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authorUlrich Drepper <drepper@redhat.com>2005-01-06 11:32:24 +0000
committerUlrich Drepper <drepper@redhat.com>2005-01-06 11:32:24 +0000
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2004-12-29 Jakub Jelinek <jakub@redhat.com> * sysdeps/ia64/fpu/libm_support.h (__libm_error_support): Use libc_hidden_proto instead of HIDDEN_PROTO. * sysdeps/ia64/fpu/libm-symbols.h (HIDDEN_PROTO): Remove. (__libm_error_support): If ASSEMBLER and in libc, define to HIDDEN_JUMPTARGET(__libm_error_support). 2004-12-28 David Mosberger <davidm@hpl.hp.com> * sysdeps/ia64/fpu/Makefile (duplicated-routines): New macro. (sysdep_routines): Replace libm_ldexp{,f,l} and libm_scalbn{,f,l} with $(duplicated-routines). (libm-sysdep_routines): Likewise, but substitute "s_" prefix for "m_" prefix. 2004-12-27 David Mosberger <davidm@hpl.hp.com> * sysdeps/ia64/fpu/libm-symbols.h: Add include of <sysdep.h> and undefine "ret" macro. Add __libm_error_support hidden definitions. * sysdeps/ia64/fpu/e_lgamma_r.c: Remove CVS-id comment. Add missing portion of copyright statement. * sysdeps/ia64/fpu/e_lgammaf_r.c: Likewise. * sysdeps/ia64/fpu/e_lgammal_r.c: Likewise. * sysdeps/ia64/fpu/w_lgamma.c: Remove CVS-id comment. Add missing portion of copyright statement. (__ieee754_lgamma): Rename from lgamma(). Make lgamma() a weak alias. (__ieee754_gamma): Likewise. * sysdeps/ia64/fpu/w_lgammaf.c: Likewise. * sysdeps/ia64/fpu/w_lgammal.c: Likewise. 2004-12-09 H. J. Lu <hjl@lucon.org> * sysdeps/ia64/fpu/s_nextafterl.c: Remove. * sysdeps/ia64/fpu/s_nexttoward.c: Likewise. * sysdeps/ia64/fpu/s_nexttowardf.c: Likewise. * sysdeps/ia64/fpu/e_atan2l.S: Remove (duplicate of e_atan2l.c). * sysdeps/ia64/fpu/e_expl.S: Likewise. * sysdeps/ia64/fpu/e_logl.c: Remove (conflicts with e_logl.S). 2004-11-18 David Mosberger <davidm@hpl.hp.com> * sysdeps/ia64/fpu/README: New file. * sysdeps/ia64/fpu/gen_import_file_list: New file. * sysdeps/ia64/fpu/import_check: Likewise. * sysdeps/ia64/fpu/import_diffs: Likewise. * sysdeps/ia64/fpu/import_file.awk: Likewise. * sysdeps/ia64/fpu/import_intel_libm: Likewise. * sysdeps/ia64/fpu/libm-symbols.h: Likewise. * sysdeps/ia64/fpu/e_acos.S: Update from Intel libm v2.1+. * sysdeps/ia64/fpu/e_acosf.S: Likewise. * sysdeps/ia64/fpu/e_acosl.S: Likewise. * sysdeps/ia64/fpu/e_asin.S: Likewise. * sysdeps/ia64/fpu/e_asinf.S: Likewise. * sysdeps/ia64/fpu/e_asinl.S: Likewise. * sysdeps/ia64/fpu/e_atan2.S: Likewise. * sysdeps/ia64/fpu/e_atan2f.S: Likewise. * sysdeps/ia64/fpu/e_cosh.S: Likewise. * sysdeps/ia64/fpu/e_coshf.S: Likewise. * sysdeps/ia64/fpu/e_coshl.S: Likewise. * sysdeps/ia64/fpu/e_exp.S: Likewise. * sysdeps/ia64/fpu/e_expf.S: Likewise. * sysdeps/ia64/fpu/e_fmod.S: Likewise. * sysdeps/ia64/fpu/e_fmodf.S: Likewise. * sysdeps/ia64/fpu/e_fmodl.S: Likewise. * sysdeps/ia64/fpu/e_hypot.S: Likewise. * sysdeps/ia64/fpu/e_hypotf.S: Likewise. * sysdeps/ia64/fpu/e_hypotl.S: Likewise. * sysdeps/ia64/fpu/e_log.S: Likewise. * sysdeps/ia64/fpu/e_log2.S: Likewise. * sysdeps/ia64/fpu/e_log2f.S: Likewise. * sysdeps/ia64/fpu/e_log2l.S: Likewise. * sysdeps/ia64/fpu/e_logf.S: Likewise. * sysdeps/ia64/fpu/e_pow.S: Likewise. * sysdeps/ia64/fpu/e_powf.S: Likewise. * sysdeps/ia64/fpu/e_powl.S: Likewise. * sysdeps/ia64/fpu/e_remainder.S: Likewise. * sysdeps/ia64/fpu/e_remainderf.S: Likewise. * sysdeps/ia64/fpu/e_remainderl.S: Likewise. * sysdeps/ia64/fpu/e_scalb.S: Likewise. * sysdeps/ia64/fpu/e_scalbf.S: Likewise. * sysdeps/ia64/fpu/e_scalbl.S: Likewise. * sysdeps/ia64/fpu/e_sinh.S: Likewise. * sysdeps/ia64/fpu/e_sinhf.S: Likewise. * sysdeps/ia64/fpu/e_sinhl.S: Likewise. * sysdeps/ia64/fpu/e_sqrt.S: Likewise. * sysdeps/ia64/fpu/e_sqrtf.S: Likewise. * sysdeps/ia64/fpu/e_sqrtl.S: Likewise. * sysdeps/ia64/fpu/libm_error.c: Likewise. * sysdeps/ia64/fpu/libm_reduce.c: Likewise. * sysdeps/ia64/fpu/libm_support.h: Likewise. * sysdeps/ia64/fpu/s_atan.S: Likewise. * sysdeps/ia64/fpu/s_atanf.S: Likewise. * sysdeps/ia64/fpu/s_atanl.S: Likewise. * sysdeps/ia64/fpu/s_cbrt.S: Likewise. * sysdeps/ia64/fpu/s_cbrtf.S: Likewise. * sysdeps/ia64/fpu/s_cbrtl.S: Likewise. * sysdeps/ia64/fpu/s_ceil.S: Likewise. * sysdeps/ia64/fpu/s_ceilf.S: Likewise. * sysdeps/ia64/fpu/s_ceill.S: Likewise. * sysdeps/ia64/fpu/s_cos.S: Likewise. * sysdeps/ia64/fpu/s_cosf.S: Likewise. * sysdeps/ia64/fpu/s_cosl.S: Likewise. * sysdeps/ia64/fpu/s_expm1.S: Likewise. * sysdeps/ia64/fpu/s_expm1f.S: Likewise. * sysdeps/ia64/fpu/s_expm1l.S: Likewise. * sysdeps/ia64/fpu/s_fabs.S: Likewise. * sysdeps/ia64/fpu/s_fabsf.S: Likewise. * sysdeps/ia64/fpu/s_fabsl.S: Likewise. * sysdeps/ia64/fpu/s_floor.S: Likewise. * sysdeps/ia64/fpu/s_floorf.S: Likewise. * sysdeps/ia64/fpu/s_floorl.S: Likewise. * sysdeps/ia64/fpu/s_frexp.c: Likewise. * sysdeps/ia64/fpu/s_frexpf.c: Likewise. * sysdeps/ia64/fpu/s_frexpl.c: Likewise. * sysdeps/ia64/fpu/s_ilogb.S: Likewise. * sysdeps/ia64/fpu/s_ilogbf.S: Likewise. * sysdeps/ia64/fpu/s_ilogbl.S: Likewise. * sysdeps/ia64/fpu/s_log1p.S: Likewise. * sysdeps/ia64/fpu/s_log1pf.S: Likewise. * sysdeps/ia64/fpu/s_log1pl.S: Likewise. * sysdeps/ia64/fpu/s_logb.S: Likewise. * sysdeps/ia64/fpu/s_logbf.S: Likewise. * sysdeps/ia64/fpu/s_logbl.S: Likewise. * sysdeps/ia64/fpu/s_modf.S: Likewise. * sysdeps/ia64/fpu/s_modff.S: Likewise. * sysdeps/ia64/fpu/s_modfl.S: Likewise. * sysdeps/ia64/fpu/s_nearbyint.S: Likewise. * sysdeps/ia64/fpu/s_nearbyintf.S: Likewise. * sysdeps/ia64/fpu/s_nearbyintl.S: Likewise. * sysdeps/ia64/fpu/s_rint.S: Likewise. * sysdeps/ia64/fpu/s_rintf.S: Likewise. * sysdeps/ia64/fpu/s_rintl.S: Likewise. * sysdeps/ia64/fpu/s_round.S: Likewise. * sysdeps/ia64/fpu/s_roundf.S: Likewise. * sysdeps/ia64/fpu/s_roundl.S: Likewise. * sysdeps/ia64/fpu/s_significand.S: Likewise. * sysdeps/ia64/fpu/s_significandf.S: Likewise. * sysdeps/ia64/fpu/s_significandl.S: Likewise. * sysdeps/ia64/fpu/s_tan.S: Likewise. * sysdeps/ia64/fpu/s_tanf.S: Likewise. * sysdeps/ia64/fpu/s_tanl.S: Likewise. * sysdeps/ia64/fpu/s_trunc.S: Likewise. * sysdeps/ia64/fpu/s_truncf.S: Likewise. * sysdeps/ia64/fpu/s_truncl.S: Likewise. * sysdeps/ia64/fpu/e_acosh.S: New file from Intel libm v2.1+. * sysdeps/ia64/fpu/e_acoshf.S: Likewise. * sysdeps/ia64/fpu/e_acoshl.S: Likewise. * sysdeps/ia64/fpu/e_atanh.S: Likewise. * sysdeps/ia64/fpu/e_atanhf.S: Likewise. * sysdeps/ia64/fpu/e_atanhl.S: Likewise. * sysdeps/ia64/fpu/e_exp10.S: Likewise. * sysdeps/ia64/fpu/e_exp10f.S: Likewise. * sysdeps/ia64/fpu/e_exp10l.S: Likewise. * sysdeps/ia64/fpu/e_exp2.S: Likewise. * sysdeps/ia64/fpu/e_exp2f.S: Likewise. * sysdeps/ia64/fpu/e_exp2l.S: Likewise. * sysdeps/ia64/fpu/e_lgamma_r.S: Likewise. * sysdeps/ia64/fpu/e_lgammaf_r.S: Likewise. * sysdeps/ia64/fpu/e_lgammal_r.S: Likewise. * sysdeps/ia64/fpu/e_logl.S: Likewise. * sysdeps/ia64/fpu/libm_frexp.S: Likewise. * sysdeps/ia64/fpu/libm_frexpf.S: Likewise. * sysdeps/ia64/fpu/libm_frexpl.S: Likewise. * sysdeps/ia64/fpu/s_libm_ldexp.S: Likewise. * sysdeps/ia64/fpu/s_libm_ldexpf.S: Likewise. * sysdeps/ia64/fpu/s_libm_ldexpl.S: Likewise. * sysdeps/ia64/fpu/s_libm_scalbn.S: Likewise. * sysdeps/ia64/fpu/s_libm_scalbnf.S: Likewise. * sysdeps/ia64/fpu/s_libm_scalbnl.S: Likewise. * sysdeps/ia64/fpu/libm_lgamma.S: Likewise. * sysdeps/ia64/fpu/libm_lgammaf.S: Likewise. * sysdeps/ia64/fpu/libm_lgammal.S: Likewise. * sysdeps/ia64/fpu/libm_sincos.S: Likewise. * sysdeps/ia64/fpu/libm_sincos_large.S: Likewise. * sysdeps/ia64/fpu/libm_sincosf.S: Likewise. * sysdeps/ia64/fpu/libm_sincosl.S: Likewise. * sysdeps/ia64/fpu/libm_scalblnf.S: Likewise. * sysdeps/ia64/fpu/s_asinh.S: Likewise. * sysdeps/ia64/fpu/s_asinhf.S: Likewise. * sysdeps/ia64/fpu/s_asinhl.S: Likewise. * sysdeps/ia64/fpu/s_erf.S: Likewise. * sysdeps/ia64/fpu/s_erfc.S: Likewise. * sysdeps/ia64/fpu/s_erfcf.S: Likewise. * sysdeps/ia64/fpu/s_erfcl.S: Likewise. * sysdeps/ia64/fpu/s_erff.S: Likewise. * sysdeps/ia64/fpu/s_erfl.S: Likewise. * sysdeps/ia64/fpu/s_fdim.S: Likewise. * sysdeps/ia64/fpu/s_fdimf.S: Likewise. * sysdeps/ia64/fpu/s_fdiml.S: Likewise. * sysdeps/ia64/fpu/s_fma.S: Likewise. * sysdeps/ia64/fpu/s_fmaf.S: Likewise. * sysdeps/ia64/fpu/s_fmal.S: Likewise. * sysdeps/ia64/fpu/s_fmax.S: Likewise. * sysdeps/ia64/fpu/s_fmaxf.S: Likewise. * sysdeps/ia64/fpu/s_fmaxl.S: Likewise. * sysdeps/ia64/fpu/s_ldexp.c: Likewise. * sysdeps/ia64/fpu/s_ldexpf.c: Likewise. * sysdeps/ia64/fpu/s_ldexpl.c: Likewise. * sysdeps/ia64/fpu/s_nextafter.S: Likewise. * sysdeps/ia64/fpu/s_nextafterf.S: Likewise. * sysdeps/ia64/fpu/s_nextafterl.S: Likewise. * sysdeps/ia64/fpu/s_nexttoward.S: Likewise. * sysdeps/ia64/fpu/s_nexttowardf.S: Likewise. * sysdeps/ia64/fpu/s_nexttowardl.S: Likewise. * sysdeps/ia64/fpu/s_tanh.S: Likewise. * sysdeps/ia64/fpu/s_tanhf.S: Likewise. * sysdeps/ia64/fpu/s_tanhl.S: Likewise. * sysdeps/ia64/fpu/s_scalblnf.c: Likewise. * sysdeps/ia64/fpu/w_lgamma.c: Likewise. * sysdeps/ia64/fpu/w_lgammaf.c: Likewise. * sysdeps/ia64/fpu/w_lgammal.c: Likewise. * sysdeps/ia64/fpu/w_tgamma.S: Likewise. * sysdeps/ia64/fpu/w_tgammaf.S: Likewise. * sysdeps/ia64/fpu/w_tgammal.S: Likewise. * sysdeps/ia64/fpu/e_gamma_r.c: New empty dummy-file. * sysdeps/ia64/fpu/e_gammaf_r.c: Likewise. * sysdeps/ia64/fpu/e_gammal_r.c: Likewise. * sysdeps/ia64/fpu/w_acosh.c: Likewise. * sysdeps/ia64/fpu/w_acoshf.c: Likewise. * sysdeps/ia64/fpu/w_acoshl.c: Likewise. * sysdeps/ia64/fpu/w_atanh.c: Likewise. * sysdeps/ia64/fpu/w_atanhf.c: Likewise. * sysdeps/ia64/fpu/w_atanhl.c: Likewise. * sysdeps/ia64/fpu/w_exp10.c: Likewise. * sysdeps/ia64/fpu/w_exp10f.c: Likewise. * sysdeps/ia64/fpu/w_exp10l.c: Likewise. * sysdeps/ia64/fpu/w_exp2.c: Likewise. * sysdeps/ia64/fpu/w_exp2f.c: Likewise. * sysdeps/ia64/fpu/w_exp2l.c: Likewise. * sysdeps/ia64/fpu/w_expl.c: Likewise. * sysdeps/ia64/fpu/e_expl.S: Likewise. * sysdeps/ia64/fpu/w_lgamma_r.c: Likewise. * sysdeps/ia64/fpu/w_lgammaf_r.c: Likewise. * sysdeps/ia64/fpu/w_lgammal_r.c: Likewise. * sysdeps/ia64/fpu/w_log2.c: Likewise. * sysdeps/ia64/fpu/w_log2f.c: Likewise. * sysdeps/ia64/fpu/w_log2l.c: Likewise. * sysdeps/ia64/fpu/w_sinh.c: Likewise. * sysdeps/ia64/fpu/w_sinhf.c: Likewise. * sysdeps/ia64/fpu/w_sinhl.c: Likewise. * sysdeps/ia64/fpu/libm_atan2_reg.S: Remove. * sysdeps/ia64/fpu/s_ldexp.S: Likewise. * sysdeps/ia64/fpu/s_ldexpf.S: Likewise. * sysdeps/ia64/fpu/s_ldexpl.S: Likewise. * sysdeps/ia64/fpu/s_scalbn.S: Likewise. * sysdeps/ia64/fpu/s_scalbnf.S: Likewise. * sysdeps/ia64/fpu/s_scalbnl.S: Likewise. * sysdeps/ia64/fpu/s_sincos.c: Make it an empty dummy-file. * sysdeps/ia64/fpu/s_sincosf.c: Likewise. * sysdeps/ia64/fpu/s_sincosl.c: Likewise. * sysdeps/ia64/fpu/e_atan2l.S: Add "Not needed" comment. * sysdeps/ia64/fpu/s_copysign.S: Add __libm_copysign{,f,l} alias for use by libm_error.c * sysdeps/ia64/fpu/Makefile (libm-sysdep_routines): Remove libm_atan2_reg, libm_tan, libm_frexp4{f,l}. Mention s_erfc{,f,l}, libm_frexp{,f,l}, libm_ldexp{,f,l}, libm_sincos{,f,l}, libm_sincos_large, libm_lgamma{,f,l}, libm_scalbn{,f,l}, libm_scalblnf. (sysdep_routines): Remove libm_frexp4{,f,l}. Mention libm_frexp{,f,l}, libm_ldexp{,f,l}, and libm_scalbn{,f,l}. (sysdep-CPPFLAGS): Add -include libm-symbols.h, -D__POSIX__, _D_LIB_VERSIONIMF=_LIB_VERSION, -DSIZE_LONG_INT_64, and -DSIZE_LONG_LONG_INT_64.
