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-rw-r--r--sysdeps/ia64/fpu/s_log1p.S2314
1 files changed, 1419 insertions, 895 deletions
diff --git a/sysdeps/ia64/fpu/s_log1p.S b/sysdeps/ia64/fpu/s_log1p.S
index e1e6dcc80b..0d96c14a55 100644
--- a/sysdeps/ia64/fpu/s_log1p.S
+++ b/sysdeps/ia64/fpu/s_log1p.S
@@ -1,10 +1,10 @@
-.file "log1p.s"
+.file "log1p.s"
-
-// Copyright (c) 2000 - 2005, Intel Corporation
+// Copyright (C) 2000, 2001, Intel Corporation
// All rights reserved.
-//
-// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
+// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
@@ -20,1084 +20,1608 @@
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
-
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
-// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
-// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
-// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
+// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
-// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
-// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-//
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
// Intel Corporation is the author of this code, and requests that all
-// problem reports or change requests be submitted to it directly at
-// http://www.intel.com/software/products/opensource/libraries/num.htm.
+// problem reports or change requests be submitted to it directly at
+// http://developer.intel.com/opensource.
//
// History
//==============================================================
-// 02/02/00 Initial version
-// 04/04/00 Unwind support added
-// 08/15/00 Bundle added after call to __libm_error_support to properly
+// 2/02/00 Initial version
+// 4/04/00 Unwind support added
+// 8/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
-// 06/29/01 Improved speed of all paths
-// 05/20/02 Cleaned up namespace and sf0 syntax
-// 10/02/02 Improved performance by basing on log algorithm
-// 02/10/03 Reordered header: .section, .global, .proc, .align
-// 04/18/03 Eliminate possible WAW dependency warning
-// 03/31/05 Reformatted delimiters between data tables
-//
-// API
-//==============================================================
-// double log1p(double)
//
-// log1p(x) = log(x+1)
+// *********************************************************************
//
-// Overview of operation
-//==============================================================
-// Background
-// ----------
+// Function: log1p(x) = ln(x+1), for double precision x values
//
-// This algorithm is based on fact that
-// log1p(x) = log(1+x) and
-// log(a b) = log(a) + log(b).
-// In our case we have 1+x = 2^N f, where 1 <= f < 2.
-// So
-// log(1+x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f)
+// *********************************************************************
//
-// To calculate log(f) we do following
-// log(f) = log(f * frcpa(f) / frcpa(f)) =
-// = log(f * frcpa(f)) + log(1/frcpa(f))
+// Accuracy: Very accurate for double precision values
//
-// According to definition of IA-64's frcpa instruction it's a
-// floating point that approximates 1/f using a lookup on the
-// top of 8 bits of the input number's + 1 significand with relative
-// error < 2^(-8.886). So we have following
+// *********************************************************************
//
-// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256
+// Resources Used:
//
-// and
+// Floating-Point Registers: f8 (Input and Return Value)
+// f9,f33-f55,f99
//
-// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) =
-// = log(1 + r) + T
+// General Purpose Registers:
+// r32-r53
+// r54-r57 (Used to pass arguments to error handling routine)
//
-// The first value can be computed by polynomial P(r) approximating
-// log(1 + r) on |r| < 1/256 and the second is precomputed tabular
-// value defined by top 8 bit of f.
+// Predicate Registers: p6-p15
//
-// Finally we have that log(1+x) ~ (N*log(2) + T) + P(r)
+// *********************************************************************
//
-// Note that if input argument is close to 0.0 (in our case it means
-// that |x| < 1/256) we can use just polynomial approximation
-// because 1+x = 2^0 * f = f = 1 + r and
-// log(1+x) = log(1 + r) ~ P(r)
+// IEEE Special Conditions:
//
+// Denormal fault raised on denormal inputs
+// Overflow exceptions cannot occur
+// Underflow exceptions raised when appropriate for log1p
+// (Error Handling Routine called for underflow)
+// Inexact raised when appropriate by algorithm
//
-// Implementation
-// --------------
+// log1p(inf) = inf
+// log1p(-inf) = QNaN
+// log1p(+/-0) = +/-0
+// log1p(-1) = -inf
+// log1p(SNaN) = QNaN
+// log1p(QNaN) = QNaN
+// log1p(EM_special Values) = QNaN
//
-// 1. |x| >= 2^(-8), and x > -1
-// InvX = frcpa(x+1)
-// r = InvX*(x+1) - 1
-// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)),
-// all coefficients are calcutated in quad and rounded to double
-// precision. A7,A6,A5,A4 are stored in memory whereas A3 and A2
-// created with setf.
+// *********************************************************************
//
-// N = float(n) where n is true unbiased exponent of x
+// Computation is based on the following kernel.
//
-// T is tabular value of log(1/frcpa(x)) calculated in quad precision
-// and represented by two floating-point numbers 64-bit Thi and 32-bit Tlo.
-// To load Thi,Tlo we get bits from 55 to 62 of register format significand
-// as index and calculate two addresses
-// ad_Thi = Thi_table_base_addr + 8 * index
-// ad_Tlo = Tlo_table_base_addr + 4 * index
+// ker_log_64( in_FR : X,
+// in_FR : E,
+// in_FR : Em1,
+// in_GR : Expo_Range,
+// out_FR : Y_hi,
+// out_FR : Y_lo,
+// out_FR : Scale,
+// out_PR : Safe )
+//
+// Overview
//
-// L1 (log(2)) is calculated in quad
-// precision and represented by two floating-point 64-bit numbers L1hi,L1lo
-// stored in memory.
