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3a327316ad
Continuing the preparation for additional _FloatN / _FloatNx aliases, this patch makes long double functions in sysdeps/ia64/fpu use libm_alias_ldouble macros, so that they can have _Float64x aliases added in future. Most ia64 libm functions are defined using ia64-specific macros in libm-symbols.h. These are left unchanged, with libm-alias-ldouble.h included from libm-symbols.h (and the expectation that other libm-alias-*.h headers will be included from there as well in future), and libm_alias_ldouble_other then being used in most cases to define aliases for any additional types (currently the empty set). Functions that used weak_alias are converted to use libm_alias_ldouble. Tested (compilation only) with build-many-glibcs.py for ia64, including that installed stripped shared libraries are unchanged by the patch. * sysdeps/ia64/fpu/libm-symbols.h: Include <libm-alias-ldouble.h>. * sysdeps/ia64/fpu/e_acoshl.S (acoshl): Use libm_alias_ldouble_other. * sysdeps/ia64/fpu/e_acosl.S (acosl): Likewise. * sysdeps/ia64/fpu/e_asinl.S (asinl): Likewise. * sysdeps/ia64/fpu/e_atanhl.S (atanhl): Likewise. * sysdeps/ia64/fpu/e_coshl.S (coshl): Likewise. * sysdeps/ia64/fpu/e_exp10l.S (exp10l): Likewise. * sysdeps/ia64/fpu/e_exp2l.S (exp2l): Likewise. * sysdeps/ia64/fpu/e_fmodl.S (fmodl): Likewise. * sysdeps/ia64/fpu/e_hypotl.S (hypotl): Likewise. * sysdeps/ia64/fpu/e_lgammal_r.c (lgammal_r): Define using libm_alias_ldouble_r. * sysdeps/ia64/fpu/e_log2l.S (log2l): Use libm_alias_ldouble_other. * sysdeps/ia64/fpu/e_logl.S (logl): Likewise. (log10l): Likewise. * sysdeps/ia64/fpu/e_powl.S (powl): Likewise. * sysdeps/ia64/fpu/e_remainderl.S (remainderl): Likewise. * sysdeps/ia64/fpu/e_sinhl.S (sinhl): Likewise. * sysdeps/ia64/fpu/e_sqrtl.S (sqrtl): Likewise. * sysdeps/ia64/fpu/libm_sincosl.S (sincosl): Likewise. * sysdeps/ia64/fpu/s_asinhl.S (asinhl): Likewise. * sysdeps/ia64/fpu/s_atanl.S (atanl): Likewise. (atan2l): Likewise. * sysdeps/ia64/fpu/s_cbrtl.S (cbrtl): Likewise. * sysdeps/ia64/fpu/s_ceill.S (ceill): Likewise. * sysdeps/ia64/fpu/s_copysign.S (copysignl): Define using libm_alias_ldouble. * sysdeps/ia64/fpu/s_cosl.S (sinl): Use libm_alias_ldouble_other. (cosl): Likewise. * sysdeps/ia64/fpu/s_erfcl.S (erfcl): Likewise. * sysdeps/ia64/fpu/s_erfl.S (erfl): Likewise. * sysdeps/ia64/fpu/s_expm1l.S (expm1l): Likewise. (expl): Likewise. * sysdeps/ia64/fpu/s_fabsl.S (fabsl): Likewise. * sysdeps/ia64/fpu/s_fdiml.S (fdiml): Likewise. * sysdeps/ia64/fpu/s_floorl.S (floorl): Likewise. * sysdeps/ia64/fpu/s_fmal.S (fmal): Likewise. * sysdeps/ia64/fpu/s_fmaxl.S (fmaxl): Likewise. * sysdeps/ia64/fpu/s_frexpl.c (frexpl): Likewise. * sysdeps/ia64/fpu/s_ldexpl.c (ldexpl): Likewise. * sysdeps/ia64/fpu/s_log1pl.S (log1pl): Likewise. * sysdeps/ia64/fpu/s_logbl.S (logbl): Likewise. * sysdeps/ia64/fpu/s_modfl.S (modfl): Likewise. * sysdeps/ia64/fpu/s_nearbyintl.S (nearbyintl): Define using libm_alias_ldouble. * sysdeps/ia64/fpu/s_nextafterl.S (nextafterl): Use libm_alias_ldouble_other. * sysdeps/ia64/fpu/s_rintl.S (rintl): Likewise. * sysdeps/ia64/fpu/s_roundl.S (roundl): Likewise. * sysdeps/ia64/fpu/s_scalbnl.c (scalbnl): Define using libm_alias_ldouble. * sysdeps/ia64/fpu/s_tanhl.S (tanhl): Use libm_alias_ldouble_other. * sysdeps/ia64/fpu/s_tanl.S (tanl): Likewise. * sysdeps/ia64/fpu/s_truncl.S (truncl): Likewise. * sysdeps/ia64/fpu/w_lgammal_main.c [BUILD_LGAMMA && !USE_AS_COMPAT] (lgammal): Likewise. * sysdeps/ia64/fpu/w_tgammal_compat.S (tgammal): Likewise.
