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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_cosf.S
parent591aeaf7a99bc9aa9179f013114d92496952dced (diff)
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ia64: relocate out of ports/ subdir
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+.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#