code bài tính Sin(x). Giúp mình

[cake1990]

Tính giá trị Sin(x) với x nhập từ bàn phím
Sin(x) =x -3x/3!+ 5x/5!-7x/7!+...+ (-1)nx2n + 1/(2n+1)! với x tính theo radian

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[minhthu1987]

Tính giá trị Sin(x) với x nhập từ bàn phím
Sin(x) =x -3x/3!+ 5x/5!-7x/7!+...+ (-1)nx2n + 1/(2n+1)! với x tính theo radian

Peter thấy công thức này của cậu sai đó! Cậu hãy tham khảo các bài viết liên quan vấn đề này tại:

1. http://forums.congdongcviet.com/showthread.php?t=25498

2. http://forums.congdongcviet.com/showthread.php?t=35154

3. http://forums.congdongcviet.com/showthread.php?t=12164

4. Và một số kết quả khác: http://www.google.com.vn/#hl=vi&q=+s...6703146cb5c95f.

Chúc thành công!

[khamnamkhoa]

Mình thấy không bài nào trong số những bài của bạn Peter đưa ra là chính xác nên mình xin góp ý ở đây. Xin lưu ý là mặc dù thoạt nhìn thì bài toán rất dễ nhưng mình biết là rất ít người có thể xác định hoàn toàn bản chất của vấn đề của điều này

Thuật toán rất đơn giản:

Nếu số đưa vào là [IMG]http:/jet.oops.jp/cgi/mimetex.cgi?\pm\infty[/IMG], kết quả trả ra sẽ là [IMG]http:/jet.oops.jp/cgi/mimetex.cgi?NaN[/IMG]
40px
Nếu số đưa vào là [IMG]http:/jet.oops.jp/cgi/mimetex.cgi?NaN[/IMG], kết quả trả ra cũng sẽ là [IMG]http:/jet.oops.jp/cgi/mimetex.cgi?NaN[/IMG]

Nếu số đưa vào thuộc dạng không chuẩn (denormalize), kết quả trả về là giá trị của khai triển Maclaurin cho 3 số hạng đầu tiên.

Nếu không thuộc các trường hợp trên (dạng chuẩn: normalize) thì chúng ta mới có thể áp dụng công thức Maclaurin chính tắc với sai số epsilon như các bài ở trên.

Thuật toán trên được lấy từ Math Package của hãng Intel nên các bạn có thể an tâm về độ chính xác. Thuật toán cụ thể bạn có thể đọc ở đây (thật ra họ không hoàn toàn dùng khai triển Maclaurin mà còn dùng thêm cả thuật toán CORDIC để tăng tốc độ hội tụ)