1346 lines
35 KiB
ArmAsm
1346 lines
35 KiB
ArmAsm
.file "asinhl.s"
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// Copyright (c) 2000 - 2003, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2000 by the Intel Numerics Group, Intel Corporation
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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//*********************************************************************
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//
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// History:
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// 09/04/01 Initial version
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// 09/13/01 Performance improved, symmetry problems fixed
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// 10/10/01 Performance improved, split issues removed
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// 12/11/01 Changed huges_logp to not be global
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 02/10/03 Reordered header: .section, .global, .proc, .align;
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// used data8 for long double table values
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//
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//*********************************************************************
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//
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// API
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//==============================================================
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// long double asinhl(long double);
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//
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// Overview of operation
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//==============================================================
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//
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// There are 6 paths:
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// 1. x = 0, [S,Q]Nan or +/-INF
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// Return asinhl(x) = x + x;
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//
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// 2. x = + denormal
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// Return asinhl(x) = x - x^2;
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//
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// 3. x = - denormal
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// Return asinhl(x) = x + x^2;
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//
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// 4. 'Near 0': max denormal < |x| < 1/128
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// Return asinhl(x) = sign(x)*(x+x^3*(c3+x^2*(c5+x^2*(c7+x^2*(c9)))));
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//
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// 5. 'Huges': |x| > 2^63
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// Return asinhl(x) = sign(x)*(logl(2*x));
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//
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// 6. 'Main path': 1/128 < |x| < 2^63
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// b_hi + b_lo = x + sqrt(x^2 + 1);
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// asinhl(x) = sign(x)*(log_special(b_hi, b_lo));
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//
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// Algorithm description
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//==============================================================
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//
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// Main path algorithm
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// ( thanks to Peter Markstein for the idea of sqrt(x^2+1) computation! )
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// *************************************************************************
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//
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// There are 3 parts of x+sqrt(x^2+1) computation:
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//
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// 1) p2 = (p2_hi+p2_lo) = x^2+1 obtaining
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// ------------------------------------
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// p2_hi = x2_hi + 1, where x2_hi = x * x;
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// p2_lo = x2_lo + p1_lo, where
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// x2_lo = FMS(x*x-x2_hi),
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// p1_lo = (1 - p2_hi) + x2_hi;
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//
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// 2) g = (g_hi+g_lo) = sqrt(p2) = sqrt(p2_hi+p2_lo)
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// ----------------------------------------------
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// r = invsqrt(p2_hi) (8-bit reciprocal square root approximation);
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// g = p2_hi * r (first 8 bit-approximation of sqrt);
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//
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// h = 0.5 * r;
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// e = 0.5 - g * h;
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// g = g * e + g (second 16 bit-approximation of sqrt);
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//
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// h = h * e + h;
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// e = 0.5 - g * h;
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// g = g * e + g (third 32 bit-approximation of sqrt);
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//
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// h = h * e + h;
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// e = 0.5 - g * h;
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// g_hi = g * e + g (fourth 64 bit-approximation of sqrt);
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//
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// Remainder computation:
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// h = h * e + h;
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// d = (p2_hi - g_hi * g_hi) + p2_lo;
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// g_lo = d * h;
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//
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// 3) b = (b_hi + b_lo) = x + g, where g = (g_hi + g_lo) = sqrt(x^2+1)
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// -------------------------------------------------------------------
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// b_hi = (g_hi + x) + gl;
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// b_lo = (g_hi - b_hi) + x + gl;
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//
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// Now we pass b presented as sum b_hi + b_lo to special version
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// of logl function which accept a pair of arguments as
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// 'mutiprecision' value.
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//
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// Special log algorithm overview
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// ================================
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// Here we use a table lookup method. The basic idea is that in
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// order to compute logl(Arg) = logl (Arg-1) for an argument Arg in [1,2),
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// we construct a value G such that G*Arg is close to 1 and that
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// logl(1/G) is obtainable easily from a table of values calculated
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// beforehand. Thus
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//
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// logl(Arg) = logl(1/G) + logl((G*Arg - 1))
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//
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// Because |G*Arg - 1| is small, the second term on the right hand
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// side can be approximated by a short polynomial. We elaborate
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// this method in four steps.
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//
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// Step 0: Initialization
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//
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// We need to calculate logl( X ). Obtain N, S_hi such that
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//
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// X = 2^N * ( S_hi + S_lo ) exactly
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//
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// where S_hi in [1,2) and S_lo is a correction to S_hi in the sense
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// that |S_lo| <= ulp(S_hi).