Diffstat (limited to 'sysdeps/ia64/fpu/s_tanl.S')
-rw-r--r--sysdeps/ia64/fpu/s_tanl.S3028
1 files changed, 1601 insertions, 1427 deletions
diff --git a/sysdeps/ia64/fpu/s_tanl.S b/sysdeps/ia64/fpu/s_tanl.S
index e13e6c6cbd..345a059c5f 100644
--- a/sysdeps/ia64/fpu/s_tanl.S
+++ b/sysdeps/ia64/fpu/s_tanl.S
@@ -1,10 +1,10 @@
-.file "tanl.s"
+.file "tancotl.s"
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2003, 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
@@ -35,50 +35,77 @@
//
// 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:
//
-// 2/02/2000 (hand-optimized)
-// 4/04/00 Unwind support added
+// 02/02/00 (hand-optimized)
+// 04/04/00 Unwind support added
// 12/28/00 Fixed false invalid flags
+// 02/06/02 Improved speed
+// 05/07/02 Changed interface to __libm_pi_by_2_reduce
+// 05/30/02 Added cotl
+// 02/10/03 Reordered header: .section, .global, .proc, .align;
+// used data8 for long double table values
+// 05/15/03 Reformatted data tables
//
-// *********************************************************************
+//*********************************************************************
//
-// Function: tanl(x) = tangent(x), for double-extended precision x values
+// Functions: tanl(x) = tangent(x), for double-extended precision x values
+// cotl(x) = cotangent(x), for double-extended precision x values
//
-// *********************************************************************
+//*********************************************************************
//
// Resources Used:
//
// Floating-Point Registers: f8 (Input and Return Value)
// f9-f15
-// f32-f112
+// f32-f121
//
// General Purpose Registers:
-// r32-r48
-// r49-r50 (Used to pass arguments to pi_by_2 reduce routine)
+// r14-r26,r32-r57
//
// Predicate Registers: p6-p15
//
-// *********************************************************************
+//*********************************************************************
//
-// IEEE Special Conditions:
+// IEEE Special Conditions for tanl:
//
// Denormal fault raised on denormal inputs
// Overflow exceptions do not occur
-// Underflow exceptions raised when appropriate for tan
+// Underflow exceptions raised when appropriate for tan
// (No specialized error handling for this routine)
// Inexact raised when appropriate by algorithm
//
-// tan(SNaN) = QNaN
-// tan(QNaN) = QNaN
-// tan(inf) = QNaN
-// tan(+/-0) = +/-0
+// tanl(SNaN) = QNaN
+// tanl(QNaN) = QNaN
+// tanl(inf) = QNaN
+// tanl(+/-0) = +/-0
+//
+//*********************************************************************
+//
+// IEEE Special Conditions for cotl:
+//
+// Denormal fault raised on denormal inputs
+// Overflow exceptions occur at zero and near zero
+// Underflow exceptions do not occur
+// Inexact raised when appropriate by algorithm
+//
+// cotl(SNaN) = QNaN
+// cotl(QNaN) = QNaN
+// cotl(inf) = QNaN
+// cotl(+/-0) = +/-Inf and error handling is called
+//
+//*********************************************************************
//
-// *********************************************************************
+// Below are mathematical and algorithmic descriptions for tanl.
+// For cotl we use next identity cot(x) = -tan(x + Pi/2).
+// So, to compute cot(x) we just need to increment N (N = N + 1)
+// and invert sign of the computed result.
+//
+//*********************************************************************
//
// Mathematical Description
//
@@ -106,13 +133,13 @@
// -------
//
// tan(r + c) = r + c + r^3/3 ...accurately
-// -cot(r + c) = -1/(r+c) + r/3 ...accurately
+// -cot(r + c) = -1/(r+c) + r/3 ...accurately
//
// Case 4:
// -------
//
// tan(r + c) = r + c + r^3/3 + 2r^5/15 ...accurately
-// -cot(r + c) = -1/(r+c) + r/3 + r^3/45 ...accurately
+// -cot(r + c) = -1/(r+c) + r/3 + r^3/45 ...accurately
//
//
// The only cases left are Cases 1 and 3 of the argument reduction
@@ -143,13 +170,13 @@
// Since Arg = N pi/4 + r + c accurately, we have
//
// tan(Arg) = tan(r+c) for N even,
-// = -cot(r+c) otherwise.
+// = -cot(r+c) otherwise.
//
// Here for this case, both tan(r) and -cot(r) can be approximated
// by simple polynomials:
//
// tan(r) = r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19
-// -cot(r) = -1/r + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13
+// -cot(r) = -1/r + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13
//
// accurately. Since |r| is relatively small, tan(r+c) and
// -cot(r+c) can be accurately approximated by replacing r with
@@ -178,21 +205,21 @@
// The required calculation is either
//
// tan(r + c) = tan(r) + correction, or
-// -cot(r + c) = -cot(r) + correction.
+// -cot(r + c) = -cot(r) + correction.
//
// Specifically,
//
// tan(r + c) = tan(r) + c tan'(r) + O(c^2)
-// = tan(r) + c sec^2(r) + O(c^2)
-// = tan(r) + c SEC_sq ...accurately
+// = tan(r) + c sec^2(r) + O(c^2)
+// = tan(r) + c SEC_sq ...accurately
// as long as SEC_sq approximates sec^2(r)
// to, say, 5 bits or so.
//
// Similarly,
//
-// -cot(r + c) = -cot(r) - c cot'(r) + O(c^2)
-// = -cot(r) + c csc^2(r) + O(c^2)
-// = -cot(r) + c CSC_sq ...accurately
+// -cot(r + c) = -cot(r) - c cot'(r) + O(c^2)
+// = -cot(r) + c csc^2(r) + O(c^2)
+// = -cot(r) + c CSC_sq ...accurately
// as long as CSC_sq approximates csc^2(r)
// to, say, 5 bits or so.
//
@@ -208,14 +235,14 @@
// where
//
// B = 2^k * 1.b_1 b_2 ... b_5 1
-// x = |r| - B
+// x = |r| - B
//
// Now,
// tan(B) + tan(x)
// tan( B + x ) = ------------------------
// 1 - tan(B)*tan(x)
//
-// / \
+// / \
// | tan(B) + tan(x) |
// = tan(B) + | ------------------------ - tan(B) |
@@ -248,7 +275,7 @@
// cot( B + x ) = ------------------------
// tan(B) + tan(x)
//
-// / \
+// / \
// | 1 - tan(B)*tan(x) |
// = cot(B) + | ----------------------- - cot(B) |
@@ -273,7 +300,7 @@
// Arg = N * pi/2 + r + c ...accurately
//
// tan(Arg) = tan(r) + correction if N is even;
-// = -cot(r) + correction otherwise.
+// = -cot(r) + correction otherwise.
//
// For Cases 2 and 4,
//
@@ -292,8 +319,8 @@
// tan(Arg) = r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19
// + c*(1 + r^2) N even
//
-// = -1/(r+c) + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13
-// + Q1_1*c N odd
+// = -1/(r+c) + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13
+// + Q1_1*c N odd
//
// Case normal_r: 2^(-2) <= |r| <= pi/4
//
@@ -304,15 +331,15 @@
//
// tan(Arg) = tan(r) + c*sec^2(r)
// = tan( sgn_r * (B+x) ) + c * sec^2(|r|)
-// = sgn_r * ( tan(B+x) + sgn_r*c*sec^2(|r|) )
-// = sgn_r * ( tan(B+x) + sgn_r*c*sec^2(B) )
+// = sgn_r * ( tan(B+x) + sgn_r*c*sec^2(|r|) )
+// = sgn_r * ( tan(B+x) + sgn_r*c*sec^2(B) )
//
// since B approximates |r| to 2^(-6) in relative accuracy.
//
// / (1/[sin(B)*cos(B)]) * tan(x)
// tan(Arg) = sgn_r * | tan(B) + --------------------------------
// \ cot(B) - tan(x)
-// \
+// \
// + CORR |
// /
@@ -324,15 +351,15 @@
//
// tan(Arg) = -cot(r) + c*csc^2(r)
// = -cot( sgn_r * (B+x) ) + c * csc^2(|r|)
-// = sgn_r * ( -cot(B+x) + sgn_r*c*csc^2(|r|) )
-// = sgn_r * ( -cot(B+x) + sgn_r*c*csc^2(B) )
+// = sgn_r * ( -cot(B+x) + sgn_r*c*csc^2(|r|) )
+// = sgn_r * ( -cot(B+x) + sgn_r*c*csc^2(B) )
//
// since B approximates |r| to 2^(-6) in relative accuracy.
//
// / (1/[sin(B)*cos(B)]) * tan(x)
// tan(Arg) = sgn_r * | -cot(B) + --------------------------------
// \ tan(B) + tan(x)
-// \
+// \
// + CORR |
// /
@@ -356,8 +383,8 @@
// For N even,
//
// rsq := r * r
-// Result := c + r * rsq * P1_1
-// Result := r + Result ...in user-defined rounding
+// Poly := c + r * rsq * P1_1
+// Result := r + Poly ...in user-defined rounding
//
// For N odd,
// S_hi := -frcpa(r) ...8 bits
@@ -375,8 +402,8 @@
// For N even,
//
// rsq := r * r
-// Result := c + r * rsq * (P1_1 + rsq * P1_2)
-// Result := r + Result ...in user-defined rounding
+// Poly := c + r * rsq * (P1_1 + rsq * P1_2)
+// Result := r + Poly ...in user-defined rounding
//
// For N odd,
// S_hi := -frcpa(r) ...8 bits
@@ -414,8 +441,8 @@
// Poly2 := P1_4 + rsq*(P1_5 + rsq*(P1_6 + ... rsq*P1_9))
// CORR := c * ( 1 + rsq )
// Poly := Poly1 + r_to_the_8*Poly2
-// Result := r*Poly + CORR
-// Result := r + Result ...in user-defined rounding
+// Poly := r*Poly + CORR
+// Result := r + Poly ...in user-defined rounding
// ...note that Poly1 and r_to_the_8 can be computed in parallel
// ...with Poly2 (Poly1 is intentionally set to be much
// ...shorter than Poly2 so that r_to_the_8 and CORR can be hidden)
@@ -434,8 +461,8 @@
// rsq := r*r
// P := Q1_1 + rsq*(Q1_2 + rsq*(Q1_3 + ... + rsq*Q1_7))
//
-// Result := r*P + S_lo
-// Result := S_hi + Result ...in user-defined rounding
+// Poly := r*P + S_lo
+// Result := S_hi + Poly ...in user-defined rounding
//
//
// Algorithm for the case of normal_r
@@ -454,7 +481,7 @@
// / (1/[sin(B)*cos(B)]) * tan(x)
// sgn_r * | tan(B) + -------------------------------- +
// \ cot(B) - tan(x)
-// \
+// \
// CORR |
// /
@@ -463,7 +490,7 @@
// calculated beforehand and stored in a table. Specifically,
// the table values are
//
-// tan(B) as T_hi + T_lo;
+// tan(B) as T_hi + T_lo;
// cot(B) as C_hi + C_lo;
// 1/[sin(B)*cos(B)] as SC_inv
//
@@ -559,7 +586,7 @@
// / (1/[sin(B)*cos(B)]) * tan(x)
// sgn_r * | -cot(B) + -------------------------------- +
// \ tan(B) + tan(x)
-// \
+// \
// CORR |
// /
@@ -568,7 +595,7 @@
// calculated beforehand and stored in a table. Specifically,
// the table values are
//
-// tan(B) as T_hi + T_lo;
+// tan(B) as T_hi + T_lo;
// cot(B) as C_hi + C_lo;
// 1/[sin(B)*cos(B)] as SC_inv
//
@@ -675,254 +702,382 @@
//
//
-#include "libm_support.h"
-
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
-.align 128
-
-TANL_BASE_CONSTANTS:
-ASM_TYPE_DIRECTIVE(TANL_BASE_CONSTANTS,@object)
-data4 0x4B800000, 0xCB800000, 0x38800000, 0xB8800000 // two**24, -two**24
- // two**-14, -two**-14
-data4 0x4E44152A, 0xA2F9836E, 0x00003FFE, 0x00000000 // two_by_pi
-data4 0xCE81B9F1, 0xC84D32B0, 0x00004016, 0x00000000 // P_0
-data4 0x2168C235, 0xC90FDAA2, 0x00003FFF, 0x00000000 // P_1
-data4 0xFC8F8CBB, 0xECE675D1, 0x0000BFBD, 0x00000000 // P_2
-data4 0xACC19C60, 0xB7ED8FBB, 0x0000BF7C, 0x00000000 // P_3
-data4 0x5F000000, 0xDF000000, 0x00000000, 0x00000000 // two_to_63, -two_to_63
-data4 0x6EC6B45A, 0xA397E504, 0x00003FE7, 0x00000000 // Inv_P_0
-data4 0xDBD171A1, 0x8D848E89, 0x0000BFBF, 0x00000000 // d_1
-data4 0x18A66F8E, 0xD5394C36, 0x0000BF7C, 0x00000000 // d_2
-data4 0x2168C234, 0xC90FDAA2, 0x00003FFE, 0x00000000 // PI_BY_4
-data4 0x2168C234, 0xC90FDAA2, 0x0000BFFE, 0x00000000 // MPI_BY_4
-data4 0x3E800000, 0xBE800000, 0x00000000, 0x00000000 // two**-2, -two**-2
-data4 0x2F000000, 0xAF000000, 0x00000000, 0x00000000 // two**-33, -two**-33
-data4 0xAAAAAABD, 0xAAAAAAAA, 0x00003FFD, 0x00000000 // P1_1
-data4 0x88882E6A, 0x88888888, 0x00003FFC, 0x00000000 // P1_2
-data4 0x0F0177B6, 0xDD0DD0DD, 0x00003FFA, 0x00000000 // P1_3
-data4 0x646B8C6D, 0xB327A440, 0x00003FF9, 0x00000000 // P1_4
-data4 0x1D5F7D20, 0x91371B25, 0x00003FF8, 0x00000000 // P1_5
-data4 0x61C67914, 0xEB69A5F1, 0x00003FF6, 0x00000000 // P1_6
-data4 0x019318D2, 0xBEDD37BE, 0x00003FF5, 0x00000000 // P1_7
-data4 0x3C794015, 0x9979B146, 0x00003FF4, 0x00000000 // P1_8
-data4 0x8C6EB58A, 0x8EBD21A3, 0x00003FF3, 0x00000000 // P1_9
-data4 0xAAAAAAB4, 0xAAAAAAAA, 0x00003FFD, 0x00000000 // Q1_1
-data4 0x0B5FC93E, 0xB60B60B6, 0x00003FF9, 0x00000000 // Q1_2
-data4 0x0C9BBFBF, 0x8AB355E0, 0x00003FF6, 0x00000000 // Q1_3
-data4 0xCBEE3D4C, 0xDDEBBC89, 0x00003FF2, 0x00000000 // Q1_4
-data4 0x5F80BBB6, 0xB3548A68, 0x00003FEF, 0x00000000 // Q1_5
-data4 0x4CED5BF1, 0x91362560, 0x00003FEC, 0x00000000 // Q1_6
-data4 0x8EE92A83, 0xF189D95A, 0x00003FE8, 0x00000000 // Q1_7
-data4 0xAAAB362F, 0xAAAAAAAA, 0x00003FFD, 0x00000000 // P2_1
-data4 0xE97A6097, 0x88888886, 0x00003FFC, 0x00000000 // P2_2
-data4 0x25E716A1, 0xDD108EE0, 0x00003FFA, 0x00000000 // P2_3
+RODATA
+.align 16
+
+LOCAL_OBJECT_START(TANL_BASE_CONSTANTS)
+
+tanl_table_1:
+data8 0xA2F9836E4E44152A, 0x00003FFE // two_by_pi
+data8 0xC84D32B0CE81B9F1, 0x00004016 // P_0
+data8 0xC90FDAA22168C235, 0x00003FFF // P_1
+data8 0xECE675D1FC8F8CBB, 0x0000BFBD // P_2
+data8 0xB7ED8FBBACC19C60, 0x0000BF7C // P_3
+LOCAL_OBJECT_END(TANL_BASE_CONSTANTS)
+
+LOCAL_OBJECT_START(tanl_table_2)
+data8 0xC90FDAA22168C234, 0x00003FFE // PI_BY_4
+data8 0xA397E5046EC6B45A, 0x00003FE7 // Inv_P_0
+data8 0x8D848E89DBD171A1, 0x0000BFBF // d_1
+data8 0xD5394C3618A66F8E, 0x0000BF7C // d_2
+data4 0x3E800000 // two**-2
+data4 0xBE800000 // -two**-2
+data4 0x00000000 // pad
+data4 0x00000000 // pad
+LOCAL_OBJECT_END(tanl_table_2)
+
+LOCAL_OBJECT_START(tanl_table_p1)
+data8 0xAAAAAAAAAAAAAABD, 0x00003FFD // P1_1
+data8 0x8888888888882E6A, 0x00003FFC // P1_2
+data8 0xDD0DD0DD0F0177B6, 0x00003FFA // P1_3
+data8 0xB327A440646B8C6D, 0x00003FF9 // P1_4
+data8 0x91371B251D5F7D20, 0x00003FF8 // P1_5
+data8 0xEB69A5F161C67914, 0x00003FF6 // P1_6