.file "libm_sincos.s"  // Copyright (c) 2002 - 2005, Intel Corporation// All rights reserved.//// Contributed 2002 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/produc...ibrariesum.htm.//// History//==============================================================// 02/01/02 Initial version// 02/18/02 Large arguments processing routine is excluded.//          External interface entry points are added// 03/13/02 Corrected restore of predicate registers// 03/19/02 Added stack unwind around call to __libm_cis_large// 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// 02/11/04 cis is moved to the separate file.// 03/31/05 Reformatted delimiters between data tables//// API//==============================================================// 1) void sincos(double, double*s, double*c)// 2) __libm_sincos - internal LIBM function, that accepts//    argument in f8 and returns cosine through f8, sine through f9//// 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) + C[m] 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] + 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 -> r39 // predicate registers used:// p6 -> p14//// floating-point registers used// f9 -> f15// f32 -> f67 // Assembly macros//============================================================== cis_Arg                     = f8 cis_Sin_res                 = f9cis_Cos_res                 = f8 cis_NORM_f8                 = f10cis_W                       = f11cis_int_Nfloat              = f12cis_Nfloat                  = f13 cis_r                       = f14cis_rsq                     = f15cis_rcub                    = f32 cis_Inv_Pi_by_16            = f33cis_Pi_by_16_hi             = f34cis_Pi_by_16_lo             = f35 cis_Inv_Pi_by_64            = f36cis_Pi_by_16_lowest         = f37cis_r_exact                 = f38  cis_P1                      = f39cis_Q1                      = f40cis_P2                      = f41cis_Q2                      = f42cis_P3                      = f43cis_Q3                      = f44cis_P4                      = f45cis_Q4                      = f46 cis_P_temp1                 = f47cis_P_temp2                 = f48 cis_Q_temp1                 = f49cis_Q_temp2                 = f50 cis_P                       = f51 cis_SIG_INV_PI_BY_16_2TO61  = f52cis_RSHF_2TO61              = f53cis_RSHF                    = f54cis_2TOM61                  = f55cis_NFLOAT                  = f56cis_W_2TO61_RSH             = f57 cis_tmp                     = f58 cis_Sm_sin                  = f59cis_Cm_sin                  = f60 cis_Sm_cos                  = f61cis_Cm_cos                  = f62 cis_srsq_sin                = f63cis_srsq_cos                = f64 cis_Q_sin                   = f65cis_Q_cos                   = f66cis_Q                       = f67 ///////////////////////////////////////////////////////////// cis_pResSin                 = r33cis_pResCos                 = r34 cis_GR_sig_inv_pi_by_16     = r14cis_GR_rshf_2to61           = r15cis_GR_rshf                 = r16cis_GR_exp_2tom61           = r17cis_GR_n                    = r18cis_GR_n_sin                = r19cis_exp_limit               = r20cis_r_signexp               = r21cis_AD_1                    = r22cis_r_sincos                = r23cis_r_exp                   = r24cis_r_17_ones               = r25cis_GR_m_sin                = r26cis_GR_32m_sin              = r26cis_GR_n_cos                = r27cis_GR_m_cos                = r28cis_GR_32m_cos              = r28cis_AD_2_sin                = r29cis_AD_2_cos                = r30cis_gr_tmp                  = r31 GR_SAVE_B0                  = r35GR_SAVE_GP                  = r36rB0_SAVED                   = r37GR_SAVE_PFS                 = r38GR_SAVE_PR                  = r39 RODATA .align 16// Pi/16 partsLOCAL_OBJECT_START(double_cis_pi)   data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part   data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part   data8 0xA4093822299F31D0, 0x00003F7A // pi/16 3rd partLOCAL_OBJECT_END(double_cis_pi) // Coefficients for polynomialsLOCAL_OBJECT_START(double_cis_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 // Q1LOCAL_OBJECT_END(double_cis_pq_k4) // Sincos table (S[m], C[m])LOCAL_OBJECT_START(double_sin_cos_beta_k4)data8 0x0000000000000000 , 0x00000000 // sin( 0 pi/16)  S0data8 0x8000000000000000 , 0x00003fff // cos( 0 pi/16)  C0//data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin( 1 pi/16)  S1data8 0xfb14be7fbae58157 , 0x00003ffe // cos( 1 pi/16)  C1//data8 0xc3ef1535754b168e , 0x00003ffd // sin( 2 pi/16)  S2data8 0xec835e79946a3146 , 0x00003ffe // cos( 2 pi/16)  C2//data8 0x8e39d9cd73464364 , 0x00003ffe // sin( 3 pi/16)  S3data8 0xd4db3148750d181a , 0x00003ffe // cos( 3 pi/16)  C3//data8 0xb504f333f9de6484 , 0x00003ffe // sin( 4 pi/16)  S4data8 0xb504f333f9de6484 , 0x00003ffe // cos( 4 pi/16)  C4//data8 0xd4db3148750d181a , 0x00003ffe // sin( 5 pi/16)  C3data8 0x8e39d9cd73464364 , 0x00003ffe // cos( 5 pi/16)  S3//data8 0xec835e79946a3146 , 0x00003ffe // sin( 6 pi/16)  C2data8 0xc3ef1535754b168e , 0x00003ffd // cos( 6 pi/16)  S2//data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 7 pi/16)  C1data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos( 7 pi/16)  S1//data8 0x8000000000000000 , 0x00003fff // sin( 8 pi/16)  C0data8 0x0000000000000000 , 0x00000000 // cos( 8 pi/16)  S0//data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 9 pi/16)  C1data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos( 9 pi/16)  -S1//data8 0xec835e79946a3146 , 0x00003ffe // sin(10 pi/16)  C2data8 0xc3ef1535754b168e , 0x0000bffd // cos(10 pi/16)  -S2//data8 0xd4db3148750d181a , 0x00003ffe // sin(11 pi/16)  C3data8 0x8e39d9cd73464364 , 0x0000bffe // cos(11 pi/16)  -S3//data8 0xb504f333f9de6484 , 0x00003ffe // sin(12 pi/16)  S4data8 0xb504f333f9de6484 , 0x0000bffe // cos(12 pi/16)  -S4//data8 0x8e39d9cd73464364 , 0x00003ffe // sin(13 pi/16) S3data8 0xd4db3148750d181a , 0x0000bffe // cos(13 pi/16) -C3//data8 0xc3ef1535754b168e , 0x00003ffd // sin(14 pi/16) S2data8 0xec835e79946a3146 , 0x0000bffe // cos(14 pi/16) -C2//data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin(15 pi/16) S1data8 0xfb14be7fbae58157 , 0x0000bffe // cos(15 pi/16) -C1//data8 0x0000000000000000 , 0x00000000 // sin(16 pi/16) S0data8 0x8000000000000000 , 0x0000bfff // cos(16 pi/16) -C0//data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(17 pi/16) -S1data8 0xfb14be7fbae58157 , 0x0000bffe // cos(17 pi/16) -C1//data8 0xc3ef1535754b168e , 0x0000bffd // sin(18 pi/16) -S2data8 0xec835e79946a3146 , 0x0000bffe // cos(18 pi/16) -C2//data8 0x8e39d9cd73464364 , 0x0000bffe // sin(19 pi/16) -S3data8 0xd4db3148750d181a , 0x0000bffe // cos(19 pi/16) -C3//data8 0xb504f333f9de6484 , 0x0000bffe // sin(20 pi/16) -S4data8 0xb504f333f9de6484 , 0x0000bffe // cos(20 pi/16) -S4//data8 0xd4db3148750d181a , 0x0000bffe // sin(21 pi/16) -C3data8 0x8e39d9cd73464364 , 0x0000bffe // cos(21 pi/16) -S3//data8 0xec835e79946a3146 , 0x0000bffe // sin(22 pi/16) -C2data8 0xc3ef1535754b168e , 0x0000bffd // cos(22 pi/16) -S2//data8 0xfb14be7fbae58157 , 0x0000bffe // sin(23 pi/16) -C1data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos(23 pi/16) -S1//data8 0x8000000000000000 , 0x0000bfff // sin(24 pi/16) -C0data8 0x0000000000000000 , 0x00000000 // cos(24 pi/16) S0//data8 0xfb14be7fbae58157 , 0x0000bffe // sin(25 pi/16) -C1data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos(25 pi/16) S1//data8 0xec835e79946a3146 , 0x0000bffe // sin(26 pi/16) -C2data8 0xc3ef1535754b168e , 0x00003ffd // cos(26 pi/16) S2//data8 0xd4db3148750d181a , 0x0000bffe // sin(27 pi/16) -C3data8 0x8e39d9cd73464364 , 0x00003ffe // cos(27 pi/16) S3//data8 0xb504f333f9de6484 , 0x0000bffe // sin(28 pi/16) -S4data8 0xb504f333f9de6484 , 0x00003ffe // cos(28 pi/16) S4//data8 0x8e39d9cd73464364 , 0x0000bffe // sin(29 pi/16) -S3data8 0xd4db3148750d181a , 0x00003ffe // cos(29 pi/16) C3//data8 0xc3ef1535754b168e , 0x0000bffd // sin(30 pi/16) -S2data8 0xec835e79946a3146 , 0x00003ffe // cos(30 pi/16) C2//data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(31 pi/16) -S1data8 0xfb14be7fbae58157 , 0x00003ffe // cos(31 pi/16) C1//data8 0x0000000000000000 , 0x00000000 // sin(32 pi/16) S0data8 0x8000000000000000 , 0x00003fff // cos(32 pi/16) C0LOCAL_OBJECT_END(double_sin_cos_beta_k4) .section .text GLOBAL_IEEE754_ENTRY(sincos)// cis_GR_sig_inv_pi_by_16 = significand of 16/pi{ .mlx      getf.exp      cis_r_signexp       = cis_Arg      movl          cis_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A }// cis_GR_rshf_2to61 = 1.1000 2^(63+63-2){ .mlx      addl          cis_AD_1                = @ltoff(double_cis_pi), gp      movl          cis_GR_rshf_2to61       = 0x47b8000000000000};; { .mfi      ld8           cis_AD_1            = [cis_AD_1]      fnorm.s1      cis_NORM_f8         = cis_Arg      cmp.eq        p13, p14            = r0, r0 // p13 set for sincos}// cis_GR_exp_2tom61 = exponent of scaling factor 2^-61{ .mib      mov           cis_GR_exp_2tom61   = 0xffff-61      nop.i         0      br.cond.sptk  _CIS_COMMON};;GLOBAL_IEEE754_END(sincos) GLOBAL_LIBM_ENTRY(__libm_sincos)// cis_GR_sig_inv_pi_by_16 = significand of 16/pi{ .mlx      getf.exp      cis_r_signexp       = cis_Arg      movl          cis_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A}// cis_GR_rshf_2to61 = 1.1000 2^(63+63-2){ .mlx      addl          cis_AD_1            = @ltoff(double_cis_pi), gp      movl          cis_GR_rshf_2to61   = 0x47b8000000000000};; // p14 set for __libm_sincos and cis{ .mfi      ld8           cis_AD_1            = [cis_AD_1]      fnorm.s1      cis_NORM_f8         = cis_Arg      cmp.eq        p14, p13            = r0, r0}// cis_GR_exp_2tom61 = exponent of scaling factor 2^-61{ .mib      mov           cis_GR_exp_2tom61   = 0xffff-61      nop.i         0      nop.b         0};; _CIS_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      cis_SIG_INV_PI_BY_16_2TO61 = cis_GR_sig_inv_pi_by_16      fclass.m      p6,p0                      = cis_Arg, 0xe7 // if x=0,inf,nan      addl          cis_gr_tmp                 = -1, r0}// 1.1000 2^63 for right shift{ .mlx      setf.d        cis_RSHF_2TO61             = cis_GR_rshf_2to61      movl          cis_GR_rshf                = 0x43e8000000000000};; //  Form another constant//  2^-61 for scaling Nfloat//  0x1001a is register_bias + 27.//  So if f8 >= 2^27, go to large arguments routine{ .mfi      alloc         GR_SAVE_PFS         = ar.pfs, 3, 5, 0, 0      fclass.m      p11,p0              = cis_Arg, 0x0b // Test for x=unorm      mov           cis_exp_limit       = 0x1001a}{ .mib      setf.exp      cis_2TOM61          = cis_GR_exp_2tom61      nop.i         0(p6)  br.cond.spnt  _CIS_SPECIAL_ARGS};; //  Load the two pieces of pi/16//  Form another constant//  1.1000...000 * 2^63, the right shift constant{ .mmb      ldfe          cis_Pi_by_16_hi     = [cis_AD_1],16      setf.d        