2.5-18.1

1 files changed, 463 insertions, 541 deletions

diff --git a/sysdeps/ia64/fpu/s_tanf.S b/sysdeps/ia64/fpu/s_tanf.S
index a84009e2fe..193d7568a5 100644
--- a/sysdeps/ia64/fpu/s_tanf.S
+++ b/sysdeps/ia64/fpu/s_tanf.S
@@ -1,10 +1,10 @@
-.file "tanf.s"
+.file "tancotf.s"
 
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2005, Intel Corporation
 // All rights reserved.
-// 
-// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
-// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
+//
+// 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
@@ -20,7 +20,7 @@
 // * 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
@@ -32,739 +32,661 @@
 // 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://developer.intel.com/opensource.
+// http://www.intel.com/software/products/opensource/libraries/num.htm.
 //
 // History
 //==============================================================
-// 2/02/00: Initial version
-// 4/04/00  Unwind support added
+// 02/02/00 Initial version
+// 04/04/00 Unwind support added
 // 12/27/00 Improved speed
+// 02/21/01 Updated to call tanl
+// 05/30/02 Improved speed, added cotf.
+// 11/25/02 Added explicit completer on fnorm
+// 02/10/03 Reordered header: .section, .global, .proc, .align
+// 04/17/03 Eliminated redundant stop bits
+// 03/31/05 Reformatted delimiters between data tables
 //
-// API
+// APIs
 //==============================================================
-// float tan( float x);
+// float tanf(float)
+// float cotf(float)
 //
-// Overview of operation
+// Algorithm Description for tanf
 //==============================================================
-// If the input value in radians is |x| >= 1.xxxxx 2^10 call the
-// older slower version.
+// The tanf function computes the principle value of the tangent of x,
+// where x is radian argument.
 //
-// The new algorithm is used when |x| <= 1.xxxxx 2^9.
+// There are 5 paths:
+// 1. x = +/-0.0
+//    Return tanf(x) = +/-0.0
 //
-// Represent the input X as Nfloat * pi/2 + r
-//    where r can be negative and |r| <= pi/4
+// 2. x = [S,Q]NaN
+//    Return tanf(x) = QNaN
 //
-//     tan_W  = x * 2/pi
-//     Nfloat = round_int(tan_W)
+// 3. x = +/-Inf
+//    Return tanf(x) = QNaN
 //
-//     tan_r  = x - Nfloat * (pi/2)_hi
-//     tan_r  = tan_r - Nfloat * (pi/2)_lo
+// 4. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is even, |r|<Pi/4
+//    Return tanf(x) = P19(r) = A1*r + A3*r^3 + A5*r^5 + ... + A19*r^19 =
+//    = r*(A1 + A3*t + A5*t^2 + ... + A19*t^9) = r*P9(t), where t = r^2
 //
-// We have two paths: p8, when Nfloat is even and p9. when Nfloat is odd.
-// p8: tan(X) =  tan(r)
-// p9: tan(X) = -cot(r)
+// 5. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is odd, |r|<Pi/4
+//    Return tanf(x) = -1/r + P11(r) = -1/r + B1*r + B3*r^3 + ... + B11*r^11 =
+//    = -1/r + r*(B1 + B3*t + B5*t^2 + ... + B11*t^5) = -1/r + r*P11(t),
+//    where t = r^2
 //
-// Each is evaluated as a series. The p9 path requires 1/r.
+// Algorithm Description for cotf
+//==============================================================
+// The cotf function computes the principle value of the cotangent of x,
+// where x is radian argument.
 //
-// The coefficients used in the series are stored in a table as
-// are the pi constants.
+// There are 5 paths:
+// 1. x = +/-0.0
+//    Return cotf(x) = +/-Inf and error handling is called
 //
-// Registers used
-//==============================================================
+// 2. x = [S,Q]NaN
+//    Return cotf(x) = QNaN
 //
-// predicate registers used:  
-// p6-10
+// 3. x = +/-Inf
+//    Return cotf(x) = QNaN
 //
-// floating-point registers used:  
-// f10-15, f32-105
+// 4. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is odd, |r|<Pi/4
+//    Return cotf(x) = P19(-r) = A1*(-r) + A3*(-r^3) + ... + A19*(-r^19) =
+//    = -r*(A1 + A3*t + A5*t^2 + ... + A19*t^9) = -r*P9(t), where t = r^2
+//
+// 5. x = r + (Pi/2)*N, N = RoundInt(x*(2/Pi)), N is even, |r|<Pi/4
+//    Return cotf(x) = 1/r + P11(-r) = 1/r + B1*(-r) + ... + B11*(-r^11) =
+//    = 1/r - r*(B1 + B3*t + B5*t^2 + ... + B11*t^5) = 1/r - r*P11(t),
+//    where t = r^2
+//
+//    We set p10 and clear p11 if computing tanf, vice versa for cotf.
+//
+//
+// Registers used
+//==============================================================
+// Floating Point registers used:
 // f8, input
+// f32 -> f80
 //
-// general registers used
-// r14-18, r32-43
+// General registers used:
+// r14 -> r23, r32 -> r39
+//
+// Predicate registers used:
+// p6 -> p13
 //
-
-#include "libm_support.h"
-
 // Assembly macros
 //==============================================================
-TAN_INV_PI_BY_2_2TO64        = f10
-TAN_RSHF_2TO64               = f11
-TAN_2TOM64                   = f12
-TAN_RSHF                     = f13
-TAN_W_2TO64_RSH              = f14
-TAN_NFLOAT                   = f15
-
-tan_Inv_Pi_by_2              = f32
-tan_Pi_by_2_hi               = f33
-tan_Pi_by_2_lo               = f34
-
-
-tan_P0                       = f35
-tan_P1                       = f36
-tan_P2                       = f37
-tan_P3                       = f38 
-tan_P4                       = f39 
-tan_P5                       = f40 
-tan_P6                       = f41
-tan_P7                       = f42
-tan_P8                       = f43 
-tan_P9                       = f44 
-tan_P10                      = f45 
-tan_P11                      = f46
