| .file "libm_sincosf.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 |
| // 02/26/02 Added temporary return of results in r8, r9 |
| // 03/13/02 Corrected restore of predicate registers |
| // 03/19/02 Added stack unwind around call to __libm_cisf_large |
| // 09/05/02 Work range is widened by reduction strengthen (2 parts of Pi/16) |
| // 02/10/03 Reordered header: .section, .global, .proc, .align |
| // 02/11/04 cisf is moved to the separate file. |
| // 03/31/05 Reformatted delimiters between data tables |
| |
| // API |
| //============================================================== |
| // 1) void sincosf(float, float*s, float*c) |
| // 2) __libm_sincosf - 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) 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^2p2 |
| // Q = q1 + r^2q2 |
| // |
| // rcub = r * rsq |
| // Sin(r) = r + rcub * P |
| // = r + r^3p1 + r^5p2 = Sin(r) |
| // |
| // 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) |
| // 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 -> r49 |
| |
| // predicate registers used: |
| // p6 -> p14 |
| |
| // floating-point registers used |
| // f9 -> f15 |
| // f32 -> f100 |
| |
| // Assembly macros |
| //============================================================== |
| |
| cisf_Arg = f8 |
| |
| cisf_Sin_res = f9 |
| cisf_Cos_res = f8 |
| |
| |
| cisf_NORM_f8 = f10 |
| cisf_W = f11 |
| cisf_int_Nfloat = f12 |
| cisf_Nfloat = f13 |
| |
| cisf_r = f14 |
| cisf_r_exact = f68 |
| cisf_rsq = f15 |
| cisf_rcub = f32 |
| |
| cisf_Inv_Pi_by_16 = f33 |
| cisf_Pi_by_16_hi = f34 |
| cisf_Pi_by_16_lo = f35 |
| |
| cisf_Inv_Pi_by_64 = f36 |
| cisf_Pi_by_64_hi = f37 |
| cisf_Pi_by_64_lo = f38 |
| |
| |
| cisf_P1 = f39 |
| cisf_Q1 = f40 |
| cisf_P2 = f41 |
| cisf_Q2 = f42 |
| cisf_P3 = f43 |
| cisf_Q3 = f44 |
| cisf_P4 = f45 |
| cisf_Q4 = f46 |
| |
| cisf_P_temp1 = f47 |
| cisf_P_temp2 = f48 |
| |
| cisf_Q_temp1 = f49 |
| cisf_Q_temp2 = f50 |
| |
| cisf_P = f51 |
| |
| cisf_SIG_INV_PI_BY_16_2TO61 = f52 |
| cisf_RSHF_2TO61 = f53 |
| cisf_RSHF = f54 |
| cisf_2TOM61 = f55 |
| cisf_NFLOAT = f56 |
| cisf_W_2TO61_RSH = f57 |
| |
| cisf_tmp = f58 |
| |
| cisf_Sm_sin = f59 |
| cisf_Cm_sin = f60 |
| |
| cisf_Sm_cos = f61 |
| cisf_Cm_cos = f62 |
| |
| cisf_srsq_sin = f63 |
| cisf_srsq_cos = f64 |
| |
| cisf_Q_sin = f65 |
| cisf_Q_cos = f66 |
| cisf_Q = f67 |
| |
| ///////////////////////////////////////////////////////////// |
| |
| cisf_pResSin = r33 |
| cisf_pResCos = r34 |
| |
| cisf_exp_limit = r35 |
| cisf_r_signexp = r36 |
| cisf_AD_beta_table = r37 |
| cisf_r_sincos = r38 |
| |
| cisf_r_exp = r39 |
| cisf_r_17_ones = r40 |
| |
| cisf_GR_sig_inv_pi_by_16 = r14 |
| cisf_GR_rshf_2to61 = r15 |
| cisf_GR_rshf = r16 |
| cisf_GR_exp_2tom61 = r17 |
| cisf_GR_n = r18 |
| |
| cisf_GR_n_sin = r19 |
| cisf_GR_m_sin = r41 |