+// The method consists of three cases.
//
-// And final result = ((L1hi*N + Thi) + (N*L1lo + Tlo)) + P(r)
+// If |X+Em1| < 2^(-80) use case log1p_small;
+// elseif |X+Em1| < 2^(-7) use case log_near1;
+// else use case log_regular;
//
+// Case log1p_small:
//
-// 2. 2^(-80) <= |x| < 2^(-8)
-// r = x
-// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)),
-// A7,A6,A5,A4,A3,A2 are the same as in case |x| >= 1/256
+// log( 1 + (X+Em1) ) can be approximated by (X+Em1).
//
-// And final results
-// log(1+x) = P(r)
+// Case log_near1:
//
-// 3. 0 < |x| < 2^(-80)
-// Although log1p(x) is basically x, we would like to preserve the inexactness
-// nature as well as consistent behavior under different rounding modes.
-// We can do this by computing the result as
+// log( 1 + (X+Em1) ) can be approximated by a simple polynomial
+// in W = X+Em1. This polynomial resembles the truncated Taylor
+// series W - W^/2 + W^3/3 - ...
+//
+// Case log_regular:
//
-// log1p(x) = x - x*x
+// Here we use a table lookup method. The basic idea is that in
+// order to compute log(Arg) for an argument Arg in [1,2), we
+// construct a value G such that G*Arg is close to 1 and that
+// log(1/G) is obtainable easily from a table of values calculated
+// beforehand. Thus
//
+// log(Arg) = log(1/G) + log(G*Arg)
+// = log(1/G) + log(1 + (G*Arg - 1))
//
-// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are
-// filtered and processed on special branches.
+// Because |G*Arg - 1| is small, the second term on the right hand
+// side can be approximated by a short polynomial. We elaborate
+// this method in four steps.
//
-
+// Step 0: Initialization
//
-// Special values
-//==============================================================
+// We need to calculate log( E + X ). Obtain N, S_hi, S_lo such that
//
-// log1p(-1) = -inf // Call error support
+// E + X = 2^N * ( S_hi + S_lo ) exactly
//
-// log1p(+qnan) = +qnan
-// log1p(-qnan) = -qnan
-// log1p(+snan) = +qnan
-// log1p(-snan) = -qnan
+// where S_hi in [1,2) and S_lo is a correction to S_hi in the sense
+// that |S_lo| <= ulp(S_hi).
//
-// log1p(x),x<-1= QNAN Indefinite // Call error support
-// log1p(-inf) = QNAN Indefinite
-// log1p(+inf) = +inf
-// log1p(+/-0) = +/-0
+// Step 1: Argument Reduction
//
+// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate
//
-// Registers used
-//==============================================================
-// Floating Point registers used:
-// f8, input
-// f7 -> f15, f32 -> f40
+// G := G_1 * G_2 * G_3
+// r := (G * S_hi - 1) + G * S_lo
+//
+// These G_j's have the property that the product is exactly
+// representable and that |r| < 2^(-12) as a result.
+//
+// Step 2: Approximation
+//
+//
+// log(1 + r) is approximated by a short polynomial poly(r).
+//
+// Step 3: Reconstruction
+//
+//
+// Finally, log( E + X ) is given by
+//
+// log( E + X ) = log( 2^N * (S_hi + S_lo) )
+// ~=~ N*log(2) + log(1/G) + log(1 + r)
+// ~=~ N*log(2) + log(1/G) + poly(r).
+//
+// **** Algorithm ****
+//
+// Case log1p_small:
+//
+// Although log(1 + (X+Em1)) is basically X+Em1, we would like to
+// preserve the inexactness nature as well as consistent behavior
+// under different rounding modes. Note that this case can only be
+// taken if E is set to be 1.0. In this case, Em1 is zero, and that
+// X can be very tiny and thus the final result can possibly underflow.
+// Thus, we compare X against a threshold that is dependent on the
+// input Expo_Range. If |X| is smaller than this threshold, we set
+// SAFE to be FALSE.
+//
+// The result is returned as Y_hi, Y_lo, and in the case of SAFE
+// is FALSE, an additional value Scale is also returned.
+//
+// W := X + Em1
+// Threshold := Threshold_Table( Expo_Range )
+// Tiny := Tiny_Table( Expo_Range )
+//
+// If ( |W| > Threshold ) then
+// Y_hi := W
+// Y_lo := -W*W
+// Else
+// Y_hi := W
+// Y_lo := -Tiny
+// Scale := 2^(-100)
+// Safe := FALSE
+// EndIf
+//
+//
+// One may think that Y_lo should be -W*W/2; however, it does not matter
+// as Y_lo will be rounded off completely except for the correct effect in
+// directed rounding. Clearly -W*W is simplier to compute. Moreover,
+// because of the difference in exponent value, Y_hi + Y_lo or
+// Y_hi + Scale*Y_lo is always inexact.