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//
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// For the special version of logl: S_lo = b_lo
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// !-----------------------------------------------!
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//
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// Step 1: Argument Reduction
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//
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// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate
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//
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// G := G_1 * G_2 * G_3
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// r := (G * S_hi - 1) + G * S_lo
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//
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// These G_j's have the property that the product is exactly
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// representable and that |r| < 2^(-12) as a result.
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//
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// Step 2: Approximation
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//
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// logl(1 + r) is approximated by a short polynomial poly(r).
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//
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// Step 3: Reconstruction
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//
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// Finally,
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//
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// logl( X ) = logl( 2^N * (S_hi + S_lo) )
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// ~=~ N*logl(2) + logl(1/G) + logl(1 + r)
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// ~=~ N*logl(2) + logl(1/G) + poly(r).
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//
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// For detailed description see logl or log1pl function, regular path.
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//
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// Registers used
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//==============================================================
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// Floating Point registers used:
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// f8, input
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// f32 -> f101 (70 registers)
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// General registers used:
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// r32 -> r57 (26 registers)
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// Predicate registers used:
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// p6 -> p11
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// p6 for '0, NaNs, Inf' path
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// p7 for '+ denormals' path
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// p8 for 'near 0' path
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// p9 for 'huges' path
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// p10 for '- denormals' path
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// p11 for negative values
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//
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// Data tables
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//==============================================================
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RODATA
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.align 64
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// C7, C9 'near 0' polynomial coefficients
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LOCAL_OBJECT_START(Poly_C_near_0_79)
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data8 0xF8DC939BBEDD5A54, 0x00003FF9
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data8 0xB6DB6DAB21565AC5, 0x0000BFFA
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LOCAL_OBJECT_END(Poly_C_near_0_79)
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// C3, C5 'near 0' polynomial coefficients
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LOCAL_OBJECT_START(Poly_C_near_0_35)
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data8 0x999999999991D582, 0x00003FFB
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data8 0xAAAAAAAAAAAAAAA9, 0x0000BFFC
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LOCAL_OBJECT_END(Poly_C_near_0_35)
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// Q coeffs
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LOCAL_OBJECT_START(Constants_Q)
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data4 0x00000000,0xB1721800,0x00003FFE,0x00000000
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data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
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data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000
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data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000
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data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000