+data8 0xBEDD37BE019318D2, 0x00003FF5 // P1_7
+data8 0x9979B1463C794015, 0x00003FF4 // P1_8
+data8 0x8EBD21A38C6EB58A, 0x00003FF3 // P1_9
+LOCAL_OBJECT_END(tanl_table_p1)
+
+LOCAL_OBJECT_START(tanl_table_q1)
+data8 0xAAAAAAAAAAAAAAB4, 0x00003FFD // Q1_1
+data8 0xB60B60B60B5FC93E, 0x00003FF9 // Q1_2
+data8 0x8AB355E00C9BBFBF, 0x00003FF6 // Q1_3
+data8 0xDDEBBC89CBEE3D4C, 0x00003FF2 // Q1_4
+data8 0xB3548A685F80BBB6, 0x00003FEF // Q1_5
+data8 0x913625604CED5BF1, 0x00003FEC // Q1_6
+data8 0xF189D95A8EE92A83, 0x00003FE8 // Q1_7
+LOCAL_OBJECT_END(tanl_table_q1)
+
+LOCAL_OBJECT_START(tanl_table_p2)
+data8 0xAAAAAAAAAAAB362F, 0x00003FFD // P2_1
+data8 0x88888886E97A6097, 0x00003FFC // P2_2
+data8 0xDD108EE025E716A1, 0x00003FFA // P2_3
+LOCAL_OBJECT_END(tanl_table_p2)
+
+LOCAL_OBJECT_START(tanl_table_tm2)
//
// Entries T_hi double-precision memory format
// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64)
// Entries T_lo single-precision memory format
// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64)
//
-data4 0x62400794, 0x3FD09BC3, 0x23A05C32, 0x00000000
-data4 0xDFFBC074, 0x3FD124A9, 0x240078B2, 0x00000000
-data4 0x5BD4920F, 0x3FD1AE23, 0x23826B8E, 0x00000000
-data4 0x15E2701D, 0x3FD23835, 0x22D31154, 0x00000000
-data4 0x63739C2D, 0x3FD2C2E4, 0x2265C9E2, 0x00000000
-data4 0xAFEEA48B, 0x3FD34E36, 0x245C05EB, 0x00000000
-data4 0x7DBB35D1, 0x3FD3DA31, 0x24749F2D, 0x00000000
-data4 0x67321619, 0x3FD466DA, 0x2462CECE, 0x00000000
-data4 0x1F94A4D5, 0x3FD4F437, 0x246D0DF1, 0x00000000
-data4 0x740C3E6D, 0x3FD5824D, 0x240A85B5, 0x00000000
-data4 0x4CB1E73D, 0x3FD61123, 0x23F96E33, 0x00000000
-data4 0xAD9EA64B, 0x3FD6A0BE, 0x247C5393, 0x00000000
-data4 0xB804FD01, 0x3FD73125, 0x241F3B29, 0x00000000
-data4 0xAB53EE83, 0x3FD7C25E, 0x2479989B, 0x00000000
-data4 0xE6640EED, 0x3FD8546F, 0x23B343BC, 0x00000000
-data4 0xE8AF1892, 0x3FD8E75F, 0x241454D1, 0x00000000
-data4 0x53928BDA, 0x3FD97B35, 0x238613D9, 0x00000000
-data4 0xEB9DE4DE, 0x3FDA0FF6, 0x22859FA7, 0x00000000
-data4 0x99ECF92D, 0x3FDAA5AB, 0x237A6D06, 0x00000000
-data4 0x6D8F1796, 0x3FDB3C5A, 0x23952F6C, 0x00000000
-data4 0x9CFB8BE4, 0x3FDBD40A, 0x2280FC95, 0x00000000
-data4 0x87943100, 0x3FDC6CC3, 0x245D2EC0, 0x00000000
-data4 0xB736C500, 0x3FDD068C, 0x23C4AD7D, 0x00000000
-data4 0xE1DDBC31, 0x3FDDA16D, 0x23D076E6, 0x00000000
-data4 0xEB515A93, 0x3FDE3D6E, 0x244809A6, 0x00000000
-data4 0xE6E9E5F1, 0x3FDEDA97, 0x220856C8, 0x00000000
-data4 0x1963CE69, 0x3FDF78F1, 0x244BE993, 0x00000000
-data4 0x7D635BCE, 0x3FE00C41, 0x23D21799, 0x00000000
-data4 0x1C302CD3, 0x3FE05CAB, 0x248A1B1D, 0x00000000
-data4 0xDB6A1FA0, 0x3FE0ADB9, 0x23D53E33, 0x00000000
-data4 0x4A20BA81, 0x3FE0FF72, 0x24DB9ED5, 0x00000000
-data4 0x153FA6F5, 0x3FE151D9, 0x24E9E451, 0x00000000
+data8 0x3FD09BC362400794
+data4 0x23A05C32, 0x00000000
+data8 0x3FD124A9DFFBC074
+data4 0x240078B2, 0x00000000
+data8 0x3FD1AE235BD4920F
+data4 0x23826B8E, 0x00000000
+data8 0x3FD2383515E2701D
+data4 0x22D31154, 0x00000000
+data8 0x3FD2C2E463739C2D
+data4 0x2265C9E2, 0x00000000
+data8 0x3FD34E36AFEEA48B
+data4 0x245C05EB, 0x00000000
+data8 0x3FD3DA317DBB35D1
+data4 0x24749F2D, 0x00000000
+data8 0x3FD466DA67321619
+data4 0x2462CECE, 0x00000000
+data8 0x3FD4F4371F94A4D5
+data4 0x246D0DF1, 0x00000000
+data8 0x3FD5824D740C3E6D
+data4 0x240A85B5, 0x00000000
+data8 0x3FD611234CB1E73D
+data4 0x23F96E33, 0x00000000
+data8 0x3FD6A0BEAD9EA64B
+data4 0x247C5393, 0x00000000
+data8 0x3FD73125B804FD01
+data4 0x241F3B29, 0x00000000
+data8 0x3FD7C25EAB53EE83
+data4 0x2479989B, 0x00000000
+data8 0x3FD8546FE6640EED
+data4 0x23B343BC, 0x00000000
+data8 0x3FD8E75FE8AF1892
+data4 0x241454D1, 0x00000000
+data8 0x3FD97B3553928BDA
+data4 0x238613D9, 0x00000000
+data8 0x3FDA0FF6EB9DE4DE
+data4 0x22859FA7, 0x00000000
+data8 0x3FDAA5AB99ECF92D
+data4 0x237A6D06, 0x00000000
+data8 0x3FDB3C5A6D8F1796
+data4 0x23952F6C, 0x00000000
+data8 0x3FDBD40A9CFB8BE4
+data4 0x2280FC95, 0x00000000
+data8 0x3FDC6CC387943100
+data4 0x245D2EC0, 0x00000000
+data8 0x3FDD068CB736C500
+data4 0x23C4AD7D, 0x00000000
+data8 0x3FDDA16DE1DDBC31
+data4 0x23D076E6, 0x00000000
+data8 0x3FDE3D6EEB515A93
+data4 0x244809A6, 0x00000000
+data8 0x3FDEDA97E6E9E5F1
+data4 0x220856C8, 0x00000000
+data8 0x3FDF78F11963CE69
+data4 0x244BE993, 0x00000000
+data8 0x3FE00C417D635BCE
+data4 0x23D21799, 0x00000000
+data8 0x3FE05CAB1C302CD3
+data4 0x248A1B1D, 0x00000000
+data8 0x3FE0ADB9DB6A1FA0
+data4 0x23D53E33, 0x00000000
+data8 0x3FE0FF724A20BA81
+data4 0x24DB9ED5, 0x00000000
+data8 0x3FE151D9153FA6F5
+data4 0x24E9E451, 0x00000000
+LOCAL_OBJECT_END(tanl_table_tm2)
+
+LOCAL_OBJECT_START(tanl_table_tm1)
//
// Entries T_hi double-precision memory format
// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64)
// Entries T_lo single-precision memory format
// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64)
//
-data4 0xBA1BE39E, 0x3FE1CEC4, 0x24B60F9E, 0x00000000
-data4 0x5ABD9B2D, 0x3FE277E4, 0x248C2474, 0x00000000
-data4 0x0272B110, 0x3FE32418, 0x247B8311, 0x00000000
-data4 0x890E2DF0, 0x3FE3D38B, 0x24C55751, 0x00000000
-data4 0x46236871, 0x3FE4866D, 0x24E5BC34, 0x00000000
-data4 0x45E044B0, 0x3FE53CEE, 0x24001BA4, 0x00000000
-data4 0x82EC06E4, 0x3FE5F742, 0x24B973DC, 0x00000000
-data4 0x25DF43F9, 0x3FE6B5A1, 0x24895440, 0x00000000
-data4 0xCAFD348C, 0x3FE77844, 0x240021CA, 0x00000000
-data4 0xCEED6B92, 0x3FE83F6B, 0x24C45372, 0x00000000
-data4 0xA34F3665, 0x3FE90B58, 0x240DAD33, 0x00000000
-data4 0x2C1E56B4, 0x3FE9DC52, 0x24F846CE, 0x00000000
-data4 0x27041578, 0x3FEAB2A4, 0x2323FB6E, 0x00000000
-data4 0x9DD8C373, 0x3FEB8E9F, 0x24B3090B, 0x00000000
-data4 0x65C9AA7B, 0x3FEC709B, 0x2449F611, 0x00000000
-data4 0xACCF8435, 0x3FED58F4, 0x23616A7E, 0x00000000
-data4 0x97635082, 0x3FEE480F, 0x24C2FEAE, 0x00000000
-data4 0xF0ACC544, 0x3FEF3E57, 0x242CE964, 0x00000000
-data4 0xF7E06E4B, 0x3FF01E20, 0x2480D3EE, 0x00000000
-data4 0x8A798A69, 0x3FF0A125, 0x24DB8967, 0x00000000
+data8 0x3FE1CEC4BA1BE39E
+data4 0x24B60F9E, 0x00000000
+data8 0x3FE277E45ABD9B2D
+data4 0x248C2474, 0x00000000
+data8 0x3FE324180272B110
+data4 0x247B8311, 0x00000000
+data8 0x3FE3D38B890E2DF0
+data4 0x24C55751, 0x00000000
+data8 0x3FE4866D46236871
+data4 0x24E5BC34, 0x00000000
+data8 0x3FE53CEE45E044B0
+data4 0x24001BA4, 0x00000000
+data8 0x3FE5F74282EC06E4
+data4 0x24B973DC, 0x00000000
+data8 0x3FE6B5A125DF43F9
+data4 0x24895440, 0x00000000
+data8 0x3FE77844CAFD348C
+data4 0x240021CA, 0x00000000
+data8 0x3FE83F6BCEED6B92
+data4 0x24C45372, 0x00000000
+data8 0x3FE90B58A34F3665
+data4 0x240DAD33, 0x00000000
+data8 0x3FE9DC522C1E56B4
+data4 0x24F846CE, 0x00000000
+data8 0x3FEAB2A427041578
+data4 0x2323FB6E, 0x00000000
+data8 0x3FEB8E9F9DD8C373
+data4 0x24B3090B, 0x00000000
+data8 0x3FEC709B65C9AA7B
+data4 0x2449F611, 0x00000000
+data8 0x3FED58F4ACCF8435
+data4 0x23616A7E, 0x00000000
+data8 0x3FEE480F97635082
+data4 0x24C2FEAE, 0x00000000
+data8 0x3FEF3E57F0ACC544
+data4 0x242CE964, 0x00000000
+data8 0x3FF01E20F7E06E4B
+data4 0x2480D3EE, 0x00000000
+data8 0x3FF0A1258A798A69
+data4 0x24DB8967, 0x00000000
+LOCAL_OBJECT_END(tanl_table_tm1)
+
+LOCAL_OBJECT_START(tanl_table_cm2)
//
// Entries C_hi double-precision memory format
// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64)
// Entries C_lo single-precision memory format
// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64)
//
-data4 0xE63EFBD0, 0x400ED3E2, 0x259D94D4, 0x00000000
-data4 0xC515DAB5, 0x400DDDB4, 0x245F0537, 0x00000000
-data4 0xBE19A79F, 0x400CF57A, 0x25D4EA9F, 0x00000000
-data4 0xD15298ED, 0x400C1A06, 0x24AE40A0, 0x00000000
-data4 0x164B2708, 0x400B4A4C, 0x25A5AAB6, 0x00000000
-data4 0x5285B068, 0x400A855A, 0x25524F18, 0x00000000
-data4 0x3FFA549F, 0x4009CA5A, 0x24C999C0, 0x00000000
-data4 0x646AF623, 0x4009188A, 0x254FD801, 0x00000000
-data4 0x6084D0E7, 0x40086F3C, 0x2560F5FD, 0x00000000
-data4 0xA29A76EE, 0x4007CDD2, 0x255B9D19, 0x00000000
-data4 0x6C8ECA95, 0x400733BE, 0x25CB021B, 0x00000000
-data4 0x1F8DDC52, 0x4006A07E, 0x24AB4722, 0x00000000
-data4 0xC298AD58, 0x4006139B, 0x252764E2, 0x00000000
-data4 0xBAD7164B, 0x40058CAB, 0x24DAF5DB, 0x00000000
-data4 0xAE31A5D3, 0x40050B4B, 0x25EA20F4, 0x00000000
-data4 0x89F85A8A, 0x40048F21, 0x2583A3E8, 0x00000000
-data4 0xA862380D, 0x400417DA, 0x25DCC4CC, 0x00000000
-data4 0x1088FCFE, 0x4003A52B, 0x2430A492, 0x00000000
-data4 0xCD3527D5, 0x400336CC, 0x255F77CF, 0x00000000
-data4 0x5760766D, 0x4002CC7F, 0x25DA0BDA, 0x00000000
-data4 0x11CE02E3, 0x40026607, 0x256FF4A2, 0x00000000
-data4 0xD37BBE04, 0x4002032C, 0x25208AED, 0x00000000
-data4 0x7F050775, 0x4001A3BD, 0x24B72DD6, 0x00000000
-data4 0xA554848A, 0x40014789, 0x24AB4DAA, 0x00000000
-data4 0x323E81B7, 0x4000EE65, 0x2584C440, 0x00000000
-data4 0x21CF1293, 0x40009827, 0x25C9428D, 0x00000000
-data4 0x3D415EEB, 0x400044A9, 0x25DC8482, 0x00000000
-data4 0xBD72C577, 0x3FFFE78F, 0x257F5070, 0x00000000
-data4 0x75EFD28E, 0x3FFF4AC3, 0x23EBBF7A, 0x00000000
-data4 0x60B52DDE, 0x3FFEB2AF, 0x22EECA07, 0x00000000
-data4 0x35204180, 0x3FFE1F19, 0x24191079, 0x00000000
-data4 0x54F7E60A, 0x3FFD8FCA, 0x248D3058, 0x00000000
+data8 0x400ED3E2E63EFBD0
+data4 0x259D94D4, 0x00000000
+data8 0x400DDDB4C515DAB5
+data4 0x245F0537, 0x00000000
+data8 0x400CF57ABE19A79F
+data4 0x25D4EA9F, 0x00000000
+data8 0x400C1A06D15298ED
+data4 0x24AE40A0, 0x00000000
+data8 0x400B4A4C164B2708
+data4 0x25A5AAB6, 0x00000000
+data8 0x400A855A5285B068
+data4 0x25524F18, 0x00000000
+data8 0x4009CA5A3FFA549F
+data4 0x24C999C0, 0x00000000
+data8 0x4009188A646AF623
+data4 0x254FD801, 0x00000000
+data8 0x40086F3C6084D0E7
+data4 0x2560F5FD, 0x00000000
+data8 0x4007CDD2A29A76EE
+data4 0x255B9D19, 0x00000000
+data8 0x400733BE6C8ECA95
+data4 0x25CB021B, 0x00000000
+data8 0x4006A07E1F8DDC52
+data4 0x24AB4722, 0x00000000
+data8 0x4006139BC298AD58
+data4 0x252764E2, 0x00000000
+data8 0x40058CABBAD7164B
+data4 0x24DAF5DB, 0x00000000
+data8 0x40050B4BAE31A5D3
+data4 0x25EA20F4, 0x00000000
+data8 0x40048F2189F85A8A
+data4 0x2583A3E8, 0x00000000
+data8 0x400417DAA862380D
+data4 0x25DCC4CC, 0x00000000
+data8 0x4003A52B1088FCFE
+data4 0x2430A492, 0x00000000
+data8 0x400336CCCD3527D5
+data4 0x255F77CF, 0x00000000
+data8 0x4002CC7F5760766D
+data4 0x25DA0BDA, 0x00000000
+data8 0x4002660711CE02E3
+data4 0x256FF4A2, 0x00000000
+data8 0x4002032CD37BBE04
+data4 0x25208AED, 0x00000000
+data8 0x4001A3BD7F050775
+data4 0x24B72DD6, 0x00000000
+data8 0x40014789A554848A
+data4 0x24AB4DAA, 0x00000000
+data8 0x4000EE65323E81B7
+data4 0x2584C440, 0x00000000
+data8 0x4000982721CF1293
+data4 0x25C9428D, 0x00000000
+data8 0x400044A93D415EEB
+data4 0x25DC8482, 0x00000000
+data8 0x3FFFE78FBD72C577
+data4 0x257F5070, 0x00000000
+data8 0x3FFF4AC375EFD28E
+data4 0x23EBBF7A, 0x00000000
+data8 0x3FFEB2AF60B52DDE
+data4 0x22EECA07, 0x00000000
+data8 0x3FFE1F1935204180
+data4 0x24191079, 0x00000000
+data8 0x3FFD8FCA54F7E60A
+data4 0x248D3058, 0x00000000
+LOCAL_OBJECT_END(tanl_table_cm2)
+
+LOCAL_OBJECT_START(tanl_table_cm1)
//
// Entries C_hi double-precision memory format
// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64)
// Entries C_lo single-precision memory format
// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64)
//
-data4 0x79F6FADE, 0x3FFCC06A, 0x239C7886, 0x00000000
-data4 0x891662A6, 0x3FFBB91F, 0x250BD191, 0x00000000
-data4 0x529F155D, 0x3FFABFB6, 0x256CC3E6, 0x00000000
-data4 0x2E964AE9, 0x3FF9D300, 0x250843E3, 0x00000000
-data4 0x89DCB383, 0x3FF8F1EF, 0x2277C87E, 0x00000000
-data4 0x7C87DBD6, 0x3FF81B93, 0x256DA6CF, 0x00000000
-data4 0x1042EDE4, 0x3FF74F14, 0x2573D28A, 0x00000000
-data4 0x1784B360, 0x3FF68BAF, 0x242E489A, 0x00000000
-data4 0x7C923C4C, 0x3FF5D0B5, 0x2532D940, 0x00000000
-data4 0xF418EF20, 0x3FF51D88, 0x253C7DD6, 0x00000000
-data4 0x02F88DAE, 0x3FF4719A, 0x23DB59BF, 0x00000000
-data4 0x49DA0788, 0x3FF3CC66, 0x252B4756, 0x00000000
-data4 0x0B980DB8, 0x3FF32D77, 0x23FE585F, 0x00000000
-data4 0xE56C987A, 0x3FF2945F, 0x25378A63, 0x00000000
-data4 0xB16523F6, 0x3FF200BD, 0x247BB2E0, 0x00000000
-data4 0x8CE27778, 0x3FF17235, 0x24446538, 0x00000000
-data4 0xFDEFE692, 0x3FF0E873, 0x2514638F, 0x00000000
-data4 0x33154062, 0x3FF0632C, 0x24A7FC27, 0x00000000
-data4 0xB3EF115F, 0x3FEFC42E, 0x248FD0FE, 0x00000000
-data4 0x135D26F6, 0x3FEEC9E8, 0x2385C719, 0x00000000
+data8 0x3FFCC06A79F6FADE
+data4 0x239C7886, 0x00000000
+data8 0x3FFBB91F891662A6
+data4 0x250BD191, 0x00000000
+data8 0x3FFABFB6529F155D
+data4 0x256CC3E6, 0x00000000
+data8 0x3FF9D3002E964AE9
+data4 0x250843E3, 0x00000000
+data8 0x3FF8F1EF89DCB383
+data4 0x2277C87E, 0x00000000
+data8 0x3FF81B937C87DBD6
+data4 0x256DA6CF, 0x00000000
+data8 0x3FF74F141042EDE4
+data4 0x2573D28A, 0x00000000
+data8 0x3FF68BAF1784B360
+data4 0x242E489A, 0x00000000
+data8 0x3FF5D0B57C923C4C
+data4 0x2532D940, 0x00000000
+data8 0x3FF51D88F418EF20