+//
+// Case log_near1:
+//
+// Here we compute a simple polynomial. To exploit parallelism, we split
+// the polynomial into two portions.
+//
+// W := X + Em1
+// Wsq := W * W
+// W4 := Wsq*Wsq
+// W6 := W4*Wsq
+// Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4))
+// Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8)))
+// set lsb(Y_lo) to be 1
+//
+// Case log_regular:
+//
+// We present the algorithm in four steps.
+//
+// Step 0. Initialization
+// ----------------------
+//
+// Z := X + E
+// N := unbaised exponent of Z
+// S_hi := 2^(-N) * Z
+// S_lo := 2^(-N) * { (max(X,E)-Z) + min(X,E) }
+//
+// Note that S_lo is always 0 for the case E = 0.
+//
+// Step 1. Argument Reduction
+// --------------------------
+//
+// Let
+//
+// Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63
+//
+// We obtain G_1, G_2, G_3 by the following steps.
+//
+//
+// Define X_0 := 1.d_1 d_2 ... d_14. This is extracted
+// from S_hi.
+//
+// Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated
+// to lsb = 2^(-4).
+//
+// Define index_1 := [ d_1 d_2 d_3 d_4 ].
+//
+// Fetch Z_1 := (1/A_1) rounded UP in fixed point with
+// fixed point lsb = 2^(-15).
+// Z_1 looks like z_0.z_1 z_2 ... z_15
+// Note that the fetching is done using index_1.
+// A_1 is actually not needed in the implementation
+// and is used here only to explain how is the value
+// Z_1 defined.
+//
+// Fetch G_1 := (1/A_1) truncated to 21 sig. bits.
+// floating pt. Again, fetching is done using index_1. A_1
+// explains how G_1 is defined.
+//
+// Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14)
+// = 1.0 0 0 0 d_5 ... d_14
+// This is accomplised by integer multiplication.
+// It is proved that X_1 indeed always begin
+// with 1.0000 in fixed point.
+//
+//
+// Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1
+// truncated to lsb = 2^(-8). Similar to A_1,
+// A_2 is not needed in actual implementation. It
+// helps explain how some of the values are defined.
+//
+// Define index_2 := [ d_5 d_6 d_7 d_8 ].
+//
+// Fetch Z_2 := (1/A_2) rounded UP in fixed point with
+// fixed point lsb = 2^(-15). Fetch done using index_2.
+// Z_2 looks like z_0.z_1 z_2 ... z_15
+//
+// Fetch G_2 := (1/A_2) truncated to 21 sig. bits.
+// floating pt.
+//
+// Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14)
+// = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14
+// This is accomplised by integer multiplication.
+// It is proved that X_2 indeed always begin
+// with 1.00000000 in fixed point.
+//
+//
+// Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1.
+// This is 2^(-14) + X_2 truncated to lsb = 2^(-13).
+//
+// Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ].
+//
+// Fetch G_3 := (1/A_3) truncated to 21 sig. bits.
+// floating pt. Fetch is done using index_3.
//
-// General registers used:
-// r8 -> r11
-// r14 -> r20
+// Compute G := G_1 * G_2 * G_3.
+//
+// This is done exactly since each of G_j only has 21 sig. bits.
+//
+// Compute
+//
+// r := (G*S_hi - 1) + G*S_lo using 2 FMA operations.
+//
+// thus, r approximates G*(S_hi+S_lo) - 1 to within a couple of
+// rounding errors.
+//
+//
+// Step 2. Approximation
+// ---------------------
+//
+// This step computes an approximation to log( 1 + r ) where r is the
+// reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13);
+// thus log(1+r) can be approximated by a short polynomial:
+//
+// log(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5
+//
+//
+// Step 3. Reconstruction
+// ----------------------
+//
+// This step computes the desired result of log(X+E):
+//
+// log(X+E) = log( 2^N * (S_hi + S_lo) )
+// = N*log(2) + log( S_hi + S_lo )
+// = N*log(2) + log(1/G) +
+// log(1 + C*(S_hi+S_lo) - 1 )
+//
+// log(2), log(1/G_j) are stored as pairs of (single,double) numbers:
+// log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are
+// single-precision numbers and the low parts are double precision
+// numbers. These have the property that
+//
+// N*log2_hi + SUM ( log1byGj_hi )
+//
+// is computable exactly in double-extended precision (64 sig. bits).
