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Diffstat (limited to 'sysdeps/ia64/fpu/s_cos.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_cos.S | 768 |
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diff --git a/sysdeps/ia64/fpu/s_cos.S b/sysdeps/ia64/fpu/s_cos.S deleted file mode 100644 index fc121fce19..0000000000 --- a/sysdeps/ia64/fpu/s_cos.S +++ /dev/null @@ -1,768 +0,0 @@ -.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# - |