-tan_P12                      = f47 
-tan_P13                      = f48
-tan_P14                      = f49
-tan_P15                      = f50
-
-tan_Q0                       = f51 
-tan_Q1                       = f52 
-tan_Q2                       = f53 
-tan_Q3                       = f54 
-tan_Q4                       = f55 
-tan_Q5                       = f56 
-tan_Q6                       = f57 
-tan_Q7                       = f58 
-tan_Q8                       = f59
-tan_Q9                       = f60
-tan_Q10                      = f61
-
-tan_r                        = f62
-tan_rsq                      = f63
-tan_rcube                    = f64
-
-tan_v18                      = f65
-tan_v16                      = f66
-tan_v17                      = f67
-tan_v12                      = f68
-tan_v13                      = f69
-tan_v7                       = f70
-tan_v8                       = f71
-tan_v4                       = f72
-tan_v5                       = f73
-tan_v15                      = f74
-tan_v11                      = f75
-tan_v14                      = f76
-tan_v3                       = f77
-tan_v6                       = f78
-tan_v10                      = f79
-tan_v2                       = f80
-tan_v9                       = f81
-tan_v1                       = f82
-tan_int_Nfloat               = f83 
-tan_Nfloat                   = f84 
-
-tan_NORM_f8                  = f85 
-tan_W                        = f86
-
-tan_y0                       = f87
-tan_d                        = f88 
-tan_y1                       = f89 
-tan_dsq                      = f90 
-tan_y2                       = f91 
-tan_d4                       = f92 
-tan_inv_r                    = f93 
-
-tan_z1                       = f94
-tan_z2                       = f95
-tan_z3                       = f96
-tan_z4                       = f97
-tan_z5                       = f98
-tan_z6                       = f99
-tan_z7                       = f100
-tan_z8                       = f101
-tan_z9                       = f102
-tan_z10                      = f103
-tan_z11                      = f104
-tan_z12                      = f105
-
-
-/////////////////////////////////////////////////////////////
-
-tan_GR_sig_inv_pi_by_2       = r14
-tan_GR_rshf_2to64            = r15
-tan_GR_exp_2tom64            = r16
-tan_GR_n                     = r17
-tan_GR_rshf                  = r18
-
-tan_AD                       = r33
-tan_GR_10009                 = r34 
-tan_GR_17_ones               = r35 
-tan_GR_N_odd_even            = r36 
-tan_GR_N                     = r37 
-tan_signexp                  = r38
-tan_exp                      = r39
-tan_ADQ                      = r40
-
-GR_SAVE_PFS                  = r41 
-GR_SAVE_B0                   = r42       
-GR_SAVE_GP                   = r43      
-
-
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
+// integer registers
+rExp                        = r14
+rSignMask                   = r15
+rRshf                       = r16
+rScFctrExp                  = r17
+rIntN                       = r18
+rSigRcpPiby2                = r19
+rScRshf                     = r20
+rCoeffA                     = r21
+rCoeffB                     = r22
+rExpCut                     = r23
+
+GR_SAVE_B0                  = r33
+GR_SAVE_PFS                 = r34
+GR_SAVE_GP                  = r35
+GR_Parameter_X              = r36
+GR_Parameter_Y              = r37
+GR_Parameter_RESULT         = r38
+GR_Parameter_Tag            = r39
+
+//==============================================================
+// floating point registers
+fScRcpPiby2                 = f32
+fScRshf                     = f33
+fNormArg                    = f34
+fScFctr                     = f35
+fRshf                       = f36
+fShiftedN                   = f37
+fN                          = f38
+fR                          = f39
+fA01                        = f40
+fA03                        = f41
+fA05                        = f42
+fA07                        = f43
+fA09                        = f44
+fA11                        = f45
+fA13                        = f46
+fA15                        = f47
+fA17                        = f48
+fA19                        = f49
+fB01                        = f50
+fB03                        = f51
+fB05                        = f52
+fB07                        = f53
+fB09                        = f54
+fB11                        = f55
+fA03_01                     = f56
+fA07_05                     = f57
+fA11_09                     = f58
+fA15_13                     = f59
+fA19_17                     = f60
+fA11_05                     = f61
+fA19_13                     = f62
+fA19_05                     = f63
+fRbyA03_01                  = f64
+fB03_01                     = f65
+fB07_05                     = f66
+fB11_09                     = f67
+fB11_05                     = f68
+fRbyB03_01                  = f69
+fRbyB11_01                  = f70
+fRp2                        = f71
+fRp4                        = f72
+fRp8                        = f73
+fRp5                        = f74
+fY0                         = f75
+fY1                         = f76
+fD                          = f77
+fDp2                        = f78
+fInvR                       = f79
+fPiby2                      = f80
+//==============================================================
 
