1156 lines
31 KiB
ArmAsm
1156 lines
31 KiB
ArmAsm
.file "atanhl.s"
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// Copyright (c) 2001 - 2003, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2001 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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// 09/10/01 Initial version
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// 12/11/01 Corrected .restore syntax
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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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//*********************************************************************
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//
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// Function: atanhl(x) computes the principle value of the inverse
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// hyperbolic tangent of x.
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//
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//*********************************************************************
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//
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// Resources Used:
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//
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// Floating-Point Registers: f8 (Input and Return Value)
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// f33-f73
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//
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// General Purpose Registers:
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// r32-r52
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// r49-r52 (Used to pass arguments to error handling routine)
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//
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// Predicate Registers: p6-p15
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//
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//*********************************************************************
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//
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// IEEE Special Conditions:
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//
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// atanhl(inf) = QNaN
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// atanhl(-inf) = QNaN
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// atanhl(+/-0) = +/-0
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// atanhl(1) = +inf
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// atanhl(-1) = -inf
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// atanhl(|x|>1) = QNaN
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// atanhl(SNaN) = QNaN
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// atanhl(QNaN) = QNaN
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//
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//*********************************************************************
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//
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// Overview
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//
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// The method consists of two cases.
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//
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// If |x| < 1/32 use case atanhl_near_zero;
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// else use case atanhl_regular;
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//
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// Case atanhl_near_zero:
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//
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// atanhl(x) can be approximated by the Taylor series expansion
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// up to order 17.
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//
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// Case atanhl_regular:
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//
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// Here we use formula atanhl(x) = sign(x)*log1pl(2*|x|/(1-|x|))/2 and
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// calculation is subdivided into two stages. The first stage is
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// calculating of X = 2*|x|/(1-|x|). The second one is calculating of
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// sign(x)*log1pl(X)/2. To obtain required accuracy we use precise division
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// algorythm output of which is a pair of two extended precision values those
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// approximate result of division with accuracy higher than working
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// precision. This pair is passed to modified log1pl function.
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//
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//
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// 1. calculating of X = 2*|x|/(1-|x|)
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// ( based on Peter Markstein's "IA-64 and Elementary Functions" book )
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// ********************************************************************
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//
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// a = 2*|x|
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// b = 1 - |x|
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// b_lo = |x| - (1 - b)
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//
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// y = frcpa(b) initial approximation of 1/b
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// q = a*y initial approximation of a/b
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//
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// e = 1 - b*y
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// e2 = e + e^2
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// e1 = e^2
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// y1 = y + y*e2 = y + y*(e+e^2)
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//
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// e3 = e + e1^2
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// y2 = y + y1*e3 = y + y*(e+e^2+..+e^6)
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//
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// r = a - b*q
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// e = 1 - b*y2
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// X = q + r*y2 high part of a/b
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//
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// y3 = y2 + y2*e4
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// r1 = a - b*X
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// r1 = r1 - b_lo*X
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// X_lo = r1*y3 low part of a/b
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//
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// 2. special log1p algorithm overview
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// ***********************************
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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) = log1pl (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)
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// = logl(1/G) + logl(1 + (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 several 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 + X_lo + 1). Obtain N, S_hi such that
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//
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// X + X_lo + 1 = 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 log1p we add X_lo to S_lo (S_lo = S_lo + X_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, log1pl(X + X_lo) = logl(X + X_lo + 1) is given by
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//
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// logl(X + X_lo + 1) = 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 log1p1 function, regular path.
