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Diffstat (limited to 'sysdeps/ia64/fpu/s_cos.S')
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diff --git a/sysdeps/ia64/fpu/s_cos.S b/sysdeps/ia64/fpu/s_cos.S new file mode 100644 index 0000000..5f5cdc1 --- /dev/null +++ b/sysdeps/ia64/fpu/s_cos.S @@ -0,0 +1,767 @@ +.file "sincos.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 Work range is widened by reduction strengthen (3 parts of Pi/16) +// 02/10/03 Reordered header: .section, .global, .proc, .align +// 08/08/03 Improved performance +// 10/28/04 Saved sincos_r_sincos to avoid clobber by dynamic loader +// 03/31/05 Reformatted delimiters between data tables + +// API +//============================================================== +// double sin( double x); +// double cos( double 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)) - +// nfloat * LOWEST(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 and LOW parts are rounded to zero values, +// and LOWEST is rounded to nearest one. +// +// 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 + r^6 q3 + ... = Series for Cos +// Sin(r) = r + r^3 p1 + r^5 p2 + r^7 p3 + ... = 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^2p2 + r^4p3 + r^6p4 +// Q = q1 + r^2q2 + r^4q3 + r^6q4 +// +// rcub = r * rsq +// Sin(r) = r + rcub * P +// = r + r^3p1 + r^5p2 + r^7p3 + r^9p4 + ... = 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 + rcub * P +// +// Answer = S[m] Cos(r) + [Cm] P +// +// Cos(r) = 1 + rsq Q +// Cos(r) = 1 + r^2 Q +// Cos(r) = 1 + r^2 (q1 + r^2q2 + r^4q3 + r^6q4) +// Cos(r) = 1 + r^2q1 + r^4q2 + r^6q3 + r^8q4 + ... +// +// S[m] Cos(r) = S[m](1 + rsq Q) +// S[m] Cos(r) = S[m] + Sm 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 -> r26 +// r32 -> r35 + +// predicate registers used: +// p6 -> p11 + +// floating-point registers used +// f9 -> f15 +// f32 -> f61 + +// Assembly macros +//============================================================== +sincos_NORM_f8 = f9 +sincos_W = f10 +sincos_int_Nfloat = f11 +sincos_Nfloat = f12 + +sincos_r = f13 +sincos_rsq = f14 +sincos_rcub = f15 +sincos_save_tmp = f15 + +sincos_Inv_Pi_by_16 = f32 +sincos_Pi_by_16_1 = f33 +sincos_Pi_by_16_2 = f34 + +sincos_Inv_Pi_by_64 = f35 + +sincos_Pi_by_16_3 = f36 + +sincos_r_exact = f37 + +sincos_Sm = f38 +sincos_Cm = f39 + +sincos_P1 = f40 +sincos_Q1 = f41 +sincos_P2 = f42 +sincos_Q2 = f43 +sincos_P3 = f44 +sincos_Q3 = f45 +sincos_P4 = f46 +sincos_Q4 = f47 + +sincos_P_temp1 = f48 +sincos_P_temp2 = f49 + +sincos_Q_temp1 = f50 +sincos_Q_temp2 = f51 + +sincos_P = f52 +sincos_Q = f53 + +sincos_srsq = f54 + +sincos_SIG_INV_PI_BY_16_2TO61 = f55 +sincos_RSHF_2TO61 = f56 +sincos_RSHF = f57 +sincos_2TOM61 = f58 +sincos_NFLOAT = f59 +sincos_W_2TO61_RSH = f60 + +fp_tmp = f61 + +///////////////////////////////////////////////////////////// + +sincos_GR_sig_inv_pi_by_16 = r14 +sincos_GR_rshf_2to61 = r15 +sincos_GR_rshf = r16 +sincos_GR_exp_2tom61 = r17 +sincos_GR_n = r18 +sincos_GR_m = r19 +sincos_GR_32m = r19 +sincos_GR_all_ones = r19 +sincos_AD_1 = r20 +sincos_AD_2 = r21 +sincos_exp_limit = r22 +sincos_r_signexp = r23 +sincos_r_17_ones = r24 +sincos_r_sincos = r25 +sincos_r_exp = r26 + +GR_SAVE_PFS = r33 +GR_SAVE_B0 = r34 +GR_SAVE_GP = r35 +GR_SAVE_r_sincos = r36 + + +RODATA + +// Pi/16 parts +.align 16 +LOCAL_OBJECT_START(double_sincos_pi) + data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part + data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part + data8 0xA4093822299F31D0, 0x00003F7A // pi/16 3rd part +LOCAL_OBJECT_END(double_sincos_pi) + +// Coefficients for polynomials +LOCAL_OBJECT_START(double_sincos_pq_k4) + data8 0x3EC71C963717C63A // P4 + data8 0x3EF9FFBA8F191AE6 // Q4 + data8 0xBF2A01A00F4E11A8 // P3 + data8 0xBF56C16C05AC77BF // Q3 + data8 0x3F8111111110F167 // P2 + data8 0x3FA555555554DD45 // Q2 + data8 0xBFC5555555555555 // P1 + data8 0xBFDFFFFFFFFFFFFC // Q1 +LOCAL_OBJECT_END(double_sincos_pq_k4) + +// Sincos table (S[m], C[m]) +LOCAL_OBJECT_START(double_sin_cos_beta_k4) + +data8 0x0000000000000000 , 0x00000000 // sin( 0 pi/16) S0 +data8 0x8000000000000000 , 0x00003fff // cos( 0 pi/16) C0 +// +data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin( 1 pi/16) S1 +data8 0xfb14be7fbae58157 , 0x00003ffe // cos( 1 pi/16) C1 +// +data8 0xc3ef1535754b168e , 0x00003ffd // sin( 2 pi/16) S2 +data8 0xec835e79946a3146 , 0x00003ffe // cos( 2 pi/16) C2 +// +data8 0x8e39d9cd73464364 , 0x00003ffe // sin( 3 pi/16) S3 +data8 0xd4db3148750d181a , 0x00003ffe // cos( 3 pi/16) C3 +// +data8 0xb504f333f9de6484 , 0x00003ffe // sin( 4 pi/16) S4 +data8 0xb504f333f9de6484 , 0x00003ffe // cos( 4 pi/16) C4 +// +data8 0xd4db3148750d181a , 0x00003ffe // sin( 5 pi/16) C3 +data8 0x8e39d9cd73464364 , 0x00003ffe // cos( 5 pi/16) S3 +// +data8 0xec835e79946a3146 , 0x00003ffe // sin( 6 pi/16) C2 +data8 0xc3ef1535754b168e , 0x00003ffd // cos( 6 pi/16) S2 +// +data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 7 pi/16) C1 +data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos( 7 pi/16) S1 +// +data8 0x8000000000000000 , 0x00003fff // sin( 8 pi/16) C0 +data8 0x0000000000000000 , 0x00000000 // cos( 8 pi/16) S0 +// +data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 9 pi/16) C1 +data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos( 9 pi/16) -S1 +// +data8 0xec835e79946a3146 , 0x00003ffe // sin(10 pi/16) C2 +data8 0xc3ef1535754b168e , 0x0000bffd // cos(10 pi/16) -S2 +// +data8 0xd4db3148750d181a , 0x00003ffe // sin(11 pi/16) C3 +data8 0x8e39d9cd73464364 , 0x0000bffe // cos(11 pi/16) -S3 +// +data8 0xb504f333f9de6484 , 0x00003ffe // sin(12 pi/16) S4 +data8 0xb504f333f9de6484 , 0x0000bffe // cos(12 pi/16) -S4 +// +data8 0x8e39d9cd73464364 , 0x00003ffe // sin(13 pi/16) S3 +data8 0xd4db3148750d181a , 0x0000bffe // cos(13 pi/16) -C3 +// +data8 0xc3ef1535754b168e , 0x00003ffd // sin(14 pi/16) S2 +data8 0xec835e79946a3146 , 0x0000bffe // cos(14 pi/16) -C2 +// +data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin(15 pi/16) S1 +data8 0xfb14be7fbae58157 , 0x0000bffe // cos(15 pi/16) -C1 +// +data8 0x0000000000000000 , 0x00000000 // sin(16 pi/16) S0 +data8 0x8000000000000000 , 0x0000bfff // cos(16 pi/16) -C0 +// +data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(17 pi/16) -S1 +data8 0xfb14be7fbae58157 , 0x0000bffe // cos(17 pi/16) -C1 +// +data8 0xc3ef1535754b168e , 0x0000bffd // sin(18 pi/16) -S2 +data8 0xec835e79946a3146 , 0x0000bffe // cos(18 pi/16) -C2 +// +data8 0x8e39d9cd73464364 , 0x0000bffe // sin(19 pi/16) -S3 +data8 0xd4db3148750d181a , 0x0000bffe // cos(19 pi/16) -C3 +// +data8 0xb504f333f9de6484 , 0x0000bffe // sin(20 pi/16) -S4 +data8 0xb504f333f9de6484 , 0x0000bffe // cos(20 pi/16) -S4 +// +data8 0xd4db3148750d181a , 0x0000bffe // sin(21 pi/16) -C3 +data8 0x8e39d9cd73464364 , 0x0000bffe // cos(21 pi/16) -S3 +// +data8 0xec835e79946a3146 , 0x0000bffe // sin(22 pi/16) -C2 +data8 0xc3ef1535754b168e , 0x0000bffd // cos(22 pi/16) -S2 +// +data8 0xfb14be7fbae58157 , 0x0000bffe // sin(23 pi/16) -C1 +data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos(23 pi/16) -S1 +// +data8 0x8000000000000000 , 0x0000bfff // sin(24 pi/16) -C0 +data8 0x0000000000000000 , 0x00000000 // cos(24 pi/16) S0 +// +data8 0xfb14be7fbae58157 , 0x0000bffe // sin(25 pi/16) -C1 +data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos(25 pi/16) S1 +// +data8 0xec835e79946a3146 , 0x0000bffe // sin(26 pi/16) -C2 +data8 0xc3ef1535754b168e , 0x00003ffd // cos(26 pi/16) S2 +// +data8 0xd4db3148750d181a , 0x0000bffe // sin(27 pi/16) -C3 +data8 0x8e39d9cd73464364 , 0x00003ffe // cos(27 pi/16) S3 +// +data8 0xb504f333f9de6484 , 0x0000bffe // sin(28 pi/16) -S4 +data8 0xb504f333f9de6484 , 0x00003ffe // cos(28 pi/16) S4 +// +data8 0x8e39d9cd73464364 , 0x0000bffe // sin(29 pi/16) -S3 +data8 0xd4db3148750d181a , 0x00003ffe // cos(29 pi/16) C3 +// +data8 0xc3ef1535754b168e , 0x0000bffd // sin(30 pi/16) -S2 +data8 0xec835e79946a3146 , 0x00003ffe // cos(30 pi/16) C2 +// +data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(31 pi/16) -S1 +data8 0xfb14be7fbae58157 , 0x00003ffe // cos(31 pi/16) C1 +// +data8 0x0000000000000000 , 0x00000000 // sin(32 pi/16) S0 +data8 0x8000000000000000 , 0x00003fff // cos(32 pi/16) C0 +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(sin) + +{ .mlx + getf.exp sincos_r_signexp = f8 + movl sincos_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A // signd of 16/pi +} +{ .mlx + addl sincos_AD_1 = @ltoff(double_sincos_pi), gp + movl sincos_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) +} +;; + +{ .mfi + ld8 sincos_AD_1 = [sincos_AD_1] + fnorm.s0 sincos_NORM_f8 = f8 // Normalize argument + cmp.eq p8,p9 = r0, r0 // set p8 (clear p9) for sin +} +{ .mib + mov sincos_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 + mov sincos_r_sincos = 0x0 // sincos_r_sincos = 0 for sin + br.cond.sptk _SINCOS_COMMON // go to common part +} +;; + +GLOBAL_IEEE754_END(sin) + +GLOBAL_IEEE754_ENTRY(cos) + +{ .mlx + getf.exp sincos_r_signexp = f8 + movl sincos_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A // signd of 16/pi +} +{ .mlx + addl sincos_AD_1 = @ltoff(double_sincos_pi), gp + movl sincos_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) +} +;; + +{ .mfi + ld8 sincos_AD_1 = [sincos_AD_1] + fnorm.s1 sincos_NORM_f8 = f8 // Normalize argument + cmp.eq p9,p8 = r0, r0 // set p9 (clear p8) for cos +} +{ .mib + mov sincos_GR_exp_2tom61 = 0xffff-61 // exp of scale 2^-61 + mov sincos_r_sincos = 0x8 // sincos_r_sincos = 8 for cos + nop.b 999 +} +;; + +//////////////////////////////////////////////////////// +// All entry points end up here. +// If from sin, sincos_r_sincos is 0 and p8 is true +// If from cos, sincos_r_sincos is 8 = 2^(k-1) and p9 is true +// We add sincos_r_sincos to N + +///////////// Common sin and cos part ////////////////// +_SINCOS_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 +{ .mfi + setf.sig sincos_SIG_INV_PI_BY_16_2TO61 = sincos_GR_sig_inv_pi_by_16 + fclass.m p6,p0 = f8, 0xe7 // if x = 0,inf,nan + mov sincos_exp_limit = 0x1001a +} +{ .mlx + setf.d sincos_RSHF_2TO61 = sincos_GR_rshf_2to61 + movl sincos_GR_rshf = 0x43e8000000000000 // 1.1 2^63 +} // Right shift +;; + +// Form another constant +// 2^-61 for scaling Nfloat +// 0x1001a is register_bias + 27. +// So if f8 >= 2^27, go to large argument routines +{ .mfi + alloc r32 = ar.pfs, 1, 4, 0, 0 + fclass.m p11,p0 = f8, 0x0b // Test for x=unorm + mov sincos_GR_all_ones = -1 // For "inexect" constant create +} +{ .mib + setf.exp sincos_2TOM61 = sincos_GR_exp_2tom61 + nop.i 999 +(p6) br.cond.spnt _SINCOS_SPECIAL_ARGS +} +;; + +// Load the two pieces of pi/16 +// Form another constant +// 1.1000...000 * 2^63, the right shift constant +{ .mmb + ldfe sincos_Pi_by_16_1 = [sincos_AD_1],16 + setf.d sincos_RSHF = sincos_GR_rshf +(p11) br.cond.spnt _SINCOS_UNORM // Branch if x=unorm +} +;; + +_SINCOS_COMMON2: +// Return here if x=unorm +// Create constant used to set inexact +{ .mmi + ldfe sincos_Pi_by_16_2 = [sincos_AD_1],16 + setf.sig fp_tmp = sincos_GR_all_ones + nop.i 999 +};; + +// Select exponent (17 lsb) +{ .mfi + ldfe sincos_Pi_by_16_3 = [sincos_AD_1],16 + nop.f 999 + dep.z sincos_r_exp = sincos_r_signexp, 0, 17 +};; + +// Polynomial coefficients (Q4, P4, Q3, P3, Q2, Q1, P2, P1) loading +// p10 is true if we must call routines to handle larger arguments +// p10 is true if f8 exp is >= 0x1001a (2^27) +{ .mmb + ldfpd sincos_P4,sincos_Q4 = [sincos_AD_1],16 + cmp.ge p10,p0 = sincos_r_exp,sincos_exp_limit +(p10) br.cond.spnt _SINCOS_LARGE_ARGS // Go to "large args" routine +};; + +// sincos_W = x * sincos_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 + ldfpd sincos_P3,sincos_Q3 = [sincos_AD_1],16 + fma.s1 sincos_W_2TO61_RSH = sincos_NORM_f8,sincos_SIG_INV_PI_BY_16_2TO61,sincos_RSHF_2TO61 + nop.i 999 +};; + +// get N = (int)sincos_int_Nfloat +// sincos_NFLOAT = Round_Int_Nearest(sincos_W) +// This is done by scaling back by 2^-61 and subtracting the shift constant +{ .mmf + getf.sig sincos_GR_n = sincos_W_2TO61_RSH + ldfpd sincos_P2,sincos_Q2 = [sincos_AD_1],16 + fms.s1 sincos_NFLOAT = sincos_W_2TO61_RSH,sincos_2TOM61,sincos_RSHF +};; + +// sincos_r = -sincos_Nfloat * sincos_Pi_by_16_1 + x +{ .mfi + ldfpd sincos_P1,sincos_Q1 = [sincos_AD_1],16 + fnma.s1 sincos_r = sincos_NFLOAT, sincos_Pi_by_16_1, sincos_NORM_f8 + nop.i 999 +};; + +// Add 2^(k-1) (which is in sincos_r_sincos) to N +{ .mmi + add sincos_GR_n = sincos_GR_n, sincos_r_sincos +;; +// Get M (least k+1 bits of N) + and sincos_GR_m = 0x1f,sincos_GR_n + nop.i 999 +};; + +// sincos_r = sincos_r -sincos_Nfloat * sincos_Pi_by_16_2 +{ .mfi + nop.m 999 + fnma.s1 sincos_r = sincos_NFLOAT, sincos_Pi_by_16_2, sincos_r + shl sincos_GR_32m = sincos_GR_m,5 +};; + +// Add 32*M to address of sin_cos_beta table +// For sin denorm. - set uflow +{ .mfi + add sincos_AD_2 = sincos_GR_32m, sincos_AD_1 +(p8) fclass.m.unc p10,p0 = f8,0x0b + nop.i 999 +};; + +// Load Sin and Cos table value using obtained index m (sincosf_AD_2) +{ .mfi + ldfe sincos_Sm = [sincos_AD_2],16 + nop.f 999 + nop.i 999 +};; + +// get rsq = r*r +{ .mfi + ldfe sincos_Cm = [sincos_AD_2] + fma.s1 sincos_rsq = sincos_r, sincos_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 +};; + +// sincos_r_exact = sincos_r -sincos_Nfloat * sincos_Pi_by_16_3 +{ .mfi + nop.m 999 + fnma.s1 sincos_r_exact = sincos_NFLOAT, sincos_Pi_by_16_3, sincos_r + nop.i 999 +};; + +// Polynomials calculation +// P_1 = P4*r^2 + P3 +// Q_2 = Q4*r^2 + Q3 +{ .mfi + nop.m 999 + fma.s1 sincos_P_temp1 = sincos_rsq, sincos_P4, sincos_P3 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 sincos_Q_temp1 = sincos_rsq, sincos_Q4, sincos_Q3 + nop.i 999 +};; + +// get rcube = r^3 and S[m]*r^2 +{ .mfi + nop.m 999 + fmpy.s1 sincos_srsq = sincos_Sm,sincos_rsq + nop.i 999 +} +{ .mfi + nop.m 999 + fmpy.s1 sincos_rcub = sincos_r_exact, sincos_rsq + nop.i 999 +};; + +// Polynomials calculation +// Q_2 = Q_1*r^2 + Q2 +// P_1 = P_1*r^2 + P2 +{ .mfi + nop.m 999 + fma.s1 sincos_Q_temp2 = sincos_rsq, sincos_Q_temp1, sincos_Q2 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 sincos_P_temp2 = sincos_rsq, sincos_P_temp1, sincos_P2 + nop.i 999 +};; + +// Polynomials calculation +// Q = Q_2*r^2 + Q1 +// P = P_2*r^2 + P1 +{ .mfi + nop.m 999 + fma.s1 sincos_Q = sincos_rsq, sincos_Q_temp2, sincos_Q1 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 sincos_P = sincos_rsq, sincos_P_temp2, sincos_P1 + 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 sincos_Q = sincos_srsq,sincos_Q, sincos_Sm + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 sincos_P = sincos_rcub,sincos_P, sincos_r_exact + nop.i 999 +};; + +// If sin(denormal), force underflow to be set +{ .mfi + nop.m 999 +(p10) fmpy.d.s0 fp_tmp = sincos_NORM_f8,sincos_NORM_f8 + nop.i 999 +};; + +// Final calculation +// result = C[m]*P + Q +{ .mfb + nop.m 999 + fma.d.s0 f8 = sincos_Cm, sincos_P, sincos_Q + br.ret.sptk b0 // Exit for common path +};; + +////////// x = 0/Inf/NaN path ////////////////// +_SINCOS_SPECIAL_ARGS: +.pred.rel "mutex",p8,p9 +// sin(+/-0) = +/-0 +// sin(Inf) = NaN +// sin(NaN) = NaN +{ .mfi + nop.m 999 +(p8) fma.d.s0 f8 = f8, f0, f0 // sin(+/-0,NaN,Inf) + nop.i 999 +} +// cos(+/-0) = 1.0 +// cos(Inf) = NaN +// cos(NaN) = NaN +{ .mfb + nop.m 999 +(p9) fma.d.s0 f8 = f8, f0, f1 // cos(+/-0,NaN,Inf) + br.ret.sptk b0 // Exit for x = 0/Inf/NaN path +};; + +_SINCOS_UNORM: +// Here if x=unorm +{ .mfb + getf.exp sincos_r_signexp = sincos_NORM_f8 // Get signexp of x + fcmp.eq.s0 p11,p0 = f8, f0 // Dummy op to set denorm flag + br.cond.sptk _SINCOS_COMMON2 // Return to main path +};; + +GLOBAL_IEEE754_END(cos) + +//////////// x >= 2^27 - large arguments routine call //////////// +LOCAL_LIBM_ENTRY(__libm_callout_sincos) +_SINCOS_LARGE_ARGS: +.prologue +{ .mfi + mov GR_SAVE_r_sincos = sincos_r_sincos // Save sin or cos + 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 sincos_save_tmp = sincos_GR_all_ones// inexact set + nop.b 999 +(p8) br.call.sptk.many b0 = __libm_sin_large# // sin(large_X) + +};; + +{ .mbb + cmp.ne p9,p0 = GR_SAVE_r_sincos, r0 // set p9 if cos + nop.b 999 +(p9) br.call.sptk.many b0 = __libm_cos_large# // cos(large_X) +};; + +{ .mfi + mov gp = GR_SAVE_GP + fma.d.s0 f8 = f8, f1, f0 // Round result to double + mov b0 = GR_SAVE_B0 +} +// Force inexact set +{ .mfi + nop.m 999 + fmpy.s0 sincos_save_tmp = sincos_save_tmp, sincos_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_sincos) + +.type __libm_sin_large#,@function +.global __libm_sin_large# +.type __libm_cos_large#,@function +.global __libm_cos_large# |