cis_RSHF            = cis_GR_rshf(p11) br.cond.spnt  _CIS_UNORM          // Branch if x=unorm};; _CIS_COMMON2:// Return here if x=unorm// Create constant inexact set{ .mmi      ldfe          cis_Pi_by_16_lo     = [cis_AD_1],16      setf.sig      cis_tmp             = cis_gr_tmp      nop.i         0};; // Select exponent (17 lsb){ .mfi      ldfe          cis_Pi_by_16_lowest = [cis_AD_1],16      nop.f         0      dep.z         cis_r_exp           = cis_r_signexp, 0, 17};; // Start loading P, Q coefficients// p10 is true if we must call routines to handle larger arguments// p10 is true if f8 exp is > 0x1001a{ .mmb      ldfpd         cis_P4,cis_Q4       = [cis_AD_1],16      cmp.ge        p10, p0             = cis_r_exp, cis_exp_limit(p10) br.cond.spnt  _CIS_LARGE_ARGS // go to |x| >= 2^27 path};; // cis_W = x * cis_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         cis_P3,cis_Q3       = [cis_AD_1],16      fma.s1 cis_W_2TO61_RSH = cis_NORM_f8,cis_SIG_INV_PI_BY_16_2TO61,cis_RSHF_2TO61      nop.i  0};; // get N = (int)cis_int_Nfloat// cis_NFLOAT = Round_Int_Nearest(cis_W){ .mmf      getf.sig      cis_GR_n            = cis_W_2TO61_RSH      ldfpd  cis_P2,cis_Q2   = [cis_AD_1],16      fms.s1        cis_NFLOAT          = cis_W_2TO61_RSH,cis_2TOM61,cis_RSHF};; // cis_r = -cis_Nfloat * cis_Pi_by_16_hi + x{ .mfi      ldfpd         cis_P1,cis_Q1       = [cis_AD_1], 16      fnma.s1       cis_r               = cis_NFLOAT,cis_Pi_by_16_hi,cis_NORM_f8      nop.i         0};; // Add 2^(k-1) (which is in cis_r_sincos) to N{ .mmi      add           cis_GR_n_cos        = 0x8, cis_GR_n;;//Get M (least k+1 bits of N)      and           cis_GR_m_sin        = 0x1f,cis_GR_n      and           cis_GR_m_cos        = 0x1f,cis_GR_n_cos};; { .mmi      nop.m         0      nop.m         0      shl           cis_GR_32m_sin      = cis_GR_m_sin,5};; // Add 32*M to address of sin_cos_beta table// cis_r =  cis_r -cis_Nfloat * cis_Pi_by_16_lo{ .mfi      add           cis_AD_2_sin        = cis_GR_32m_sin, cis_AD_1      fnma.s1       cis_r               = cis_NFLOAT, cis_Pi_by_16_lo,  cis_r      shl           cis_GR_32m_cos      = cis_GR_m_cos,5};; // Add 32*M to address of sin_cos_beta table{ .mmf      ldfe          cis_Sm_sin          = [cis_AD_2_sin],16      add           cis_AD_2_cos        = cis_GR_32m_cos, cis_AD_1      fclass.m.unc  p10,p0              = cis_Arg,0x0b  // den. input - uflow};; { .mfi      ldfe          cis_Sm_cos          = [cis_AD_2_cos], 16      nop.i         0};; { .mfi      ldfe          cis_Cm_sin          = [cis_AD_2_sin]      fma.s1        cis_rsq             = cis_r, cis_r,   f0  // get r^2      nop.i         0}// fmpy forces inexact flag{ .mfi      nop.m         0      fmpy.s0       cis_tmp             = cis_tmp,cis_tmp      nop.i         0};; { .mfi      nop.m         0      fnma.s1       cis_r_exact         = cis_NFLOAT, cis_Pi_by_16_lowest, cis_r      nop.i         0};; { .mfi      ldfe          cis_Cm_cos          = [cis_AD_2_cos]      fma.s1        cis_P_temp1         = cis_rsq, cis_P4, cis_P3      nop.i         0} { .mfi      nop.m         0      fma.s1        cis_Q_temp1         = cis_rsq, cis_Q4, cis_Q3      nop.i         0};; { .mfi      nop.m         0      fmpy.s1       cis_srsq_sin        = cis_Sm_sin, cis_rsq      nop.i         0}{ .mfi      nop.m         0      fmpy.s1       cis_srsq_cos        = cis_Sm_cos,cis_rsq      nop.i         0};; { .mfi      nop.m         0      fma.s1        cis_Q_temp2         = cis_rsq, cis_Q_temp1, cis_Q2      nop.i         0}{ .mfi      nop.m         0      fma.s1        cis_P_temp2         = cis_rsq, cis_P_temp1, cis_P2      