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//
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//*********************************************************************
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RODATA
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.align 64
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// ************* DO NOT CHANGE THE ORDER OF THESE TABLES *************
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LOCAL_OBJECT_START(Constants_TaylorSeries)
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data8 0xF0F0F0F0F0F0F0F1,0x00003FFA // C17
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data8 0x8888888888888889,0x00003FFB // C15
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data8 0x9D89D89D89D89D8A,0x00003FFB // C13
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data8 0xBA2E8BA2E8BA2E8C,0x00003FFB // C11
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data8 0xE38E38E38E38E38E,0x00003FFB // C9
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data8 0x9249249249249249,0x00003FFC // C7
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data8 0xCCCCCCCCCCCCCCCD,0x00003FFC // C5
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data8 0xAAAAAAAAAAAAAAAA,0x00003FFD // C3
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data4 0x3f000000 // 1/2
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data4 0x00000000 // pad
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data4 0x00000000
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data4 0x00000000
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LOCAL_OBJECT_END(Constants_TaylorSeries)
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LOCAL_OBJECT_START(Constants_Q)
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data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 // log2_hi
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data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 // log2_lo
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data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 // Q4
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data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 // Q3
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data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 // Q2
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data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 // Q1
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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
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data4 0x3F7FC408,0x3A6FFC1D
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|
data8 0xBD9B7C4762DC7872
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data4 0x3F7FBC10,0x3A87F20B
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|
data8 0xBDC3725E3F89154A
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data4 0x3F7FB410,0x3A97F68B
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|
data8 0xBD93519D62B9D392
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|
data4 0x3F7FAC18,0x3AA7EB86
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|
data8 0x3DC184410F21BD9D
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|
data4 0x3F7FA420,0x3AB7E101
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|
data8 0xBDA64B952245E0A6
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|
data4 0x3F7F9C20,0x3AC7E701
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|
data8 0x3DB4B0ECAABB34B8
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|
data4 0x3F7F9428,0x3AD7DD7B
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|
data8 0x3D9923376DC40A7E
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|
data4 0x3F7F8C30,0x3AE7D474
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|
data8 0x3DC6E17B4F2083D3
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|
data4 0x3F7F8438,0x3AF7CBED
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|
data8 0x3DAE314B811D4394
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|
data4 0x3F7F7C40,0x3B03E1F3
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|
data8 0xBDD46F21B08F2DB1
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|
data4 0x3F7F7448,0x3B0BDE2F
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|
data8 0xBDDC30A46D34522B
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|
data4 0x3F7F6C50,0x3B13DAAA
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|
data8 0x3DCB0070B1F473DB
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|
data4 0x3F7F6458,0x3B1BD766
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|
data8 0xBDD65DDC6AD282FD
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|
data4 0x3F7F5C68,0x3B23CC5C
|
|
data8 0xBDCDAB83F153761A
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|
data4 0x3F7F5470,0x3B2BC997
|
|
data8 0xBDDADA40341D0F8F
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|
data4 0x3F7F4C78,0x3B33C711
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|
data8 0x3DCD1BD7EBC394E8
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|
data4 0x3F7F4488,0x3B3BBCC6
|
|
data8 0xBDC3532B52E3E695