-.align 16
 
-double_tan_constants:
-ASM_TYPE_DIRECTIVE(double_tan_constants,@object)
-//   data8 0xA2F9836E4E44152A, 0x00003FFE // 2/pi
-   data8 0xC90FDAA22168C234, 0x00003FFF // pi/2 hi
-
-   data8 0xBEEA54580DDEA0E1 // P14 
-   data8 0x3ED3021ACE749A59 // P15
-   data8 0xBEF312BD91DC8DA1 // P12 
-   data8 0x3EFAE9AFC14C5119 // P13
-   data8 0x3F2F342BF411E769 // P8
-   data8 0x3F1A60FC9F3B0227 // P9
-   data8 0x3EFF246E78E5E45B // P10
-   data8 0x3F01D9D2E782875C // P11
-   data8 0x3F8226E34C4499B6 // P4
-   data8 0x3F6D6D3F12C236AC // P5
-   data8 0x3F57DA1146DCFD8B // P6
-   data8 0x3F43576410FE3D75 // P7
-   data8 0x3FD5555555555555 // P0
-   data8 0x3FC11111111111C2 // P1
-   data8 0x3FABA1BA1BA0E850 // P2
-   data8 0x3F9664F4886725A7 // P3
-ASM_SIZE_DIRECTIVE(double_tan_constants)
-
-double_Q_tan_constants:
-ASM_TYPE_DIRECTIVE(double_Q_tan_constants,@object)
-   data8 0xC4C6628B80DC1CD1, 0x00003FBF // pi/2 lo
-   data8 0x3E223A73BA576E48 // Q8
-   data8 0x3DF54AD8D1F2CA43 // Q9
-   data8 0x3EF66A8EE529A6AA // Q4
-   data8 0x3EC2281050410EE6 // Q5
-   data8 0x3E8D6BB992CC3CF5 // Q6
-   data8 0x3E57F88DE34832E4 // Q7
-   data8 0x3FD5555555555555 // Q0
-   data8 0x3F96C16C16C16DB8 // Q1
-   data8 0x3F61566ABBFFB489 // Q2
-   data8 0x3F2BBD77945C1733 // Q3
-   data8 0x3D927FB33E2B0E04 // Q10
-ASM_SIZE_DIRECTIVE(double_Q_tan_constants)
-
-
-   
-.align 32
-.global tanf#
-#ifdef _LIBC
-.global __tanf#
-#endif
-
-////////////////////////////////////////////////////////
+RODATA
+.align 16
 
+LOCAL_OBJECT_START(coeff_A)
+data8 0x3FF0000000000000 // A1  = 1.00000000000000000000e+00
+data8 0x3FD5555556BCE758 // A3  = 3.33333334641442641606e-01
+data8 0x3FC111105C2DAE48 // A5  = 1.33333249100689099175e-01
+data8 0x3FABA1F876341060 // A7  = 5.39701122561673229739e-02
+data8 0x3F965FB86D12A38D // A9  = 2.18495194027670719750e-02
+data8 0x3F8265F62415F9D6 // A11 = 8.98353860497717439465e-03
+data8 0x3F69E3AE64CCF58D // A13 = 3.16032468108912746342e-03
+data8 0x3F63920D09D0E6F6 // A15 = 2.38897844840557235331e-03
+LOCAL_OBJECT_END(coeff_A)
+
+LOCAL_OBJECT_START(coeff_B)
+data8 0xC90FDAA22168C235, 0x3FFF // pi/2
+data8 0x3FD55555555358DB // B1  = 3.33333333326107426583e-01
+data8 0x3F96C16C252F643F // B3  = 2.22222230621336129239e-02
+data8 0x3F61566243AB3C60 // B5  = 2.11638633968606896785e-03
+data8 0x3F2BC1169BD4438B // B7  = 2.11748132564551094391e-04
+data8 0x3EF611B4CEA056A1 // B9  = 2.10467959860990200942e-05
+data8 0x3EC600F9E32194BF // B11 = 2.62305891234274186608e-06
+data8 0xBF42BA7BCC177616 // A17 =-5.71546981685324877205e-04
+data8 0x3F4F2614BC6D3BB8 // A19 = 9.50584530849832782542e-04
+LOCAL_OBJECT_END(coeff_B)
 
 
 .section .text
-.proc  tanf#
-#ifdef _LIBC
-.proc  __tanf#
-#endif
-.align 32
-tanf:
-#ifdef _LIBC
-__tanf:
-#endif
-// The initial fnorm will take any unmasked faults and
-// normalize any single/double unorms
+
+LOCAL_LIBM_ENTRY(cotf)
 
 { .mlx
-      alloc          r32=ar.pfs,1,11,0,0               
-      movl tan_GR_sig_inv_pi_by_2 = 0xA2F9836E4E44152A // significand of 2/pi
+      getf.exp  rExp        = f8                    // ***** Get 2ˆ17 * s + E
+      movl      rSigRcpPiby2= 0xA2F9836E4E44152A    // significand of 2/Pi
 }
 { .mlx
-      addl           tan_AD   = @ltoff(double_tan_constants), gp
-      movl tan_GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+63+1)
+      addl      rCoeffA     = @ltoff(coeff_A), gp
+      movl      rScRshf     = 0x47e8000000000000    // 1.5*2^(63+63+1)
 }
 ;;
 
