosf_P1 = f40 +sincosf_Q1 = f41 +sincosf_P2 = f42 +sincosf_Q2 = f43 +sincosf_P3 = f44 +sincosf_Q3 = f45 +sincosf_P4 = f46 +sincosf_Q4 = f47 + +sincosf_P_temp1 = f48 +sincosf_P_temp2 = f49 + +sincosf_Q_temp1 = f50 +sincosf_Q_temp2 = f51 + +sincosf_P = f52 +sincosf_Q = f53 + +sincosf_srsq = f54 + +sincosf_SIG_INV_PI_BY_16_2TO61 = f55 +sincosf_RSHF_2TO61 = f56 +sincosf_RSHF = f57 +sincosf_2TOM61 = f58 +sincosf_NFLOAT = f59 +sincosf_W_2TO61_RSH = f60 + +fp_tmp = f61 + +///////////////////////////////////////////////////////////// + +sincosf_AD_1 = r33 +sincosf_AD_2 = r34 +sincosf_exp_limit = r35 +sincosf_r_signexp = r36 +sincosf_AD_beta_table = r37 +sincosf_r_sincos = r38 + +sincosf_r_exp = r39 +sincosf_r_17_ones = r40 + +sincosf_GR_sig_inv_pi_by_16 = r14 +sincosf_GR_rshf_2to61 = r15 +sincosf_GR_rshf = r16 +sincosf_GR_exp_2tom61 = r17 +sincosf_GR_n = r18 +sincosf_GR_m = r19 +sincosf_GR_32m = r19 +sincosf_GR_all_ones = r19 + +gr_tmp = r41 +GR_SAVE_PFS = r41 +GR_SAVE_B0 = r42 +GR_SAVE_GP = r43 + +RODATA +.align 16 + +// Pi/16 parts +LOCAL_OBJECT_START(double_sincosf_pi) + data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part + data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part +LOCAL_OBJECT_END(double_sincosf_pi) + +// Coefficients for polynomials +LOCAL_OBJECT_START(double_sincosf_pq_k4) + data8 0x3F810FABB668E9A2 // P2 + data8 0x3FA552E3D6DE75C9 // Q2 + data8 0xBFC555554447BC7F // P1 + data8 0xBFDFFFFFC447610A // Q1 +LOCAL_OBJECT_END(double_sincosf_pq_k4) + +// Sincos table (S[m], C[m]) +LOCAL_OBJECT_START(double_sin_cos_beta_k4) + data8 0x0000000000000000 // sin ( 0 Pi / 16 ) + data8 0x3FF0000000000000 // cos ( 0 Pi / 16 ) +// + data8 0x3FC8F8B83C69A60B // sin ( 1 Pi / 16 ) + data8 0x3FEF6297CFF75CB0 // cos ( 1 Pi / 16 ) +// + data8 0x3FD87DE2A6AEA963 // sin ( 2 Pi / 16 ) + data8 0x3FED906BCF328D46 // cos ( 2 Pi / 16 ) +// + data8 0x3FE1C73B39AE68C8 // sin ( 3 Pi / 16 ) + data8 0x3FEA9B66290EA1A3 // cos ( 3 Pi / 16 ) +// + data8 0x3FE6A09E667F3BCD // sin ( 4 Pi / 16 ) + data8 0x3FE6A09E667F3BCD // cos ( 4 Pi / 16 ) +// + data8 0x3FEA9B66290EA1A3 // sin ( 5 Pi / 16 ) + data8 0x3FE1C73B39AE68C8 // cos ( 5 Pi / 16 ) +// + data8 0x3FED906BCF328D46 // sin ( 6 Pi / 16 ) + data8 0x3FD87DE2A6AEA963 // cos ( 6 Pi / 16 ) +// + data8 0x3FEF6297CFF75CB0 // sin ( 7 Pi / 16 ) + data8 0x3FC8F8B83C69A60B // cos ( 7 Pi / 16 ) +// + data8 0x3FF0000000000000 // sin ( 8 Pi / 16 ) + data8 0x0000000000000000 // cos ( 8 Pi / 16 ) +// + data8 0x3FEF6297CFF75CB0 // sin ( 9 Pi / 16 ) + data8 0xBFC8F8B83C69A60B // cos ( 9 Pi / 16 ) +// + data8 0x3FED906BCF328D46 // sin ( 10 Pi / 16 ) + data8 0xBFD87DE2A6AEA963 // cos ( 10 Pi / 16 ) +// + data8 