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|
data4 0x3F7F3C90,0x3B43BAC0
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|
data8 0xBDA3961EE846B3DE
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|
data4 0x3F7F34A0,0x3B4BB0F4
|
|
data8 0xBDDADF06785778D4
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|
data4 0x3F7F2CA8,0x3B53AF6D
|
|
data8 0x3DCC3ED1E55CE212
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|
data4 0x3F7F24B8,0x3B5BA620
|
|
data8 0xBDBA31039E382C15
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|
data4 0x3F7F1CC8,0x3B639D12
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|
data8 0x3D635A0B5C5AF197
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|
data4 0x3F7F14D8,0x3B6B9444
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|
data8 0xBDDCCB1971D34EFC
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|
data4 0x3F7F0CE0,0x3B7393BC
|
|
data8 0x3DC7450252CD7ADA
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|
data4 0x3F7F04F0,0x3B7B8B6D
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|
data8 0xBDB68F177D7F2A42
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|
LOCAL_OBJECT_END(Constants_G_H_h3)
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|
|
|
|
|
|
|
// Floating Point Registers
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|
|
|
FR_C17 = f50
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|
FR_C15 = f51
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|
FR_C13 = f52
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|
FR_C11 = f53
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|
FR_C9 = f54
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|
FR_C7 = f55
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|
FR_C5 = f56
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FR_C3 = f57
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|
FR_x2 = f58
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|
FR_x3 = f59
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|
FR_x4 = f60
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|
FR_x8 = f61
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|
|
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FR_Rcp = f61
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|
|
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FR_A = f33
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|
FR_R1 = f33
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|
|
|
FR_E1 = f34
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|
FR_E3 = f34
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|
FR_Y2 = f34
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|
FR_Y3 = f34
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|
|
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FR_E2 = f35
|
|
FR_Y1 = f35
|
|
|
|
FR_B = f36
|
|
FR_Y0 = f37
|
|
FR_E0 = f38
|
|
FR_E4 = f39
|
|
FR_Q0 = f40
|
|
FR_R0 = f41
|
|
FR_B_lo = f42
|
|
|
|
FR_abs_x = f43
|
|
FR_Bp = f44
|
|
FR_Bn = f45
|
|
FR_Yp = f46
|
|
FR_Yn = f47
|
|
|
|
FR_X = f48
|
|
FR_BB = f48
|
|
FR_X_lo = f49
|
|
|
|
FR_G = f50
|
|
FR_Y_hi = f51
|
|
FR_H = f51
|
|
FR_h = f52
|
|
FR_G2 = f53
|
|
FR_H2 = f54
|
|
FR_h2 = f55
|
|
FR_G3 = f56
|
|
FR_H3 = f57
|
|
FR_h3 = f58
|
|
|
|
FR_Q4 = f59
|
|
FR_poly_lo = f59
|
|
FR_Y_lo = f59
|
|
|
|
FR_Q3 = f60
|
|
FR_Q2 = f61
|
|
|
|
FR_Q1 = f62
|
|
FR_poly_hi = f62
|
|
|
|
FR_float_N = f63
|
|
|
|
FR_AA = f64
|
|
FR_S_lo = f64
|
|
|
|
FR_S_hi = f65
|
|
FR_r = f65
|
|
|
|
FR_log2_hi = f66
|
|
FR_log2_lo = f67
|
|
FR_Z = f68
|
|
FR_2_to_minus_N = f69
|
|
FR_rcub = f70
|
|
FR_rsq = f71
|
|
FR_05r = f72
|
|
FR_Half = f73
|
|
|
|
FR_Arg_X = f50
|
|
FR_Arg_Y = f0
|
|
FR_RESULT = f8
|
|
|
|
|
|
|
|
// General Purpose Registers
|
|
|
|
GR_ad_05 = r33
|
|
GR_Index1 = r34
|
|
GR_ArgExp = r34
|
|
GR_Index2 = r35
|
|
GR_ExpMask = r35
|
|
GR_NearZeroBound = r36
|
|
GR_signif = r36
|
|
GR_X_0 = r37
|
|
GR_X_1 = r37
|
|
GR_X_2 = r38
|
|
GR_Index3 = r38
|
|
GR_minus_N = r39
|
|
GR_Z_1 = r40
|
|
GR_Z_2 = r40
|
|
GR_N = r41
|
|
GR_Bias = r42
|
|
GR_M = r43
|
|
GR_ad_taylor = r44
|
|
GR_ad_taylor_2 = r45
|
|
GR_ad2_tbl_3 = r45
|
|
GR_ad_tbl_1 = r46
|
|
GR_ad_tbl_2 = r47
|
|
GR_ad_tbl_3 = r48
|
|
GR_ad_q = r49
|
|
GR_ad_z_1 = r50
|
|
GR_ad_z_2 = r51
|
|
GR_ad_z_3 = r52
|
|
|
|
//
|
|
// Added for unwind support
|
|
//
|
|
GR_SAVE_PFS = r46
|
|
GR_SAVE_B0 = r47
|
|
GR_SAVE_GP = r48
|
|
GR_Parameter_X = r49
|
|
GR_Parameter_Y = r50
|
|
GR_Parameter_RESULT = r51
|
|
GR_Parameter_TAG = r52
|
|
|
|
|
|
|
|
.section .text
|
|
GLOBAL_LIBM_ENTRY(atanhl)
|
|
|
|
{ .mfi
|
|
alloc r32 = ar.pfs,0,17,4,0
|
|
fnma.s1 FR_Bp = f8,f1,f1 // b = 1 - |arg| (for x>0)
|
|
mov GR_ExpMask = 0x1ffff
|
|
}
|
|
{ .mfi
|
|
addl GR_ad_taylor = @ltoff(Constants_TaylorSeries),gp
|
|
fma.s1 FR_Bn = f8,f1,f1 // b = 1 - |arg| (for x<0)
|
|
mov GR_NearZeroBound = 0xfffa // biased exp of 1/32
|
|
};;
|
|
{ .mfi
|
|
getf.exp GR_ArgExp = f8
|
|
fcmp.lt.s1 p6,p7 = f8,f0 // is negative?
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ld8 GR_ad_taylor = [GR_ad_taylor]
|
|
fmerge.s FR_abs_x = f1,f8
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m p8,p0 = f8,0x1C7 // is arg NaT,Q/SNaN or +/-0 ?
