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-rw-r--r--sysdeps/ia64/fpu/s_tanf.S1004
1 files changed, 541 insertions, 463 deletions
diff --git a/sysdeps/ia64/fpu/s_tanf.S b/sysdeps/ia64/fpu/s_tanf.S
index 193d7568a5..a84009e2fe 100644
--- a/sysdeps/ia64/fpu/s_tanf.S
+++ b/sysdeps/ia64/fpu/s_tanf.S
@@ -1,10 +1,10 @@
-.file "tancotf.s"
+.file "tanf.s"
-
-// Copyright (c) 2000 - 2005, Intel Corporation
+// Copyright (C) 2000, 2001, Intel Corporation
// All rights reserved.
-//
-// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// 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.
//
// 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
@@ -32,661 +32,739 @@
// 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.
+// http://developer.intel.com/opensource.
//
// History
//==============================================================
-// 02/02/00 Initial version
-// 04/04/00 Unwind support added
+// 2/02/00: Initial version
+// 4/04/00 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
//
-// APIs
+// API
//==============================================================
-// float tanf(float)
-// float cotf(float)
+// float tan( float x);
//
-// Algorithm Description for tanf
+// Overview of operation
//==============================================================
-// The tanf function computes the principle value of the tangent of x,
-// where x is radian argument.
-//
-// There are 5 paths:
-// 1. x = +/-0.0
-// Return tanf(x) = +/-0.0
+// If the input value in radians is |x| >= 1.xxxxx 2^10 call the
+// older slower version.
//
-// 2. x = [S,Q]NaN
-// Return tanf(x) = QNaN
+// The new algorithm is used when |x| <= 1.xxxxx 2^9.
//
-// 3. x = +/-Inf
-// Return tanf(x) = QNaN
+// Represent the input X as Nfloat * pi/2 + r
+// where r can be negative and |r| <= pi/4
//
-// 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
+// tan_W = x * 2/pi
+// Nfloat = round_int(tan_W)
//
-// 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
-//
-// Algorithm Description for cotf
-//==============================================================
-// The cotf function computes the principle value of the cotangent of x,
-// where x is radian argument.
+// tan_r = x - Nfloat * (pi/2)_hi
+// tan_r = tan_r - Nfloat * (pi/2)_lo
//
-// There are 5 paths:
-// 1. x = +/-0.0
-// Return cotf(x) = +/-Inf and error handling is called
+// 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)
//
-// 2. x = [S,Q]NaN
-// Return cotf(x) = QNaN
-//
-// 3. x = +/-Inf
-// Return cotf(x) = QNaN
-//
-// 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.
+// Each is evaluated as a series. The p9 path requires 1/r.
//
+// The coefficients used in the series are stored in a table as
+// are the pi constants.
//
// Registers used
//==============================================================
-// Floating Point registers used:
-// f8, input
-// f32 -> f80
//
-// General registers used:
-// r14 -> r23, r32 -> r39
+// predicate registers used:
+// p6-10
//
-// Predicate registers used:
-// p6 -> p13
+// floating-point registers used:
+// f10-15, f32-105
+// f8, input
+//
+// general registers used
+// r14-18, r32-43
//
-// Assembly macros
-//==============================================================
-// 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
-//==============================================================
+#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
-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)
+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