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data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000
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LOCAL_OBJECT_END(Constants_Q)
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// Z1 - 16 bit fixed
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LOCAL_OBJECT_START(Constants_Z_1)
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data4 0x00008000
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data4 0x00007879
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data4 0x000071C8
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data4 0x00006BCB
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data4 0x00006667
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data4 0x00006187
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data4 0x00005D18
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data4 0x0000590C
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data4 0x00005556
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data4 0x000051EC
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data4 0x00004EC5
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data4 0x00004BDB
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data4 0x00004925
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data4 0x0000469F
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data4 0x00004445
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data4 0x00004211
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LOCAL_OBJECT_END(Constants_Z_1)
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// G1 and H1 - IEEE single and h1 - IEEE double
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LOCAL_OBJECT_START(Constants_G_H_h1)
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data4 0x3F800000,0x00000000
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data8 0x0000000000000000
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data4 0x3F70F0F0,0x3D785196
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data8 0x3DA163A6617D741C
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data4 0x3F638E38,0x3DF13843
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data8 0x3E2C55E6CBD3D5BB
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data4 0x3F579430,0x3E2FF9A0
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data8 0xBE3EB0BFD86EA5E7
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data4 0x3F4CCCC8,0x3E647FD6
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data8 0x3E2E6A8C86B12760
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data4 0x3F430C30,0x3E8B3AE7
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data8 0x3E47574C5C0739BA
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data4 0x3F3A2E88,0x3EA30C68
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data8 0x3E20E30F13E8AF2F
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data4 0x3F321640,0x3EB9CEC8
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data8 0xBE42885BF2C630BD
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data4 0x3F2AAAA8,0x3ECF9927
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data8 0x3E497F3497E577C6
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data4 0x3F23D708,0x3EE47FC5
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data8 0x3E3E6A6EA6B0A5AB
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data4 0x3F1D89D8,0x3EF8947D
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data8 0xBDF43E3CD328D9BE
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data4 0x3F17B420,0x3F05F3A1
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data8 0x3E4094C30ADB090A
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data4 0x3F124920,0x3F0F4303
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data8 0xBE28FBB2FC1FE510
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data4 0x3F0D3DC8,0x3F183EBF
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data8 0x3E3A789510FDE3FA
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data4 0x3F088888,0x3F20EC80
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data8 0x3E508CE57CC8C98F
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data4 0x3F042108,0x3F29516A
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data8 0xBE534874A223106C
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LOCAL_OBJECT_END(Constants_G_H_h1)
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// Z2 - 16 bit fixed
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LOCAL_OBJECT_START(Constants_Z_2)
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data4 0x00008000
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data4 0x00007F81
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data4 0x00007F02
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data4 0x00007E85
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data4 0x00007E08
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data4 0x00007D8D
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data4 0x00007D12
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data4 0x00007C98
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data4 0x00007C20
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data4 0x00007BA8
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data4 0x00007B31
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data4 0x00007ABB
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data4 0x00007A45
