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authorMike Frysinger <vapier@gentoo.org>2014-02-15 22:07:25 -0500
committerMike Frysinger <vapier@gentoo.org>2014-02-16 01:12:38 -0500
commitc70a4b1db0cf5e813ae24b0fa96a352399eb6edf (patch)
tree5a36b0f0955682ae5232907d04fdf68589990783 /sysdeps/ia64/fpu/s_cos.S
parent591aeaf7a99bc9aa9179f013114d92496952dced (diff)
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ia64: relocate out of ports/ subdir
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+.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#