+// Finally
+//
+// Y_hi := N*log2_hi + SUM ( log1byGj_hi )
+// Y_lo := poly_hi + [ poly_lo +
+// ( SUM ( log1byGj_lo ) + N*log2_lo ) ]
+// set lsb(Y_lo) to be 1
//
-// Predicate registers used:
-// p6 -> p12
-// Assembly macros
-//==============================================================
-GR_TAG = r8
-GR_ad_1 = r8
-GR_ad_2 = r9
-GR_Exp = r10
-GR_N = r11
+#include "libm_support.h"
-GR_signexp_x = r14
-GR_exp_mask = r15
-GR_exp_bias = r16
-GR_05 = r17
-GR_A3 = r18
-GR_Sig = r19
-GR_Ind = r19
-GR_exp_x = r20
+#ifdef _LIBC
+.rodata
+#else
+.data
+#endif
+// P_7, P_6, P_5, P_4, P_3, P_2, and P_1
-GR_SAVE_B0 = r33
-GR_SAVE_PFS = r34
-GR_SAVE_GP = r35
-GR_SAVE_SP = r36
+.align 64
+Constants_P:
+ASM_TYPE_DIRECTIVE(Constants_P,@object)
+data4 0xEFD62B15,0xE3936754,0x00003FFB,0x00000000
+data4 0xA5E56381,0x8003B271,0x0000BFFC,0x00000000
+data4 0x73282DB0,0x9249248C,0x00003FFC,0x00000000
+data4 0x47305052,0xAAAAAA9F,0x0000BFFC,0x00000000
+data4 0xCCD17FC9,0xCCCCCCCC,0x00003FFC,0x00000000
+data4 0x00067ED5,0x80000000,0x0000BFFD,0x00000000
+data4 0xAAAAAAAA,0xAAAAAAAA,0x00003FFD,0x00000000
+data4 0xFFFFFFFE,0xFFFFFFFF,0x0000BFFD,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_P)
+
+// log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1
-GR_Parameter_X = r37
-GR_Parameter_Y = r38
-GR_Parameter_RESULT = r39
-GR_Parameter_TAG = r40
+.align 64
+Constants_Q:
+ASM_TYPE_DIRECTIVE(Constants_Q,@object)
+data4 0x00000000,0xB1721800,0x00003FFE,0x00000000
+data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
+data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000
+data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000
+data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000
+data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_Q)
+
+// Z1 - 16 bit fixed, G1 and H1 - IEEE single
+
+.align 64
+Constants_Z_G_H_h1:
+ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h1,@object)
+data4 0x00008000,0x3F800000,0x00000000,0x00000000,0x00000000,0x00000000
+data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000,0x617D741C,0x3DA163A6
+data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000,0xCBD3D5BB,0x3E2C55E6
+data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000,0xD86EA5E7,0xBE3EB0BF
+data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000,0x86B12760,0x3E2E6A8C
+data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000,0x5C0739BA,0x3E47574C
+data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000,0x13E8AF2F,0x3E20E30F
+data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000,0xF2C630BD,0xBE42885B
+data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000,0x97E577C6,0x3E497F34
+data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000,0xA6B0A5AB,0x3E3E6A6E
+data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000,0xD328D9BE,0xBDF43E3C
+data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000,0x0ADB090A,0x3E4094C3
+data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000,0xFC1FE510,0xBE28FBB2
+data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000,0x10FDE3FA,0x3E3A7895
+data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000,0x7CC8C98F,0x3E508CE5
+data4 0x00004211,0x3F042108,0x3F29516A,0x00000000,0xA223106C,0xBE534874
+ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h1)
+
+// Z2 - 16 bit fixed, G2 and H2 - IEEE single
+.align 64
+Constants_Z_G_H_h2:
+ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h2,@object)
+data4 0x00008000,0x3F800000,0x00000000,0x00000000,0x00000000,0x00000000
+data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000,0x22C42273,0x3DB5A116