| cisf_GR_32m_sin = r41 |
| |
| cisf_GR_n_cos = r42 |
| cisf_GR_m_cos = r43 |
| cisf_GR_32m_cos = r43 |
| |
| cisf_AD_2_sin = r44 |
| cisf_AD_2_cos = r45 |
| |
| cisf_gr_tmp = r46 |
| GR_SAVE_B0 = r47 |
| GR_SAVE_GP = r48 |
| rB0_SAVED = r49 |
| GR_SAVE_PFS = r50 |
| GR_SAVE_PR = r51 |
| cisf_AD_1 = r52 |
| |
| RODATA |
| |
| .align 16 |
| // Pi/16 parts |
| LOCAL_OBJECT_START(double_cisf_pi) |
| data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part |
| data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part |
| LOCAL_OBJECT_END(double_cisf_pi) |
| |
| // Coefficients for polynomials |
| LOCAL_OBJECT_START(double_cisf_pq_k4) |
| data8 0x3F810FABB668E9A2 // P2 |
| data8 0x3FA552E3D6DE75C9 // Q2 |
| data8 0xBFC555554447BC7F // P1 |
| data8 0xBFDFFFFFC447610A // Q1 |
| LOCAL_OBJECT_END(double_cisf_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 |
| |
| GLOBAL_IEEE754_ENTRY(sincosf) |
| // cis_GR_sig_inv_pi_by_16 = significand of 16/pi |
| { .mlx |
| alloc GR_SAVE_PFS = ar.pfs, 0, 21, 0, 0 |
| movl cisf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A // 16/pi signd |
| |
| } |
| // cis_GR_rshf_2to61 = 1.1000 2^(63+63-2) |
| { .mlx |
| addl cisf_AD_1 = @ltoff(double_cisf_pi), gp |
| movl cisf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) |
| };; |
| |
| { .mfi |
| ld8 cisf_AD_1 = [cisf_AD_1] |
| fnorm.s1 cisf_NORM_f8 = cisf_Arg |
| cmp.eq p13, p14 = r0, r0 // p13 set for sincos |
| } |
| // cis_GR_exp_2tom61 = exponent of scaling factor 2^-61 |
| { .mib |
| mov cisf_GR_exp_2tom61 = 0xffff-61 |
| nop.i 0 |
| br.cond.sptk _CISF_COMMON |
| };; |
| GLOBAL_IEEE754_END(sincosf) |
| |
| GLOBAL_LIBM_ENTRY(__libm_sincosf) |
| { .mlx |
| // cisf_GR_sig_inv_pi_by_16 = significand of 16/pi |
| alloc GR_SAVE_PFS = ar.pfs,0,21,0,0 |
| movl cisf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A |
| } |
| // cisf_GR_rshf_2to61 = 1.1000 2^(63+63-2) |
| { .mlx |
| addl cisf_AD_1 = @ltoff(double_cisf_pi), gp |
| movl cisf_GR_rshf_2to61 = 0x47b8000000000000 |
| };; |
| |
| // p14 set for __libm_sincos and cis |
| { .mfi |
| ld8 cisf_AD_1 = [cisf_AD_1] |
| fnorm.s1 cisf_NORM_f8 = cisf_Arg |
| cmp.eq p14, p13 = r0, r0 |
| } |
| // cisf_GR_exp_2tom61 = exponent of scaling factor 2^-61 |
| { .mib |
| mov cisf_GR_exp_2tom61 = 0xffff-61 |
| nop.i 0 |
| nop.b 0 |
| };; |
| |
| _CISF_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 cisf_SIG_INV_PI_BY_16_2TO61 = cisf_GR_sig_inv_pi_by_16 |
| fclass.m p6,p0 = cisf_Arg, 0xe7//if x=0,inf,nan |
| addl cisf_gr_tmp = -1, r0 |
| } |
| // cisf_GR_rshf = 1.1000 2^63 for right shift |
| { .mlx |
| setf.d cisf_RSHF_2TO61 = cisf_GR_rshf_2to61 |
| movl cisf_GR_rshf = 0x43e8000000000000 |
| };; |
| |
| // Form another constant |
| // 2^-61 for scaling Nfloat |
| // 0x10017 is register_bias + 24. |
| // So if f8 >= 2^24, go to large args routine |