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_x2 = f8,f8,f0
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
add GR_ad_z_1 = 0x0F0,GR_ad_taylor
|
|
fclass.m p9,p0 = f8,0x0a // is arg -denormal ?
|
|
add GR_ad_taylor_2 = 0x010,GR_ad_taylor
|
|
}
|
|
{ .mfi
|
|
add GR_ad_05 = 0x080,GR_ad_taylor
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_C17 = [GR_ad_taylor],32
|
|
fclass.m p10,p0 = f8,0x09 // is arg +denormal ?
|
|
add GR_ad_tbl_1 = 0x040,GR_ad_z_1 // point to Constants_G_H_h1
|
|
}
|
|
{ .mfb
|
|
add GR_ad_z_2 = 0x140,GR_ad_z_1 // point to Constants_Z_2
|
|
(p8) fma.s0 f8 = f8,f1,f0 // NaN or +/-0
|
|
(p8) br.ret.spnt b0 // exit for Nan or +/-0
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_C15 = [GR_ad_taylor_2],32
|
|
fclass.m p15,p0 = f8,0x23 // is +/-INF ?
|
|
add GR_ad_tbl_2 = 0x180,GR_ad_z_1 // point to Constants_G_H_h2
|
|
}
|
|
{ .mfb
|
|
ldfe FR_C13 = [GR_ad_taylor],32
|
|
(p9) fnma.s0 f8 = f8,f8,f8 // -denormal
|
|
(p9) br.ret.spnt b0 // exit for -denormal
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_C11 = [GR_ad_taylor_2],32
|
|
fcmp.eq.s0 p13,p0 = FR_abs_x,f1 // is |arg| = 1?
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
ldfe FR_C9 = [GR_ad_taylor],32
|
|
(p10) fma.s0 f8 = f8,f8,f8 // +denormal
|
|
(p10) br.ret.spnt b0 // exit for +denormal
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_C7 = [GR_ad_taylor_2],32
|
|
(p6) frcpa.s1 FR_Yn,p11 = f1,FR_Bn // y = frcpa(b)
|
|
and GR_ArgExp = GR_ArgExp,GR_ExpMask // biased exponent
|
|
}
|
|
{ .mfb
|
|
ldfe FR_C5 = [GR_ad_taylor],32
|
|
fnma.s1 FR_B = FR_abs_x,f1,f1 // b = 1 - |arg|
|
|
(p15) br.cond.spnt atanhl_gt_one // |arg| > 1
|
|
};;
|
|
{ .mfb
|
|
cmp.gt p14,p0 = GR_NearZeroBound,GR_ArgExp
|
|
(p7) frcpa.s1 FR_Yp,p12 = f1,FR_Bp // y = frcpa(b)
|
|
(p13) br.cond.spnt atanhl_eq_one // |arg| = 1/32
|
|
}
|
|
{ .mfb
|
|
ldfe FR_C3 = [GR_ad_taylor_2],32
|
|
fma.s1 FR_A = FR_abs_x,f1,FR_abs_x // a = 2 * |arg|
|
|
(p14) br.cond.spnt atanhl_near_zero // |arg| < 1/32
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fcmp.gt.s0 p8,p0 = FR_abs_x,f1 // is |arg| > 1 ?
|
|
nop.i 0
|
|
};;
|
|
.pred.rel "mutex",p6,p7
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fnma.s1 FR_B_lo = FR_Bn,f1,f1 // argt = 1 - (1 - |arg|)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfs FR_Half = [GR_ad_05]
|
|
(p7) fnma.s1 FR_B_lo = FR_Bp,f1,f1
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fnma.s1 FR_E0 = FR_Yn,FR_Bn,f1 // e = 1-b*y
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p6) fma.s1 FR_Y0 = FR_Yn,f1,f0
|
|
(p8) br.cond.spnt atanhl_gt_one // |arg| > 1
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fnma.s1 FR_E0 = FR_Yp,FR_Bp,f1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s1 FR_Q0 = FR_A,FR_Yn,f0 // q = a*y
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.s1 FR_Q0 = FR_A,FR_Yp,f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.s1 FR_Y0 = FR_Yp,f1,f0
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.nm p10,p0 = f8,0x1FF // test for unsupported
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_E2 = FR_E0,FR_E0,FR_E0 // e2 = e+e^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_E1 = FR_E0,FR_E0,f0 // e1 = e^2
|
|
nop.i 0
|
|
};;
|
|
{ .mfb
|
|
nop.m 0
|
|
// Return generated NaN or other value for unsupported values.