+data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000,0x21F86ED3,0x3DE620CF
+data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000,0x484F34ED,0xBDAFA07E
+data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000,0x3860BCF6,0xBDFE07F0
+data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000,0xA78093D6,0x3DEA370F
+data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000,0x72A753D0,0x3DFF5791
+data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000,0xA7EF896B,0x3DFEBE6C
+data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000,0x409ECB43,0x3E0CF156
+data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000,0xFFEF71DF,0xBE0B6F97
+data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000,0x5D59EEE8,0xBE080483
+data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000,0xA9192A74,0x3E1F91E9
+data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000,0xBF72A8CD,0xBE139A06
+data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000,0xF8FBA6CF,0x3E1D9202
+data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000,0xBA796223,0xBE1DCCC4
+data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000,0xB6B7C239,0xBE049391
+ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h2)
+
+// G3 and H3 - IEEE single and h3 -IEEE double
+.align 64
+Constants_Z_G_H_h3:
+ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h3,@object)
+data4 0x3F7FFC00,0x38800100,0x562224CD,0x3D355595
+data4 0x3F7FF400,0x39400480,0x06136FF6,0x3D8200A2
+data4 0x3F7FEC00,0x39A00640,0xE8DE9AF0,0x3DA4D68D
+data4 0x3F7FE400,0x39E00C41,0xB10238DC,0xBD8B4291
+data4 0x3F7FDC00,0x3A100A21,0x3B1952CA,0xBD89CCB8
+data4 0x3F7FD400,0x3A300F22,0x1DC46826,0xBDB10707
+data4 0x3F7FCC08,0x3A4FF51C,0xF43307DB,0x3DB6FCB9
+data4 0x3F7FC408,0x3A6FFC1D,0x62DC7872,0xBD9B7C47
+data4 0x3F7FBC10,0x3A87F20B,0x3F89154A,0xBDC3725E
+data4 0x3F7FB410,0x3A97F68B,0x62B9D392,0xBD93519D
+data4 0x3F7FAC18,0x3AA7EB86,0x0F21BD9D,0x3DC18441
+data4 0x3F7FA420,0x3AB7E101,0x2245E0A6,0xBDA64B95
+data4 0x3F7F9C20,0x3AC7E701,0xAABB34B8,0x3DB4B0EC
+data4 0x3F7F9428,0x3AD7DD7B,0x6DC40A7E,0x3D992337
+data4 0x3F7F8C30,0x3AE7D474,0x4F2083D3,0x3DC6E17B
+data4 0x3F7F8438,0x3AF7CBED,0x811D4394,0x3DAE314B
+data4 0x3F7F7C40,0x3B03E1F3,0xB08F2DB1,0xBDD46F21
+data4 0x3F7F7448,0x3B0BDE2F,0x6D34522B,0xBDDC30A4
+data4 0x3F7F6C50,0x3B13DAAA,0xB1F473DB,0x3DCB0070
+data4 0x3F7F6458,0x3B1BD766,0x6AD282FD,0xBDD65DDC
+data4 0x3F7F5C68,0x3B23CC5C,0xF153761A,0xBDCDAB83
+data4 0x3F7F5470,0x3B2BC997,0x341D0F8F,0xBDDADA40
+data4 0x3F7F4C78,0x3B33C711,0xEBC394E8,0x3DCD1BD7
+data4 0x3F7F4488,0x3B3BBCC6,0x52E3E695,0xBDC3532B
+data4 0x3F7F3C90,0x3B43BAC0,0xE846B3DE,0xBDA3961E
+data4 0x3F7F34A0,0x3B4BB0F4,0x785778D4,0xBDDADF06
+data4 0x3F7F2CA8,0x3B53AF6D,0xE55CE212,0x3DCC3ED1
+data4 0x3F7F24B8,0x3B5BA620,0x9E382C15,0xBDBA3103
+data4 0x3F7F1CC8,0x3B639D12,0x5C5AF197,0x3D635A0B
+data4 0x3F7F14D8,0x3B6B9444,0x71D34EFC,0xBDDCCB19
+data4 0x3F7F0CE0,0x3B7393BC,0x52CD7ADA,0x3DC74502
+data4 0x3F7F04F0,0x3B7B8B6D,0x7D7F2A42,0xBDB68F17
+ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h3)
+
+//
+// Exponent Thresholds and Tiny Thresholds
+// for 8, 11, 15, and 17 bit exponents
+//
+// Expo_Range Value
+//
+// 0 (8 bits) 2^(-126)
+// 1 (11 bits) 2^(-1022)
+// 2 (15 bits) 2^(-16382)
+// 3 (17 bits) 2^(-16382)
+//
+// Tiny_Table
+// ----------
+// Expo_Range Value
+//
+// 0 (8 bits) 2^(-16382)
+// 1 (11 bits) 2^(-16382)
+// 2 (15 bits) 2^(-16382)
+// 3 (17 bits) 2^(-16382)
+//
-FR_NormX = f7
-FR_RcpX = f9
-FR_r = f10
-FR_r2 = f11
-FR_r4 = f12
-FR_N = f13
-FR_Ln2hi = f14