| { .mmi |
| getf.exp cisf_r_signexp = cisf_Arg |
| setf.exp cisf_2TOM61 = cisf_GR_exp_2tom61 |
| mov cisf_exp_limit = 0x10017 |
| };; |
| |
| // Load the two pieces of pi/16 |
| // Form another constant |
| // 1.1000...000 * 2^63, the right shift constant |
| { .mmb |
| ldfe cisf_Pi_by_16_hi = [cisf_AD_1],16 |
| setf.d cisf_RSHF = cisf_GR_rshf |
| (p6) br.cond.spnt _CISF_SPECIAL_ARGS |
| };; |
| |
| { .mmi |
| ldfe cisf_Pi_by_16_lo = [cisf_AD_1],16 |
| setf.sig cisf_tmp = cisf_gr_tmp //constant for inexact set |
| nop.i 0 |
| };; |
| |
| // Start loading P, Q coefficients |
| { .mmi |
| ldfpd cisf_P2,cisf_Q2 = [cisf_AD_1],16 |
| nop.m 0 |
| dep.z cisf_r_exp = cisf_r_signexp, 0, 17 |
| };; |
| |
| // p10 is true if we must call routines to handle larger arguments |
| // p10 is true if f8 exp is >= 0x10017 |
| { .mmb |
| ldfpd cisf_P1,cisf_Q1 = [cisf_AD_1], 16 |
| cmp.ge p10, p0 = cisf_r_exp, cisf_exp_limit |
| (p10) br.cond.spnt _CISF_LARGE_ARGS // go to |x| >= 2^24 path |
| };; |
| |
| // cisf_W = x * cisf_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 0 |
| fma.s1 cisf_W_2TO61_RSH = cisf_NORM_f8,cisf_SIG_INV_PI_BY_16_2TO61,cisf_RSHF_2TO61 |
| nop.i 0 |
| };; |
| |
| // cisf_NFLOAT = Round_Int_Nearest(cisf_W) |
| { .mfi |
| nop.m 0 |
| fms.s1 cisf_NFLOAT = cisf_W_2TO61_RSH,cisf_2TOM61,cisf_RSHF |
| nop.i 0 |
| };; |
| |
| // N = (int)cisf_int_Nfloat |
| { .mfi |
| getf.sig cisf_GR_n = cisf_W_2TO61_RSH |
| nop.f 0 |
| nop.i 0 |
| };; |
| |
| // Add 2^(k-1) (which is in cisf_r_sincos) to N |
| // cisf_r = -cisf_Nfloat * cisf_Pi_by_16_hi + x |
| // cisf_r = cisf_r -cisf_Nfloat * cisf_Pi_by_16_lo |
| { .mfi |
| add cisf_GR_n_cos = 0x8, cisf_GR_n |
| fnma.s1 cisf_r = cisf_NFLOAT, cisf_Pi_by_16_hi, cisf_NORM_f8 |
| nop.i 0 |
| };; |
| |
| //Get M (least k+1 bits of N) |
| { .mmi |
| and cisf_GR_m_sin = 0x1f,cisf_GR_n |
| and cisf_GR_m_cos = 0x1f,cisf_GR_n_cos |
| nop.i 0 |
| };; |
| |
| { .mmi |
| shladd cisf_AD_2_cos = cisf_GR_m_cos,4, cisf_AD_1 |
| shladd cisf_AD_2_sin = cisf_GR_m_sin,4, cisf_AD_1 |
| nop.i 0 |
| };; |
| |
| // den. input to set uflow |
| { .mmf |
| ldfpd cisf_Sm_sin, cisf_Cm_sin = [cisf_AD_2_sin] |
| ldfpd cisf_Sm_cos, cisf_Cm_cos = [cisf_AD_2_cos] |
| fclass.m.unc p10,p0 = cisf_Arg,0x0b |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 cisf_rsq = cisf_r, cisf_r, f0 // get r^2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fmpy.s0 cisf_tmp = cisf_tmp,cisf_tmp // inexact flag |
| nop.i 0 |
| };; |
| |
| { .mmf |
| nop.m 0 |
| nop.m 0 |