 { .mfi
-      ld8 tan_AD = [tan_AD]
-      fnorm     tan_NORM_f8  = f8                      
-      mov tan_GR_exp_2tom64 = 0xffff-64 // exponent of scaling factor 2^-64
+      alloc     r32         = ar.pfs, 0, 4, 4, 0
+      fclass.m  p9, p0      = f8, 0xc3              // Test for x=nan
+      cmp.eq    p11, p10    = r0, r0                // if p11=1 we compute cotf
 }
-{ .mlx
-      nop.m 999
-      movl tan_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 for right shift
+{ .mib
+      ld8       rCoeffA     = [rCoeffA]
+      mov       rExpCut     = 0x10009               // cutoff for exponent
+      br.cond.sptk Common_Path
 }
 ;;
 
+LOCAL_LIBM_END(cotf)
 
-// Form two constants we need
-//   2/pi * 2^1 * 2^63, scaled by 2^64 since we just loaded the significand
-//   1.1000...000 * 2^(63+63+1) to right shift int(W) into the significand
-{ .mmi
-      setf.sig TAN_INV_PI_BY_2_2TO64 = tan_GR_sig_inv_pi_by_2
-      setf.d TAN_RSHF_2TO64 = tan_GR_rshf_2to64
-      mov       tan_GR_17_ones     = 0x1ffff             ;;
-}
 
+GLOBAL_IEEE754_ENTRY(tanf)
 
-// Form another constant
-//   2^-64 for scaling Nfloat
-//   1.1000...000 * 2^63, the right shift constant
-{ .mmf
-      setf.exp TAN_2TOM64 = tan_GR_exp_2tom64
-      adds tan_ADQ = double_Q_tan_constants - double_tan_constants, tan_AD
-      fclass.m.unc  p6,p0 = f8, 0x07  // Test for x=0
+{ .mlx
+      getf.exp  rExp        = f8                    // ***** Get 2ˆ17 * s + E
+      movl      rSigRcpPiby2= 0xA2F9836E4E44152A    // significand of 2/Pi
 }
-;;
-
-
-// Form another constant
-//   2^-64 for scaling Nfloat
-//   1.1000...000 * 2^63, the right shift constant
-{ .mmf
-      setf.d TAN_RSHF = tan_GR_rshf
-      ldfe      tan_Pi_by_2_hi = [tan_AD],16 
-      fclass.m.unc  p7,p0 = f8, 0x23  // Test for x=inf
+{ .mlx
+      addl      rCoeffA     = @ltoff(coeff_A), gp
+      movl      rScRshf     = 0x47e8000000000000    // 1.5*2^(63+63+1)
 }
 ;;
 
-{ .mfb
-      ldfe      tan_Pi_by_2_lo = [tan_ADQ],16           
-      fclass.m.unc  p8,p0 = f8, 0xc3  // Test for x=nan
-(p6)  br.ret.spnt    b0    ;;         // Exit for x=0
-}
-
 { .mfi
-      ldfpd     tan_P14,tan_P15 = [tan_AD],16                         
-(p7)  frcpa.s0  f8,p9=f0,f0           // Set qnan indef if x=inf
-      mov       tan_GR_10009 = 0x10009
+      alloc     r32         = ar.pfs, 0, 4, 4, 0
+      fclass.m  p9, p0      = f8, 0xc3              // Test for x=nan
+      cmp.eq    p10, p11    = r0, r0                // if p10=1 we compute tandf
 }
 { .mib
-      ldfpd      tan_Q8,tan_Q9  = [tan_ADQ],16                        
-      nop.i 999
-(p7)  br.ret.spnt    b0    ;;         // Exit for x=inf
+      ld8       rCoeffA     = [rCoeffA]
+      mov       rExpCut     = 0x10009               // cutoff for exponent
+      nop.b     0
 }
+;;
 
+// Below is common path for both tandf and cotdf
+Common_Path:
 { .mfi
-      ldfpd      tan_P12,tan_P13 = [tan_AD],16                         
-(p8)  fma.s f8=f8,f1,f8               // Set qnan if x=nan
-      nop.i 999
+      setf.sig  fScRcpPiby2 = rSigRcpPiby2          // 2^(63+1)*(2/Pi)
+      fclass.m  p8, p0      = f8, 0x23              // Test for x=inf
+      mov       rSignMask   = 0x1ffff               // mask for sign bit
 }
-{ .mib
-      ldfpd      tan_Q4,tan_Q5  = [tan_ADQ],16                        
-      nop.i 999
-(p8)  br.ret.spnt    b0    ;;         // Exit for x=nan
+{ .mlx
+      setf.d    fScRshf     = rScRshf               // 1.5*2^(63+63+1)
+      movl      rRshf       = 0x43e8000000000000    // 1.5 2^63 for right shift
 }
+;;
 
-{ .mmi
-      getf.exp  tan_signexp    = tan_NORM_f8                 
-      ldfpd      tan_P8,tan_P9  = [tan_AD],16                         
-      nop.i 999 ;;
+{ .mfi
+      and       rSignMask   = rSignMask, rExp       // clear sign bit
+(p10) fclass.m.unc p7, p0   = f8, 0x07              // Test for x=0 (for tanf)
+      mov       rScFctrExp  = 0xffff-64             // exp of scaling factor
+}
+{ .mfb
+      adds      rCoeffB     = coeff_B - coeff_A, rCoeffA
+(p9)  fma.s.s0  f8          = f8, f1, f8            // Set qnan if x=nan
+(p9)  br.ret.spnt b0                                // Exit for x=nan
 }
+;;
 
