.file "sincosf.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 Single precision version is made using double precision one as base // 02/10/03 Reordered header: .section, .global, .proc, .align // 03/31/05 Reformatted delimiters between data tables // // API //============================================================== // float sinf( float x); // float cosf( float 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) // 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 part is rounded to zero, LOW - to nearest // // 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 = Series for Cos // Sin(r) = r + r^3 p1 + r^5 p2 = 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^2*P2 // Q = Q1 + r^2*Q2 // // rcub = r * rsq // Sin(r) = r + rcub * P // = r + r^3p1 + r^5p2 = 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 + r^3 * 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) // Cos(r) = 1 + r^2q1 + r^4q2 // // 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 -> r19 // r32 -> r45 // predicate registers used: // p6 -> p14 // floating-point registers used // f9 -> f15 // f32 -> f61 // Assembly macros //============================================================== sincosf_NORM_f8 = f9 sincosf_W = f10 sincosf_int_Nfloat = f11 sincosf_Nfloat = f12 sincosf_r = f13 sincosf_rsq = f14 sincosf_rcub = f15 sincosf_save_tmp = f15 sincosf_Inv_Pi_by_16 = f32 sincosf_Pi_by_16_1 = f33 sincosf_Pi_by_16_2 = f34 sincosf_Inv_Pi_by_64 = f35 sincosf_Pi_by_16_3 = f36 sincosf_r_exact = f37 sincosf_Sm = f38 sincosf_Cm = f39 sincosf_P1 = f40 sincosf_Q1 = f41 sincosf_P2 = f42 sincosf_Q2 = f43 sincosf_P3 = f44 sincosf_Q3 = f45 sincosf_P4 = f46 sincosf_Q4 = f47 sincosf_P_temp1 = f48 sincosf_P_temp2 = f49 sincosf_Q_temp1 = f50 sincosf_Q_temp2 = f51 sincosf_P = f52 sincosf_Q = f53 sincosf_srsq = f54 sincosf_SIG_INV_PI_BY_16_2TO61 = f55 sincosf_RSHF_2TO61 = f56 sincosf_RSHF = f57 sincosf_2TOM61 = f58 sincosf_NFLOAT = f59 sincosf_W_2TO61_RSH = f60 fp_tmp = f61 ///////////////////////////////////////////////////////////// sincosf_AD_1 = r33 sincosf_AD_2 = r34 sincosf_exp_limit = r35 sincosf_r_signexp = r36 sincosf_AD_beta_table = r37 sincosf_r_sincos = r38 sincosf_r_exp = r39 sincosf_r_17_ones = r40 sincosf_GR_sig_inv_pi_by_16 = r14 sincosf_GR_rshf_2to61 = r15 sincosf_GR_rshf = r16 sincosf_GR_exp_2tom61 = r17 sincosf_GR_n = r18 sincosf_GR_m = r19 sincosf_GR_32m = r19 sincosf_GR_all_ones = r19 gr_tmp = r41 GR_SAVE_PFS = r41 GR_SAVE_B0 = r42 GR_SAVE_GP = r43 RODATA .align 16 // Pi/16 parts LOCAL_OBJECT_START(double_sincosf_pi) data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part LOCAL_OBJECT_END(double_sincosf_pi) // Coefficients for polynomials LOCAL_OBJECT_START(double_sincosf_pq_k4) data8 0x3F810FABB668E9A2 // P2 data8 0x3FA552E3D6DE75C9 // Q2 data8 0xBFC555554447BC7F // P1 data8 0xBFDFFFFFC447610A // Q1 LOCAL_OBJECT_END(double_sincosf_pq_k4) // Sincos table (S[m], C[m]) LOCAL_OBJECT_START(double_sin_cos_beta_k4) data8 0x0000000000000000 // sin ( 0 Pi / 16 ) data8 0x3FF0000000000000 // cos ( 0 Pi / 16 ) // data8 0x3FC8F8B83C69A60B // sin ( 1 Pi / 16 ) data8 0x3FEF6297CFF75CB0 // cos ( 1 Pi / 16 ) // data8 0x3FD87DE2A6AEA963 // sin ( 2 Pi / 16 ) data8 0x3FED906BCF328D46 // cos ( 2 Pi / 16 ) // data8 0x3FE1C73B39AE68C8 // sin ( 3 Pi / 