-FR_Ln2lo = f15
+.align 64
+Constants_Threshold:
+ASM_TYPE_DIRECTIVE(Constants_Threshold,@object)
+data4 0x00000000,0x80000000,0x00003F81,0x00000000
+data4 0x00000000,0x80000000,0x00000001,0x00000000
+data4 0x00000000,0x80000000,0x00003C01,0x00000000
+data4 0x00000000,0x80000000,0x00000001,0x00000000
+data4 0x00000000,0x80000000,0x00000001,0x00000000
+data4 0x00000000,0x80000000,0x00000001,0x00000000
+data4 0x00000000,0x80000000,0x00000001,0x00000000
+data4 0x00000000,0x80000000,0x00000001,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_Threshold)
-FR_A7 = f32
-FR_A6 = f33
-FR_A5 = f34
-FR_A4 = f35
-FR_A3 = f36
-FR_A2 = f37
+.align 64
+Constants_1_by_LN10:
+ASM_TYPE_DIRECTIVE(Constants_1_by_LN10,@object)
+data4 0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000
+data4 0xACCF70C8,0xD56EAABE,0x00003FBD,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_1_by_LN10)
-FR_Thi = f38
-FR_NxLn2hipThi = f38
-FR_NxLn2pT = f38
-FR_Tlo = f39
-FR_NxLn2lopTlo = f39
+FR_Input_X = f8
+FR_Neg_One = f9
+FR_E = f33
+FR_Em1 = f34
+FR_Y_hi = f34
+// Shared with Em1
+FR_Y_lo = f35
+FR_Scale = f36
+FR_X_Prime = f37
+FR_Z = f38
+FR_S_hi = f38
+// Shared with Z
+FR_W = f39
+FR_G = f40
+FR_wsq = f40
+// Shared with G
+FR_H = f41
+FR_w4 = f41
+// Shared with H
+FR_h = f42
+FR_w6 = f42
+// Shared with h
+FR_G_tmp = f43
+FR_poly_lo = f43
+// Shared with G_tmp
+FR_P8 = f43
+// Shared with G_tmp
+FR_H_tmp = f44
+FR_poly_hi = f44
+ // Shared with H_tmp
+FR_P7 = f44
+// Shared with H_tmp
+FR_h_tmp = f45
+FR_rsq = f45
+// Shared with h_tmp
+FR_P6 = f45
+// Shared with h_tmp
+FR_abs_W = f46
+FR_r = f46
+// Shared with abs_W
+FR_AA = f47
+FR_log2_hi = f47
+// Shared with AA
+FR_BB = f48
+FR_log2_lo = f48
+// Shared with BB
+FR_S_lo = f49
+FR_two_negN = f50
+FR_float_N = f51
+FR_Q4 = f52
+FR_dummy = f52
+// Shared with Q4
+FR_P4 = f52
+// Shared with Q4
+FR_Threshold = f52
+// Shared with Q4
+FR_Q3 = f53
+FR_P3 = f53
+// Shared with Q3
+FR_Tiny = f53
+// Shared with Q3
+FR_Q2 = f54
+FR_P2 = f54
+// Shared with Q2
+FR_1LN10_hi = f54
+// Shared with Q2
+FR_Q1 = f55
+FR_P1 = f55
+// Shared with Q1
+FR_1LN10_lo = f55
+// Shared with Q1
+FR_P5 = f98
+FR_SCALE = f98
+FR_Output_X_tmp = f99
-FR_Xp1 = f40
+GR_Expo_Range = r32
+GR_Table_Base = r34
+GR_Table_Base1 = r35
+GR_Table_ptr = r36
+GR_Index2 = r37
+GR_signif = r38
+GR_X_0 = r39
+GR_X_1 = r40
+GR_X_2 = r41
+GR_Z_1 = r42
+GR_Z_2 = r43
+GR_N = r44
+GR_Bias = r45
+GR_M = r46
+GR_ScaleN = r47
+GR_Index3 = r48
+GR_Perturb = r49
+GR_Table_Scale = r50
-FR_Y = f1
-FR_X = f10
-FR_RESULT = f8
+GR_SAVE_PFS = r51
+GR_SAVE_B0 = r52
+GR_SAVE_GP = r53
+GR_Parameter_X = r54
+GR_Parameter_Y = r55
+GR_Parameter_RESULT = r56
+
+GR_Parameter_TAG = r57
-// Data
-//==============================================================
-RODATA
-.align 16
-
-LOCAL_OBJECT_START(log_data)
-// coefficients of polynomial approximation
-data8 0x3FC2494104381A8E // A7
-data8 0xBFC5556D556BBB69 // A6
-data8 0x3FC999999988B5E9 // A5
-data8 0xBFCFFFFFFFF6FFF5 // A4
-//
-// hi parts of ln(1/frcpa(1+i/256)), i=0...255
-data8 0x3F60040155D5889D // 0
-data8 0x3F78121214586B54 // 1
-data8 0x3F841929F96832EF // 2
-data8 0x3F8C317384C75F06 // 3
-data8 0x3F91A6B91AC73386 // 4
-data8 0x3F95BA9A5D9AC039 // 5
-data8 0x3F99D2A8074325F3 // 6
-data8 0x3F9D6B2725979802 // 7
-data8 0x3FA0C58FA19DFAA9 // 8
-data8 0x3FA2954C78CBCE1A // 9
-data8 0x3FA4A94D2DA96C56 // 10
-data8 0x3FA67C94F2D4BB58 // 11
-data8 0x3FA85188B630F068 // 12
-data8 0x3FAA6B8ABE73AF4C // 13
-data8 0x3FAC441E06F72A9E // 14
-data8 0x3FAE1E6713606D06 // 15
-data8 0x3FAFFA6911AB9300 // 16