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data4 0x000079D1
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data4 0x0000795D
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data4 0x000078EB
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LOCAL_OBJECT_END(Constants_Z_2)
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// G2 and H2 - IEEE single and h2 - IEEE double
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LOCAL_OBJECT_START(Constants_G_H_h2)
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data4 0x3F800000,0x00000000
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data8 0x0000000000000000
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data4 0x3F7F00F8,0x3B7F875D
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data8 0x3DB5A11622C42273
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data4 0x3F7E03F8,0x3BFF015B
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data8 0x3DE620CF21F86ED3
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data4 0x3F7D08E0,0x3C3EE393
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data8 0xBDAFA07E484F34ED
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data4 0x3F7C0FC0,0x3C7E0586
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data8 0xBDFE07F03860BCF6
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data4 0x3F7B1880,0x3C9E75D2
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data8 0x3DEA370FA78093D6
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data4 0x3F7A2328,0x3CBDC97A
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data8 0x3DFF579172A753D0
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data4 0x3F792FB0,0x3CDCFE47
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data8 0x3DFEBE6CA7EF896B
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data4 0x3F783E08,0x3CFC15D0
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data8 0x3E0CF156409ECB43
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data4 0x3F774E38,0x3D0D874D
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data8 0xBE0B6F97FFEF71DF
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data4 0x3F766038,0x3D1CF49B
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data8 0xBE0804835D59EEE8
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data4 0x3F757400,0x3D2C531D
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data8 0x3E1F91E9A9192A74
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data4 0x3F748988,0x3D3BA322
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data8 0xBE139A06BF72A8CD
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data4 0x3F73A0D0,0x3D4AE46F
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data8 0x3E1D9202F8FBA6CF
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data4 0x3F72B9D0,0x3D5A1756
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data8 0xBE1DCCC4BA796223
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data4 0x3F71D488,0x3D693B9D
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data8 0xBE049391B6B7C239
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LOCAL_OBJECT_END(Constants_G_H_h2)
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// G3 and H3 - IEEE single and h3 - IEEE double
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LOCAL_OBJECT_START(Constants_G_H_h3)
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data4 0x3F7FFC00,0x38800100
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data8 0x3D355595562224CD
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data4 0x3F7FF400,0x39400480
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data8 0x3D8200A206136FF6
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data4 0x3F7FEC00,0x39A00640
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data8 0x3DA4D68DE8DE9AF0
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data4 0x3F7FE400,0x39E00C41
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data8 0xBD8B4291B10238DC
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data4 0x3F7FDC00,0x3A100A21
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data8 0xBD89CCB83B1952CA
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data4 0x3F7FD400,0x3A300F22
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data8 0xBDB107071DC46826
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data4 0x3F7FCC08,0x3A4FF51C
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|
data8 0x3DB6FCB9F43307DB
|
|
data4 0x3F7FC408,0x3A6FFC1D
|
|
data8 0xBD9B7C4762DC7872
|
|
data4 0x3F7FBC10,0x3A87F20B
|
|
data8 0xBDC3725E3F89154A
|
|
data4 0x3F7FB410,0x3A97F68B
|
|
data8 0xBD93519D62B9D392
|
|
data4 0x3F7FAC18,0x3AA7EB86
|
|
data8 0x3DC184410F21BD9D
|
|
data4 0x3F7FA420,0x3AB7E101
|
|
data8 0xBDA64B952245E0A6
|
|
data4 0x3F7F9C20,0x3AC7E701
|
|
data8 0x3DB4B0ECAABB34B8
|
|
data4 0x3F7F9428,0x3AD7DD7B
|
|
data8 0x3D9923376DC40A7E
|
|
data4 0x3F7F8C30,0x3AE7D474
|
|
data8 0x3DC6E17B4F2083D3
|
|
data4 0x3F7F8438,0x3AF7CBED
|
|
data8 0x3DAE314B811D4394
|
|
data4 0x3F7F7C40,0x3B03E1F3
|
|
data8 0xBDD46F21B08F2DB1
|
|
data4 0x3F7F7448,0x3B0BDE2F
|
|
data8 0xBDDC30A46D34522B
|
|
data4 0x3F7F6C50,0x3B13DAAA
|
|
data8 0x3DCB0070B1F473DB
|
|
data4 0x3F7F6458,0x3B1BD766
|
|
data8 0xBDD65DDC6AD282FD
|
|
data4 0x3F7F5C68,0x3B23CC5C
|
|
data8 0xBDCDAB83F153761A
|
|
data4 0x3F7F5470,0x3B2BC997
|
|
data8 0xBDDADA40341D0F8F
|
|
data4 0x3F7F4C78,0x3B33C711
|
|
data8 0x3DCD1BD7EBC394E8
|
|
data4 0x3F7F4488,0x3B3BBCC6
|
|