0x3FEA9B66290EA1A3 // sin ( 11 Pi / 16 ) + data8 0xBFE1C73B39AE68C8 // cos ( 11 Pi / 16 ) +// + data8 0x3FE6A09E667F3BCD // sin ( 12 Pi / 16 ) + data8 0xBFE6A09E667F3BCD // cos ( 12 Pi / 16 ) +// + data8 0x3FE1C73B39AE68C8 // sin ( 13 Pi / 16 ) + data8 0xBFEA9B66290EA1A3 // cos ( 13 Pi / 16 ) +// + data8 0x3FD87DE2A6AEA963 // sin ( 14 Pi / 16 ) + data8 0xBFED906BCF328D46 // cos ( 14 Pi / 16 ) +// + data8 0x3FC8F8B83C69A60B // sin ( 15 Pi / 16 ) + data8 0xBFEF6297CFF75CB0 // cos ( 15 Pi / 16 ) +// + data8 0x0000000000000000 // sin ( 16 Pi / 16 ) + data8 0xBFF0000000000000 // cos ( 16 Pi / 16 ) +// + data8 0xBFC8F8B83C69A60B // sin ( 17 Pi / 16 ) + data8 0xBFEF6297CFF75CB0 // cos ( 17 Pi / 16 ) +// + data8 0xBFD87DE2A6AEA963 // sin ( 18 Pi / 16 ) + data8 0xBFED906BCF328D46 // cos ( 18 Pi / 16 ) +// + data8 0xBFE1C73B39AE68C8 // sin ( 19 Pi / 16 ) + data8 0xBFEA9B66290EA1A3 // cos ( 19 Pi / 16 ) +// + data8 0xBFE6A09E667F3BCD // sin ( 20 Pi / 16 ) + data8 0xBFE6A09E667F3BCD // cos ( 20 Pi / 16 ) +// + data8 0xBFEA9B66290EA1A3 // sin ( 21 Pi / 16 ) + data8 0xBFE1C73B39AE68C8 // cos ( 21 Pi / 16 ) +// + data8 0xBFED906BCF328D46 // sin ( 22 Pi / 16 ) + data8 0xBFD87DE2A6AEA963 // cos ( 22 Pi / 16 ) +// + data8 0xBFEF6297CFF75CB0 // sin ( 23 Pi / 16 ) + data8 0xBFC8F8B83C69A60B // cos ( 23 Pi / 16 ) +// + data8 0xBFF0000000000000 // sin ( 24 Pi / 16 ) + data8 0x0000000000000000 // cos ( 24 Pi / 16 ) +// + data8 0xBFEF6297CFF75CB0 // sin ( 25 Pi / 16 ) + data8 0x3FC8F8B83C69A60B // cos ( 25 Pi / 16 ) +// + data8 0xBFED906BCF328D46 // sin ( 26 Pi / 16 ) + data8 0x3FD87DE2A6AEA963 // cos ( 26 Pi / 16 ) +// + data8 0xBFEA9B66290EA1A3 // sin ( 27 Pi / 16 ) + data8 0x3FE1C73B39AE68C8 // cos ( 27 Pi / 16 ) +// + data8 0xBFE6A09E667F3BCD // sin ( 28 Pi / 16 ) + data8 0x3FE6A09E667F3BCD // cos ( 28 Pi / 16 ) +// + data8 0xBFE1C73B39AE68C8 // sin ( 29 Pi / 16 ) + data8 0x3FEA9B66290EA1A3 // cos ( 29 Pi / 16 ) +// + data8 0xBFD87DE2A6AEA963 // sin ( 30 Pi / 16 ) + data8 0x3FED906BCF328D46 // cos ( 30 Pi / 16 ) +// + data8 0xBFC8F8B83C69A60B // sin ( 31 Pi / 16 ) + data8 0x3FEF6297CFF75CB0 // cos ( 31 Pi / 16 ) +// + data8 0x0000000000000000 // sin ( 32 Pi / 16 ) + data8 0x3FF0000000000000 // cos ( 32 Pi / 16 ) +LOCAL_OBJECT_END(double_sin_cos_beta_k4) + +.section .text + +//////////////////////////////////////////////////////// +// There are two entry points: sin and cos +// If from sin, p8 is true +// If from cos, p9 is true + +GLOBAL_IEEE754_ENTRY(sinf) + +{ .mlx + alloc r32 = ar.pfs,1,13,0,0 + movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi +} +{ .mlx + addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp + movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) +};; + +{ .mfi + ld8 sincosf_AD_1 = [sincosf_AD_1] + fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument + cmp.eq p8,p9 = r0, r0 // set p8 (clear p9) for sin +} +{ .mib + mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 + mov sincosf_r_sincos = 0x0 // 0 for sin + br.cond.sptk _SINCOSF_COMMON // go to common part +};; + +GLOBAL_IEEE754_END(sinf) + +GLOBAL_IEEE754_ENTRY(cosf) + +{ .mlx + alloc r32 = ar.pfs,1,13,0,0 + movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi +} +{ .mlx + addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp + movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) +};; + +{ .mfi + ld8 sincosf_AD_1 = [sincosf_AD_1] + fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument + cmp.eq p9,p8 = r0, r0 // set p9 (clear p8) for cos +} +{ .mib + mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 + mov sincosf_r_sincos = 0x8 // 8 for cos + nop.b 999 +};; + +//////////////////////////////////////////////////////// +// All entry points end up here. +// If from sin, sincosf_r_sincos is 0 and p8 is true +// If from cos, sincosf_r_sincos is 8 = 2^(k-1) and p9 is true +// We add sincosf_r_sincos to N + +///////////// Common sin and cos part ////////////////// +_SINCOSF_COMMON: + +// Form two constants we need +// 16/pi * 2^-2 * 2^63, scaled by 2^61 since we just loaded the significand +// 1.1000...000 * 2^(63+63-2) to right shift int(W) into the low significand +// fcmp used to set denormal, and invalid on snans +{ .mfi + setf.sig sincosf_SIG_INV_PI_BY_16_2TO61 = sincosf_GR_sig_inv_pi_by_16 + fclass.m p6,p0 = f8, 0xe7 // if x=0,inf,nan + mov sincosf_exp_limit = 0x10017 +} +{ .mlx + setf.d sincosf_RSHF_2TO61 = sincosf_GR_rshf_2to61 + movl sincosf_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 +};; // Right shift + +// Form another constant +// 2^-61 for scaling Nfloat +// 0x10017 is register_bias + 24. +// So if f8 >= 2^24, go to large argument routines +{ .mmi + getf.exp sincosf_r_signexp = f8 + setf.exp sincosf_2TOM61 = sincosf_GR_exp_2tom61 + addl gr_tmp = -1,r0 // For "inexect" constant create +};; + +// Load the two pieces of pi/16 +// Form another constant +// 1.1000...000 * 2^63, the right shift constant +{ .mmb + ldfe sincosf_Pi_by_16_1 = [sincosf_AD_1],16 + setf.d sincosf_RSHF = sincosf_GR_rshf +(p6) br.cond.spnt _SINCOSF_SPECIAL_ARGS +};; + +// Getting argument's exp for "large arguments" filtering +{ .mmi + ldfe sincosf_Pi_by_16_2 = [sincosf_AD_1],16 + setf.sig fp_tmp = gr_tmp // constant for inexact set + nop.i 999 +};; + +// Polynomial coefficients (Q2, Q1, P2, P1) loading +{ .mmi + ldfpd sincosf_P2,sincosf_Q2 = [sincosf_AD_1],16 + nop.m 