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Diffstat (limited to 'sysdeps/ia64/fpu/libm_sincos.S')
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diff --git a/sysdeps/ia64/fpu/libm_sincos.S b/sysdeps/ia64/fpu/libm_sincos.S new file mode 100644 index 0000000..7fda2af --- /dev/null +++ b/sysdeps/ia64/fpu/libm_sincos.S @@ -0,0 +1,783 @@ +.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# + |