nop.i         0};; { .mfi      nop.m         0      fmpy.s1       cis_rcub            = cis_r_exact, cis_rsq // get r^3      nop.i         0};; { .mfi      nop.m         0      fma.s1        cis_Q               = cis_rsq, cis_Q_temp2, cis_Q1      nop.i         0}{ .mfi      nop.m         0      fma.s1        cis_P               = cis_rsq, cis_P_temp2, cis_P1      nop.i         0};; { .mfi      nop.m         0      fma.s1        cis_Q_sin           = cis_srsq_sin,cis_Q, cis_Sm_sin      nop.i         0}{ .mfi      nop.m         0      fma.s1        cis_Q_cos           = cis_srsq_cos,cis_Q, cis_Sm_cos      nop.i         0};; { .mfi      nop.m         0      fma.s1        cis_P               = cis_rcub,cis_P, cis_r_exact // final P      nop.i         0};; // If den. arg, force underflow to be set{ .mfi      nop.m         0(p10) fmpy.d.s0     cis_tmp             = cis_Arg,cis_Arg      nop.i         0};; { .mfi      nop.m         0      fma.d.s0      cis_Sin_res         = cis_Cm_sin,cis_P,cis_Q_sin//Final sin      nop.i         0}{ .mfb      nop.m         0      fma.d.s0      cis_Cos_res         = cis_Cm_cos,cis_P,cis_Q_cos//Final cos(p14) br.ret.sptk   b0  // common exit for __libm_sincos and cis main path};; { .mmb      stfd          [cis_pResSin]       = cis_Sin_res      stfd          [cis_pResCos]       = cis_Cos_res      br.ret.sptk   b0 // common exit for sincos main path};; _CIS_SPECIAL_ARGS:// sin(+/-0) = +/-0// sin(Inf)  = NaN// sin(NaN)  = NaN{ .mfi      nop.m         999      fma.d.s0      cis_Sin_res          = cis_Arg, f0, f0 // sinf(+/-0,NaN,Inf)      nop.i         999};;// cos(+/-0) = 1.0// cos(Inf)  = NaN// cos(NaN)  = NaN{ .mfb      nop.m         999      fma.d.s0      cis_Cos_res          = cis_Arg, f0, f1 // cosf(+/-0,NaN,Inf)(p14) br.ret.sptk   b0 //spec exit for __libm_sincos and cis main path};; { .mmb      stfd          [cis_pResSin]       = cis_Sin_res      stfd          [cis_pResCos]       = cis_Cos_res      br.ret.sptk   b0 // common exit for sincos main path};; _CIS_UNORM:// Here if x=unorm{ .mfb      getf.exp      cis_r_signexp       = cis_NORM_f8 // Get signexp of x      fcmp.eq.s0    p11,p0              = cis_Arg, f0 // Dummy op to set denorm      br.cond.sptk  _CIS_COMMON2        // Return to main path};; GLOBAL_LIBM_END(__libm_sincos) ////  |x| > 2^27 path  ///////.proc _CIS_LARGE_ARGS_CIS_LARGE_ARGS:.prologue{ .mfi      nop.m         0      nop.f         0.save ar.pfs, GR_SAVE_PFS      mov           GR_SAVE_PFS         = ar.pfs};; { .mfi      mov           GR_SAVE_GP          = gp      nop.f         0.save b0, GR_SAVE_B0      mov           GR_SAVE_B0          = b0};; .body// Call of huge arguments sincos{ .mib      nop.m         0      mov           GR_SAVE_PR          = pr      br.call.sptk  b0                  = __libm_sincos_large};; { .mfi      mov           gp                  = GR_SAVE_GP      nop.f         0      mov           pr                  = GR_SAVE_PR, 0x1fffe};; { .mfi      nop.m         0      nop.f         0      mov           b0                  = GR_SAVE_B0};; { .mfi      nop.m         0      fma.d.s0      cis_Cos_res         = cis_Cos_res, f1, f0      mov           ar.pfs              = GR_SAVE_PFS}{ .mfb      nop.m         0      fma.d.s0      cis_Sin_res         = cis_Sin_res, f1, f0(p14) br.ret.sptk   b0  // exit for |x| > 2^27 path (__libm_sincos and cis)};; { .mmb      stfd          [cis_pResSin]       = cis_Sin_res      stfd          [cis_pResCos]       = cis_Cos_res      br.ret.sptk   b0 // exit for sincos |x| > 2^27 path};;.endp _CIS_LARGE_ARGS .type __libm_sincos_large#,@function.global __libm_sincos_large#