+
+////////////////////////////////////////////////////////
-.section .text
-LOCAL_LIBM_ENTRY(cotf)
+.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
{ .mlx
- getf.exp rExp = f8 // ***** Get 2ˆ17 * s + E
- movl rSigRcpPiby2= 0xA2F9836E4E44152A // significand of 2/Pi
+ alloc r32=ar.pfs,1,11,0,0
+ movl tan_GR_sig_inv_pi_by_2 = 0xA2F9836E4E44152A // significand of 2/pi
}
{ .mlx
- addl rCoeffA = @ltoff(coeff_A), gp
- movl rScRshf = 0x47e8000000000000 // 1.5*2^(63+63+1)
+ addl tan_AD = @ltoff(double_tan_constants), gp
+ movl tan_GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+63+1)
}
;;
{ .mfi
- 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
+ ld8 tan_AD = [tan_AD]
+ fnorm tan_NORM_f8 = f8
+ mov tan_GR_exp_2tom64 = 0xffff-64 // exponent of scaling factor 2^-64
}
-{ .mib
- ld8 rCoeffA = [rCoeffA]
- mov rExpCut = 0x10009 // cutoff for exponent
- br.cond.sptk Common_Path
+{ .mlx
+ nop.m 999
+ movl tan_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 for right shift
}
;;
-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)
-{ .mlx
- getf.exp rExp = f8 // ***** Get 2ˆ17 * s + E
- movl rSigRcpPiby2= 0xA2F9836E4E44152A // significand of 2/Pi
-}
-{ .mlx
- addl rCoeffA = @ltoff(coeff_A), gp
- movl rScRshf = 0x47e8000000000000 // 1.5*2^(63+63+1)
+// 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
}
;;
-{ .mfi
- 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
- ld8 rCoeffA = [rCoeffA]
- mov rExpCut = 0x10009 // cutoff for exponent
- nop.b 0
+
+// 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
}
;;
-// Below is common path for both tandf and cotdf
-Common_Path:
-{ .mfi
- 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
-}
-{ .mlx
- setf.d fScRshf = rScRshf // 1.5*2^(63+63+1)
- movl rRshf = 0x43e8000000000000 // 1.5 2^63 for right shift
+{ .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
- 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
+ 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
}
-{ .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
+{ .mib
+ ldfpd tan_Q8,tan_Q9 = [tan_ADQ],16
+ nop.i 999
+(p7) br.ret.spnt b0 ;; // Exit for x=inf
}
-;;
{ .mfi
- 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)
+ ldfpd tan_P12,tan_P13 = [tan_AD],16
+(p8) fma.s f8=f8,f1,f8 // Set qnan if x=nan
+ nop.i 999
}
-{ .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
+{ .mib
+ ldfpd tan_Q4,tan_Q5 = [tan_ADQ],16
+ nop.i 999
+(p8) br.ret.spnt b0 ;; // Exit for x=nan
}
-;;
-{ .mfi
- nop.m 0
-(p11) fclass.m.unc p6, p0 = f8, 0x07 // Test for x=0 (for cotf)
- nop.i 0
+{ .mmi
+ getf.exp tan_signexp = tan_NORM_f8
+ ldfpd tan_P8,tan_P9 = [tan_AD],16
+ nop.i 999 ;;
}
-{ .mfb
- nop.m 0
- fnorm.s0 fNormArg = f8
-(p7) br.ret.spnt b0 // Exit for x=0 (for tanf)
+
+// 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 ;;
}
-;;
-{ .mmf
- ldfpd fA01, fA03 = [rCoeffA], 16
- ldfpd fB01, fB03 = [rCoeffB], 16
- fmerge.s f10 = f8, f8 // Save input for error call
+{ .mmi
+ ldfpd tan_P10,tan_P11 = [tan_AD],16
+ nop.m 999
+ and tan_exp = tan_GR_17_ones, tan_signexp ;;
}
-;;
-{ .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
+
+// 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 ;;
}
-;;
+
{ .mmb
- ldfpd fA05, fA07 = [rCoeffA], 16
- ldfpd fB05, fB07 = [rCoeffB], 16
-(p6) br.cond.spnt __libm_error_region // call error support if cotf(+-0)
+ ldfpd tan_P4,tan_P5 = [tan_AD],16
+ nop.m 999
+(p7) br.cond.spnt L(TAN_DBX) ;;
}
-;;
+
{ .mmi
- ldfpd fA09, fA11 = [rCoeffA], 16
- ldfpd fB09, fB11 = [rCoeffB], 16
- nop.i 0