+data4 0x253C7DD6, 0x00000000
+data8 0x3FF4719A02F88DAE
+data4 0x23DB59BF, 0x00000000
+data8 0x3FF3CC6649DA0788
+data4 0x252B4756, 0x00000000
+data8 0x3FF32D770B980DB8
+data4 0x23FE585F, 0x00000000
+data8 0x3FF2945FE56C987A
+data4 0x25378A63, 0x00000000
+data8 0x3FF200BDB16523F6
+data4 0x247BB2E0, 0x00000000
+data8 0x3FF172358CE27778
+data4 0x24446538, 0x00000000
+data8 0x3FF0E873FDEFE692
+data4 0x2514638F, 0x00000000
+data8 0x3FF0632C33154062
+data4 0x24A7FC27, 0x00000000
+data8 0x3FEFC42EB3EF115F
+data4 0x248FD0FE, 0x00000000
+data8 0x3FEEC9E8135D26F6
+data4 0x2385C719, 0x00000000
+LOCAL_OBJECT_END(tanl_table_cm1)
+
+LOCAL_OBJECT_START(tanl_table_scim2)
//
// Entries SC_inv in Swapped IEEE format (extended)
// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64)
//
-data4 0x1BF30C9E, 0x839D6D4A, 0x00004001, 0x00000000
-data4 0x554B0EB0, 0x80092804, 0x00004001, 0x00000000
-data4 0xA1CF0DE9, 0xF959F94C, 0x00004000, 0x00000000
-data4 0x77378677, 0xF3086BA0, 0x00004000, 0x00000000
-data4 0xCCD4723C, 0xED154515, 0x00004000, 0x00000000
-data4 0x1C27CF25, 0xE7790944, 0x00004000, 0x00000000
-data4 0x8DDACB88, 0xE22D037D, 0x00004000, 0x00000000
-data4 0x89C73522, 0xDD2B2D8A, 0x00004000, 0x00000000
-data4 0xBB2C1171, 0xD86E1A23, 0x00004000, 0x00000000
-data4 0xDFF5E0F9, 0xD3F0E288, 0x00004000, 0x00000000
-data4 0x283BEBD5, 0xCFAF16B1, 0x00004000, 0x00000000
-data4 0x0D88DD53, 0xCBA4AFAA, 0x00004000, 0x00000000
-data4 0xCA67C43D, 0xC7CE03CC, 0x00004000, 0x00000000
-data4 0x0CA0DDB0, 0xC427BC82, 0x00004000, 0x00000000
-data4 0xF13D8CAB, 0xC0AECD57, 0x00004000, 0x00000000
-data4 0x71ECE6B1, 0xBD606C38, 0x00004000, 0x00000000
-data4 0xA44C4929, 0xBA3A0A96, 0x00004000, 0x00000000
-data4 0xE5CCCEC1, 0xB7394F6F, 0x00004000, 0x00000000
-data4 0x9637D8BC, 0xB45C1203, 0x00004000, 0x00000000
-data4 0x92CB051B, 0xB1A05528, 0x00004000, 0x00000000
-data4 0x6BA2FFD0, 0xAF04432B, 0x00004000, 0x00000000
-data4 0x7221235F, 0xAC862A23, 0x00004000, 0x00000000
-data4 0x5F00A9D1, 0xAA2478AF, 0x00004000, 0x00000000
-data4 0x81E082BF, 0xA7DDBB0C, 0x00004000, 0x00000000
-data4 0x45684FEE, 0xA5B0987D, 0x00004000, 0x00000000
-data4 0x627A8F53, 0xA39BD0F5, 0x00004000, 0x00000000
-data4 0x6EC5C8B0, 0xA19E3B03, 0x00004000, 0x00000000
-data4 0x91CD7C66, 0x9FB6C1F0, 0x00004000, 0x00000000
-data4 0x1FA3DF8A, 0x9DE46410, 0x00004000, 0x00000000
-data4 0xA8F6B888, 0x9C263139, 0x00004000, 0x00000000
-data4 0xC27B0450, 0x9A7B4968, 0x00004000, 0x00000000
-data4 0x5EE614EE, 0x98E2DB7E, 0x00004000, 0x00000000
+data8 0x839D6D4A1BF30C9E, 0x00004001
+data8 0x80092804554B0EB0, 0x00004001
+data8 0xF959F94CA1CF0DE9, 0x00004000
+data8 0xF3086BA077378677, 0x00004000
+data8 0xED154515CCD4723C, 0x00004000
+data8 0xE77909441C27CF25, 0x00004000
+data8 0xE22D037D8DDACB88, 0x00004000
+data8 0xDD2B2D8A89C73522, 0x00004000
+data8 0xD86E1A23BB2C1171, 0x00004000
+data8 0xD3F0E288DFF5E0F9, 0x00004000
+data8 0xCFAF16B1283BEBD5, 0x00004000
+data8 0xCBA4AFAA0D88DD53, 0x00004000
+data8 0xC7CE03CCCA67C43D, 0x00004000
+data8 0xC427BC820CA0DDB0, 0x00004000
+data8 0xC0AECD57F13D8CAB, 0x00004000
+data8 0xBD606C3871ECE6B1, 0x00004000
+data8 0xBA3A0A96A44C4929, 0x00004000
+data8 0xB7394F6FE5CCCEC1, 0x00004000
+data8 0xB45C12039637D8BC, 0x00004000
+data8 0xB1A0552892CB051B, 0x00004000
+data8 0xAF04432B6BA2FFD0, 0x00004000
+data8 0xAC862A237221235F, 0x00004000
+data8 0xAA2478AF5F00A9D1, 0x00004000
+data8 0xA7DDBB0C81E082BF, 0x00004000
+data8 0xA5B0987D45684FEE, 0x00004000
+data8 0xA39BD0F5627A8F53, 0x00004000
+data8 0xA19E3B036EC5C8B0, 0x00004000
+data8 0x9FB6C1F091CD7C66, 0x00004000
+data8 0x9DE464101FA3DF8A, 0x00004000
+data8 0x9C263139A8F6B888, 0x00004000
+data8 0x9A7B4968C27B0450, 0x00004000
+data8 0x98E2DB7E5EE614EE, 0x00004000
+LOCAL_OBJECT_END(tanl_table_scim2)
+
+LOCAL_OBJECT_START(tanl_table_scim1)
//
// Entries SC_inv in Swapped IEEE format (extended)
// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64)
//
-data4 0x13B2B5BA, 0x969F335C, 0x00004000, 0x00000000
-data4 0xD4C0F548, 0x93D446D9, 0x00004000, 0x00000000
-data4 0x61B798AF, 0x9147094F, 0x00004000, 0x00000000
-data4 0x758787AC, 0x8EF317CC, 0x00004000, 0x00000000
-data4 0xB99EEFDB, 0x8CD498B3, 0x00004000, 0x00000000
-data4 0xDFF8BC37, 0x8AE82A7D, 0x00004000, 0x00000000
-data4 0xE3C55D42, 0x892AD546, 0x00004000, 0x00000000
-data4 0xD15573C1, 0x8799FEA9, 0x00004000, 0x00000000
-data4 0x435A4B4C, 0x86335F88, 0x00004000, 0x00000000
-data4 0x3E93A87B, 0x84F4FB6E, 0x00004000, 0x00000000
-data4 0x80A382FB, 0x83DD1952, 0x00004000, 0x00000000
-data4 0xA4CB8C9E, 0x82EA3D7F, 0x00004000, 0x00000000
-data4 0x6861D0A8, 0x821B247C, 0x00004000, 0x00000000
-data4 0x63E8D244, 0x816EBED1, 0x00004000, 0x00000000
-data4 0x27E4CFC6, 0x80E42D91, 0x00004000, 0x00000000
-data4 0x28E64AFD, 0x807ABF8D, 0x00004000, 0x00000000
-data4 0x863B4FD8, 0x8031EF26, 0x00004000, 0x00000000
-data4 0xAE8C11FD, 0x800960AD, 0x00004000, 0x00000000
-data4 0x5FDBEC21, 0x8000E147, 0x00004000, 0x00000000
-data4 0xA07791FA, 0x80186650, 0x00004000, 0x00000000
-ASM_SIZE_DIRECTIVE(TANL_BASE_CONSTANTS)
-
-Arg = f8
+data8 0x969F335C13B2B5BA, 0x00004000
+data8 0x93D446D9D4C0F548, 0x00004000
+data8 0x9147094F61B798AF, 0x00004000
+data8 0x8EF317CC758787AC, 0x00004000
+data8 0x8CD498B3B99EEFDB, 0x00004000
+data8 0x8AE82A7DDFF8BC37, 0x00004000
+data8 0x892AD546E3C55D42, 0x00004000
+data8 0x8799FEA9D15573C1, 0x00004000
+data8 0x86335F88435A4B4C, 0x00004000
+data8 0x84F4FB6E3E93A87B, 0x00004000
+data8 0x83DD195280A382FB, 0x00004000
+data8 0x82EA3D7FA4CB8C9E, 0x00004000
+data8 0x821B247C6861D0A8, 0x00004000
+data8 0x816EBED163E8D244, 0x00004000
+data8 0x80E42D9127E4CFC6, 0x00004000
+data8 0x807ABF8D28E64AFD, 0x00004000
+data8 0x8031EF26863B4FD8, 0x00004000
+data8 0x800960ADAE8C11FD, 0x00004000
+data8 0x8000E1475FDBEC21, 0x00004000
+data8 0x80186650A07791FA, 0x00004000
+LOCAL_OBJECT_END(tanl_table_scim1)
+
+Arg = f8
+Save_Norm_Arg = f8 // For input to reduction routine
Result = f8
-fp_tmp = f9
+r = f8 // For output from reduction routine
+c = f9 // For output from reduction routine
U_2 = f10
-rsq = f11
+rsq = f11
C_hi = f12
C_lo = f13
T_hi = f14
T_lo = f15
-N_0 = f32
d_1 = f33
-MPI_BY_4 = f34
+N_0 = f34
tail = f35
tanx = f36
Cx = f37
@@ -949,8 +1104,6 @@ P1_7 = f51
P1_8 = f52
P1_9 = f53
-TWO_TO_63 = f54
-NEGTWO_TO_63 = f55
x = f56
xsq = f57
Tx = f58
@@ -966,12 +1119,10 @@ B = f67
SC_inv = f68
Pos_r = f69
N_0_fix = f70
-PI_BY_4 = f71
-NEGTWO_TO_NEG2 = f72
-TWO_TO_24 = f73
+d_2 = f71
+PI_BY_4 = f72
TWO_TO_NEG14 = f74
TWO_TO_NEG33 = f75
-NEGTWO_TO_24 = f76
NEGTWO_TO_NEG14 = f76
NEGTWO_TO_NEG33 = f77
two_by_PI = f78
@@ -982,13 +1133,14 @@ P_2 = f82
P_3 = f83
s_val = f84
w = f85
-c = f86
-r = f87
+B_mask1 = f86
+B_mask2 = f87
+w2 = f88
A = f89
a = f90
t = f91
U_1 = f92
-d_2 = f93
+NEGTWO_TO_NEG2 = f93
TWO_TO_NEG2 = f94
Q1_1 = f95
Q1_2 = f96
@@ -1009,609 +1161,641 @@ V_hiabs = f110
V = f111
Inv_P_0 = f112
+FR_inv_pi_2to63 = f113
+FR_rshf_2to64 = f114
+FR_2tom64 = f115
+FR_rshf = f116
+Norm_Arg = f117
+Abs_Arg = f118
+TWO_TO_NEG65 = f119
+fp_tmp = f120
+mOne = f121
+
+GR_sig_inv_pi = r14
+GR_rshf_2to64 = r15
+GR_exp_2tom64 = r16
+GR_rshf = r17
+GR_exp_2_to_63 = r18
+GR_exp_2_to_24 = r19
+GR_signexp_x = r20
+GR_exp_x = r21
+GR_exp_mask = r22
+GR_exp_2tom14 = r23
+GR_exp_m2tom14 = r24
+GR_exp_2tom33 = r25
+GR_exp_m2tom33 = r26
+
GR_SAVE_B0 = r33
GR_SAVE_GP = r34
GR_SAVE_PFS = r35
-delta1 = r36
+table_base = r36
table_ptr1 = r37
table_ptr2 = r38
-i_0 = r39
-i_1 = r40
-N_fix_gr = r41
-N_inc = r42
-exp_Arg = r43
-exp_r = r44
-sig_r = r45
-lookup = r46
-table_offset = r47
-Create_B = r48
+table_ptr3 = r39
+lookup = r40
+N_fix_gr = r41
+GR_exp_2tom2 = r42
+GR_exp_2tom65 = r43
+exp_r = r44
+sig_r = r45
+bmask1 = r46
+table_offset = r47
+bmask2 = r48
gr_tmp = r49
+cot_flag = r50
+
+GR_SAVE_B0 = r51
+GR_SAVE_PFS = r52
+GR_SAVE_GP = r53
+GR_Parameter_X = r54
+GR_Parameter_Y = r55
+GR_Parameter_RESULT = r56
+GR_Parameter_Tag = r57
+
.section .text
-.global tanl
-.proc tanl
-tanl:
-#ifdef _LIBC
-.global __tanl
-.proc __tanl
-__tanl:
-#endif
-{ .mfi
-alloc r32 = ar.pfs, 0,17,2,0
-(p0) fclass.m.unc p6,p0 = Arg, 0x1E7
- addl gr_tmp = -1,r0
-}
-{ .mfi
- nop.m 0
-(p0) fclass.nm.unc p7,p0 = Arg, 0x1FF
- nop.i 0
+.global __libm_tanl#
+.global __libm_cotl#
+
+.proc __libm_cotl#
+__libm_cotl:
+.endp __libm_cotl#
+LOCAL_LIBM_ENTRY(cotl)
+
+{ .mlx
+ alloc r32 = ar.pfs, 0,22,4,0
+ movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
+}
+{ .mlx
+ mov GR_exp_mask = 0x1ffff // Exponent mask
+ movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
+}
+;;
+
+// Check for NatVals, Infs , NaNs, and Zeros
+{ .mfi
+ getf.exp GR_signexp_x = Arg // Get sign and exponent of x
+ fclass.m p6,p0 = Arg, 0x1E7 // Test for natval, nan, inf, zero
+ mov cot_flag = 0x1
+}
+{ .mfb
+ addl table_base = @ltoff(TANL_BASE_CONSTANTS), gp // Pointer to table ptr
+ fnorm.s1 Norm_Arg = Arg // Normalize x
+ br.cond.sptk COMMON_PATH
};;
+LOCAL_LIBM_END(cotl)
+
+.proc __libm_tanl#
+__libm_tanl:
+.endp __libm_tanl#
+GLOBAL_IEEE754_ENTRY(tanl)
+
+{ .mlx
+ alloc r32 = ar.pfs, 0,22,4,0
+ movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
+}
+{ .mlx
+ mov GR_exp_mask = 0x1ffff // Exponent mask
+ movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
+}
+;;
+
+// Check for NatVals, Infs , NaNs, and Zeros
{ .mfi
-(p0) addl table_ptr1 = @ltoff(TANL_BASE_CONSTANTS), gp
- nop.f 999
+ getf.exp GR_signexp_x = Arg // Get sign and exponent of x
+ fclass.m p6,p0 = Arg, 0x1E7 // Test for natval, nan, inf, zero
+ mov cot_flag = 0x0
+}
+{ .mfi
+ addl table_base = @ltoff(TANL_BASE_CONSTANTS), gp // Pointer to table ptr
+ fnorm.s1 Norm_Arg = Arg // Normalize x
nop.i 0
+};;
+
+// Common path for both tanl and cotl
+COMMON_PATH:
+{ .mfi
+ setf.sig FR_inv_pi_2to63 = GR_sig_inv_pi // Form 1/pi * 2^63
+ fclass.m p9, p0 = Arg, 0x0b // Test x denormal
+ mov GR_exp_2tom64 = 0xffff - 64 // Scaling constant to compute N
+}
+{ .mlx
+ setf.d FR_rshf_2to64 = GR_rshf_2to64 // Form const 1.1000 * 2^(63+64)
+ movl GR_rshf = 0x43e8000000000000 // Form const 1.1000 * 2^63
}
;;
-{ .mmi
-(p0) ld8 table_ptr1 = [table_ptr1]
- setf.sig fp_tmp = gr_tmp // Make a constant so fmpy produces inexact
- nop.i 999
+
+// Check for everything - if false, then must be pseudo-zero or pseudo-nan.
+// Branch out to deal with special values.
+{ .mfi
+ addl gr_tmp = -1,r0
+ fclass.nm p7,p0 = Arg, 0x1FF // Test x unsupported
+ mov GR_exp_2_to_63 = 0xffff + 63 // Exponent of 2^63
+}
+{ .mfb
+ ld8 table_base = [table_base] // Get pointer to constant table
+ fms.s1 mOne = f0, f0, f1
+(p6) br.cond.spnt TANL_SPECIAL // Branch if x natval, nan, inf, zero
}
;;
-//
-// Check for NatVals, Infs , NaNs, and Zeros
-// Check for everything - if false, then must be pseudo-zero
-// or pseudo-nan.
-// Local table pointer
-//
-{ .mbb
-(p0) add table_ptr2 = 96, table_ptr1
-(p6) br.cond.spnt L(TANL_SPECIAL)
-(p7) br.cond.spnt L(TANL_SPECIAL) ;;
+{ .mmb
+ setf.sig fp_tmp = gr_tmp // Make a constant so fmpy produces inexact
+ mov GR_exp_2_to_24 = 0xffff + 24 // Exponent of 2^24
+(p9) br.cond.spnt TANL_DENORMAL // Branch if x denormal
}
+;;
+
+TANL_COMMON:
+// Return to here if x denormal
//
-// Point to Inv_P_0
-// Branch out to deal with unsupporteds and special values.
-//
-{ .mmf
-(p0) ldfs TWO_TO_24 = [table_ptr1],4
-(p0) ldfs TWO_TO_63 = [table_ptr2],4
-//
-// Load -2**24, load -2**63.
-//
-(p0) fcmp.eq.s0 p0, p6 = Arg, f1 ;;
-}
+// Do fcmp to generate Denormal exception
+// - can't do FNORM (will generate Underflow when U is unmasked!)
+// Branch out to deal with unsupporteds values.
{ .mfi
-(p0) ldfs NEGTWO_TO_63 = [table_ptr2],12
-(p0) fnorm.s1 Arg = Arg
- nop.i 999
+ setf.exp FR_2tom64 = GR_exp_2tom64 // Form 2^-64 for scaling N_float
+ fcmp.eq.s0 p0, p6 = Arg, f1 // Dummy to flag denormals
+ add table_ptr1 = 0, table_base // Point to tanl_table_1
}
-//
-// Load 2**24, Load 2**63.
-//
-{ .mmi
-(p0) ldfs NEGTWO_TO_24 = [table_ptr1],12 ;;
-//
-// Do fcmp to generate Denormal exception
-// - can't do FNORM (will generate Underflow when U is unmasked!)
-// Normalize input argument.
-//
-(p0) ldfe two_by_PI = [table_ptr1],16
- nop.i 999
+{ .mib
+ setf.d FR_rshf = GR_rshf // Form right shift const 1.1000 * 2^63
+ add table_ptr2 = 80, table_base // Point to tanl_table_2
+(p7) br.cond.spnt TANL_UNSUPPORTED // Branch if x unsupported type
}
-{ .mmi
-(p0) ldfe Inv_P_0 = [table_ptr2],16 ;;
-(p0) ldfe d_1 = [table_ptr2],16
- nop.i 999
+;;
+
+{ .mfi
+ and GR_exp_x = GR_exp_mask, GR_signexp_x // Get exponent of x
+ fmpy.s1 Save_Norm_Arg = Norm_Arg, f1 // Save x if large arg reduction
+ dep.z bmask1 = 0x7c, 56, 8 // Form mask to get 5 msb of r
+ // bmask1 = 0x7c00000000000000
}
+;;
+
//
// Decide about the paths to take:
-// PR_1 and PR_3 set if -2**24 < Arg < 2**24 - CASE 1 OR 2
-// OTHERWISE - CASE 3 OR 4
-// Load inverse of P_0 .
