.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#