-data8 0x3FB0EC139C5DA600 // 17
-data8 0x3FB1DBD2643D190B // 18
-data8 0x3FB2CC7284FE5F1C // 19
-data8 0x3FB3BDF5A7D1EE64 // 20
-data8 0x3FB4B05D7AA012E0 // 21
-data8 0x3FB580DB7CEB5701 // 22
-data8 0x3FB674F089365A79 // 23
-data8 0x3FB769EF2C6B568D // 24
-data8 0x3FB85FD927506A47 // 25
-data8 0x3FB9335E5D594988 // 26
-data8 0x3FBA2B0220C8E5F4 // 27
-data8 0x3FBB0004AC1A86AB // 28
-data8 0x3FBBF968769FCA10 // 29
-data8 0x3FBCCFEDBFEE13A8 // 30
-data8 0x3FBDA727638446A2 // 31
-data8 0x3FBEA3257FE10F79 // 32
-data8 0x3FBF7BE9FEDBFDE5 // 33
-data8 0x3FC02AB352FF25F3 // 34
-data8 0x3FC097CE579D204C // 35
-data8 0x3FC1178E8227E47B // 36
-data8 0x3FC185747DBECF33 // 37
-data8 0x3FC1F3B925F25D41 // 38
-data8 0x3FC2625D1E6DDF56 // 39
-data8 0x3FC2D1610C868139 // 40
-data8 0x3FC340C59741142E // 41
-data8 0x3FC3B08B6757F2A9 // 42
-data8 0x3FC40DFB08378003 // 43
-data8 0x3FC47E74E8CA5F7C // 44
-data8 0x3FC4EF51F6466DE4 // 45
-data8 0x3FC56092E02BA516 // 46
-data8 0x3FC5D23857CD74D4 // 47
-data8 0x3FC6313A37335D76 // 48
-data8 0x3FC6A399DABBD383 // 49
-data8 0x3FC70337DD3CE41A // 50
-data8 0x3FC77654128F6127 // 51
-data8 0x3FC7E9D82A0B022D // 52
-data8 0x3FC84A6B759F512E // 53
-data8 0x3FC8AB47D5F5A30F // 54
-data8 0x3FC91FE49096581B // 55
-data8 0x3FC981634011AA75 // 56
-data8 0x3FC9F6C407089664 // 57
-data8 0x3FCA58E729348F43 // 58
-data8 0x3FCABB55C31693AC // 59
-data8 0x3FCB1E104919EFD0 // 60
-data8 0x3FCB94EE93E367CA // 61
-data8 0x3FCBF851C067555E // 62
-data8 0x3FCC5C0254BF23A5 // 63
-data8 0x3FCCC000C9DB3C52 // 64
-data8 0x3FCD244D99C85673 // 65
-data8 0x3FCD88E93FB2F450 // 66
-data8 0x3FCDEDD437EAEF00 // 67
-data8 0x3FCE530EFFE71012 // 68
-data8 0x3FCEB89A1648B971 // 69
-data8 0x3FCF1E75FADF9BDE // 70
-data8 0x3FCF84A32EAD7C35 // 71
-data8 0x3FCFEB2233EA07CD // 72
-data8 0x3FD028F9C7035C1C // 73
-data8 0x3FD05C8BE0D9635A // 74
-data8 0x3FD085EB8F8AE797 // 75
-data8 0x3FD0B9C8E32D1911 // 76
-data8 0x3FD0EDD060B78080 // 77
-data8 0x3FD122024CF0063F // 78
-data8 0x3FD14BE2927AECD4 // 79
-data8 0x3FD180618EF18ADF // 80
-data8 0x3FD1B50BBE2FC63B // 81
-data8 0x3FD1DF4CC7CF242D // 82
-data8 0x3FD214456D0EB8D4 // 83
-data8 0x3FD23EC5991EBA49 // 84
-data8 0x3FD2740D9F870AFB // 85
-data8 0x3FD29ECDABCDFA03 // 86
-data8 0x3FD2D46602ADCCEE // 87
-data8 0x3FD2FF66B04EA9D4 // 88
-data8 0x3FD335504B355A37 // 89
-data8 0x3FD360925EC44F5C // 90
-data8 0x3FD38BF1C3337E74 // 91
-data8 0x3FD3C25277333183 // 92
-data8 0x3FD3EDF463C1683E // 93
-data8 0x3FD419B423D5E8C7 // 94
-data8 0x3FD44591E0539F48 // 95
-data8 0x3FD47C9175B6F0AD // 96
-data8 0x3FD4A8B341552B09 // 97
-data8 0x3FD4D4F39089019F // 98
-data8 0x3FD501528DA1F967 // 99
-data8 0x3FD52DD06347D4F6 // 100
-data8 0x3FD55A6D3C7B8A89 // 101
-data8 0x3FD5925D2B112A59 // 102
-data8 0x3FD5BF406B543DB1 // 103
-data8 0x3FD5EC433D5C35AD // 104
-data8 0x3FD61965CDB02C1E // 105
-data8 0x3FD646A84935B2A1 // 106
-data8 0x3FD6740ADD31DE94 // 107
-data8 0x3FD6A18DB74A58C5 // 108
-data8 0x3FD6CF31058670EC // 109
-data8 0x3FD6F180E852F0B9 // 110
-data8 0x3FD71F5D71B894EF // 111
-data8 0x3FD74D5AEFD66D5C // 112
-data8 0x3FD77B79922BD37D // 113
-data8 0x3FD7A9B9889F19E2 // 114
-data8 0x3FD7D81B037EB6A6 // 115
-data8 0x3FD8069E33827230 // 116
-data8 0x3FD82996D3EF8BCA // 117
-data8 0x3FD85855776DCBFA // 118
-data8 0x3FD8873658327CCE // 119
-data8 0x3FD8AA75973AB8CE // 120
-data8 0x3FD8D992DC8824E4 // 121
-data8 0x3FD908D2EA7D9511 // 122
-data8 0x3FD92C59E79C0E56 // 123
-data8 0x3FD95BD750EE3ED2 // 124
-data8 0x3FD98B7811A3EE5B // 125
-data8 0x3FD9AF47F33D406B // 126
-data8 0x3FD9DF270C1914A7 // 127