data8 0xBDC3532B52E3E695
|
|
data4 0x3F7F3C90,0x3B43BAC0
|
|
data8 0xBDA3961EE846B3DE
|
|
data4 0x3F7F34A0,0x3B4BB0F4
|
|
data8 0xBDDADF06785778D4
|
|
data4 0x3F7F2CA8,0x3B53AF6D
|
|
data8 0x3DCC3ED1E55CE212
|
|
data4 0x3F7F24B8,0x3B5BA620
|
|
data8 0xBDBA31039E382C15
|
|
data4 0x3F7F1CC8,0x3B639D12
|
|
data8 0x3D635A0B5C5AF197
|
|
data4 0x3F7F14D8,0x3B6B9444
|
|
data8 0xBDDCCB1971D34EFC
|
|
data4 0x3F7F0CE0,0x3B7393BC
|
|
data8 0x3DC7450252CD7ADA
|
|
data4 0x3F7F04F0,0x3B7B8B6D
|
|
data8 0xBDB68F177D7F2A42
|
|
LOCAL_OBJECT_END(Constants_G_H_h3)
|
|
|
|
// Assembly macros
|
|
//==============================================================
|
|
|
|
// Floating Point Registers
|
|
|
|
FR_Arg = f8
|
|
FR_Res = f8
|
|
FR_AX = f32
|
|
FR_XLog_Hi = f33
|
|
FR_XLog_Lo = f34
|
|
|
|
// Special logl registers
|
|
FR_Y_hi = f35
|
|
FR_Y_lo = f36
|
|
|
|
FR_Scale = f37
|
|
FR_X_Prime = f38
|
|
FR_S_hi = f39
|
|
FR_W = f40
|
|
FR_G = f41
|
|
|
|
FR_H = f42
|
|
FR_wsq = f43
|
|
FR_w4 = f44
|
|
FR_h = f45
|
|
FR_w6 = f46
|
|
|
|
FR_G2 = f47
|
|
FR_H2 = f48
|
|
FR_poly_lo = f49
|
|
FR_P8 = f50
|
|
FR_poly_hi = f51
|
|
|
|
FR_P7 = f52
|
|
FR_h2 = f53
|
|
FR_rsq = f54
|
|
FR_P6 = f55
|
|
FR_r = f56
|
|
|
|
FR_log2_hi = f57
|
|
FR_log2_lo = f58
|
|
|
|
FR_float_N = f59
|
|
FR_Q4 = f60
|
|
|
|
FR_G3 = f61
|
|
FR_H3 = f62
|
|
FR_h3 = f63
|
|
|
|
FR_Q3 = f64
|
|
FR_Q2 = f65
|
|
FR_1LN10_hi = f66
|
|
|
|
FR_Q1 = f67
|
|
FR_1LN10_lo = f68
|
|
FR_P5 = f69
|
|
FR_rcub = f70
|
|
|
|
FR_Neg_One = f71
|
|
FR_Z = f72
|
|
FR_AA = f73
|
|
FR_BB = f74
|
|
FR_S_lo = f75
|
|
FR_2_to_minus_N = f76
|
|
|
|
|
|
// Huge & Main path prolog registers
|
|
FR_Half = f77
|
|
FR_Two = f78
|
|
FR_X2 = f79
|
|
FR_P2 = f80
|
|
FR_P2L = f81
|
|
FR_Rcp = f82
|
|
FR_GG = f83
|
|
FR_HH = f84
|
|
FR_EE = f85
|
|
FR_DD = f86
|
|
FR_GL = f87
|
|
FR_A = f88
|
|
FR_AL = f89
|
|
FR_B = f90
|
|
FR_BL = f91
|
|
FR_Tmp = f92
|
|
|
|
// Near 0 & Huges path prolog registers
|
|
FR_C3 = f93
|
|
FR_C5 = f94
|
|
FR_C7 = f95
|
|
FR_C9 = f96
|
|
|
|
FR_X3 = f97
|
|
FR_X4 = f98
|
|
FR_P9 = f99
|
|
FR_P5 = f100
|
|
FR_P3 = f101
|
|
|
|
|
|
// General Purpose Registers
|
|
|
|
// General prolog registers
|
|
GR_PFS = r32
|
|
GR_TwoN7 = r40
|
|
GR_TwoP63 = r41
|
|
GR_ExpMask = r42
|
|
GR_ArgExp = r43
|
|
GR_Half = r44
|
|
|
|
// Near 0 path prolog registers
|
|
GR_Poly_C_35 = r45
|
|
GR_Poly_C_79 = r46
|
|
|
|
// Special logl registers
|
|
GR_Index1 = r34
|
|
GR_Index2 = r35
|
|
GR_signif = r36
|
|
GR_X_0 = r37
|
|
GR_X_1 = r38
|
|
GR_X_2 = r39
|
|
GR_Z_1 = r40
|
|
GR_Z_2 = r41
|
|
GR_N = r42
|
|
GR_Bias = r43
|
|
GR_M = r44
|
|
GR_Index3 = r45
|
|
GR_exp_2tom80 = r45
|
|
GR_exp_mask = r47
|
|
GR_exp_2tom7 = r48
|
|
GR_ad_ln10 = r49
|
|
GR_ad_tbl_1 = r50
|
|
GR_ad_tbl_2 = r51
|
|
GR_ad_tbl_3 = r52
|
|
GR_ad_q = r53
|
|
GR_ad_z_1 = r54
|
|
GR_ad_z_2 = r55
|
|
GR_ad_z_3 = r56
|
|
GR_minus_N = r57
|
|
|
|
|
|
|
|
.section .text
|
|
GLOBAL_LIBM_ENTRY(asinhl)
|
|
|
|
{ .mfi
|
|
alloc GR_PFS = ar.pfs,0,27,0,0
|
|
fma.s1 FR_P2 = FR_Arg, FR_Arg, f1 // p2 = x^2 + 1
|
|
mov GR_Half = 0xfffe // 0.5's exp
|
|
}
|
|
{ .mfi
|
|
addl GR_Poly_C_79 = @ltoff(Poly_C_near_0_79), gp // C7, C9 coeffs
|
|
fma.s1 FR_X2 = FR_Arg, FR_Arg, f0 // Obtain x^2
|
|
addl GR_Poly_C_35 = @ltoff(Poly_C_near_0_35), gp // C3, C5 coeffs
|
|
};;
|
|
|
|
{ .mfi
|
|
getf.exp GR_ArgExp = FR_Arg // get arument's exponent
|
|
fabs FR_AX = FR_Arg // absolute value of argument
|
|
mov GR_TwoN7 = 0xfff8 // 2^-7 exp
|
|
}
|
|
{ .mfi
|
|
ld8 GR_Poly_C_79 = [GR_Poly_C_79] // get actual coeff table address
|
|
fma.s0 FR_Two = f1, f1, f1 // construct 2.0
|
|
mov GR_ExpMask = 0x1ffff // mask for exp
|
|
};;
|
|
|
|
{ .mfi
|
|
ld8 GR_Poly_C_35 = [GR_Poly_C_35] // get actual coeff table address
|
|
fclass.m p6,p0 = FR_Arg, 0xe7 // if arg NaN inf zero
|
|
mov GR_TwoP63 = 0x1003e // 2^63 exp
|
|
}
|
|
{ .mfi
|
|
addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
setf.exp FR_Half = GR_Half // construct 0.5
|
|
fclass.m p7,p0 = FR_Arg, 0x09 // if arg + denorm
|
|
and GR_ArgExp = GR_ExpMask, GR_ArgExp // select exp
|
|
}
|
|
{ .mfb
|
|
ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1
|
|
nop.f 0
|
|
nop.b 0
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_C9 = [GR_Poly_C_79],16 // load C9
|
|
fclass.m p10,p0 = FR_Arg, 0x0a // if arg - denorm
|
|
cmp.gt p8, p0 = GR_TwoN7, GR_ArgExp // if arg < 2^-7 ('near 0')
|
|
}
|
|
{ .mfb
|
|
cmp.le p9, p0 = GR_TwoP63, GR_ArgExp // if arg > 2^63 ('huges')
|
|
(p6) fma.s0 FR_Res = FR_Arg,f1,FR_Arg // r = a + a
|
|
(p6) br.ret.spnt b0 // return
|
|
};;
|
|
// (X^2 + 1) computation
|
|
{ .mfi
|
|
(p8) ldfe FR_C5 = [GR_Poly_C_35],16 // load C5
|
|
fms.s1 FR_Tmp = f1, f1, FR_P2 // Tmp = 1 - p2
|
|
add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1
|
|
}
|
|
{ .mfb
|
|
(p8) ldfe FR_C7 = [GR_Poly_C_79],16 // load C7
|
|
(p7) fnma.s0 FR_Res = FR_Arg,FR_Arg,FR_Arg // r = a - a*a
|
|
(p7) br.ret.spnt b0 // return
|
|
};;
|
|
|
|
{ .mfi
|
|
(p8) ldfe FR_C3 = [GR_Poly_C_35],16 // load C3
|
|
fcmp.lt.s1 p11, p12 = FR_Arg, f0 // if arg is negative
|
|
add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P
|
|
}
|
|
{ .mfb
|
|
add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2
|
|
(p10) fma.s0 FR_Res = FR_Arg,FR_Arg,FR_Arg // r = a + a*a
|
|
(p10) br.ret.spnt b0 // return
|
|
};;
|
|
|
|
{ .mfi
|
|
add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2
|
|
frsqrta.s1 FR_Rcp, p0 = FR_P2 // Rcp = 1/p2 reciprocal appr.