+ ldfpd tan_Q2,tan_Q3 = [tan_ADQ],16
+ nop.m 999
+ nop.i 999 ;;
}
-;;
+
+
+// TAN_NFLOAT = Round_Int_Nearest(tan_W)
{ .mfi
- nop.m 0
- fma.s1 fShiftedN = fNormArg,fScRcpPiby2,fScRshf // x*2^70*(2/Pi)+ScRshf
- nop.i 0
+ ldfpd tan_P6,tan_P7 = [tan_AD],16
+ fms.s1 TAN_NFLOAT = TAN_W_2TO64_RSH,TAN_2TOM64,TAN_RSHF
+ nop.i 999 ;;
}
-;;
+
{ .mfi
- nop.m 0
- fms.s1 fN = fShiftedN, fScFctr, fRshf // N = Y*2^(-70) - Rshf
- nop.i 0
+ ldfd tan_Q10 = [tan_ADQ]
+ nop.f 999
+ nop.i 999 ;;
}
-;;
-.pred.rel "mutex", p10, p11
+
{ .mfi
- getf.sig rIntN = fShiftedN // get N as integer
-(p10) fnma.s1 fR = fN, fPiby2, fNormArg // R = x - (Pi/2)*N (tanf)
- nop.i 0
+ ldfpd tan_P0,tan_P1 = [tan_AD],16
+ nop.f 999
+ nop.i 999 ;;
}
+
+
{ .mfi
- nop.m 0
-(p11) fms.s1 fR = fN, fPiby2, fNormArg // R = (Pi/2)*N - x (cotf)
- nop.i 0
+ getf.sig tan_GR_n = TAN_W_2TO64_RSH
+ nop.f 999
+ nop.i 999 ;;
}
-;;
-{ .mmi
- ldfpd fA13, fA15 = [rCoeffA], 16
- ldfpd fA17, fA19 = [rCoeffB], 16
- 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 ;;
}
-;;
-Return_From_Huges:
-{ .mfi
- nop.m 0
- fma.s1 fRp2 = fR, fR, f0 // R^2
-(p11) add rIntN = 0x1, rIntN // N = N + 1 (cotf)
+
+// 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 0
- frcpa.s1 fY0, p0 = f1, fR // Y0 ~ 1/R
- tbit.z p8, p9 = rIntN, 0 // p8=1 if N is even
+ nop.m 999
+ fnma.s1 tan_r = TAN_NFLOAT, tan_Pi_by_2_lo, tan_r
+ nop.i 999 ;;
}
-;;
-// Below are mixed polynomial calculations (mixed for even and odd N)
+
{ .mfi
- nop.m 0
-(p9) fma.s1 fB03_01 = fRp2, fB03, fB01 // R^2*B3 + B1
- nop.i 0
+ nop.m 999
+ fma.s1 tan_rsq = tan_r, tan_r, f0
+ nop.i 999 ;;
}
+
+
{ .mfi
- nop.m 0
- fma.s1 fRp4 = fRp2, fRp2, f0 // R^4
- nop.i 0
+ nop.m 999
+(p9) frcpa.s1 tan_y0, p10 = f1,tan_r
+ nop.i 999 ;;
}
-;;
+
{ .mfi
- nop.m 0
-(p8) fma.s1 fA15_13 = fRp2, fA15, fA13 // R^2*A15 + A13
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v18 = tan_rsq, tan_P15, tan_P14
+ nop.i 999
}
{ .mfi
- nop.m 0
-(p8) fma.s1 fA19_17 = fRp2, fA19, fA17 // R^2*A19 + A17
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v4 = tan_rsq, tan_P1, tan_P0
+ nop.i 999 ;;
}
-;;
+
+
{ .mfi
- nop.m 0
-(p8) fma.s1 fA07_05 = fRp2, fA07, fA05 // R^2*A7 + A5
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v16 = tan_rsq, tan_P13, tan_P12
+ nop.i 999
}
{ .mfi
- nop.m 0
-(p8) fma.s1 fA11_09 = fRp2, fA11, fA09 // R^2*A11 + A9
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v17 = tan_rsq, tan_rsq, f0
+ nop.i 999 ;;
}
-;;
+
+
{ .mfi
- nop.m 0
-(p9) fma.s1 fB07_05 = fRp2, fB07, fB05 // R^2*B7 + B5
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v12 = tan_rsq, tan_P9, tan_P8
+ nop.i 999
}
{ .mfi
- nop.m 0
-(p9) fma.s1 fB11_09 = fRp2, fB11, fB09 // R^2*B11 + B9
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v13 = tan_rsq, tan_P11, tan_P10
+ nop.i 999 ;;
}
-;;
+
+
{ .mfi
- nop.m 0
-(p9) fnma.s1 fD = fR, fY0, f1 // D = 1 - R*Y0
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v7 = tan_rsq, tan_P5, tan_P4
+ nop.i 999
}
{ .mfi
- nop.m 0
-(p8) fma.s1 fA03_01 = fRp2, fA03, fA01 // R^2*A3 + A1
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v8 = tan_rsq, tan_P7, tan_P6
+ nop.i 999 ;;
}
-;;
+
+
{ .mfi
- nop.m 0
- fma.s1 fRp8 = fRp4, fRp4, f0 // R^8
- nop.i 0
+ nop.m 999
+(p9) fnma.s1 tan_d = tan_r, tan_y0, f1
+ nop.i 999
}
{ .mfi
- nop.m 0
- fma.s1 fRp5 = fR, fRp4, f0 // R^5
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v5 = tan_rsq, tan_P3, tan_P2
+ nop.i 999 ;;
}
-;;
+
+
{ .mfi
- nop.m 0
-(p8) fma.s1 fA11_05 = fRp4, fA11_09, fA07_05 // R^4*(R^2*A11 + A9) + ...