-// Set PR_6 if Arg <= -2**63
-// Are there any Infs, NaNs, or zeros?
+// Set PR_6 if |Arg| >= 2**63
+// Set PR_9 if |Arg| < 2**24 - CASE 1 OR 2
+// OTHERWISE Set PR_8 - CASE 3 OR 4
//
-{ .mmi
-(p0) ldfe P_0 = [table_ptr1],16 ;;
-(p0) ldfe d_2 = [table_ptr2],16
- nop.i 999
+// Branch out if the magnitude of the input argument is >= 2^63
+// - do this branch before the next.
+{ .mfi
+ ldfe two_by_PI = [table_ptr1],16 // Load 2/pi
+ nop.f 999
+ dep.z bmask2 = 0x41, 57, 7 // Form mask to OR to produce B
+ // bmask2 = 0x8200000000000000
}
-//
-// Set PR_8 if Arg <= -2**24
-// Set PR_6 if Arg >= 2**63
-//
-{ .mmi
-(p0) ldfe P_1 = [table_ptr1],16 ;;
-(p0) ldfe PI_BY_4 = [table_ptr2],16
- nop.i 999
+{ .mib
+ ldfe PI_BY_4 = [table_ptr2],16 // Load pi/4
+ cmp.ge p6,p0 = GR_exp_x, GR_exp_2_to_63 // Is |x| >= 2^63
+(p6) br.cond.spnt TANL_ARG_TOO_LARGE // Branch if |x| >= 2^63
}
-//
-// Set PR_8 if Arg >= 2**24
-//
+;;
+
{ .mmi
-(p0) ldfe P_2 = [table_ptr1],16 ;;
-(p0) ldfe MPI_BY_4 = [table_ptr2],16
- nop.i 999
-}
-//
-// Load P_2 and PI_BY_4
-//
-{ .mfi
-(p0) ldfe P_3 = [table_ptr1],16
- nop.f 999
- nop.i 999 ;;
-}
-{ .mfi
- nop.m 999
-(p0) fcmp.le.unc.s1 p6,p7 = Arg,NEGTWO_TO_63
- nop.i 999
+ ldfe P_0 = [table_ptr1],16 // Load P_0
+ ldfe Inv_P_0 = [table_ptr2],16 // Load Inv_P_0
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p0) fcmp.le.unc.s1 p8,p9 = Arg,NEGTWO_TO_24
- nop.i 999 ;;
+ ldfe P_1 = [table_ptr1],16 // Load P_1
+ fmerge.s Abs_Arg = f0, Norm_Arg // Get |x|
+ mov GR_exp_m2tom33 = 0x2ffff - 33 // Form signexp of -2^-33
}
{ .mfi
- nop.m 999
-(p7) fcmp.ge.s1 p6,p0 = Arg,TWO_TO_63
- nop.i 999
+ ldfe d_1 = [table_ptr2],16 // Load d_1 for 2^24 <= |x| < 2^63
+ nop.f 999
+ mov GR_exp_2tom33 = 0xffff - 33 // Form signexp of 2^-33
}
-{ .mfi
- nop.m 999
-(p9) fcmp.ge.s1 p8,p0 = Arg,TWO_TO_24
- nop.i 999 ;;
+;;
+
+{ .mmi
+ ldfe P_2 = [table_ptr1],16 // Load P_2
+ ldfe d_2 = [table_ptr2],16 // Load d_2 for 2^24 <= |x| < 2^63
+ cmp.ge p8,p0 = GR_exp_x, GR_exp_2_to_24 // Is |x| >= 2^24
}
-{ .mib
- nop.m 999
- nop.i 999
-//
-// Load P_3 and -PI_BY_4
-//
-(p6) br.cond.spnt L(TANL_ARG_TOO_LARGE) ;;
+;;
+
+// Use special scaling to right shift so N=Arg * 2/pi is in rightmost bits
+// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24
+{ .mfb
+ ldfe P_3 = [table_ptr1],16 // Load P_3
+ fma.s1 N_fix = Norm_Arg, FR_inv_pi_2to63, FR_rshf_2to64
+(p8) br.cond.spnt TANL_LARGER_ARG // Branch if 2^24 <= |x| < 2^63
}
-{ .mib
- nop.m 999
- nop.i 999
-//
-// Load 2**(-2).
-// Load -2**(-2).
-// Branch out if we have a special argument.
-// Branch out if the magnitude of the input argument is too large
-// - do this branch before the next.
+;;
+
+// Here if 0 < |x| < 2^24
+// ARGUMENT REDUCTION CODE - CASE 1 and 2
//
-(p8) br.cond.spnt L(TANL_LARGER_ARG) ;;
+{ .mmf
+ setf.exp TWO_TO_NEG33 = GR_exp_2tom33 // Form 2^-33
+ setf.exp NEGTWO_TO_NEG33 = GR_exp_m2tom33 // Form -2^-33
+ fmerge.s r = Norm_Arg,Norm_Arg // Assume r=x, ok if |x| < pi/4
}
+;;
+
//
-// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24
+// If |Arg| < pi/4, set PR_8, else pi/4 <=|Arg| < 2^24 - set PR_9.
//
+// Case 2: Convert integer N_fix back to normalized floating-point value.
{ .mfi
-(p0) ldfs TWO_TO_NEG2 = [table_ptr2],4
-// ARGUMENT REDUCTION CODE - CASE 1 and 2
-// Load 2**(-2).
-// Load -2**(-2).
-(p0) fmpy.s1 N = Arg,two_by_PI
- nop.i 999 ;;
+ getf.sig sig_r = Norm_Arg // Get sig_r if 1/4 <= |x| < pi/4
+ fcmp.lt.s1 p8,p9= Abs_Arg,PI_BY_4 // Test |x| < pi/4
+ mov GR_exp_2tom2 = 0xffff - 2 // Form signexp of 2^-2
}
{ .mfi
-(p0) ldfs NEGTWO_TO_NEG2 = [table_ptr2],12
-//
-// N = Arg * 2/pi
-//
-(p0) fcmp.lt.unc.s1 p8,p9= Arg,PI_BY_4
- nop.i 999 ;;
-}
-{ .mfi
- nop.m 999
-//
-// if Arg < pi/4, set PR_8.
-//
-(p8) fcmp.gt.s1 p8,p9= Arg,MPI_BY_4
- nop.i 999 ;;
+ ldfps TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2] // Load 2^-2, -2^-2
+ fms.s1 N = N_fix, FR_2tom64, FR_rshf // Use scaling to get N floated
+ mov N_fix_gr = r0 // Assume N=0, ok if |x| < pi/4
}
+;;
+
//
// Case 1: Is |r| < 2**(-2).
// Arg is the same as r in this case.
// r = Arg
// c = 0
//
+// Case 2: Place integer part of N in GP register.
{ .mfi
-(p8) mov N_fix_gr = r0
-//
-// if Arg > -pi/4, reset PR_8.
-// Select the case when |Arg| < pi/4 - set PR[8] = true.
-// Else Select the case when |Arg| >= pi/4 - set PR[9] = true.
-//
-(p0) fcvt.fx.s1 N_fix = N
- nop.i 999 ;;
-}
-{ .mfi
- nop.m 999
-//
-// Grab the integer part of N .
-//
-(p8) mov r = Arg
- nop.i 999
-}
-{ .mfi
- nop.m 999
-(p8) mov c = f0
- nop.i 999 ;;
-}
-{ .mfi
- nop.m 999
-(p8) fcmp.lt.unc.s1 p10, p11 = Arg, TWO_TO_NEG2
- nop.i 999 ;;
+(p9) getf.sig N_fix_gr = N_fix
+ fmerge.s c = f0, f0 // Assume c=0, ok if |x| < pi/4
+ cmp.lt p10, p0 = GR_exp_x, GR_exp_2tom2 // Test if |x| < 1/4
}
+;;
+
{ .mfi
- nop.m 999
-(p10) fcmp.gt.s1 p10,p0 = Arg, NEGTWO_TO_NEG2
- nop.i 999 ;;
+ setf.sig B_mask1 = bmask1 // Form mask to get 5 msb of r
+ nop.f 999
+ mov exp_r = GR_exp_x // Get exp_r if 1/4 <= |x| < pi/4
}
-{ .mfi
- nop.m 999
-//
-// Case 2: Place integer part of N in GP register.
-//
-(p9) fcvt.xf N = N_fix
- nop.i 999 ;;
-}
-{ .mib
-(p9) getf.sig N_fix_gr = N_fix
- nop.i 999
-//
-// Case 2: Convert integer N_fix back to normalized floating-point value.
-//
-(p10) br.cond.spnt L(TANL_SMALL_R) ;;
-}
-{ .mib
- nop.m 999
- nop.i 999
-(p8) br.cond.sptk L(TANL_NORMAL_R) ;;
+{ .mbb
+ setf.sig B_mask2 = bmask2 // Form mask to form B from r
+(p10) br.cond.spnt TANL_SMALL_R // Branch if 0 < |x| < 1/4
+(p8) br.cond.spnt TANL_NORMAL_R // Branch if 1/4 <= |x| < pi/4
}
+;;
+
+// Here if pi/4 <= |x| < 2^24
//
// Case 1: PR_3 is only affected when PR_1 is set.
//
-{ .mmi
-(p9) ldfs TWO_TO_NEG33 = [table_ptr2], 4 ;;
//
-// Case 2: Load 2**(-33).
+// Case 2: w = N * P_2
+// Case 2: s_val = -N * P_1 + Arg
//
-(p9) ldfs NEGTWO_TO_NEG33 = [table_ptr2], 4
- nop.i 999 ;;
+
+{ .mfi
+ nop.m 999
+ fnma.s1 s_val = N, P_1, Norm_Arg
+ nop.i 999
}
{ .mfi
- nop.m 999
-//
-// Case 2: Load -2**(-33).
-//
-(p9) fnma.s1 s_val = N, P_1, Arg
- nop.i 999
+ nop.m 999
+ fmpy.s1 w = N, P_2 // w = N * P_2 for |s| >= 2^-33
+ nop.i 999
}
+;;
+
+// Case 2_reduce: w = N * P_3 (change sign)
{ .mfi
- nop.m 999
-(p9) fmpy.s1 w = N, P_2
- nop.i 999 ;;
+ nop.m 999
+ fmpy.s1 w2 = N, P_3 // w = N * P_3 for |s| < 2^-33
+ nop.i 999
}
+;;
+
+// Case 1_reduce: r = s + w (change sign)
{ .mfi
- nop.m 999
-//
-// Case 2: w = N * P_2
-// Case 2: s_val = -N * P_1 + Arg
-//
-(p0) fcmp.lt.unc.s1 p9,p8 = s_val, TWO_TO_NEG33
- nop.i 999 ;;
+ nop.m 999
+ fsub.s1 r = s_val, w // r = s_val - w for |s| >= 2^-33
+ nop.i 999
}
+;;
+
+// Case 2_reduce: U_1 = N * P_2 + w
{ .mfi
- nop.m 999
+ nop.m 999
+ fma.s1 U_1 = N, P_2, w2 // U_1 = N * P_2 + w for |s| < 2^-33
+ nop.i 999
+}
+;;
+
//
// Decide between case_1 and case_2 reduce:
+// Case 1_reduce: |s| >= 2**(-33)
+// Case 2_reduce: |s| < 2**(-33)
//
-(p9) fcmp.gt.s1 p9, p8 = s_val, NEGTWO_TO_NEG33
- nop.i 999 ;;
+{ .mfi
+ nop.m 999
+ fcmp.lt.s1 p9, p8 = s_val, TWO_TO_NEG33
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-//
-// Case 1_reduce: s <= -2**(-33) or s >= 2**(-33)
-// Case 2_reduce: -2**(-33) < s < 2**(-33)
-//
-(p8) fsub.s1 r = s_val, w
- nop.i 999
+ nop.m 999
+(p9) fcmp.gt.s1 p9, p8 = s_val, NEGTWO_TO_NEG33
+ nop.i 999
}
+;;
+
+// Case 1_reduce: c = s - r
{ .mfi
- nop.m 999
-(p9) fmpy.s1 w = N, P_3
- nop.i 999 ;;
+ nop.m 999
+ fsub.s1 c = s_val, r // c = s_val - r for |s| >= 2^-33
+ nop.i 999
}
+;;
+
+// Case 2_reduce: r is complete here - continue to calculate c .
+// r = s - U_1
{ .mfi
- nop.m 999
-(p9) fma.s1 U_1 = N, P_2, w
- nop.i 999
+ nop.m 999
+(p9) fsub.s1 r = s_val, U_1
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
+(p9) fms.s1 U_2 = N, P_2, U_1
+ nop.i 999
+}
+;;
+
//
// Case 1_reduce: Is |r| < 2**(-2), if so set PR_10
-// else set PR_11.
+// else set PR_13.
//
-(p8) fsub.s1 c = s_val, r
- nop.i 999 ;;
-}
+
{ .mfi
- nop.m 999
-//
-// Case 1_reduce: r = s + w (change sign)
-// Case 2_reduce: w = N * P_3 (change sign)
-//
-(p8) fcmp.lt.unc.s1 p10, p11 = r, TWO_TO_NEG2
- nop.i 999 ;;
+ nop.m 999
+ fand B = B_mask1, r
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p10) fcmp.gt.s1 p10, p11 = r, NEGTWO_TO_NEG2
- nop.i 999 ;;
+ nop.m 999
+(p8) fcmp.lt.unc.s1 p10, p13 = r, TWO_TO_NEG2
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p9) fsub.s1 r = s_val, U_1
- nop.i 999
+(p8) getf.sig sig_r = r // Get signif of r if |s| >= 2^-33
+ nop.f 999
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-//
+(p8) getf.exp exp_r = r // Extract signexp of r if |s| >= 2^-33
+(p10) fcmp.gt.s1 p10, p13 = r, NEGTWO_TO_NEG2
+ nop.i 999
+}
+;;
+
// Case 1_reduce: c is complete here.
+// Case 1: Branch to SMALL_R or NORMAL_R.
// c = c + w (w has not been negated.)
-// Case 2_reduce: r is complete here - continue to calculate c .
-// r = s - U_1
-//
-(p9) fms.s1 U_2 = N, P_2, U_1
- nop.i 999 ;;
-}
{ .mfi
- nop.m 999
+ nop.m 999
+(p8) fsub.s1 c = c, w // c = c - w for |s| >= 2^-33
+ nop.i 999
+}
+{ .mbb
+ nop.m 999
+(p10) br.cond.spnt TANL_SMALL_R // Branch if pi/4 < |x| < 2^24 and |r|<1/4
+(p13) br.cond.sptk TANL_NORMAL_R_A // Branch if pi/4 < |x| < 2^24 and |r|>=1/4
+}
+;;
+
+
+// Here if pi/4 < |x| < 2^24 and |s| < 2^-33
//
-// Case 1_reduce: c = s - r
-// Case 2_reduce: U_1 = N * P_2 + w
+// Is i_1 = lsb of N_fix_gr even or odd?
+// if i_1 == 0, set p11, else set p12.
//
-(p8) fsub.s1 c = c, w
- nop.i 999 ;;
-}
{ .mfi
- nop.m 999
-(p9) fsub.s1 s_val = s_val, r
- nop.i 999
+ nop.m 999
+ fsub.s1 s_val = s_val, r
+ add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl)
}
-{ .mfb
- nop.m 999
+{ .mfi
+ nop.m 999
//
// Case 2_reduce:
// U_2 = N * P_2 - U_1
// Not needed until later.
//
-(p9) fadd.s1 U_2 = U_2, w
+ fadd.s1 U_2 = U_2, w2
//
// Case 2_reduce:
// s = s - r
// U_2 = U_2 + w
//
-(p10) br.cond.spnt L(TANL_SMALL_R) ;;
-}
-{ .mib
- nop.m 999
- nop.i 999
-(p11) br.cond.sptk L(TANL_NORMAL_R) ;;
+ nop.i 999
}
-{ .mii
- nop.m 999
+;;
+
//
// Case 2_reduce:
// c = c - U_2
// c is complete here
// Argument reduction ends here.
//
-(p9) extr.u i_1 = N_fix_gr, 0, 1 ;;
-(p9) cmp.eq.unc p11, p12 = 0x0000,i_1 ;;
-}
-{ .mfi
- nop.m 999
-//
-// Is i_1 even or odd?
-// if i_1 == 0, set p11, else set p12.
-//
-(p11) fmpy.s1 rsq = r, r
- nop.i 999 ;;
-}
{ .mfi
- nop.m 999
-(p12) frcpa.s1 S_hi,p0 = f1, r
- nop.i 999
+ nop.m 999
+ fmpy.s1 rsq = r, r
+ tbit.z p11, p12 = N_fix_gr, 0 ;; // Set p11 if N even, p12 if odd
}
-
-
-//
-// Case 1: Branch to SMALL_R or NORMAL_R.
-// Case 1 is done now.
-//
-
{ .mfi
-(p9) addl table_ptr1 = @ltoff(TANL_BASE_CONSTANTS), gp
-(p9) fsub.s1 c = s_val, U_1
- nop.i 999 ;;
+ nop.m 999
+(p12) frcpa.s1 S_hi,p0 = f1, r
+ nop.i 999
}
-;;
-
-{ .mmi
-(p9) ld8 table_ptr1 = [table_ptr1]
+{ .mfi
nop.m 999
+ fsub.s1 c = s_val, U_1
nop.i 999
}
;;
-
{ .mmi
-(p9) add table_ptr1 = 224, table_ptr1 ;;
-(p9) ldfe P1_1 = [table_ptr1],144
- nop.i 999 ;;
+ add table_ptr1 = 160, table_base ;; // Point to tanl_table_p1
+ ldfe P1_1 = [table_ptr1],144
+ nop.i 999 ;;
}
//
-// Get [i_1] - lsb of N_fix_gr .
// Load P1_1 and point to Q1_1 .