|
|
add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_P2L = FR_AX, FR_AX, FR_X2 //low part of p2=fma(X*X-p2)
|
|
mov GR_Bias = 0x0FFFF // Create exponent bias
|
|
};;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
(p9) fms.s1 FR_XLog_Hi = FR_Two, FR_AX, f0 // Hi of log1p arg = 2*X - 1
|
|
(p9) br.cond.spnt huges_logl // special version of log1p
|
|
};;
|
|
|
|
{ .mfb
|
|
ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi
|
|
(p8) fma.s1 FR_X3 = FR_X2, FR_Arg, f0 // x^3 = x^2 * x
|
|
(p8) br.cond.spnt near_0 // Go to near 0 branch
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_Q4 = [GR_ad_q],16 // Load Q4
|
|
fma.s1 FR_Tmp = FR_Tmp, f1, FR_X2 // Tmp = Tmp + x^2
|
|
mov GR_exp_mask = 0x1FFFF // Create exponent mask
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_Q3 = [GR_ad_q],16 // Load Q3
|
|
fma.s1 FR_GG = FR_Rcp, FR_P2, f0 // g = Rcp * p2
|
|
// 8 bit Newton Raphson iteration
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_Half, FR_Rcp, f0 // h = 0.5 * Rcp
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_Q2 = [GR_ad_q],16 // Load Q2
|
|
fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P2L = FR_Tmp, f1, FR_P2L // low part of p2 = Tmp + p2l
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_Q1 = [GR_ad_q] // Load Q1
|
|
fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g
|
|
// 16 bit Newton Raphson iteration
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g
|
|
// 32 bit Newton Raphson iteration
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g
|
|
// 64 bit Newton Raphson iteration
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_DD = FR_GG, FR_GG, FR_P2 // Remainder d = g * g - p2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_XLog_Hi = FR_AX, f1, FR_GG // bh = z + gh
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_DD = FR_DD, f1, FR_P2L // add p2l: d = d + p2l
|
|
nop.i 0
|
|
};;
|
|
|
|
|
|
{ .mfi
|
|
getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1
|
|
fmerge.ns FR_Neg_One = f1, f1 // Form -1.0
|
|
mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GL = FR_DD, FR_HH, f0 // gl = d * h
|
|
extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_XLog_Hi = FR_DD, FR_HH, FR_XLog_Hi // bh = bh + gl
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1
|
|
shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1
|
|
extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of signif.
|
|
};;
|
|
|
|
{ .mmi
|
|
ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_XLog_Lo = FR_GG, f1, FR_XLog_Hi // bl = gh - bh
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1
|
|
};;
|
|
|
|
// WE CANNOT USE GR_X_1 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL!
|
|
// "DEAD" ZONE!
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.se FR_S_hi = f1,FR_XLog_Hi // Form |x+1|
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1
|
|
ldfd FR_h = [GR_ad_tbl_1] // Load h_1
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
};;
|
|
|
|
|
|
{ .mfi
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2
|
|
fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_AX // bl = bl + x
|
|
mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2
|
|
nop.f 0
|
|
sub GR_N = GR_N, GR_Bias // sub bias from exp
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N)
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
setf.sig FR_float_N = GR_N // Put integer N into rightmost sign
|
|
setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N)
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2
|
|
};;
|
|
|
|
// WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES ("DEAD" ZONE!)
|
|
// BECAUSE OF POSSIBLE 10 CLOCKS STALL!