-// Multiply x by scaled 2/pi and add large const to shift integer part of W to 
-//   rightmost bits of significand
 { .mfi
-      ldfpd      tan_Q6,tan_Q7  = [tan_ADQ],16
-      fma.s1 TAN_W_2TO64_RSH = tan_NORM_f8,TAN_INV_PI_BY_2_2TO64,TAN_RSHF_2TO64
-      nop.i 999 ;;
+      cmp.ge    p6, p0      = rSignMask, rExpCut    // p6 = (E => 0x10009)
+(p8)  frcpa.s0  f8, p0      = f0, f0                // Set qnan indef if x=inf
+      mov GR_Parameter_Tag  = 227                   // (cotf)
 }
-
-{ .mmi
-      ldfpd      tan_P10,tan_P11 = [tan_AD],16                         
-      nop.m 999
-      and       tan_exp = tan_GR_17_ones, tan_signexp         ;;
+{ .mbb
+      ldfe      fPiby2      = [rCoeffB], 16
+(p8)  br.ret.spnt b0                                // Exit for x=inf
+(p6)  br.cond.spnt Huge_Argument                    // Branch if |x|>=2^10
 }
+;;
 
+{ .mfi
+      nop.m     0
+(p11) fclass.m.unc p6, p0   = f8, 0x07              // Test for x=0 (for cotf)
+      nop.i     0
+}
+{ .mfb
+      nop.m     0
+      fnorm.s0  fNormArg    = f8
+(p7)  br.ret.spnt b0                                // Exit for x=0 (for tanf)
+}
+;;
 
-// p7 is true if we must call DBX TAN
-// p7 is true if f8 exp is > 0x10009 (which includes all ones
-//    NAN or inf)
-{ .mmi
-      ldfpd      tan_Q0,tan_Q1  = [tan_ADQ],16                         
-      cmp.ge.unc  p7,p0 = tan_exp,tan_GR_10009               
-      nop.i 999 ;;
+{ .mmf
+      ldfpd     fA01, fA03  = [rCoeffA], 16
+      ldfpd     fB01, fB03  = [rCoeffB], 16
+      fmerge.s  f10         = f8, f8                // Save input for error call
 }
+;;
 
+{ .mmf
+      setf.exp  fScFctr     = rScFctrExp            // get as real
+      setf.d    fRshf       = rRshf                 // get right shifter as real
+(p6)  frcpa.s0  f8, p0      = f1, f8                // cotf(+-0) = +-Inf
+}
+;;
 
 { .mmb
-      ldfpd      tan_P4,tan_P5  = [tan_AD],16                         
-      nop.m 999
-(p7)  br.cond.spnt   L(TAN_DBX) ;;                                  
+      ldfpd     fA05, fA07  = [rCoeffA], 16
+      ldfpd     fB05, fB07  = [rCoeffB], 16
+(p6)  br.cond.spnt __libm_error_region    // call error support if cotf(+-0)
 }
-
+;;
 
 { .mmi
-      ldfpd      tan_Q2,tan_Q3  = [tan_ADQ],16                         
-      nop.m 999
-      nop.i 999 ;;
+      ldfpd     fA09, fA11  = [rCoeffA], 16
+      ldfpd     fB09, fB11  = [rCoeffB], 16
+      nop.i     0
 }
-
-
-
-// TAN_NFLOAT = Round_Int_Nearest(tan_W)
-{ .mfi
-      ldfpd      tan_P6,tan_P7  = [tan_AD],16                         
-      fms.s1 TAN_NFLOAT = TAN_W_2TO64_RSH,TAN_2TOM64,TAN_RSHF      
-      nop.i 999 ;;
-}
-
+;;
 
 { .mfi
-      ldfd      tan_Q10 = [tan_ADQ]
-      nop.f 999
-      nop.i 999 ;;
+      nop.m     0
+      fma.s1    fShiftedN = fNormArg,fScRcpPiby2,fScRshf // x*2^70*(2/Pi)+ScRshf
+      nop.i     0
 }
-
+;;
 
 { .mfi
-      ldfpd      tan_P0,tan_P1  = [tan_AD],16                         
-      nop.f 999
-      nop.i 999 ;;
+      nop.m     0
+      fms.s1    fN          = fShiftedN, fScFctr, fRshf // N = Y*2^(-70) - Rshf
+      nop.i     0
 }
+;;
 
-
+.pred.rel "mutex", p10, p11
 { .mfi
-      getf.sig    tan_GR_n = TAN_W_2TO64_RSH
-      nop.f 999
-      nop.i 999 ;;
+      getf.sig  rIntN       = fShiftedN             // get N as integer
+(p10) fnma.s1   fR          = fN, fPiby2, fNormArg  // R = x - (Pi/2)*N (tanf)
+      nop.i     0
 }
-
-// tan_r          = -tan_Nfloat * tan_Pi_by_2_hi + x
 { .mfi
-      ldfpd      tan_P2,tan_P3  = [tan_AD]
-      fnma.s1  tan_r      = TAN_NFLOAT, tan_Pi_by_2_hi,  tan_NORM_f8         
-      nop.i 999 ;;
+      nop.m     0
+(p11) fms.s1    fR          = fN, fPiby2, fNormArg  // R = (Pi/2)*N - x (cotf)
+      nop.i     0
 }
+;;
 