999 + nop.i 999 +};; + +// Select exponent (17 lsb) +{ .mmi + ldfpd sincosf_P1,sincosf_Q1 = [sincosf_AD_1],16 + nop.m 999 + dep.z sincosf_r_exp = sincosf_r_signexp, 0, 17 +};; + +// p10 is true if we must call routines to handle larger arguments +// p10 is true if f8 exp is >= 0x10017 (2^24) +{ .mfb + cmp.ge p10,p0 = sincosf_r_exp,sincosf_exp_limit + nop.f 999 +(p10) br.cond.spnt _SINCOSF_LARGE_ARGS // Go to "large args" routine +};; + +// sincosf_W = x * sincosf_Inv_Pi_by_16 +// Multiply x by scaled 16/pi and add large const to shift integer part of W to +// rightmost bits of significand +{ .mfi + nop.m 999 + fma.s1 sincosf_W_2TO61_RSH = sincosf_NORM_f8, sincosf_SIG_INV_PI_BY_16_2TO61, sincosf_RSHF_2TO61 + nop.i 999 +};; + +// sincosf_NFLOAT = Round_Int_Nearest(sincosf_W) +// This is done by scaling back by 2^-61 and subtracting the shift constant +{ .mfi + nop.m 999 + fms.s1 sincosf_NFLOAT = sincosf_W_2TO61_RSH,sincosf_2TOM61,sincosf_RSHF + nop.i 999 +};; + +// get N = (int)sincosf_int_Nfloat +{ .mfi + getf.sig sincosf_GR_n = sincosf_W_2TO61_RSH // integer N value + nop.f 999 + nop.i 999 +};; + +// Add 2^(k-1) (which is in sincosf_r_sincos=8) to N +// sincosf_r = -sincosf_Nfloat * sincosf_Pi_by_16_1 + x +{ .mfi + add sincosf_GR_n = sincosf_GR_n, sincosf_r_sincos + fnma.s1 sincosf_r = sincosf_NFLOAT, sincosf_Pi_by_16_1, sincosf_NORM_f8 + nop.i 999 +};; + +// Get M (least k+1 bits of N) +{ .mmi + and sincosf_GR_m = 0x1f,sincosf_GR_n // Put mask 0x1F - + nop.m 999 // - select k+1 bits + nop.i 999 +};; + +// Add 16*M to address of sin_cos_beta table +{ .mfi + shladd sincosf_AD_2 = sincosf_GR_32m, 4, sincosf_AD_1 +(p8) fclass.m.unc p10,p0 = f8,0x0b // If sin denormal input - + nop.i 999 +};; + +// Load Sin and Cos table value using obtained index m (sincosf_AD_2) +{ .mfi + ldfd sincosf_Sm = [sincosf_AD_2],8 // Sin value S[m] +(p9) fclass.m.unc p11,p0 = f8,0x0b // If cos denormal input - + nop.i 999 // - set denormal +};; + +// sincosf_r = sincosf_r -sincosf_Nfloat * sincosf_Pi_by_16_2 +{ .mfi + ldfd sincosf_Cm = [sincosf_AD_2] // Cos table value C[m] + fnma.s1 sincosf_r_exact = sincosf_NFLOAT, sincosf_Pi_by_16_2, sincosf_r + nop.i 999 +} +// get rsq = r*r +{ .mfi + nop.m 999 + fma.s1 sincosf_rsq = sincosf_r, sincosf_r, f0 // r^2 = r*r + nop.i 999 +};; + +{ .mfi + nop.m 999 + fmpy.s0 fp_tmp = fp_tmp, fp_tmp // forces inexact flag + nop.i 999 +};; + +// Polynomials calculation +// Q = Q2*r^2 + Q1 +// P = P2*r^2 + P1 +{ .mfi + nop.m 999 + fma.s1 sincosf_Q = sincosf_rsq, sincosf_Q2, sincosf_Q1 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 sincosf_P = sincosf_rsq, sincosf_P2, sincosf_P1 + nop.i 999 +};; + +// get rcube and S[m]*r^2 +{ .mfi + nop.m 999 + fmpy.s1 sincosf_srsq = sincosf_Sm,sincosf_rsq // r^2*S[m] + nop.i 999 +} +{ .mfi + nop.m 999 + fmpy.s1 sincosf_rcub = sincosf_r_exact, sincosf_rsq + nop.i 999 +};; + +// Get final P and Q +// Q = Q*S[m]*r^2 + S[m] +// P = P*r^3 + r +{ .mfi + nop.m 999 + fma.s1 sincosf_Q = sincosf_srsq,sincosf_Q, sincosf_Sm + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 sincosf_P = sincosf_rcub,sincosf_P,sincosf_r_exact + nop.i 999 +};; + +// If sinf(denormal) - force underflow to be set +.pred.rel "mutex",p10,p11 +{ .mfi + nop.m 999 +(p10) fmpy.s.s0 fp_tmp = f8,f8 // forces underflow flag + nop.i 999 // for denormal sine args +} +// If cosf(denormal) - force denormal to be set +{ .mfi + nop.m 999 +(p11) fma.s.s0 fp_tmp = f8, f1, f8 // forces denormal flag + nop.i 999 // for denormal cosine args +};; + + +// Final calculation +// result = C[m]*P + Q +{ .mfb + nop.m 999 + fma.s.s0 f8 = sincosf_Cm, sincosf_P, sincosf_Q + br.ret.sptk b0 // Exit for common path +};; + +////////// x = 0/Inf/NaN path ////////////////// +_SINCOSF_SPECIAL_ARGS: +.pred.rel "mutex",p8,p9 +// sinf(+/-0) = +/-0 +// sinf(Inf) = NaN +// sinf(NaN) = NaN +{ .mfi + nop.m 999 +(p8) fma.s.s0 f8 = f8, f0, f0 // sinf(+/-0,NaN,Inf) + nop.i 999 +} +// cosf(+/-0) = 1.0 +// cosf(Inf) = NaN +// cosf(NaN) = NaN +{ .mfb + nop.m 999 +(p9) fma.s.s0 f8 = f8, f0, f1 // cosf(+/-0,NaN,Inf) + br.ret.sptk b0 // Exit for x = 0/Inf/NaN path +};; + +GLOBAL_IEEE754_END(cosf) + +//////////// x >= 2^24 - large arguments routine call //////////// +LOCAL_LIBM_ENTRY(__libm_callout_sincosf) +_SINCOSF_LARGE_ARGS: +.prologue +{ .mfi + mov sincosf_GR_all_ones = -1 // 0xffffffff + nop.f 999 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS = ar.pfs +} +;; + +{ .mfi + mov GR_SAVE_GP = gp + nop.f 999 +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0 = b0 +} +.body + +{ .mbb + setf.sig sincosf_save_tmp = sincosf_GR_all_ones // inexact set + nop.b 999 +(p8) br.call.sptk.many b0 = __libm_sin_large# // sinf(large_X) +};; + +{ .mbb + cmp.ne p9,p0 = sincosf_r_sincos, r0 // set p9 if cos + nop.b 999 +(p9) br.call.sptk.many b0 = __libm_cos_large# // cosf(large_X) +};; + +{ .mfi + mov gp = GR_SAVE_GP + fma.s.s0 f8 = f8, f1, f0 // Round result to single + mov b0 = GR_SAVE_B0 +} +{ .mfi // force inexact set + nop.m 999 + fmpy.s0 sincosf_save_tmp = sincosf_save_tmp, sincosf_save_tmp + nop.i 999 +};; + +{ .mib + nop.m 999 + mov ar.pfs = GR_SAVE_PFS + br.ret.sptk b0 // Exit for large arguments routine call +};; +LOCAL_LIBM_END(__libm_callout_sincosf) + +.type __libm_sin_large#, @function +.global __libm_sin_large# +.type __libm_cos_large#, @function +.global __libm_cos_large# -- cgit 1.4.1