| fnma.s1 cisf_r_exact = cisf_NFLOAT, cisf_Pi_by_16_lo, cisf_r |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 cisf_P = cisf_rsq, cisf_P2, cisf_P1 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 cisf_Q = cisf_rsq, cisf_Q2, cisf_Q1 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fmpy.s1 cisf_rcub = cisf_r_exact, cisf_rsq // get r^3 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fmpy.s1 cisf_srsq_sin = cisf_Sm_sin,cisf_rsq |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fmpy.s1 cisf_srsq_cos = cisf_Sm_cos,cisf_rsq |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 cisf_P = cisf_rcub,cisf_P,cisf_r_exact |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 cisf_Q_sin = cisf_srsq_sin,cisf_Q, cisf_Sm_sin |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 cisf_Q_cos = cisf_srsq_cos,cisf_Q, cisf_Sm_cos |
| nop.i 0 |
| };; |
| |
| // If den. arg, force underflow to be set |
| { .mfi |
| nop.m 0 |
| (p10) fmpy.s.s0 cisf_tmp = cisf_Arg,cisf_Arg |
| nop.i 0 |
| };; |
| |
| //Final sin |
| { .mfi |
| nop.m 0 |
| fma.s.s0 cisf_Sin_res = cisf_Cm_sin, cisf_P, cisf_Q_sin |
| nop.i 0 |
| } |
| //Final cos |
| { .mfb |
| nop.m 0 |
| fma.s.s0 cisf_Cos_res = cisf_Cm_cos, cisf_P, cisf_Q_cos |
| (p14) br.cond.sptk _CISF_RETURN //com. exit for __libm_sincos and cis main path |
| };; |
| |
| { .mmb |
| stfs [cisf_pResSin] = cisf_Sin_res |
| stfs [cisf_pResCos] = cisf_Cos_res |
| br.ret.sptk b0 // common exit for sincos main path |
| };; |
| |
| _CISF_SPECIAL_ARGS: |
| // sinf(+/-0) = +/-0 |
| // sinf(Inf) = NaN |
| // sinf(NaN) = NaN |
| { .mfi |
| nop.m 999 |
| fma.s.s0 cisf_Sin_res = cisf_Arg, f0, f0 // sinf(+/-0,NaN,Inf) |
| nop.i 999 |
| };; |
| |
| // cosf(+/-0) = 1.0 |
| // cosf(Inf) = NaN |
| // cosf(NaN) = NaN |
| { .mfb |
| nop.m 999 |
| fma.s.s0 cisf_Cos_res = cisf_Arg, f0, f1 // cosf(+/-0,NaN,Inf) |
| (p14) br.cond.sptk _CISF_RETURN //spec exit for __libm_sincos and cis main path |
| };; |
| |
| { .mmb |
| stfs [cisf_pResSin] = cisf_Sin_res |
| stfs [cisf_pResCos] = cisf_Cos_res |
| br.ret.sptk b0 // special exit for sincos main path |
| };; |
| |
| // exit for sincos |
| // NOTE! r8 and r9 used only because of compiler issue |
| // connected with float point complex function arguments pass |
| // After fix of this issue this operations can be deleted |
| _CISF_RETURN: |
| { .mmb |
| getf.s r8 = cisf_Cos_res |
| getf.s r9 = cisf_Sin_res |
| br.ret.sptk b0 // exit for sincos |
| };; |
| GLOBAL_LIBM_END(__libm_sincosf) |
| |
| //// |x| > 2^24 path /////// |
| .proc _CISF_LARGE_ARGS |
| _CISF_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.s.s0 cisf_Cos_res = cisf_Cos_res, f1, f0 |
| mov ar.pfs = GR_SAVE_PFS |
| } |
| // exit for |x| > 2^24 path (__libm_sincos and cis) |
| { .mfb |
| nop.m 0 |
| fma.s.s0 cisf_Sin_res = cisf_Sin_res, f1, f0 |
| (p14) br.cond.sptk _CISF_RETURN |
| };; |
| |
| { .mmb |
| stfs [cisf_pResSin] = cisf_Sin_res |
| stfs [cisf_pResCos] = cisf_Cos_res |
| br.ret.sptk b0 // exit for sincos |x| > 2^24 path |
| };; |
| |
| .endp _CISF_LARGE_ARGS |
| |
| .type __libm_sincos_large#,@function |
| .global __libm_sincos_large# |
| |