-
-// p8 ==> even
-// p9 ==> odd
 { .mmi
-      and         tan_GR_N_odd_even = 0x1, tan_GR_n ;;          
-      nop.m 999
-      cmp.eq.unc  p8,p9          = tan_GR_N_odd_even, r0      ;;
-}
-
-
-// tan_r          = tan_r -tan_Nfloat * tan_Pi_by_2_lo 
-{ .mfi
-      nop.m 999
-      fnma.s1  tan_r      = TAN_NFLOAT, tan_Pi_by_2_lo,  tan_r      
-      nop.i 999 ;;
+      ldfpd     fA13, fA15  = [rCoeffA], 16
+      ldfpd     fA17, fA19  = [rCoeffB], 16
+      nop.i     0
 }
+;;
 
-
+Return_From_Huges:
 { .mfi
-      nop.m 999
-      fma.s1   tan_rsq    = tan_r, tan_r,   f0                      
-      nop.i 999 ;;
+      nop.m     0
+      fma.s1    fRp2        = fR, fR, f0            // R^2
+(p11) add       rIntN       = 0x1, rIntN            // N = N + 1 (cotf)
 }
-
+;;
 
 { .mfi
-      nop.m 999
-(p9)  frcpa.s1   tan_y0, p10 = f1,tan_r                  
-      nop.i 999  ;;
+      nop.m     0
+      frcpa.s1  fY0, p0     = f1, fR                // Y0 ~ 1/R
+      tbit.z    p8, p9      = rIntN, 0              // p8=1 if N is even
 }
+;;
 
-
+// Below are mixed polynomial calculations (mixed for even and odd N)
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v18 = tan_rsq, tan_P15, tan_P14        
-      nop.i 999
+      nop.m     0
+(p9)  fma.s1    fB03_01     = fRp2, fB03, fB01      // R^2*B3 + B1
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v4  = tan_rsq, tan_P1, tan_P0          
-      nop.i 999  ;;
+      nop.m     0
+      fma.s1    fRp4        = fRp2, fRp2, f0        // R^4
+      nop.i     0
 }
-
-
+;;
 
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v16 = tan_rsq, tan_P13, tan_P12        
-      nop.i 999 
+      nop.m     0
+(p8)  fma.s1    fA15_13     = fRp2, fA15, fA13      // R^2*A15 + A13
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v17 = tan_rsq, tan_rsq, f0             
-      nop.i 999 ;;
+      nop.m     0
+(p8)  fma.s1    fA19_17     = fRp2, fA19, fA17      // R^2*A19 + A17
+      nop.i     0
 }
-
-
+;;
 
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v12 = tan_rsq, tan_P9, tan_P8          
-      nop.i 999 
+      nop.m     0
+(p8)  fma.s1    fA07_05     = fRp2, fA07, fA05      // R^2*A7 + A5
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v13 = tan_rsq, tan_P11, tan_P10        
-      nop.i 999 ;;
+      nop.m     0
+(p8)  fma.s1    fA11_09     = fRp2, fA11, fA09      // R^2*A11 + A9
+      nop.i     0
 }
-
-
+;;
 
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v7  = tan_rsq, tan_P5, tan_P4          
-      nop.i 999 
+      nop.m     0
+(p9)  fma.s1    fB07_05     = fRp2, fB07, fB05      // R^2*B7 + B5
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v8  = tan_rsq, tan_P7, tan_P6          
-      nop.i 999 ;;
+      nop.m     0
+(p9)  fma.s1    fB11_09     = fRp2, fB11, fB09      // R^2*B11 + B9
+      nop.i     0
 }
-
-
+;;
 
 { .mfi
-      nop.m 999
-(p9)  fnma.s1    tan_d   = tan_r, tan_y0, f1   
-      nop.i 999 
+      nop.m     0
+(p9)  fnma.s1   fD          = fR, fY0, f1           // D = 1 - R*Y0
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v5  = tan_rsq, tan_P3, tan_P2          
-      nop.i 999 ;;
+      nop.m     0
+(p8)  fma.s1    fA03_01     = fRp2, fA03, fA01      // R^2*A3 + A1
+      nop.i     0
 }
-
-
+;;
 
 { .mfi
-      nop.m 999
-(p9)  fma.s1  tan_z11 = tan_rsq, tan_Q9, tan_Q8         
-      nop.i 999
+      nop.m     0
+      fma.s1    fRp8        = fRp4, fRp4, f0        // R^8
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p9)  fma.s1  tan_z12 = tan_rsq, tan_rsq, f0            
-      nop.i 999 ;;
+      nop.m     0
+      fma.s1    fRp5        = fR, fRp4, f0          // R^5
+      nop.i     0
 }
-
+;;
 
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v15 = tan_v17, tan_v18, tan_v16        
-      nop.i 999 
+      nop.m     0
+(p8)  fma.s1    fA11_05     = fRp4, fA11_09, fA07_05 // R^4*(R^2*A11 + A9) + ...
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p9)  fma.s1  tan_z7 = tan_rsq, tan_Q5, tan_Q4          
-      nop.i 999 ;;
+      nop.m     0
+(p8)  fma.s1    fA19_13     = fRp4, fA19_17, fA15_13 // R^4*(R^2*A19 + A17) + ..
+      nop.i     0
 }
-
+;;
 
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v11 = tan_v17, tan_v13, tan_v12        
-      nop.i 999
+      nop.m     0
+(p9)  fma.s1    fB11_05     = fRp4, fB11_09, fB07_05 // R^4*(R^2*B11 + B9) + ...
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p9)  fma.s1  tan_z8 = tan_rsq, tan_Q7, tan_Q6          
-      nop.i 999 ;;
+      nop.m     0
+(p9)  fma.s1    fRbyB03_01  = fR, fB03_01, f0       // R*(R^2*B3 + B1)
+      nop.i     0
 }
-
-
+;;
 