//
{ .mfi
-(p9) ldfe Q1_1 = [table_ptr1] , 0
+ ldfe Q1_1 = [table_ptr1]
//
// N even: rsq = r * Z
// N odd: S_hi = frcpa(r)
//
-(p12) fmerge.ns S_hi = S_hi, S_hi
- nop.i 999
+(p12) fmerge.ns S_hi = S_hi, S_hi
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// Case 2_reduce:
// c = s - U_1
//
-(p9) fsub.s1 c = c, U_2
- nop.i 999 ;;
+(p9) fsub.s1 c = c, U_2
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
+ nop.m 999
+(p12) fma.s1 poly1 = S_hi, r, f1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: Change sign of S_hi
//
-(p11) fmpy.s1 rsq = rsq, P1_1
- nop.i 999 ;;
+(p11) fmpy.s1 rsq = rsq, P1_1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999 ;;
+ nop.m 999
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: rsq = rsq * P1_1
// N odd: poly1 = 1.0 + S_hi * r 16 bits partial account for necessary
//
-(p11) fma.s1 Result = r, rsq, c
- nop.i 999 ;;
+(p11) fma.s1 Poly = r, rsq, c
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// N even: Result = c + r * rsq
+// N even: Poly = c + r * rsq
// N odd: S_hi = S_hi + S_hi*poly1 16 bits account for necessary
//
-(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
+(p12) fma.s1 poly1 = S_hi, r, f1
+(p11) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// N even: Result = Result + r
+// N even: Result = Poly + r
// N odd: poly1 = 1.0 + S_hi * r 32 bits partial
//
-(p11) fadd.s0 Result = r, Result
- nop.i 999 ;;
+(p14) fadd.s0 Result = r, Poly // for tanl
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p15) fms.s0 Result = r, mOne, Poly // for cotl
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999 ;;
+ nop.m 999
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: Result1 = Result + r
// N odd: S_hi = S_hi * poly1 + S_hi 32 bits
//
-(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
+(p12) fma.s1 poly1 = S_hi, r, f1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: poly1 = S_hi * r + 1.0 64 bits partial
//
-(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999 ;;
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: poly1 = S_hi * poly + 1.0 64 bits
//
-(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
+(p12) fma.s1 poly1 = S_hi, r, f1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: poly1 = S_hi * r + 1.0
//
-(p12) fma.s1 poly1 = S_hi, c, poly1
- nop.i 999 ;;
+(p12) fma.s1 poly1 = S_hi, c, poly1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: poly1 = S_hi * c + poly1
//
-(p12) fmpy.s1 S_lo = S_hi, poly1
- nop.i 999 ;;
+(p12) fmpy.s1 S_lo = S_hi, poly1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: S_lo = S_hi * poly1
//
-(p12) fma.s1 S_lo = Q1_1, r, S_lo
- nop.i 999
+(p12) fma.s1 S_lo = Q1_1, r, S_lo
+(p12) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: Result = S_hi + S_lo
//
-(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
- nop.i 999 ;;
+ fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
+ nop.i 999 ;;
}
-{ .mfb
- nop.m 999
+{ .mfi
+ nop.m 999
//
// N odd: S_lo = S_lo + Q1_1 * r
//
-(p12) fadd.s0 Result = S_hi, S_lo
-(p0) br.ret.sptk b0 ;;
+(p14) fadd.s0 Result = S_hi, S_lo // for tanl
+ nop.i 999
+}
+{ .mfb
+ nop.m 999
+(p15) fms.s0 Result = S_hi, mOne, S_lo // for cotl
+ br.ret.sptk b0 ;; // Exit for pi/4 <= |x| < 2^24 and |s| < 2^-33
}
-L(TANL_LARGER_ARG):
-
+TANL_LARGER_ARG:
+// Here if 2^24 <= |x| < 2^63
//
// ARGUMENT REDUCTION CODE - CASE 3 and 4
//
-{ .mfi
-(p0) addl table_ptr1 = @ltoff(TANL_BASE_CONSTANTS), gp
-(p0) fmpy.s1 N_0 = Arg, Inv_P_0
- nop.i 999
+{ .mmf
+ mov GR_exp_2tom14 = 0xffff - 14 // Form signexp of 2^-14
+ mov GR_exp_m2tom14 = 0x2ffff - 14 // Form signexp of -2^-14
+ fmpy.s1 N_0 = Norm_Arg, Inv_P_0
}
;;
{ .mmi
-(p0) ld8 table_ptr1 = [table_ptr1]
- nop.m 999
+ setf.exp TWO_TO_NEG14 = GR_exp_2tom14 // Form 2^-14
+ setf.exp NEGTWO_TO_NEG14 = GR_exp_m2tom14// Form -2^-14
nop.i 999
}
;;
@@ -1622,661 +1806,605 @@ L(TANL_LARGER_ARG):
// N_0 = Arg * Inv_P_0
//
{ .mmi
-(p0) add table_ptr1 = 8, table_ptr1 ;;
-//
-// Point to 2*-14
-//
-(p0) ldfs TWO_TO_NEG14 = [table_ptr1], 4
- nop.i 999 ;;
+ add table_ptr2 = 144, table_base ;; // Point to 2^-2
+ ldfps TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2]
+ nop.i 999
}
-//
-// Load 2**(-14).
-//
-{ .mmi
-(p0) ldfs NEGTWO_TO_NEG14 = [table_ptr1], 180 ;;
+;;
+
//
// N_0_fix = integer part of N_0 .
-// Adjust table_ptr1 to beginning of table.
//
-(p0) ldfs TWO_TO_NEG2 = [table_ptr1], 4
- nop.i 999 ;;
-}
//
// Make N_0 the integer part.
//
{ .mfi
-(p0) ldfs NEGTWO_TO_NEG2 = [table_ptr1]
-//
-// Load -2**(-14).
-//
-(p0) fcvt.fx.s1 N_0_fix = N_0
- nop.i 999 ;;
+ nop.m 999
+ fcvt.fx.s1 N_0_fix = N_0
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p0) fcvt.xf N_0 = N_0_fix
- nop.i 999 ;;
+ setf.sig B_mask1 = bmask1 // Form mask to get 5 msb of r
+ fcvt.xf N_0 = N_0_fix
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p0) fnma.s1 ArgPrime = N_0, P_0, Arg
- nop.i 999
+ setf.sig B_mask2 = bmask2 // Form mask to form B from r
+ fnma.s1 ArgPrime = N_0, P_0, Norm_Arg
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p0) fmpy.s1 w = N_0, d_1
- nop.i 999 ;;
+ nop.m 999
+ fmpy.s1 w = N_0, d_1
+ nop.i 999 ;;
}
-{ .mfi
- nop.m 999
//
// ArgPrime = -N_0 * P_0 + Arg
// w = N_0 * d_1
//
-(p0) fmpy.s1 N = ArgPrime, two_by_PI
- nop.i 999 ;;
-}
-{ .mfi
- nop.m 999
//
// N = ArgPrime * 2/pi
//
-(p0) fcvt.fx.s1 N_fix = N
- nop.i 999 ;;
-}
+// fcvt.fx.s1 N_fix = N
+// Use special scaling to right shift so N=Arg * 2/pi is in rightmost bits
+// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24
{ .mfi
- nop.m 999
-//
-// N_fix is the integer part.
-//
-(p0) fcvt.xf N = N_fix
- nop.i 999 ;;
+ nop.m 999
+ fma.s1 N_fix = ArgPrime, FR_inv_pi_2to63, FR_rshf_2to64
+
+ nop.i 999 ;;
}
+// Convert integer N_fix back to normalized floating-point value.
{ .mfi
-(p0) getf.sig N_fix_gr = N_fix
- nop.f 999
- nop.i 999 ;;
+ nop.m 999
+ fms.s1 N = N_fix, FR_2tom64, FR_rshf // Use scaling to get N floated
+ nop.i 999
}
-{ .mfi
- nop.m 999
+;;
+
//
// N is the integer part of the reduced-reduced argument.
// Put the integer in a GP register.
//
-(p0) fnma.s1 s_val = N, P_1, ArgPrime
- nop.i 999
-}
{ .mfi
- nop.m 999
-(p0) fnma.s1 w = N, P_2, w
- nop.i 999 ;;
+ getf.sig N_fix_gr = N_fix
+ nop.f 999
+ nop.i 999
}
-{ .mfi
- nop.m 999
+;;
+
//
// s_val = -N*P_1 + ArgPrime
// w = -N*P_2 + w
//
-(p0) fcmp.lt.unc.s1 p11, p10 = s_val, TWO_TO_NEG14
- nop.i 999 ;;
-}
-{ .mfi
- nop.m 999
-(p11) fcmp.gt.s1 p11, p10 = s_val, NEGTWO_TO_NEG14
- nop.i 999 ;;
-}
{ .mfi
- nop.m 999
-//
-// Case 3: r = s_val + w (Z complete)
-// Case 4: U_hi = N_0 * d_1
-//
-(p10) fmpy.s1 V_hi = N, P_2
- nop.i 999
+ nop.m 999
+ fnma.s1 s_val = N, P_1, ArgPrime
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p11) fmpy.s1 U_hi = N_0, d_1
- nop.i 999 ;;
+ nop.m 999
+ fnma.s1 w = N, P_2, w
+ nop.i 999
}
-{ .mfi
- nop.m 999
-//
-// Case 3: r = s_val + w (Z complete)
+;;
+
+// Case 4: V_hi = N * P_2
// Case 4: U_hi = N_0 * d_1
-//
-(p11) fmpy.s1 V_hi = N, P_2
- nop.i 999
-}
{ .mfi
- nop.m 999
-(p11) fmpy.s1 U_hi = N_0, d_1
- nop.i 999 ;;
+ nop.m 999
+ fmpy.s1 V_hi = N, P_2 // V_hi = N * P_2 for |s| < 2^-14
+ nop.i 999
}
{ .mfi
- nop.m 999
-//
-// Decide between case 3 and 4:
-// Case 3: s <= -2**(-14) or s >= 2**(-14)
-// Case 4: -2**(-14) < s < 2**(-14)
-//
-(p10) fadd.s1 r = s_val, w
- nop.i 999
+ nop.m 999
+ fmpy.s1 U_hi = N_0, d_1 // U_hi = N_0 * d_1 for |s| < 2^-14
+ nop.i 999
}
+;;
+
+// Case 3: r = s_val + w (Z complete)
+// Case 4: w = N * P_3
{ .mfi
- nop.m 999
-(p11) fmpy.s1 w = N, P_3
- nop.i 999 ;;
+ nop.m 999
+ fadd.s1 r = s_val, w // r = s_val + w for |s| >= 2^-14
+ nop.i 999
}
{ .mfi
- nop.m 999
-//
-// Case 4: We need abs of both U_hi and V_hi - dont
-// worry about switched sign of V_hi .
-//
-(p11) fsub.s1 A = U_hi, V_hi
- nop.i 999
+ nop.m 999
+ fmpy.s1 w2 = N, P_3 // w = N * P_3 for |s| < 2^-14
+ nop.i 999
}
-{ .mfi
- nop.m 999
-//
+;;
+
// Case 4: A = U_hi + V_hi
// Note: Worry about switched sign of V_hi, so subtract instead of add.
-//
-(p11) fnma.s1 V_lo = N, P_2, V_hi
- nop.i 999 ;;
+// Case 4: V_lo = -N * P_2 - V_hi (U_hi is in place of V_hi in writeup)
+// Note: the (-) is still missing for V_hi.
+{ .mfi
+ nop.m 999
+ fsub.s1 A = U_hi, V_hi // A = U_hi - V_hi for |s| < 2^-14
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p11) fms.s1 U_lo = N_0, d_1, U_hi
- nop.i 999 ;;
+ nop.m 999
+ fnma.s1 V_lo = N, P_2, V_hi // V_lo = V_hi - N * P_2 for |s| < 2^-14
+ nop.i 999
}
+;;
+
+// Decide between case 3 and 4:
+// Case 3: |s| >= 2**(-14) Set p10
+// Case 4: |s| < 2**(-14) Set p11
+//
+// Case 4: U_lo = N_0 * d_1 - U_hi
{ .mfi
- nop.m 999
-(p11) fabs V_hiabs = V_hi
- nop.i 999
+ nop.m 999
+ fms.s1 U_lo = N_0, d_1, U_hi // U_lo = N_0*d_1 - U_hi for |s| < 2^-14
+ nop.i 999
}
{ .mfi
- nop.m 999
-//
-// Case 4: V_hi = N * P_2
-// w = N * P_3
-// Note the product does not include the (-) as in the writeup
-// so (-) missing for V_hi and w .
-(p10) fadd.s1 r = s_val, w
- nop.i 999 ;;
+ nop.m 999
+ fcmp.lt.s1 p11, p10 = s_val, TWO_TO_NEG14
+ nop.i 999
}
+;;
+
+// Case 4: We need abs of both U_hi and V_hi - dont
+// worry about switched sign of V_hi.
{ .mfi
- nop.m 999
-//
-// Case 3: c = s_val - r
-// Case 4: U_lo = N_0 * d_1 - U_hi
-//
-(p11) fabs U_hiabs = U_hi
- nop.i 999
+ nop.m 999
+ fabs V_hiabs = V_hi // |V_hi| for |s| < 2^-14
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p11) fmpy.s1 w = N, P_3
- nop.i 999 ;;
+ nop.m 999
+(p11) fcmp.gt.s1 p11, p10 = s_val, NEGTWO_TO_NEG14
+ nop.i 999
}
+;;
+
+// Case 3: c = s_val - r
{ .mfi
- nop.m 999
-//
-// Case 4: Set P_12 if U_hiabs >= V_hiabs
-//
-(p11) fadd.s1 C_hi = s_val, A
- nop.i 999 ;;
+ nop.m 999
+ fabs U_hiabs = U_hi // |U_hi| for |s| < 2^-14
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
+ fsub.s1 c = s_val, r // c = s_val - r for |s| >= 2^-14
+ nop.i 999
+}
+;;
+
+// For Case 3, |s| >= 2^-14, determine if |r| < 1/4
//
// Case 4: C_hi = s_val + A
//
-(p11) fadd.s1 t = U_lo, V_lo
- nop.i 999 ;;
-}
{ .mfi
- nop.m 999
-//
-// Case 3: Is |r| < 2**(-2), if so set PR_7
-// else set PR_8.
-// Case 3: If PR_7 is set, prepare to branch to Small_R.
-// Case 3: If PR_8 is set, prepare to branch to Normal_R.
-//
-(p10) fsub.s1 c = s_val, r
- nop.i 999 ;;
+ nop.m 999
+(p11) fadd.s1 C_hi = s_val, A // C_hi = s_val + A for |s| < 2^-14
+ nop.i 999
}
{ .mfi
- nop.m 999
-//
-// Case 3: c = (s - r) + w (c complete)
-//
-(p11) fcmp.ge.unc.s1 p12, p13 = U_hiabs, V_hiabs
- nop.i 999
+ nop.m 999
+(p10) fcmp.lt.unc.s1 p14, p15 = r, TWO_TO_NEG2
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p11) fms.s1 w = N_0, d_2, w
- nop.i 999 ;;
+ getf.sig sig_r = r // Get signif of r if |s| >= 2^-33
+ fand B = B_mask1, r
+ nop.i 999
}
+;;
+
+// Case 4: t = U_lo + V_lo
{ .mfi
- nop.m 999
-//
-// Case 4: V_hi = N * P_2
-// w = N * P_3
-// Note the product does not include the (-) as in the writeup
-// so (-) missing for V_hi and w .
-//
-(p10) fcmp.lt.unc.s1 p14, p15 = r, TWO_TO_NEG2
- nop.i 999 ;;
+ getf.exp exp_r = r // Extract signexp of r if |s| >= 2^-33
+(p11) fadd.s1 t = U_lo, V_lo // t = U_lo + V_lo for |s| < 2^-14
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p14) fcmp.gt.s1 p14, p15 = r, NEGTWO_TO_NEG2
- nop.i 999 ;;
+ nop.i 999
}
-{ .mfb
- nop.m 999
+;;
+
+// Case 3: c = (s - r) + w (c complete)
+{ .mfi
+ nop.m 999
+(p10) fadd.s1 c = c, w // c = c + w for |s| >= 2^-14
+ nop.i 999
+}
+{ .mbb
+ nop.m 999
+(p14) br.cond.spnt TANL_SMALL_R // Branch if 2^24 <= |x| < 2^63 and |r|< 1/4
+(p15) br.cond.sptk TANL_NORMAL_R_A // Branch if 2^24 <= |x| < 2^63 and |r|>=1/4
+}
+;;
+
+
+// Here if 2^24 <= |x| < 2^63 and |s| < 2^-14 >>>>>>> Case 4.
//
-// Case 4: V_lo = -N * P_2 - V_hi (U_hi is in place of V_hi in writeup)
-// Note: the (-) is still missing for V_hi .
+// Case 4: Set P_12 if U_hiabs >= V_hiabs
// Case 4: w = w + N_0 * d_2
// Note: the (-) is now incorporated in w .
-//
-(p10) fadd.s1 c = c, w
-//
-// Case 4: t = U_lo + V_lo
-// Note: remember V_lo should be (-), subtract instead of add. NO
-//
-(p14) br.cond.spnt L(TANL_SMALL_R) ;;
-}
-{ .mib
- nop.m 999
- nop.i 999
-(p15) br.cond.spnt L(TANL_NORMAL_R) ;;
-}
{ .mfi
- nop.m 999
-//
-// Case 3: Vector off when |r| < 2**(-2). Recall that PR_3 will be true.
-// The remaining stuff is for Case 4.
-//
-(p12) fsub.s1 a = U_hi, A
-(p11) extr.u i_1 = N_fix_gr, 0, 1 ;;
+ add table_ptr1 = 160, table_base // Point to tanl_table_p1
+ fcmp.ge.unc.s1 p12, p13 = U_hiabs, V_hiabs
+ nop.i 999
}
{ .mfi
- nop.m 999
-//
-// Case 4: C_lo = s_val - C_hi
-//
-(p11) fadd.s1 t = t, w
- nop.i 999
+ nop.m 999
+ fms.s1 w2 = N_0, d_2, w2
+ nop.i 999
}
+;;
+
+// Case 4: C_lo = s_val - C_hi
{ .mfi
- nop.m 999
-(p13) fadd.s1 a = V_hi, A
- nop.i 999 ;;
+ ldfe P1_1 = [table_ptr1], 16 // Load P1_1
+ fsub.s1 C_lo = s_val, C_hi
+ nop.i 999
}
-
-
+;;
//
// Case 4: a = U_hi - A
// a = V_hi - A (do an add to account for missing (-) on V_hi
//
-
{ .mfi
-(p11) addl table_ptr1 = @ltoff(TANL_BASE_CONSTANTS), gp
-(p11) fsub.s1 C_lo = s_val, C_hi
- nop.i 999
+ ldfe P1_2 = [table_ptr1], 128 // Load P1_2
+(p12) fsub.s1 a = U_hi, A
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p13) fadd.s1 a = V_hi, A
+ nop.i 999
}
;;
+// Case 4: t = U_lo + V_lo + w
+{ .mfi
+ ldfe Q1_1 = [table_ptr1], 16 // Load Q1_1
+ fadd.s1 t = t, w2
+ nop.i 999
+}
+;;
-
-//
// Case 4: a = (U_hi - A) + V_hi
// a = (V_hi - A) + U_hi
// In each case account for negative missing form V_hi .