16 ) data8 0x3FEA9B66290EA1A3 // cos ( 3 Pi / 16 ) // data8 0x3FE6A09E667F3BCD // sin ( 4 Pi / 16 ) data8 0x3FE6A09E667F3BCD // cos ( 4 Pi / 16 ) // data8 0x3FEA9B66290EA1A3 // sin ( 5 Pi / 16 ) data8 0x3FE1C73B39AE68C8 // cos ( 5 Pi / 16 ) // data8 0x3FED906BCF328D46 // sin ( 6 Pi / 16 ) data8 0x3FD87DE2A6AEA963 // cos ( 6 Pi / 16 ) // data8 0x3FEF6297CFF75CB0 // sin ( 7 Pi / 16 ) data8 0x3FC8F8B83C69A60B // cos ( 7 Pi / 16 ) // data8 0x3FF0000000000000 // sin ( 8 Pi / 16 ) data8 0x0000000000000000 // cos ( 8 Pi / 16 ) // data8 0x3FEF6297CFF75CB0 // sin ( 9 Pi / 16 ) data8 0xBFC8F8B83C69A60B // cos ( 9 Pi / 16 ) // data8 0x3FED906BCF328D46 // sin ( 10 Pi / 16 ) data8 0xBFD87DE2A6AEA963 // cos ( 10 Pi / 16 ) // data8 0x3FEA9B66290EA1A3 // sin ( 11 Pi / 16 ) data8 0xBFE1C73B39AE68C8 // cos ( 11 Pi / 16 ) // data8 0x3FE6A09E667F3BCD // sin ( 12 Pi / 16 ) data8 0xBFE6A09E667F3BCD // cos ( 12 Pi / 16 ) // data8 0x3FE1C73B39AE68C8 // sin ( 13 Pi / 16 ) data8 0xBFEA9B66290EA1A3 // cos ( 13 Pi / 16 ) // data8 0x3FD87DE2A6AEA963 // sin ( 14 Pi / 16 ) data8 0xBFED906BCF328D46 // cos ( 14 Pi / 16 ) // data8 0x3FC8F8B83C69A60B // sin ( 15 Pi / 16 ) data8 0xBFEF6297CFF75CB0 // cos ( 15 Pi / 16 ) // data8 0x0000000000000000 // sin ( 16 Pi / 16 ) data8 0xBFF0000000000000 // cos ( 16 Pi / 16 ) // data8 0xBFC8F8B83C69A60B // sin ( 17 Pi / 16 ) data8 0xBFEF6297CFF75CB0 // cos ( 17 Pi / 16 ) // data8 0xBFD87DE2A6AEA963 // sin ( 18 Pi / 16 ) data8 0xBFED906BCF328D46 // cos ( 18 Pi / 16 ) // data8 0xBFE1C73B39AE68C8 // sin ( 19 Pi / 16 ) data8 0xBFEA9B66290EA1A3 // cos ( 19 Pi / 16 ) // data8 0xBFE6A09E667F3BCD // sin ( 20 Pi / 16 ) data8 0xBFE6A09E667F3BCD // cos ( 20 Pi / 16 ) // data8 0xBFEA9B66290EA1A3 // sin ( 21 Pi / 16 ) data8 0xBFE1C73B39AE68C8 // cos ( 21 Pi / 16 ) // data8 0xBFED906BCF328D46 // sin ( 22 Pi / 16 ) data8 0xBFD87DE2A6AEA963 // cos ( 22 Pi / 16 ) // data8 0xBFEF6297CFF75CB0 // sin ( 23 Pi / 16 ) data8 0xBFC8F8B83C69A60B // cos ( 23 Pi / 16 ) // data8 0xBFF0000000000000 // sin ( 24 Pi / 16 ) data8 0x0000000000000000 // cos ( 24 Pi / 16 ) // data8 0xBFEF6297CFF75CB0 // sin ( 25 Pi / 16 ) data8 0x3FC8F8B83C69A60B // cos ( 25 Pi / 16 ) // data8 0xBFED906BCF328D46 // sin ( 26 Pi / 16 ) data8 0x3FD87DE2A6AEA963 // cos ( 26 Pi / 16 ) // data8 0xBFEA9B66290EA1A3 // sin ( 27 Pi / 16 ) data8 0x3FE1C73B39AE68C8 // cos ( 27 Pi / 16 ) // data8 0xBFE6A09E667F3BCD // sin ( 28 Pi / 16 ) data8 0x3FE6A09E667F3BCD // cos ( 28 Pi / 16 ) // data8 0xBFE1C73B39AE68C8 // sin ( 29 Pi / 16 ) data8 0x3FEA9B66290EA1A3 // cos ( 29 Pi / 16 ) // data8 0xBFD87DE2A6AEA963 // sin ( 30 Pi / 16 ) data8 0x3FED906BCF328D46 // cos ( 30 Pi / 16 ) // data8 0xBFC8F8B83C69A60B // sin ( 31 Pi / 16 ) data8 0x3FEF6297CFF75CB0 // cos ( 31 Pi / 16 ) // data8 0x0000000000000000 // sin ( 32 Pi / 16 ) data8 0x3FF0000000000000 // cos ( 32 Pi / 16 ) 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(sinf) { .mlx alloc r32 = ar.pfs,1,13,0,0 movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi } { .mlx addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) };; { .mfi ld8 sincosf_AD_1 = [sincosf_AD_1] fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument cmp.eq p8,p9 = r0, r0 // set p8 (clear p9) for sin } { .mib mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 