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v14 = tan_v17, tan_v17, f0             
-      nop.i 999 
+      nop.m     0
+(p9)  fma.s1    fY1         = fY0, fD, fY0          // Y1 = Y0*D + Y0
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p9)  fma.s1  tan_z3 = tan_rsq, tan_Q1, tan_Q0          
-      nop.i 999 ;; 
+      nop.m     0
+(p9)  fma.s1    fDp2        = fD, fD, f0            // D^2
+      nop.i     0
 }
-
-
-
+;;
 
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v3 = tan_v17, tan_v5, tan_v4           
-      nop.i 999
+      nop.m     0
+   // R^8*(R^6*A19 + R^4*A17 + R^2*A15 + A13) + R^6*A11 + R^4*A9 + R^2*A7 + A5
+(p8)  fma.d.s1  fA19_05     = fRp8, fA19_13, fA11_05
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v6 = tan_v17, tan_v8, tan_v7           
-      nop.i 999 ;;
+      nop.m     0
+(p8)  fma.d.s1  fRbyA03_01  = fR, fA03_01, f0       // R*(R^2*A3 + A1)
+      nop.i     0
 }
-
-
+;;
 
 { .mfi
-      nop.m 999
-(p9)  fma.s1     tan_y1  = tan_y0, tan_d, tan_y0    
-      nop.i 999 
+      nop.m     0
+(p9)  fma.d.s1  fInvR       = fY1, fDp2, fY1        // 1/R = Y1*D^2 + Y1
+      nop.i     0
 }
 { .mfi
-      nop.m 999
-(p9)  fma.s1     tan_dsq = tan_d, tan_d, f0        
-      nop.i 999 ;; 
+      nop.m     0
+   // R^5*(R^6*B11 + R^4*B9 + R^2*B7 + B5) + R^3*B3 + R*B1
+(p9)  fma.d.s1  fRbyB11_01  = fRp5, fB11_05, fRbyB03_01
+      nop.i     0
 }
+;;
 
-
+.pred.rel "mutex", p8, p9
 { .mfi
-      nop.m 999
-(p9)  fma.s1  tan_z10 = tan_z12, tan_Q10, tan_z11       
-      nop.i 999 
+      nop.m     0
+   // Result = R^5*(R^14*A19 + R^12*A17 + R^10*A15 + ...) + R^3*A3 + R*A1
+(p8)  fma.s.s0  f8          = fRp5, fA19_05, fRbyA03_01
+      nop.i 0
 }
-{ .mfi
-      nop.m 999
-(p9)  fma.s1  tan_z9  = tan_z12, tan_z12,f0             
-      nop.i 999 ;;
+{ .mfb
+      nop.m     0
+   // Result = -1/R + R^11*B11 + R^9*B9 + R^7*B7 + R^5*B5 + R^3*B3 + R*B1
+(p9)  fnma.s.s0 f8          = f1, fInvR, fRbyB11_01
+      br.ret.sptk b0                                // exit for main path
 }
+;;
 
-
-{ .mfi
-      nop.m 999
-(p9)  fma.s1  tan_z4 = tan_rsq, tan_Q3, tan_Q2          
-      nop.i 999 
-}
-{ .mfi
-      nop.m 999
-(p9)  fma.s1  tan_z6  = tan_z12, tan_z8, tan_z7         
-      nop.i 999 ;; 
-}
+GLOBAL_IEEE754_END(tanf)
 
 
+LOCAL_LIBM_ENTRY(__libm_callout)
+Huge_Argument:
+.prologue
 
 { .mfi
-      nop.m 999
-(p8)  fma.s1  tan_v10 = tan_v14, tan_v15, tan_v11        
-      nop.i 999 ;; 
+      nop.m 0
+      fmerge.s f9 = f0,f0
+.save ar.pfs,GR_SAVE_PFS
+      mov  GR_SAVE_PFS=ar.pfs
 }
-
-
+;;
 
 { .mfi
-      nop.m 999
-(p9)  fma.s1     tan_y2  = tan_y1, tan_d, tan_y0         
-      nop.i 999 
-}
-{ .mfi
-      nop.m 999
-(p9)  fma.s1     tan_d4  = tan_dsq, tan_dsq, tan_d       
-      nop.i 999  ;;
+      mov GR_SAVE_GP=gp
+      nop.f 0
+.save b0, GR_SAVE_B0
+      mov GR_SAVE_B0=b0
 }
 
-
-{ .mfi
+.body
+{ .mmb
       nop.m 999
-(p8)  fma.s1  tan_v2 = tan_v14, tan_v6, tan_v3           
-      nop.i 999
-}
-{ .mfi
       nop.m 999
-(p8)  fma.s1  tan_v9 = tan_v14, tan_v14, f0              
-      nop.i 999 ;;
+(p10) br.cond.sptk.many  call_tanl ;;
 }
 
-
-{ .mfi
+// Here if we should call cotl (p10=0, p11=1)
+{ .mmb
       nop.m 999
-(p9)  fma.s1  tan_z2  = tan_z12, tan_z4, tan_z3         
-      nop.i 999 
-}
-{ .mfi
       nop.m 999
-(p9)  fma.s1  tan_z5  = tan_z9, tan_z10, tan_z6         
-      nop.i 999  ;;
+      br.call.sptk.many  b0=__libm_cotl# ;;
 }
 