|
|
(p10) fma.s0 f8 = f8, f0, f0
|
|
(p10) br.ret.spnt b0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y1 = FR_Y0,FR_E2,FR_Y0 // y1 = y+y*e2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_E3 = FR_E1,FR_E1,FR_E0 // e3 = e+e1^2
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_B_lo = FR_abs_x,f1,FR_B_lo // b_lo = argt-|arg|
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y2 = FR_Y1,FR_E3,FR_Y0 // y2 = y+y1*e3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_R0 = FR_B,FR_Q0,FR_A // r = a-b*q
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_E4 = FR_B,FR_Y2,f1 // e4 = 1-b*y2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_X = FR_R0,FR_Y2,FR_Q0 // x = q+r*y2
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Z = FR_X,f1,f1 // x+1
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fnma.s1 FR_Half = FR_Half,f1,f0 // sign(arg)/2
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y3 = FR_Y2,FR_E4,FR_Y2 // y3 = y2+y2*e4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_R1 = FR_B,FR_X,FR_A // r1 = a-b*x
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
getf.sig GR_signif = FR_Z // get significand of x+1
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
|
|
{ .mfi
|
|
add GR_ad_q = -0x060,GR_ad_z_1
|
|
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 significand
|
|
};;
|
|
{ .mfi
|
|
ld4 GR_Z_1 = [GR_ad_z_1] // load Z_1
|
|
fmax.s1 FR_AA = FR_X,f1 // for S_lo,form AA = max(X,1.0)
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_tbl_1 = GR_Index1,4,GR_ad_tbl_1 // point to G_1
|
|
nop.f 0
|
|
mov GR_Bias = 0x0FFFF // 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_Z // form |x+1|
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
getf.exp GR_N = FR_Z // get N = exponent of x+1
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfd FR_h = [GR_ad_tbl_1] // load h_1
|
|
fnma.s1 FR_R1 = FR_B_lo,FR_X,FR_R1 // r1 = r1-b_lo*x
|
|
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
|
|
};;
|
|
//
|
|
// For performance,don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mfi
|
|
ldfe FR_log2_lo = [GR_ad_q],16 // load log2_lo
|
|
nop.f 0
|
|
sub GR_N = GR_N,GR_Bias
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_Q4 = [GR_ad_q],16 // load Q4
|
|
fms.s1 FR_S_lo = FR_AA,f1,FR_Z // form S_lo = AA - Z
|
|
sub GR_minus_N = GR_Bias,GR_N // form exponent of 2^(-N)
|
|
};;
|
|
{ .mmf
|
|
ldfe FR_Q3 = [GR_ad_q],16 // load Q3
|
|
// put integer N into rightmost significand
|
|
setf.sig FR_float_N = GR_N
|
|
fmin.s1 FR_BB = FR_X,f1 // for S_lo,form BB = min(X,1.0)
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_Q2 = [GR_ad_q],16 // load Q2
|
|
nop.f 0
|
|
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
|
|
};;
|
|
{ .mfi
|
|
ldfps FR_G2,FR_H2 = [GR_ad_tbl_2],8 // load G_2,H_2
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
ldfd FR_h2 = [GR_ad_tbl_2] // load h_2
|
|
fma.s1 FR_S_lo = FR_S_lo,f1,FR_BB // S_lo = S_lo + BB
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
setf.exp FR_2_to_minus_N = GR_minus_N // form 2^(-N)
|
|
fma.s1 FR_X_lo = FR_R1,FR_Y3,f0 // x_lo = r1*y3
|
|
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
|
|
};;
|
|
//
|
|
// For performance,don't use result of pmpyshr2.u for 4 cycles
|
|
//
|
|
{ .mfi
|
|
add GR_ad2_tbl_3 = 8,GR_ad_tbl_3
|
|
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
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
//
|
|
// Now GR_X_2 can be used
|
|
//
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
extr.u GR_Index3 = GR_X_2,1,5 // extract bits 1-5 of X_2
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_S_lo = FR_S_lo,f1,FR_X_lo // S_lo = S_lo + Arg_lo
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .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