//
-
-
-{ .mmi
-(p11) ld8 table_ptr1 = [table_ptr1]
+{ .mfi
+ ldfe Q1_2 = [table_ptr1], 16 // Load Q1_2
+(p12) fsub.s1 a = a, V_hi
+ nop.i 999
+}
+{ .mfi
nop.m 999
+(p13) fsub.s1 a = U_hi, a
nop.i 999
}
;;
-
//
// Case 4: C_lo = (s_val - C_hi) + A
//
-{ .mmi
-(p11) add table_ptr1 = 224, table_ptr1 ;;
-(p11) ldfe P1_1 = [table_ptr1], 16
- nop.i 999 ;;
-}
{ .mfi
-(p11) ldfe P1_2 = [table_ptr1], 128
-//
-// Case 4: w = U_lo + V_lo + w
-//
-(p12) fsub.s1 a = a, V_hi
- nop.i 999 ;;
-}
-//
-// Case 4: r = C_hi + C_lo
-//
-{ .mfi
-(p11) ldfe Q1_1 = [table_ptr1], 16
-(p11) fadd.s1 C_lo = C_lo, A
- nop.i 999 ;;
+ nop.m 999
+ fadd.s1 C_lo = C_lo, A
+ nop.i 999 ;;
}
//
-// Case 4: c = C_hi - r
-// Get [i_1] - lsb of N_fix_gr.
+// Case 4: t = t + a
//
{ .mfi
-(p11) ldfe Q1_2 = [table_ptr1], 16
- nop.f 999
- nop.i 999 ;;
+ nop.m 999
+ fadd.s1 t = t, a
+ nop.i 999
}
+;;
+
+// Case 4: C_lo = C_lo + t
+// Case 4: r = C_hi + C_lo
{ .mfi
- nop.m 999
-(p13) fsub.s1 a = U_hi, a
- nop.i 999 ;;
+ nop.m 999
+ fadd.s1 C_lo = C_lo, t
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p11) fadd.s1 t = t, a
- nop.i 999 ;;
+ nop.m 999
+ fadd.s1 r = C_hi, C_lo
+ nop.i 999
}
-{ .mfi
- nop.m 999
+;;
+
//
-// Case 4: t = t + a
+// Case 4: c = C_hi - r
//
-(p11) fadd.s1 C_lo = C_lo, t
- nop.i 999 ;;
-}
{ .mfi
- nop.m 999
-//
-// Case 4: C_lo = C_lo + t
-//
-(p11) fadd.s1 r = C_hi, C_lo
- nop.i 999 ;;
+ nop.m 999
+ fsub.s1 c = C_hi, r
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p11) fsub.s1 c = C_hi, r
- nop.i 999
+ nop.m 999
+ fmpy.s1 rsq = r, r
+ add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl)
}
-{ .mfi
- nop.m 999
-//
+;;
+
// Case 4: c = c + C_lo finished.
-// Is i_1 even or odd?
-// if i_1 == 0, set PR_4, else set PR_5.
//
-// r and c have been computed.
-// We known whether this is the sine or cosine routine.
-// Make sure ftz mode is set - should be automatic when using wre
-(p0) fmpy.s1 rsq = r, r
- nop.i 999 ;;
-}
+// Is i_1 = lsb of N_fix_gr even or odd?
+// if i_1 == 0, set PR_11, else set PR_12.
+//
{ .mfi
- nop.m 999
-(p11) fadd.s1 c = c , C_lo
-(p11) cmp.eq.unc p11, p12 = 0x0000, i_1 ;;
+ nop.m 999
+ fadd.s1 c = c , C_lo
+ tbit.z p11, p12 = N_fix_gr, 0
}
+;;
+
+// r and c have been computed.
{ .mfi
- nop.m 999
+ nop.m 999
(p12) frcpa.s1 S_hi, p0 = f1, r
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: Change sign of S_hi
//
-(p11) fma.s1 Result = rsq, P1_2, P1_1
- nop.i 999 ;;
+(p11) fma.s1 Poly = rsq, P1_2, P1_1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 P = rsq, Q1_2, Q1_1
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: Result = S_hi + S_lo (User supplied rounding mode for C1)
//
-(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
- nop.i 999 ;;
+ fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: rsq = r * r
// N odd: S_hi = frcpa(r)
//
(p12) fmerge.ns S_hi = S_hi, S_hi
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: rsq = rsq * P1_2 + P1_1
// N odd: poly1 = 1.0 + S_hi * r 16 bits partial account for necessary
//
-(p11) fmpy.s1 Result = rsq, Result
- nop.i 999 ;;
+(p11) fmpy.s1 Poly = rsq, Poly
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 poly1 = S_hi, r,f1
- nop.i 999
+(p11) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// N even: Result = Result * rsq
+// N even: Poly = Poly * rsq
// N odd: S_hi = S_hi + S_hi*poly1 16 bits account for necessary
//
-(p11) fma.s1 Result = r, Result, c
- nop.i 999 ;;
+(p11) fma.s1 Poly = r, Poly, c
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: S_hi = S_hi * poly1 + S_hi 32 bits
//
-(p11) fadd.s0 Result= r, Result
- nop.i 999 ;;
+(p14) fadd.s0 Result = r, Poly // for tanl
+ nop.i 999 ;;
}
+
+.pred.rel "mutex",p15,p12
{ .mfi
- nop.m 999
+ nop.m 999
+(p15) fms.s0 Result = r, mOne, Poly // for cotl
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// N even: Result = Result * r + c
+// N even: Poly = Poly * r + c
// N odd: poly1 = 1.0 + S_hi * r 32 bits partial
//
(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// N even: Result1 = Result + r (Rounding mode S0)
+// N even: Result = Poly + r (Rounding mode S0)
// N odd: poly1 = S_hi * r + 1.0 64 bits partial
//
(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: poly1 = S_hi * poly + S_hi 64 bits
//
(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: poly1 = S_hi * r + 1.0
//
(p12) fma.s1 poly1 = S_hi, c, poly1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: poly1 = S_hi * c + poly1
//
(p12) fmpy.s1 S_lo = S_hi, poly1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: S_lo = S_hi * poly1
//
(p12) fma.s1 S_lo = P, r, S_lo
- nop.i 999 ;;
+(p12) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl
+}
+
+{ .mfi
+ nop.m 999
+(p14) fadd.s0 Result = S_hi, S_lo // for tanl
+ nop.i 999
}
{ .mfb
- nop.m 999
+ nop.m 999
//
// N odd: S_lo = S_lo + r * P
//
-(p12) fadd.s0 Result = S_hi, S_lo
-(p0) br.ret.sptk b0 ;;
+(p15) fms.s0 Result = S_hi, mOne, S_lo // for cotl
+ br.ret.sptk b0 ;; // Exit for 2^24 <= |x| < 2^63 and |s| < 2^-14
}
-L(TANL_SMALL_R):
-{ .mii
- nop.m 999
-(p0) extr.u i_1 = N_fix_gr, 0, 1 ;;
-(p0) cmp.eq.unc p11, p12 = 0x0000, i_1
-}
+TANL_SMALL_R:
+// Here if |r| < 1/4
+// r and c have been computed.
+// *****************************************************************
+// *****************************************************************
+// *****************************************************************
+// N odd: S_hi = frcpa(r)
+// Get [i_1] - lsb of N_fix_gr. Set p11 if N even, p12 if N odd.
+// N even: rsq = r * r
{ .mfi
- nop.m 999
-(p0) fmpy.s1 rsq = r, r
- nop.i 999 ;;
+ add table_ptr1 = 160, table_base // Point to tanl_table_p1
+ frcpa.s1 S_hi, p0 = f1, r // S_hi for N odd
+ add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl)
}
{ .mfi
-(p0) addl table_ptr1 = @ltoff(TANL_BASE_CONSTANTS), gp
-(p12) frcpa.s1 S_hi, p0 = f1, r
- nop.i 999
+ add table_ptr2 = 400, table_base // Point to Q1_7
+ fmpy.s1 rsq = r, r
+ nop.i 999
}
;;
-
{ .mmi
-(p0) ld8 table_ptr1 = [table_ptr1]
- nop.m 999
- nop.i 999
+ ldfe P1_1 = [table_ptr1], 16
+;;
+ ldfe P1_2 = [table_ptr1], 16
+ tbit.z p11, p12 = N_fix_gr, 0
}
;;
-// *****************************************************************
-// *****************************************************************
-// *****************************************************************
-
-{ .mmi
-(p0) add table_ptr1 = 224, table_ptr1 ;;
-(p0) ldfe P1_1 = [table_ptr1], 16
- nop.i 999 ;;
-}
-// r and c have been computed.
-// We known whether this is the sine or cosine routine.
-// Make sure ftz mode is set - should be automatic when using wre
-// |r| < 2**(-2)
{ .mfi
-(p0) ldfe P1_2 = [table_ptr1], 16
-(p11) fmpy.s1 r_to_the_8 = rsq, rsq
- nop.i 999 ;;
+ ldfe P1_3 = [table_ptr1], 96
+ nop.f 999
+ nop.i 999
}
-//
-// Set table_ptr1 to beginning of constant table.
-// Get [i_1] - lsb of N_fix_gr.
-//
+;;
+
{ .mfi
-(p0) ldfe P1_3 = [table_ptr1], 96
-//
-// N even: rsq = r * r
-// N odd: S_hi = frcpa(r)
-//
+(p11) ldfe P1_9 = [table_ptr1], -16
(p12) fmerge.ns S_hi = S_hi, S_hi
- nop.i 999 ;;
+ nop.i 999
}
-//
-// Is i_1 even or odd?
-// if i_1 == 0, set PR_11.
-// if i_1 != 0, set PR_12.
-//
{ .mfi
-(p11) ldfe P1_9 = [table_ptr1], -16
+ nop.m 999
+(p11) fmpy.s1 r_to_the_8 = rsq, rsq
+ nop.i 999
+}
+;;
+
//
// N even: Poly2 = P1_7 + Poly2 * rsq
// N odd: poly2 = Q1_5 + poly2 * rsq
//
+{ .mfi
+(p11) ldfe P1_8 = [table_ptr1], -16
(p11) fadd.s1 CORR = rsq, f1
- nop.i 999 ;;
+ nop.i 999
}
-{ .mmi
-(p11) ldfe P1_8 = [table_ptr1], -16 ;;
+;;
+
//
// N even: Poly1 = P1_2 + P1_3 * rsq
-// N odd: poly1 = 1.0 + S_hi * r
+// N odd: poly1 = 1.0 + S_hi * r
// 16 bits partial account for necessary (-1)
//
+{ .mmi
(p11) ldfe P1_7 = [table_ptr1], -16
- nop.i 999 ;;
+;;
+(p11) ldfe P1_6 = [table_ptr1], -16
+ nop.i 999
}
+;;
+
//
// N even: Poly1 = P1_1 + Poly1 * rsq
// N odd: S_hi = S_hi + S_hi * poly1) 16 bits account for necessary
//
-{ .mfi
-(p11) ldfe P1_6 = [table_ptr1], -16
//
// N even: Poly2 = P1_5 + Poly2 * rsq
// N odd: poly2 = Q1_3 + poly2 * rsq
//
+{ .mfi
+(p11) ldfe P1_5 = [table_ptr1], -16
(p11) fmpy.s1 r_to_the_8 = r_to_the_8, r_to_the_8
- nop.i 999 ;;
+ nop.i 999
}
+{ .mfi
+ nop.m 999
+(p12) fma.s1 poly1 = S_hi, r, f1
+ nop.i 999
+}
+;;
+
//
// N even: Poly1 = Poly1 * rsq
// N odd: poly1 = 1.0 + S_hi * r 32 bits partial
//
-{ .mfi
-(p11) ldfe P1_5 = [table_ptr1], -16
-(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
-}
//
// N even: CORR = CORR * c
@@ -2290,44 +2418,30 @@ L(TANL_SMALL_R):
{ .mmf
(p11) ldfe P1_4 = [table_ptr1], -16
-(p0) addl table_ptr2 = @ltoff(TANL_BASE_CONSTANTS), gp
-(p11) fmpy.s1 CORR = CORR, c
-}
-;;
-
-
-{ .mmi
-(p0) ld8 table_ptr2 = [table_ptr2]
nop.m 999
- nop.i 999
+(p11) fmpy.s1 CORR = CORR, c
}
;;
-
-{ .mii
-(p0) add table_ptr2 = 464, table_ptr2
- nop.i 999 ;;
- nop.i 999
-}
{ .mfi
- nop.m 999
+ nop.m 999
(p11) fma.s1 Poly1 = P1_3, rsq, P1_2
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
-(p0) ldfe Q1_7 = [table_ptr2], -16
+(p12) ldfe Q1_7 = [table_ptr2], -16
(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
-(p0) ldfe Q1_6 = [table_ptr2], -16
+(p12) ldfe Q1_6 = [table_ptr2], -16
(p11) fma.s1 Poly2 = P1_9, rsq, P1_8
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mmi
-(p0) ldfe Q1_5 = [table_ptr2], -16 ;;
+(p12) ldfe Q1_5 = [table_ptr2], -16 ;;
(p12) ldfe Q1_4 = [table_ptr2], -16
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
(p12) ldfe Q1_3 = [table_ptr2], -16
@@ -2336,735 +2450,795 @@ L(TANL_SMALL_R):
// N odd: poly2 = Q1_6 + Q1_7 * rsq
//
(p11) fma.s1 Poly1 = Poly1, rsq, P1_1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
(p12) ldfe Q1_2 = [table_ptr2], -16
(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
(p12) ldfe Q1_1 = [table_ptr2], -16
(p11) fma.s1 Poly2 = Poly2, rsq, P1_7
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: CORR = rsq + 1
// N even: r_to_the_8 = rsq * rsq
//
(p11) fmpy.s1 Poly1 = Poly1, rsq
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 poly2 = Q1_7, rsq, Q1_6
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p11) fma.s1 Poly2 = Poly2, rsq, P1_6
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 poly2 = poly2, rsq, Q1_5
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p11) fma.s1 Poly2= Poly2, rsq, P1_5
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 poly2 = poly2, rsq, Q1_4
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: r_to_the_8 = r_to_the_8 * r_to_the_8
// N odd: poly1 = S_hi * r + 1.0 64 bits partial
//
(p11) fma.s1 Poly2 = Poly2, rsq, P1_4
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// N even: Result = CORR + Poly * r
+// N even: Poly = CORR + Poly * r
// N odd: P = Q1_1 + poly2 * rsq
//
(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 poly2 = poly2, rsq, Q1_3
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: Poly2 = P1_4 + Poly2 * rsq
// N odd: poly2 = Q1_2 + poly2 * rsq
//
(p11) fma.s1 Poly = Poly2, r_to_the_8, Poly1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 poly1 = S_hi, c, poly1
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 poly2 = poly2, rsq, Q1_2
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: Poly = Poly1 + Poly2 * r_to_the_8
// N odd: S_hi = S_hi * poly1 + S_hi 64 bits
//
-(p11) fma.s1 Result = Poly, r, CORR
- nop.i 999 ;;
+(p11) fma.s1 Poly = Poly, r, CORR
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
-// N even: Result = r + Result (User supplied rounding mode)
+// N even: Result = r + Poly (User supplied rounding mode)
// N odd: poly1 = S_hi * c + poly1
//
(p12) fmpy.s1 S_lo = S_hi, poly1
- nop.i 999
+(p11) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fma.s1 P = poly2, rsq, Q1_1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: poly1 = S_hi * r + 1.0
//
//
// N odd: S_lo = S_hi * poly1
//
-(p11) fadd.s0 Result = Result, r
- nop.i 999 ;;
+(p14) fadd.s0 Result = Poly, r // for tanl
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
+(p15) fms.s0 Result = Poly, mOne, r // for cotl
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
//
// N odd: S_lo = Q1_1 * c + S_lo
//
(p12) fma.s1 S_lo = Q1_1, c, S_lo
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
- nop.i 999 ;;
+ nop.m 999
+ fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: Result = S_lo + r * P
//
(p12) fma.s1 Result = P, r, S_lo
- nop.i 999 ;;
+(p12) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl
}
-{ .mfb
- nop.m 999
+
//
// N odd: Result = Result + S_hi (user supplied rounding mode)
//
-(p12) fadd.s0 Result = Result, S_hi
-(p0) br.ret.sptk b0 ;;
+{ .mfi
+ nop.m 999
+(p14) fadd.s0 Result = Result, S_hi // for tanl
+ nop.i 999
+}
+{ .mfb
+ nop.m 999
+(p15) fms.s0 Result = Result, mOne, S_hi // for cotl
+ br.ret.sptk b0 ;; // Exit |r| < 1/4 path
}
-L(TANL_NORMAL_R):
-{ .mfi
-(p0) getf.sig sig_r = r
+TANL_NORMAL_R:
+// Here if 1/4 <= |x| < pi/4 or if |x| >= 2^63 and |r| >= 1/4
// *******************************************************************
// *******************************************************************
// *******************************************************************
//
// r and c have been computed.
-// Make sure ftz mode is set - should be automatic when using wre
-//
//
-// Get [i_1] - lsb of N_fix_gr alone.
-//
-(p0) fmerge.s Pos_r = f1, r
-(p0) extr.u i_1 = N_fix_gr, 0, 1 ;;
-}
-{ .mfi
- nop.m 999
-(p0) fmerge.s sgn_r = r, f1
-(p0) cmp.eq.unc p11, p12 = 0x0000, i_1 ;;
-}
-{ .mfi
- nop.m 999
- nop.f 999
-(p0) extr.u lookup = sig_r, 58, 5
-}
-{ .mlx
- nop.m 999
-(p0) movl Create_B = 0x8200000000000000 ;;
-}
{ .mfi
-(p0) addl table_ptr1 = @ltoff(TANL_BASE_CONSTANTS), gp
- nop.f 999
-(p0) dep Create_B = lookup, Create_B, 58, 5
-}
-;;
-
-
-//
-// Get [i_1] - lsb of N_fix_gr alone.
-// Pos_r = abs (r)
-//
-
-
-{ .mmi
-(p0) ld8 table_ptr1 = [table_ptr1]
nop.m 999
+ fand B = B_mask1, r
nop.i 999
}
;;
-
+TANL_NORMAL_R_A:
+// Enter here if pi/4 <= |x| < 2^63 and |r| >= 1/4
+// Get the 5 bits or r for the lookup. 1.xxxxx ....
{ .mmi
- nop.m 999
-(p0) setf.sig B = Create_B
-//
-// Set table_ptr1 and table_ptr2 to base address of
-// constant table.
-//
-(p0) add table_ptr1 = 480, table_ptr1 ;;
-}
-{ .mmb
- nop.m 999
-//
-// Is i_1 or i_0 == 0 ?
-// Create the constant 1 00000 1000000000000000000000...
-//
-(p0) ldfe P2_1 = [table_ptr1], 16
- nop.b 999
+ add table_ptr1 = 416, table_base // Point to tanl_table_p2
+ mov GR_exp_2tom65 = 0xffff - 65 // Scaling constant for B
+ extr.u lookup = sig_r, 58, 5
}
+;;
+
{ .mmi
- nop.m 999 ;;
-(p0) getf.exp exp_r = Pos_r
- nop.i 999
+ ldfe P2_1 = [table_ptr1], 16
+ setf.exp TWO_TO_NEG65 = GR_exp_2tom65 // 2^-65 for scaling B if exp_r=-2
+ add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl)
}
-//
-// Get r's exponent
-// Get r's significand
-//
-{ .mmi
-(p0) ldfe P2_2 = [table_ptr1], 16 ;;
-//
-// Get the 5 bits or r for the lookup. 1.xxxxx ....
-// from sig_r.