-
 { .mfi
-      nop.m 999
-(p9)  fma.s1     tan_inv_r = tan_d4, tan_y2, tan_y0      
-      nop.i 999 
+      mov gp        = GR_SAVE_GP
+      fnorm.s.s0 f8 = f8
+      mov b0        = GR_SAVE_B0
 }
-{ .mfi
+;;
+
+{ .mib
       nop.m 999
-(p8)  fma.s1   tan_rcube  = tan_rsq, tan_r,   f0
-      nop.i 999  ;;
+      mov ar.pfs    = GR_SAVE_PFS
+      br.ret.sptk     b0
+;;
 }
 
-
-
-{ .mfi
+// Here if we should call tanl (p10=1, p11=0)
+call_tanl:
+{ .mmb
       nop.m 999
-(p8)  fma.s1  tan_v1 = tan_v9, tan_v10, tan_v2           
-      nop.i 999 
-}
-{ .mfi
       nop.m 999
-(p9)  fma.s1  tan_z1  = tan_z9, tan_z5, tan_z2          
-      nop.i 999   ;;
+      br.call.sptk.many  b0=__libm_tanl# ;;
 }
 
-
-
 { .mfi
-      nop.m 999
-(p8)  fma.s.s0  f8  = tan_v1, tan_rcube, tan_r             
-      nop.i 999  
+      mov gp        = GR_SAVE_GP
+      fnorm.s.s0 f8 = f8
+      mov b0        = GR_SAVE_B0
 }
-{ .mfb
+;;
+
+{ .mib
       nop.m 999
-(p9)  fms.s.s0  f8  = tan_r, tan_z1, tan_inv_r        
-      br.ret.sptk    b0 ;;    
+      mov ar.pfs    = GR_SAVE_PFS
+      br.ret.sptk     b0
+;;
 }
-.endp tanf#
-ASM_SIZE_DIRECTIVE(tanf#)
+
+LOCAL_LIBM_END(__libm_callout)
+
+.type __libm_tanl#,@function
+.global __libm_tanl#
+.type __libm_cotl#,@function
+.global __libm_cotl#
 
 
-.proc __libm_callout
-__libm_callout:
-L(TAN_DBX): 
+LOCAL_LIBM_ENTRY(__libm_error_region)
 .prologue
 
+// (1)
 { .mfi
-        nop.m 0
-     fmerge.s f9 = f0,f0 
+      add           GR_Parameter_Y=-32,sp        // Parameter 2 value
+      nop.f         0
 .save   ar.pfs,GR_SAVE_PFS
-        mov  GR_SAVE_PFS=ar.pfs
+      mov           GR_SAVE_PFS=ar.pfs           // Save ar.pfs
 }
-;;
-
 { .mfi
-        mov GR_SAVE_GP=gp
-        nop.f 0
+.fframe 64
+      add sp=-64,sp                              // Create new stack
+      nop.f 0
+      mov GR_SAVE_GP=gp                          // Save gp
+};;
+
+// (2)
+{ .mmi
+      stfs [GR_Parameter_Y] = f1,16              // STORE Parameter 2 on stack
+      add GR_Parameter_X = 16,sp                 // Parameter 1 address
 .save   b0, GR_SAVE_B0
-        mov GR_SAVE_B0=b0
-}
+      mov GR_SAVE_B0=b0                          // Save b0
+};;
 
 .body
-{ .mfb
-      nop.m 999
-      nop.f 999
-       br.call.sptk.many  b0=__libm_tan# ;;
-}
-
-
-{ .mfi
-       mov gp        = GR_SAVE_GP
-      fnorm.s     f8 = f8
-       mov b0        = GR_SAVE_B0 
+// (3)
+{ .mib
+      stfs [GR_Parameter_X] = f10                // STORE Parameter 1 on stack
+      add   GR_Parameter_RESULT = 0,GR_Parameter_Y  // Parameter 3 address
+      nop.b 0
 }
-;;
-
+{ .mib
+      stfs [GR_Parameter_Y] = f8                 // STORE Parameter 3 on stack
+      add   GR_Parameter_Y = -16,GR_Parameter_Y
+      br.call.sptk b0=__libm_error_support#      // Call error handling function
+};;
+{ .mmi
+      nop.m 0
+      nop.m 0
+      add   GR_Parameter_RESULT = 48,sp
+};;
 
+// (4)
+{ .mmi
+      ldfs  f8 = [GR_Parameter_RESULT]           // Get return result off stack
+.restore sp
+      add   sp = 64,sp                           // Restore stack pointer
+      mov   b0 = GR_SAVE_B0                      // Restore return address
+};;
 { .mib
-         nop.m 999
-      mov ar.pfs    = GR_SAVE_PFS
-      br.ret.sptk     b0
-;;
-}
+      mov   gp = GR_SAVE_GP                      // Restore gp
+      mov   ar.pfs = GR_SAVE_PFS                 // Restore ar.pfs
+      br.ret.sptk     b0                         // Return
+};;
 
+LOCAL_LIBM_END(__libm_error_region)
 
-.endp  __libm_callout
-ASM_SIZE_DIRECTIVE(__libm_callout)
+.type   __libm_error_support#,@function
+.global __libm_error_support#
 
-.type __libm_tan#,@function
-.global __libm_tan#