| .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 |
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| // 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# |
| |