mov sincosf_r_sincos = 0x0 // 0 for sin br.cond.sptk _SINCOSF_COMMON // go to common part };; GLOBAL_IEEE754_END(sinf) GLOBAL_IEEE754_ENTRY(cosf) { .mlx alloc r32 = ar.pfs,1,13,0,0 movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi } { .mlx addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) };; { .mfi ld8 sincosf_AD_1 = [sincosf_AD_1] fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument cmp.eq p9,p8 = r0, r0 // set p9 (clear p8) for cos } { .mib mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 mov sincosf_r_sincos = 0x8 // 8 for cos nop.b 999 };; //////////////////////////////////////////////////////// // All entry points end up here. // If from sin, sincosf_r_sincos is 0 and p8 is true // If from cos, sincosf_r_sincos is 8 = 2^(k-1) and p9 is true // We add sincosf_r_sincos to N ///////////// Common sin and cos part ////////////////// _SINCOSF_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 sincosf_SIG_INV_PI_BY_16_2TO61 = sincosf_GR_sig_inv_pi_by_16 fclass.m p6,p0 = f8, 0xe7 // if x=0,inf,nan mov sincosf_exp_limit = 0x10017 } { .mlx setf.d sincosf_RSHF_2TO61 = sincosf_GR_rshf_2to61 movl sincosf_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 };; // Right shift // Form another constant // 2^-61 for scaling Nfloat // 0x10017 is register_bias + 24. // So if f8 >= 2^24, go to large argument routines { .mmi getf.exp sincosf_r_signexp = f8 setf.exp sincosf_2TOM61 = sincosf_GR_exp_2tom61 addl gr_tmp = -1,r0 // For "inexect" constant create };; // Load the two pieces of pi/16 // Form another constant // 1.1000...000 * 2^63, the right shift constant { .mmb ldfe sincosf_Pi_by_16_1 = [sincosf_AD_1],16 setf.d sincosf_RSHF = sincosf_GR_rshf (p6) br.cond.spnt _SINCOSF_SPECIAL_ARGS };; // Getting argument's exp for "large arguments" filtering { .mmi ldfe sincosf_Pi_by_16_2 = [sincosf_AD_1],16 setf.sig fp_tmp = gr_tmp // constant for inexact set nop.i 999 };; // Polynomial coefficients (Q2, Q1, P2, P1) loading { .mmi ldfpd sincosf_P2,sincosf_Q2 = [sincosf_AD_1],16 nop.m 999 nop.i 999 };; // Select exponent (17 lsb) { .mmi ldfpd sincosf_P1,sincosf_Q1 = [sincosf_AD_1],16 nop.m 999 dep.z sincosf_r_exp = sincosf_r_signexp, 0, 17 };; // p10 is true if we must call routines to handle larger arguments // p10 is true if f8 exp is >= 0x10017 (2^24) { .mfb cmp.ge p10,p0 = sincosf_r_exp,sincosf_exp_limit nop.f 999 (p10) br.cond.spnt _SINCOSF_LARGE_ARGS // Go to "large args" routine };; // sincosf_W = x * sincosf_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 nop.m 999 fma.s1 sincosf_W_2TO61_RSH = sincosf_NORM_f8, sincosf_SIG_INV_PI_BY_16_2TO61, sincosf_RSHF_2TO61 nop.i 999 };; // sincosf_NFLOAT = Round_Int_Nearest(sincosf_W) // This is done by scaling back by 2^-61 and subtracting the shift constant { .mfi nop.m 999 fms.s1 sincosf_NFLOAT = sincosf_W_2TO61_RSH,sincosf_2TOM61,sincosf_RSHF nop.i 999 };; // get N = (int)sincosf_int_Nfloat { .mfi getf.sig sincosf_GR_n = sincosf_W_2TO61_RSH // integer N value nop.f 999 nop.i 999 };; // Add 2^(k-1) (which is in sincosf_r_sincos=8) to N // sincosf_r = -sincosf_Nfloat * sincosf_Pi_by_16_1 + x { .mfi add sincosf_GR_n = sincosf_GR_n, sincosf_r_sincos fnma.s1 sincosf_r = sincosf_NFLOAT, sincosf_Pi_by_16_1, sincosf_NORM_f8 nop.i 999 };; // Get M (least k+1 bits of N) { .mmi and