- nop.i 0
+ nop.m 999
+(p9) fma.s1 tan_z11 = tan_rsq, tan_Q9, tan_Q8
+ nop.i 999
}
{ .mfi
- nop.m 0
-(p8) fma.s1 fA19_13 = fRp4, fA19_17, fA15_13 // R^4*(R^2*A19 + A17) + ..
- nop.i 0
+ nop.m 999
+(p9) fma.s1 tan_z12 = tan_rsq, tan_rsq, f0
+ nop.i 999 ;;
}
-;;
+
{ .mfi
- nop.m 0
-(p9) fma.s1 fB11_05 = fRp4, fB11_09, fB07_05 // R^4*(R^2*B11 + B9) + ...
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v15 = tan_v17, tan_v18, tan_v16
+ nop.i 999
}
{ .mfi
- nop.m 0
-(p9) fma.s1 fRbyB03_01 = fR, fB03_01, f0 // R*(R^2*B3 + B1)
- nop.i 0
+ nop.m 999
+(p9) fma.s1 tan_z7 = tan_rsq, tan_Q5, tan_Q4
+ nop.i 999 ;;
}
-;;
+
{ .mfi
- nop.m 0
-(p9) fma.s1 fY1 = fY0, fD, fY0 // Y1 = Y0*D + Y0
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v11 = tan_v17, tan_v13, tan_v12
+ nop.i 999
}
{ .mfi
- nop.m 0
-(p9) fma.s1 fDp2 = fD, fD, f0 // D^2
- nop.i 0
+ nop.m 999
+(p9) fma.s1 tan_z8 = tan_rsq, tan_Q7, tan_Q6
+ nop.i 999 ;;
}
-;;
+
+
{ .mfi
- 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
+ nop.m 999
+(p8) fma.s1 tan_v14 = tan_v17, tan_v17, f0
+ nop.i 999
}
{ .mfi
- nop.m 0
-(p8) fma.d.s1 fRbyA03_01 = fR, fA03_01, f0 // R*(R^2*A3 + A1)
- nop.i 0
+ nop.m 999
+(p9) fma.s1 tan_z3 = tan_rsq, tan_Q1, tan_Q0
+ nop.i 999 ;;
}
-;;
+
+
+
{ .mfi
- nop.m 0
-(p9) fma.d.s1 fInvR = fY1, fDp2, fY1 // 1/R = Y1*D^2 + Y1
- nop.i 0
+ nop.m 999
+(p8) fma.s1 tan_v3 = tan_v17, tan_v5, tan_v4
+ nop.i 999
}
{ .mfi
- 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
+ nop.m 999
+(p8) fma.s1 tan_v6 = tan_v17, tan_v8, tan_v7
+ nop.i 999 ;;
}
-;;
-.pred.rel "mutex", p8, p9
+
+
{ .mfi
- 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
+ nop.m 999
+(p9) fma.s1 tan_y1 = tan_y0, tan_d, tan_y0
+ 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_dsq = tan_d, tan_d, f0
+ nop.i 999 ;;
}
-;;
-GLOBAL_IEEE754_END(tanf)
+{ .mfi
+ nop.m 999
+(p9) fma.s1 tan_z10 = tan_z12, tan_Q10, tan_z11
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p9) fma.s1 tan_z9 = tan_z12, tan_z12,f0
+ nop.i 999 ;;
+}
-LOCAL_LIBM_ENTRY(__libm_callout)
-Huge_Argument:
-.prologue
{ .mfi
- nop.m 0
- fmerge.s f9 = f0,f0
-.save ar.pfs,GR_SAVE_PFS
- mov GR_SAVE_PFS=ar.pfs
+ 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 ;;
+}
+
+
{ .mfi
- mov GR_SAVE_GP=gp
- nop.f 0
-.save b0, GR_SAVE_B0
- mov GR_SAVE_B0=b0
+ nop.m 999
+(p8) fma.s1 tan_v10 = tan_v14, tan_v15, tan_v11
+ nop.i 999 ;;
}
-.body
-{ .mmb
+
+
+{ .mfi
nop.m 999
+(p9) fma.s1 tan_y2 = tan_y1, tan_d, tan_y0
+ nop.i 999
+}
+{ .mfi
nop.m 999
-(p10) br.cond.sptk.many call_tanl ;;
+(p9) fma.s1 tan_d4 = tan_dsq, tan_dsq, tan_d
+ nop.i 999 ;;
}
