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-rw-r--r--sysdeps/ia64/fpu/s_tanf.S1004
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#