sincosf_GR_m = 0x1f,sincosf_GR_n // Put mask 0x1F - nop.m 999 // - select k+1 bits nop.i 999 };; // Add 16*M to address of sin_cos_beta table { .mfi shladd sincosf_AD_2 = sincosf_GR_32m, 4, sincosf_AD_1 (p8) fclass.m.unc p10,p0 = f8,0x0b // If sin denormal input - nop.i 999 };; // Load Sin and Cos table value using obtained index m (sincosf_AD_2) { .mfi ldfd sincosf_Sm = [sincosf_AD_2],8 // Sin value S[m] (p9) fclass.m.unc p11,p0 = f8,0x0b // If cos denormal input - nop.i 999 // - set denormal };; // sincosf_r = sincosf_r -sincosf_Nfloat * sincosf_Pi_by_16_2 { .mfi ldfd sincosf_Cm = [sincosf_AD_2] // Cos table value C[m] fnma.s1 sincosf_r_exact = sincosf_NFLOAT, sincosf_Pi_by_16_2, sincosf_r nop.i 999 } // get rsq = r*r { .mfi nop.m 999 fma.s1 sincosf_rsq = sincosf_r, sincosf_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 };; // Polynomials calculation // Q = Q2*r^2 + Q1 // P = P2*r^2 + P1 { .mfi nop.m 999 fma.s1 sincosf_Q = sincosf_rsq, sincosf_Q2, sincosf_Q1 nop.i 999 } { .mfi nop.m 999 fma.s1 sincosf_P = sincosf_rsq, sincosf_P2, sincosf_P1 nop.i 999 };; // get rcube and S[m]*r^2 { .mfi nop.m 999 fmpy.s1 sincosf_srsq = sincosf_Sm,sincosf_rsq // r^2*S[m] nop.i 999 } { .mfi nop.m 999 fmpy.s1 sincosf_rcub = sincosf_r_exact, sincosf_rsq 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 sincosf_Q = sincosf_srsq,sincosf_Q, sincosf_Sm nop.i 999 } { .mfi nop.m 999 fma.s1 sincosf_P = sincosf_rcub,sincosf_P,sincosf_r_exact nop.i 999 };; // If sinf(denormal) - force underflow to be set .pred.rel "mutex",p10,p11 { .mfi nop.m 999 (p10) fmpy.s.s0 fp_tmp = f8,f8 // forces underflow flag nop.i 999 // for denormal sine args } // If cosf(denormal) - force denormal to be set { .mfi nop.m 999 (p11) fma.s.s0 fp_tmp = f8, f1, f8 // forces denormal flag nop.i 999 // for denormal cosine args };; // Final calculation // result = C[m]*P + Q { .mfb nop.m 999 fma.s.s0 f8 = sincosf_Cm, sincosf_P, sincosf_Q br.ret.sptk b0 // Exit for common path };; ////////// x = 0/Inf/NaN path ////////////////// _SINCOSF_SPECIAL_ARGS: .pred.rel "mutex",p8,p9 // sinf(+/-0) = +/-0 // sinf(Inf) = NaN // sinf(NaN) = NaN { .mfi nop.m 999 (p8) fma.s.s0 f8 = f8, f0, f0 // sinf(+/-0,NaN,Inf) nop.i 999 } // cosf(+/-0) = 1.0 // cosf(Inf) = NaN // cosf(NaN) = NaN { .mfb nop.m 999 (p9) fma.s.s0 f8 = f8, f0, f1 // cosf(+/-0,NaN,Inf) br.ret.sptk b0 // Exit for x = 0/Inf/NaN path };; GLOBAL_IEEE754_END(cosf) //////////// x >= 2^24 - large arguments routine call //////////// LOCAL_LIBM_ENTRY(__libm_callout_sincosf) _SINCOSF_LARGE_ARGS: .prologue { .mfi mov sincosf_GR_all_ones = -1 // 0xffffffff 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 sincosf_save_tmp = sincosf_GR_all_ones // inexact set nop.b 999 (p8) br.call.sptk.many b0 = __libm_sin_large# // sinf(large_X) };; { .mbb cmp.ne p9,p0 = sincosf_r_sincos, r0 // set p9 if cos nop.b 999 (p9) br.call.sptk.many b0 = __libm_cos_large# // cosf(large_X) };; { .mfi mov gp = GR_SAVE_GP fma.s.s0 f8 = f8, f1, f0 // Round result to single mov b0 = GR_SAVE_B0 } { .mfi // force inexact set nop.m 999 fmpy.s0 sincosf_save_tmp = sincosf_save_tmp, sincosf_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_sincosf) .type __libm_sin_large#, @function .global __libm_sin_large# .type __libm_cos_large#, @function .global __libm_cos_large#