|
|
// So we can negate Q coefficients there for negative values
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s1 FR_Q1 = FR_Q1, FR_Neg_One, f0 // Negate Q1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_GL // bl = bl + gl
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s1 FR_Q2 = FR_Q2, FR_Neg_One, f0 // Negate Q2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s1 FR_Q3 = FR_Q3, FR_Neg_One, f0 // Negate Q3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s1 FR_Q4 = FR_Q4, FR_Neg_One, f0 // Negate Q4
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
};;
|
|
|
|
{ .mfi
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
|
|
fcvt.xf FR_float_N = FR_float_N
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_S_lo = FR_XLog_Lo, FR_2_to_minus_N, f0 //S_lo=S_lo*2^-N
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+H
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h=N*log2_lo+h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_r = FR_G, FR_S_lo, FR_r // r=G*S_lo+(G*S_hi-1)
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
};;
|
|
|
|
.pred.rel "mutex",p12,p11
|
|
{ .mfi
|
|
nop.m 0
|
|
(p12) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fms.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r
|
|
nop.i 0
|
|
};;
|
|
|
|
|
|
.pred.rel "mutex",p12,p11
|
|
{ .mfi
|
|
nop.m 0
|
|
(p12) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fms.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo
|
|
// Y_lo=poly_hi+poly_lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s0 FR_Y_hi = FR_Y_hi, FR_Neg_One, f0 // FR_Y_hi sign for neg
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi
|
|
br.ret.sptk b0 // Common exit for 2^-7 < x < inf
|
|
};;
|
|
|
|
// * SPECIAL VERSION OF LOGL FOR HUGE ARGUMENTS *
|
|
|
|
huges_logl:
|
|
{ .mfi
|
|
getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1
|
|
fmerge.ns FR_Neg_One = f1, f1 // Form -1.0
|
|
mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7
|
|
};;
|
|
|
|
{ .mfi
|
|
add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1
|
|
nop.f 0
|
|
add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P
|
|
}
|
|
{ .mfi
|
|
add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2
|
|
nop.f 0
|
|
add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif
|
|
}
|
|
{ .mfi
|
|
add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1
|
|
nop.f 0
|
|
extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of signif.
|
|
};;
|
|
|
|
{ .mfi
|
|
ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1
|
|
nop.f 0
|
|
mov GR_exp_mask = 0x1FFFF // Create exponent mask
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1
|
|
nop.f 0
|
|
mov GR_Bias = 0x0FFFF // Create exponent bias
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1
|
|
fmerge.se FR_S_hi = f1,FR_XLog_Hi // Form |x+1|
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1
|
|
ldfd FR_h = [GR_ad_tbl_1] // Load h_1
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi
|
|
nop.f 0
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1
|
|
};;
|
|
|
|
// WE CANNOT USE GR_X_1 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL!
|
|
// "DEAD" ZONE!
|
|
|
|
{ .mmi
|
|
ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo
|
|
sub GR_N = GR_N, GR_Bias
|
|
mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_Q4 = [GR_ad_q],16 // Load Q4
|
|
nop.f 0
|
|
sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N)
|
|
};;
|
|
|
|
{ .mmf
|
|
ldfe FR_Q3 = [GR_ad_q],16 // Load Q3
|
|
setf.sig FR_float_N = GR_N // Put integer N into rightmost sign
|
|
nop.f 0
|
|
};;
|
|
|
|
{ .mmi
|
|
nop.m 0
|
|
ldfe FR_Q2 = [GR_ad_q],16 // Load Q2
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfe FR_Q1 = [GR_ad_q] // Load Q1
|
|
shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N)
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2
|
|
};;
|
|
|
|
// WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL!
|
|
// "DEAD" ZONE!
|
|
// JUST HAVE TO INSERT 3 NOP CYCLES (nothing to do here)
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s1 FR_Q4 = FR_Q4, FR_Neg_One, f0 // Negate Q4
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
};;
|
|
|
|
{ .mfi
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3
|
|
fcvt.xf FR_float_N = FR_float_N
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s1 FR_Q3 = FR_Q3, FR_Neg_One, f0 // Negate Q3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3
|
|
(p11) fma.s1 FR_Q2 = FR_Q2, FR_Neg_One, f0 // Negate Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s1 FR_Q1 = FR_Q1, FR_Neg_One, f0 // Negate Q1
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
|
|
fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmf
|
|
nop.m 0
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+H
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h=N*log2_lo+h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
};;
|
|
|
|
.pred.rel "mutex",p12,p11
|
|
{ .mfi
|
|
nop.m 0
|
|
(p12) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fms.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r
|
|
nop.i 0
|
|
};;
|
|
|
|
|
|
.pred.rel "mutex",p12,p11
|
|
{ .mfi
|
|
nop.m 0
|
|
(p12) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fms.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo=poly_hi+poly_lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s0 FR_Y_hi = FR_Y_hi, FR_Neg_One, f0 // FR_Y_hi sign for neg
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi
|
|
br.ret.sptk b0 // Common exit for 2^-7 < x < inf
|
|
};;
|
|
|
|
// NEAR ZERO POLYNOMIAL INTERVAL
|
|
near_0:
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_X4 = FR_X2, FR_X2, f0 // x^4 = x^2 * x^2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P9 = FR_C9,FR_X2,FR_C7 // p9 = C9*x^2 + C7
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P5 = FR_C5,FR_X2,FR_C3 // p5 = C5*x^2 + C3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P3 = FR_P9,FR_X4,FR_P5 // p3 = p9*x^4 + p5
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s0 FR_Res = FR_P3,FR_X3,FR_Arg // res = p3*C3 + x
|
|
br.ret.sptk b0 // Near 0 path return
|
|
};;
|
|
|
|
GLOBAL_LIBM_END(asinhl)
|
|
libm_alias_ldouble_other (asinh, asinh)
|