.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/products/opensource/libraries/num.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 = f9 cis_Cos_res = f8 cis_NORM_f8 = f10 cis_W = f11 cis_int_Nfloat = f12 cis_Nfloat = f13 cis_r = f14 cis_rsq = f15 cis_rcub = f32 cis_Inv_Pi_by_16 = f33 cis_Pi_by_16_hi = f34 cis_Pi_by_16_lo = f35 cis_Inv_Pi_by_64 = f36 cis_Pi_by_16_lowest = f37 cis_r_exact = f38 cis_P1 = f39 cis_Q1 = f40 cis_P2 = f41 cis_Q2 = f42 cis_P3 = f43 cis_Q3 = f44 cis_P4 = f45 cis_Q4 = f46 cis_P_temp1 = f47 cis_P_temp2 = f48 cis_Q_temp1 = f49 cis_Q_temp2 = f50 cis_P = f51 cis_SIG_INV_PI_BY_16_2TO61 = f52 cis_RSHF_2TO61 = f53 cis_RSHF = f54 cis_2TOM61 = f55 cis_NFLOAT = f56 cis_W_2TO61_RSH = f57 cis_tmp = f58 cis_Sm_sin = f59 cis_Cm_sin = f60 cis_Sm_cos = f61 cis_Cm_cos = f62 cis_srsq_sin = f63 cis_srsq_cos = f64 cis_Q_sin = f65 cis_Q_cos = f66 cis_Q = f67 ///////////////////////////////////////////////////////////// cis_pResSin = r33 cis_pResCos = r34 cis_GR_sig_inv_pi_by_16 = r14 cis_GR_rshf_2to61 = r15 cis_GR_rshf = r16 cis_GR_exp_2tom61 = r17 cis_GR_n = r18 cis_GR_n_sin = r19 cis_exp_limit = r20 cis_r_signexp = r21 cis_AD_1 = r22 cis_r_sincos = r23 cis_r_exp = r24 cis_r_17_ones = r25 cis_GR_m_sin = r26 cis_GR_32m_sin = r26 cis_GR_n_cos = r27 cis_GR_m_cos = r28 cis_GR_32m_cos = r28 cis_AD_2_sin = r29 cis_AD_2_cos = r30 cis_gr_tmp = r31 GR_SAVE_B0 = r35 GR_SAVE_GP = r36 rB0_SAVED = r37 GR_SAVE_PFS = r38 GR_SAVE_PR = r39 RODATA .align 16 // Pi/16 parts LOCAL_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 part LOCAL_OBJECT_END(double_cis_pi) // Coefficients for polynomials LOCAL_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 // Q1 LOCAL_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) 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 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#