-// Here if we should call cotl (p10=0, p11=1)
-{ .mmb
+
+{ .mfi
nop.m 999
+(p8) fma.s1 tan_v2 = tan_v14, tan_v6, tan_v3
+ nop.i 999
+}
+{ .mfi
nop.m 999
- br.call.sptk.many b0=__libm_cotl# ;;
+(p8) fma.s1 tan_v9 = tan_v14, tan_v14, f0
+ nop.i 999 ;;
}
+
{ .mfi
- mov gp = GR_SAVE_GP
- fnorm.s.s0 f8 = f8
- mov b0 = GR_SAVE_B0
+ nop.m 999
+(p9) fma.s1 tan_z2 = tan_z12, tan_z4, tan_z3
+ nop.i 999
}
-;;
-
-{ .mib
+{ .mfi
nop.m 999
- mov ar.pfs = GR_SAVE_PFS
- br.ret.sptk b0
-;;
+(p9) fma.s1 tan_z5 = tan_z9, tan_z10, tan_z6
+ nop.i 999 ;;
}
-// Here if we should call tanl (p10=1, p11=0)
-call_tanl:
-{ .mmb
+
+{ .mfi
nop.m 999
+(p9) fma.s1 tan_inv_r = tan_d4, tan_y2, tan_y0
+ nop.i 999
+}
+{ .mfi
nop.m 999
- br.call.sptk.many b0=__libm_tanl# ;;
+(p8) fma.s1 tan_rcube = tan_rsq, tan_r, f0
+ nop.i 999 ;;
}
+
+
{ .mfi
- mov gp = GR_SAVE_GP
- fnorm.s.s0 f8 = f8
- mov b0 = GR_SAVE_B0
+ nop.m 999
+(p8) fma.s1 tan_v1 = tan_v9, tan_v10, tan_v2
+ nop.i 999
}
-;;
-
-{ .mib
+{ .mfi
nop.m 999
- mov ar.pfs = GR_SAVE_PFS
- br.ret.sptk b0
-;;
+(p9) fma.s1 tan_z1 = tan_z9, tan_z5, tan_z2
+ nop.i 999 ;;
}
-LOCAL_LIBM_END(__libm_callout)
-.type __libm_tanl#,@function
-.global __libm_tanl#
-.type __libm_cotl#,@function
-.global __libm_cotl#
+
+{ .mfi
+ nop.m 999
+(p8) fma.s.s0 f8 = tan_v1, tan_rcube, tan_r
+ nop.i 999
+}
+{ .mfb
+ nop.m 999
+(p9) fms.s.s0 f8 = tan_r, tan_z1, tan_inv_r
+ br.ret.sptk b0 ;;
+}
+.endp tanf#
+ASM_SIZE_DIRECTIVE(tanf#)
-LOCAL_LIBM_ENTRY(__libm_error_region)
+.proc __libm_callout
+__libm_callout:
+L(TAN_DBX):
.prologue
-// (1)
{ .mfi
- add GR_Parameter_Y=-32,sp // Parameter 2 value
- nop.f 0
+ nop.m 0
+ fmerge.s f9 = f0,f0
.save ar.pfs,GR_SAVE_PFS
- mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
+ mov GR_SAVE_PFS=ar.pfs
}
-{ .mfi
-.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
+{ .mfi
+ mov GR_SAVE_GP=gp
+ nop.f 0
.save b0, GR_SAVE_B0
- mov GR_SAVE_B0=b0 // Save b0
-};;
+ mov GR_SAVE_B0=b0
+}
.body
-// (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
+{ .mfb
+ nop.m 999
+ nop.f 999
+ br.call.sptk.many b0=__libm_tan# ;;
}
-{ .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
-};;
+
+{ .mfi
+ mov gp = GR_SAVE_GP
+ fnorm.s f8 = f8
+ mov b0 = GR_SAVE_B0
+}
+;;
+
+
{ .mib
- mov gp = GR_SAVE_GP // Restore gp
- mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
- br.ret.sptk b0 // Return
-};;
+ nop.m 999
+ mov ar.pfs = GR_SAVE_PFS
+ br.ret.sptk b0
+;;
+}
-LOCAL_LIBM_END(__libm_error_region)
-.type __libm_error_support#,@function
-.global __libm_error_support#
+.endp __libm_callout
+ASM_SIZE_DIRECTIVE(__libm_callout)
+.type __libm_tan#,@function
+.global __libm_tan#