|
|
shladd GR_ad2_tbl_3 = GR_Index3,4,GR_ad2_tbl_3 // point to h_3
|
|
fma.s1 FR_Q1 = FR_Q1,FR_Half,f0 // sign(arg)*Q1/2
|
|
nop.i 0
|
|
};;
|
|
{ .mmi
|
|
ldfps FR_G3,FR_H3 = [GR_ad_tbl_3],8 // load G_3,H_3
|
|
ldfd FR_h3 = [GR_ad2_tbl_3] // load h_3
|
|
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
|
|
// S_lo = S_lo * 2^(-N)
|
|
fma.s1 FR_S_lo = FR_S_lo,FR_2_to_minus_N,f0
|
|
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
|
|
// Y_hi = N * log2_hi + H
|
|
fma.s1 FR_Y_hi = FR_float_N,FR_log2_hi,FR_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_05r = FR_r,FR_Half,f0 // sign(arg)*r/2
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo * r + Q2
|
|
fma.s1 FR_poly_lo = FR_poly_lo,FR_r,FR_Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq,FR_r,f0 // rcub = r^3
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_hi = sing(arg)*(Q1*r^2 + r)/2
|
|
fma.s1 FR_poly_hi = FR_Q1,FR_rsq,FR_05r
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
// poly_lo = poly_lo*r^3 + h
|
|
fma.s1 FR_poly_lo = FR_poly_lo,FR_rcub,FR_h
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
// Y_lo = poly_hi + poly_lo/2
|
|
fma.s0 FR_Y_lo = FR_poly_lo,FR_Half,FR_poly_hi
|
|
nop.i 0
|
|
};;
|
|
{ .mfb
|
|
nop.m 0
|
|
// Result = arctanh(x) = Y_hi/2 + Y_lo
|
|
fma.s0 f8 = FR_Y_hi,FR_Half,FR_Y_lo
|
|
br.ret.sptk b0
|
|
};;
|
|
|
|
// Taylor's series
|
|
atanhl_near_zero:
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_x3 = FR_x2,f8,f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_x4 = FR_x2,FR_x2,f0
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_C17 = FR_C17,FR_x2,FR_C15
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_C13 = FR_C13,FR_x2,FR_C11
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_C9 = FR_C9,FR_x2,FR_C7
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_C5 = FR_C5,FR_x2,FR_C3
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_x8 = FR_x4,FR_x4,f0
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_C17 = FR_C17,FR_x4,FR_C13
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_C9 = FR_C9,FR_x4,FR_C5
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_C17 = FR_C17,FR_x8,FR_C9
|
|
nop.i 0
|
|
};;
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s0 f8 = FR_C17,FR_x3,f8
|
|
br.ret.sptk b0
|
|
};;
|
|
|
|
atanhl_eq_one:
|
|
{ .mfi
|
|
nop.m 0
|
|
frcpa.s0 FR_Rcp,p0 = f1,f0 // get inf,and raise Z flag
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_Arg_X = f8, f8
|
|
nop.i 0
|
|
};;
|
|
{ .mfb
|
|
mov GR_Parameter_TAG = 130
|
|
fmerge.s FR_RESULT = f8,FR_Rcp // result is +-inf
|
|
br.cond.sptk __libm_error_region // exit if |x| = 1.0
|
|
};;
|
|
|
|
atanhl_gt_one:
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_Arg_X = f8, f8
|
|
nop.i 0
|
|
};;
|
|
{ .mfb
|
|
mov GR_Parameter_TAG = 129
|
|
frcpa.s0 FR_RESULT,p0 = f0,f0 // get QNaN,and raise invalid
|
|
br.cond.sptk __libm_error_region // exit if |x| > 1.0
|
|
};;
|
|
|
|
GLOBAL_LIBM_END(atanhl)
|
|
LOCAL_LIBM_ENTRY(__libm_error_region)
|
|
.prologue
|
|
{ .mfi
|
|
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
|
|
}
|
|
{ .mfi
|
|
.fframe 64
|
|
add sp=-64,sp // Create new stack
|
|
nop.f 0
|
|
mov GR_SAVE_GP=gp // Save gp
|
|
};;
|
|
{ .mmi
|
|
stfe [GR_Parameter_Y] = FR_Arg_Y,16 // Save 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
|
|
};;
|
|
.body
|
|
{ .mib
|
|
stfe [GR_Parameter_X] = FR_Arg_X // Store Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y
|
|
nop.b 0 // Parameter 3 address
|
|
}
|
|
{ .mib
|
|
stfe [GR_Parameter_Y] = FR_RESULT // 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
|
|
};;
|
|
{ .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#
|