-// Grab lsb of exp of B
-//
-(p0) ldfe P2_3 = [table_ptr1], 16
- nop.i 999 ;;
+;;
+
+.pred.rel "mutex",p11,p12
+// B = 2^63 * 1.xxxxx 100...0
+{ .mfi
+ ldfe P2_2 = [table_ptr1], 16
+ for B = B_mask2, B
+ mov table_offset = 512 // Assume table offset is 512
}
-{ .mii
- nop.m 999
-(p0) andcm table_offset = 0x0001, exp_r ;;
-(p0) shl table_offset = table_offset, 9 ;;
+;;
+
+{ .mfi
+ ldfe P2_3 = [table_ptr1], 16
+ fmerge.s Pos_r = f1, r
+ tbit.nz p8,p9 = exp_r, 0
}
-{ .mii
- nop.m 999
-//
-// Deposit 0 00000 1000000000000000000000... on
-// 1 xxxxx yyyyyyyyyyyyyyyyyyyyyy...,
-// getting rid of the ys.
+;;
+
// Is B = 2** -2 or B= 2** -1? If 2**-1, then
// we want an offset of 512 for table addressing.
-//
-(p0) shladd table_offset = lookup, 4, table_offset ;;
-//
-// B = ........ 1xxxxx 1000000000000000000...
-//
-(p0) add table_ptr1 = table_ptr1, table_offset ;;
-}
-{ .mmb
- nop.m 999
-//
-// B = ........ 1xxxxx 1000000000000000000...
-// Convert B so it has the same exponent as Pos_r
-//
-(p0) ldfd T_hi = [table_ptr1], 8
- nop.b 999 ;;
+{ .mii
+ add table_ptr2 = 1296, table_base // Point to tanl_table_cm2
+(p9) shladd table_offset = lookup, 4, table_offset
+(p8) shladd table_offset = lookup, 4, r0
}
+;;
+{ .mmi
+ add table_ptr1 = table_ptr1, table_offset // Point to T_hi
+ add table_ptr2 = table_ptr2, table_offset // Point to C_hi
+ add table_ptr3 = 2128, table_base // Point to tanl_table_scim2
+}
+;;
+{ .mmi
+ ldfd T_hi = [table_ptr1], 8 // Load T_hi
+;;
+ ldfd C_hi = [table_ptr2], 8 // Load C_hi
+ add table_ptr3 = table_ptr3, table_offset // Point to SC_inv
+}
+;;
//
// x = |r| - B
-// Load T_hi.
-// Load C_hi.
//
-
-{ .mmf
-(p0) addl table_ptr2 = @ltoff(TANL_BASE_CONSTANTS), gp
-(p0) ldfs T_lo = [table_ptr1]
-(p0) fmerge.se B = Pos_r, B
+// Convert B so it has the same exponent as Pos_r before subtracting
+{ .mfi
+ ldfs T_lo = [table_ptr1] // Load T_lo
+(p9) fnma.s1 x = B, FR_2tom64, Pos_r
+ nop.i 999
}
-;;
-
-
-{ .mmi
-(p0) ld8 table_ptr2 = [table_ptr2]
+{ .mfi
nop.m 999
+(p8) fnma.s1 x = B, TWO_TO_NEG65, Pos_r
nop.i 999
}
;;
-
-{ .mii
-(p0) add table_ptr2 = 1360, table_ptr2
- nop.i 999 ;;
-(p0) add table_ptr2 = table_ptr2, table_offset ;;
+{ .mfi
+ ldfs C_lo = [table_ptr2] // Load C_lo
+ nop.f 999
+ nop.i 999
}
+;;
+
{ .mfi
-(p0) ldfd C_hi = [table_ptr2], 8
-(p0) fsub.s1 x = Pos_r, B
- nop.i 999 ;;
+ ldfe SC_inv = [table_ptr3] // Load SC_inv
+ fmerge.s sgn_r = r, f1
+ tbit.z p11, p12 = N_fix_gr, 0 // p11 if N even, p12 if odd
+
}
-{ .mii
-(p0) ldfs C_lo = [table_ptr2],255
- nop.i 999 ;;
+;;
+
//
// xsq = x * x
// N even: Tx = T_hi * x
-// Load T_lo.
-// Load C_lo - increment pointer to get SC_inv
-// - cant get all the way, do an add later.
-//
-(p0) add table_ptr2 = 569, table_ptr2 ;;
-}
//
// N even: Tx1 = Tx + 1
// N odd: Cx1 = 1 - Cx
//
+
{ .mfi
-(p0) ldfe SC_inv = [table_ptr2], 0
- nop.f 999
- nop.i 999 ;;
-}
-{ .mfi
- nop.m 999
-(p0) fmpy.s1 xsq = x, x
- nop.i 999
+ nop.m 999
+ fmpy.s1 xsq = x, x
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p11) fmpy.s1 Tx = T_hi, x
- nop.i 999 ;;
-}
-{ .mfi
- nop.m 999
-(p12) fmpy.s1 Cx = C_hi, x
- nop.i 999 ;;
+ nop.i 999
}
-{ .mfi
- nop.m 999
+;;
+
//
// N odd: Cx = C_hi * x
//
-(p0) fma.s1 P = P2_3, xsq, P2_2
- nop.i 999
-}
{ .mfi
- nop.m 999
+ nop.m 999
+(p12) fmpy.s1 Cx = C_hi, x
+ nop.i 999
+}
+;;
//
// N even and odd: P = P2_3 + P2_2 * xsq
//
+{ .mfi
+ nop.m 999
+ fma.s1 P = P2_3, xsq, P2_2
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
(p11) fadd.s1 Tx1 = Tx, f1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: D = C_hi - tanx
// N odd: D = T_hi + tanx
//
(p11) fmpy.s1 CORR = SC_inv, T_hi
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p0) fmpy.s1 Sx = SC_inv, x
- nop.i 999 ;;
+ nop.m 999
+ fmpy.s1 Sx = SC_inv, x
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fmpy.s1 CORR = SC_inv, C_hi
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fsub.s1 V_hi = f1, Cx
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p0) fma.s1 P = P, xsq, P2_1
- nop.i 999
+ nop.m 999
+ fma.s1 P = P, xsq, P2_1
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even and odd: P = P2_1 + P * xsq
//
(p11) fma.s1 V_hi = Tx, Tx1, f1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: Result = sgn_r * tail + T_hi (user rounding mode for C1)
// N odd: Result = sgn_r * tail + C_hi (user rounding mode for C1)
//
-(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
- nop.i 999 ;;
+ fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p0) fmpy.s1 CORR = CORR, c
- nop.i 999 ;;
+ nop.m 999
+ fmpy.s1 CORR = CORR, c
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fnma.s1 V_hi = Cx,V_hi,f1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: V_hi = Tx * Tx1 + 1
// N odd: Cx1 = 1 - Cx * Cx1
//
-(p0) fmpy.s1 P = P, xsq
- nop.i 999
+ fmpy.s1 P = P, xsq
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even and odd: P = P * xsq
//
(p11) fmpy.s1 V_hi = V_hi, T_hi
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even and odd: tail = P * tail + V_lo
//
(p11) fmpy.s1 T_hi = sgn_r, T_hi
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p0) fmpy.s1 CORR = CORR, sgn_r
- nop.i 999 ;;
+ nop.m 999
+ fmpy.s1 CORR = CORR, sgn_r
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fmpy.s1 V_hi = V_hi,C_hi
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: V_hi = T_hi * V_hi
// N odd: V_hi = C_hi * V_hi
//
-(p0) fma.s1 tanx = P, x, x
- nop.i 999
+ fma.s1 tanx = P, x, x
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fnmpy.s1 C_hi = sgn_r, C_hi
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: V_lo = 1 - V_hi + C_hi
// N odd: V_lo = 1 - V_hi + T_hi
//
(p11) fadd.s1 CORR = CORR, T_lo
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fsub.s1 CORR = CORR, C_lo
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even and odd: tanx = x + x * P
// N even and odd: Sx = SC_inv * x
//
(p11) fsub.s1 D = C_hi, tanx
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fadd.s1 D = T_hi, tanx
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N odd: CORR = SC_inv * C_hi
// N even: CORR = SC_inv * T_hi
//
-(p0) fnma.s1 D = V_hi, D, f1
- nop.i 999 ;;
+ fnma.s1 D = V_hi, D, f1
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even and odd: D = 1 - V_hi * D
// N even and odd: CORR = CORR * c
//
-(p0) fma.s1 V_hi = V_hi, D, V_hi
- nop.i 999 ;;
+ fma.s1 V_hi = V_hi, D, V_hi
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even and odd: V_hi = V_hi + V_hi * D
// N even and odd: CORR = sgn_r * CORR
//
(p11) fnma.s1 V_lo = V_hi, C_hi, f1
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fnma.s1 V_lo = V_hi, T_hi, f1
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: CORR = COOR + T_lo
// N odd: CORR = CORR - C_lo
//
(p11) fma.s1 V_lo = tanx, V_hi, V_lo
- nop.i 999
+ tbit.nz p15, p0 = cot_flag, 0 // p15=1 if we compute cotl
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fnma.s1 V_lo = tanx, V_hi, V_lo
- nop.i 999 ;;
+ nop.i 999 ;;
}
+
{ .mfi
- nop.m 999
+ nop.m 999
+(p15) fms.s1 T_hi = f0, f0, T_hi // to correct result's sign for cotl
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p15) fms.s1 C_hi = f0, f0, C_hi // to correct result's sign for cotl
+ nop.i 999
+};;
+
+{ .mfi
+ nop.m 999
+(p15) fms.s1 sgn_r = f0, f0, sgn_r // to correct result's sign for cotl
+ nop.i 999
+};;
+
+{ .mfi
+ nop.m 999
//
// N even: V_lo = V_lo + V_hi * tanx
// N odd: V_lo = V_lo - V_hi * tanx
//
(p11) fnma.s1 V_lo = C_lo, V_hi, V_lo
- nop.i 999
+ nop.i 999
}
{ .mfi
- nop.m 999
+ nop.m 999
(p12) fnma.s1 V_lo = T_lo, V_hi, V_lo
- nop.i 999 ;;
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: V_lo = V_lo - V_hi * C_lo
// N odd: V_lo = V_lo - V_hi * T_lo
//
-(p0) fmpy.s1 V_lo = V_hi, V_lo
- nop.i 999 ;;
+ fmpy.s1 V_lo = V_hi, V_lo
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even and odd: V_lo = V_lo * V_hi
//
-(p0) fadd.s1 tail = V_hi, V_lo
- nop.i 999 ;;
+ fadd.s1 tail = V_hi, V_lo
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even and odd: tail = V_hi + V_lo
//
-(p0) fma.s1 tail = tail, P, V_lo
- nop.i 999 ;;
+ fma.s1 tail = tail, P, V_lo
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even: T_hi = sgn_r * T_hi
// N odd : C_hi = -sgn_r * C_hi
//
-(p0) fma.s1 tail = tail, Sx, CORR
- nop.i 999 ;;
+ fma.s1 tail = tail, Sx, CORR
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even and odd: tail = Sx * tail + CORR
//
-(p0) fma.s1 tail = V_hi, Sx, tail
- nop.i 999 ;;
+ fma.s1 tail = V_hi, Sx, tail
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
+ nop.m 999
//
// N even an odd: tail = Sx * V_hi + tail
//
(p11) fma.s0 Result = sgn_r, tail, T_hi
- nop.i 999
+ nop.i 999
}
{ .mfb
- nop.m 999
+ nop.m 999
(p12) fma.s0 Result = sgn_r, tail, C_hi
-(p0) br.ret.sptk b0 ;;
+ br.ret.sptk b0 ;; // Exit for 1/4 <= |r| < pi/4
}
-L(TANL_SPECIAL):
+TANL_DENORMAL:
+// Here if x denormal
{ .mfb
- nop.m 999
-(p0) fmpy.s0 Arg = Arg, f0
-(p0) br.ret.sptk b0 ;;
+ getf.exp GR_signexp_x = Norm_Arg // Get sign and exponent of x
+ nop.f 999
+ br.cond.sptk TANL_COMMON // Return to common code
}
+;;
+
+
+TANL_SPECIAL:
+TANL_UNSUPPORTED:
//
// Code for NaNs, Unsupporteds, Infs, or +/- zero ?
// Invalid raised for Infs and SNaNs.
//
-.endp tanl
-ASM_SIZE_DIRECTIVE(tanl)
+{ .mfi
+ nop.m 999
+ fmerge.s f10 = f8, f8 // Save input for error call
+ tbit.nz p6, p7 = cot_flag, 0 // p6=1 if we compute cotl
+}
+;;
-// *******************************************************************
-// *******************************************************************
-// *******************************************************************
-//
-// Special Code to handle very large argument case.
-// Call int pi_by_2_reduce(&x,&r,&c)
-// for |arguments| >= 2**63
-// (Arg or x) is in f8
-// Address to save r and c as double
-// *******************************************************************
-// *******************************************************************
-// *******************************************************************
+{ .mfi
+ nop.m 999
+(p6) fclass.m p6, p7 = f8, 0x7 // Test for zero (cotl only)
+ nop.i 999
+}
+;;
+
+.pred.rel "mutex", p6, p7
+{ .mfi
+(p6) mov GR_Parameter_Tag = 225 // (cotl)
+(p6) frcpa.s0 f8, p0 = f1, f8 // cotl(+-0) = +-Inf
+ nop.i 999
+}
+{ .mfb
+ nop.m 999
+(p7) fmpy.s0 f8 = f8, f0
+(p7) br.ret.sptk b0
+}
+;;
+
+GLOBAL_IEEE754_END(tanl)
-.proc __libm_callout
-__libm_callout:
-L(TANL_ARG_TOO_LARGE):
+LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
+
+// (1)
{ .mfi
- add r50=-32,sp // Parameter: r address
- nop.f 0
+ add GR_Parameter_Y=-32,sp // Parameter 2 value
+ nop.f 0
.save ar.pfs,GR_SAVE_PFS
- mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
+ mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
{ .mfi
.fframe 64
- add sp=-64,sp // Create new stack
- nop.f 0
- mov GR_SAVE_GP=gp // Save gp
+ add sp=-64,sp // Create new stack
+ nop.f 0
+ mov GR_SAVE_GP=gp // Save gp
};;
+
+// (2)
{ .mmi
- stfe [r50] = f0,16 // Clear Parameter r on stack
- add r49 = 16,sp // Parameter x address
+ stfe [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 // Save b0
+ mov GR_SAVE_B0=b0 // Save b0
};;
+
.body
+// (3)
{ .mib
- stfe [r50] = f0,-16 // Clear Parameter c on stack
- nop.i 0
- nop.b 0
+ stfe [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
+ add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
+ nop.b 0
}
{ .mib
- stfe [r49] = Arg // Store Parameter x on stack
- nop.i 0
-(p0) br.call.sptk b0=__libm_pi_by_2_reduce# ;;
+ stfe [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
+ ldfe 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
+ 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)
+
+.type __libm_error_support#,@function
+.global __libm_error_support#
+
+
+// *******************************************************************
+// *******************************************************************
+// *******************************************************************
//
-// Load 2^-2
+// Special Code to handle very large argument case.
+// Call int __libm_pi_by_2_reduce(x,r,c) for |arguments| >= 2**63
+// The interface is custom:
+// On input:
+// (Arg or x) is in f8
+// On output:
+// r is in f8
+// c is in f9
+// N is in r8
+// We know also that __libm_pi_by_2_reduce preserves f10-15, f71-127. We
+// use this to eliminate save/restore of key fp registers in this calling
+// function.
//
+// *******************************************************************
+// *******************************************************************
+// *******************************************************************
+
+LOCAL_LIBM_ENTRY(__libm_callout)
+TANL_ARG_TOO_LARGE:
+.prologue
+{ .mfi
+ add table_ptr2 = 144, table_base // Point to 2^-2
+ nop.f 999
+.save ar.pfs,GR_SAVE_PFS
+ mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
+}
+;;
+
+// Load 2^-2, -2^-2
{ .mmi
-(p0) ldfe Arg =[r49],16
+ ldfps TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2]
+ setf.sig B_mask1 = bmask1 // Form mask to get 5 msb of r
+.save b0, GR_SAVE_B0
+ mov GR_SAVE_B0=b0 // Save b0
+};;
+
+.body
//
-// Call argument reduction
+// Call argument reduction with x in f8
+// Returns with N in r8, r in f8, c in f9
+// Assumes f71-127 are preserved across the call
//
-(p0) ldfs TWO_TO_NEG2 = [table_ptr2],4
-// Get Arg off stack
-// Get r off stack - hi order part
-// Get c off stack - lo order part
-(p0) mov N_fix_gr = r8 ;;
-}
-{ .mmb
-(p0) ldfe r =[r50],16
-(p0) ldfs NEGTWO_TO_NEG2 = [table_ptr2],4
- nop.b 999 ;;
+{ .mib
+ setf.sig B_mask2 = bmask2 // Form mask to form B from r
+ mov GR_SAVE_GP=gp // Save gp
+ br.call.sptk b0=__libm_pi_by_2_reduce#
}
+;;
+
+//
+// Is |r| < 2**(-2)
+//
{ .mfi
-(p0) ldfe c =[r50],-32
- nop.f 999
- nop.i 999 ;;
+ getf.sig sig_r = r // Extract significand of r
+ fcmp.lt.s1 p6, p0 = r, TWO_TO_NEG2
+ mov gp = GR_SAVE_GP // Restore gp
}
+;;
+
{ .mfi
-.restore sp
- add sp = 64,sp // Restore stack pointer
+ getf.exp exp_r = r // Extract signexp of r
+ nop.f 999
+ mov b0 = GR_SAVE_B0 // Restore return address
+}
+;;
+
//
-// Is |r| < 2**(-2)
+// Get N_fix_gr
//
-(p0) fcmp.lt.unc.s1 p6, p0 = r, TWO_TO_NEG2
-mov b0 = GR_SAVE_B0 // Restore return address
-};;
{ .mfi
- mov gp = GR_SAVE_GP // Restore gp
-(p6) fcmp.gt.unc.s1 p6, p0 = r, NEGTWO_TO_NEG2
- mov ar.pfs = GR_SAVE_PFS // Restore gp
-};;
+ mov N_fix_gr = r8
+(p6) fcmp.gt.unc.s1 p6, p0 = r, NEGTWO_TO_NEG2
+ mov ar.pfs = GR_SAVE_PFS // Restore pfs
+}
+;;
+
{ .mbb
- nop.m 999
-(p6) br.cond.spnt L(TANL_SMALL_R)
-(p0) br.cond.sptk L(TANL_NORMAL_R) ;;
+ nop.m 999
+(p6) br.cond.spnt TANL_SMALL_R // Branch if |r| < 1/4
+ br.cond.sptk TANL_NORMAL_R // Branch if 1/4 <= |r| < pi/4
}
+;;
-.endp __libm_callout
-ASM_SIZE_DIRECTIVE(__libm_callout)
+LOCAL_LIBM_END(__libm_callout)
.type __libm_pi_by_2_reduce#,@function
.global __libm_pi_by_2_reduce#