-data8 0x3FDA0325ED14FDA4 // 128
-data8 0x3FDA33440224FA78 // 129
-data8 0x3FDA57725E80C382 // 130
-data8 0x3FDA87D0165DD199 // 131
-data8 0x3FDAAC2E6C03F895 // 132
-data8 0x3FDADCCC6FDF6A81 // 133
-data8 0x3FDB015B3EB1E790 // 134
-data8 0x3FDB323A3A635948 // 135
-data8 0x3FDB56FA04462909 // 136
-data8 0x3FDB881AA659BC93 // 137
-data8 0x3FDBAD0BEF3DB164 // 138
-data8 0x3FDBD21297781C2F // 139
-data8 0x3FDC039236F08818 // 140
-data8 0x3FDC28CB1E4D32FC // 141
-data8 0x3FDC4E19B84723C1 // 142
-data8 0x3FDC7FF9C74554C9 // 143
-data8 0x3FDCA57B64E9DB05 // 144
-data8 0x3FDCCB130A5CEBAF // 145
-data8 0x3FDCF0C0D18F326F // 146
-data8 0x3FDD232075B5A201 // 147
-data8 0x3FDD490246DEFA6B // 148
-data8 0x3FDD6EFA918D25CD // 149
-data8 0x3FDD9509707AE52F // 150
-data8 0x3FDDBB2EFE92C554 // 151
-data8 0x3FDDEE2F3445E4AE // 152
-data8 0x3FDE148A1A2726CD // 153
-data8 0x3FDE3AFC0A49FF3F // 154
-data8 0x3FDE6185206D516D // 155
-data8 0x3FDE882578823D51 // 156
-data8 0x3FDEAEDD2EAC990C // 157
-data8 0x3FDED5AC5F436BE2 // 158
-data8 0x3FDEFC9326D16AB8 // 159
-data8 0x3FDF2391A21575FF // 160
-data8 0x3FDF4AA7EE03192C // 161
-data8 0x3FDF71D627C30BB0 // 162
-data8 0x3FDF991C6CB3B379 // 163
-data8 0x3FDFC07ADA69A90F // 164
-data8 0x3FDFE7F18EB03D3E // 165
-data8 0x3FE007C053C5002E // 166
-data8 0x3FE01B942198A5A0 // 167
-data8 0x3FE02F74400C64EA // 168
-data8 0x3FE04360BE7603AC // 169
-data8 0x3FE05759AC47FE33 // 170
-data8 0x3FE06B5F1911CF51 // 171
-data8 0x3FE078BF0533C568 // 172
-data8 0x3FE08CD9687E7B0E // 173
-data8 0x3FE0A10074CF9019 // 174
-data8 0x3FE0B5343A234476 // 175
-data8 0x3FE0C974C89431CD // 176
-data8 0x3FE0DDC2305B9886 // 177
-data8 0x3FE0EB524BAFC918 // 178
-data8 0x3FE0FFB54213A475 // 179
-data8 0x3FE114253DA97D9F // 180
-data8 0x3FE128A24F1D9AFF // 181
-data8 0x3FE1365252BF0864 // 182
-data8 0x3FE14AE558B4A92D // 183
-data8 0x3FE15F85A19C765B // 184
-data8 0x3FE16D4D38C119FA // 185
-data8 0x3FE18203C20DD133 // 186
-data8 0x3FE196C7BC4B1F3A // 187
-data8 0x3FE1A4A738B7A33C // 188
-data8 0x3FE1B981C0C9653C // 189
-data8 0x3FE1CE69E8BB106A // 190
-data8 0x3FE1DC619DE06944 // 191
-data8 0x3FE1F160A2AD0DA3 // 192
-data8 0x3FE2066D7740737E // 193
-data8 0x3FE2147DBA47A393 // 194
-data8 0x3FE229A1BC5EBAC3 // 195
-data8 0x3FE237C1841A502E // 196
-data8 0x3FE24CFCE6F80D9A // 197
-data8 0x3FE25B2C55CD5762 // 198
-data8 0x3FE2707F4D5F7C40 // 199
-data8 0x3FE285E0842CA383 // 200
-data8 0x3FE294294708B773 // 201
-data8 0x3FE2A9A2670AFF0C // 202
-data8 0x3FE2B7FB2C8D1CC0 // 203
-data8 0x3FE2C65A6395F5F5 // 204
-data8 0x3FE2DBF557B0DF42 // 205
-data8 0x3FE2EA64C3F97654 // 206
-data8 0x3FE3001823684D73 // 207
-data8 0x3FE30E97E9A8B5CC // 208
-data8 0x3FE32463EBDD34E9 // 209
-data8 0x3FE332F4314AD795 // 210
-data8 0x3FE348D90E7464CF // 211
-data8 0x3FE35779F8C43D6D // 212
-data8 0x3FE36621961A6A99 // 213
-data8 0x3FE37C299F3C366A // 214
-data8 0x3FE38AE2171976E7 // 215
-data8 0x3FE399A157A603E7 // 216
-data8 0x3FE3AFCCFE77B9D1 // 217
-data8 0x3FE3BE9D503533B5 // 218
-data8 0x3FE3CD7480B4A8A2 // 219
-data8 0x3FE3E3C43918F76C // 220
-data8 0x3FE3F2ACB27ED6C6 // 221
-data8 0x3FE4019C2125CA93 // 222
-data8 0x3FE4181061389722 // 223
-data8 0x3FE42711518DF545 // 224
-data8 0x3FE436194E12B6BF // 225
-data8 0x3FE445285D68EA69 // 226
-data8 0x3FE45BCC464C893A // 227
-data8 0x3FE46AED21F117FC // 228
-data8 0x3FE47A1527E8A2D3 // 229
-data8 0x3FE489445EFFFCCB // 230
-data8 0x3FE4A018BCB69835 // 231
-data8 0x3FE4AF5A0C9D65D7 // 232
-data8 0x3FE4BEA2A5BDBE87 // 233
-data8 0x3FE4CDF28F10AC46 // 234
-data8 0x3FE4DD49CF994058 // 235
-data8 0x3FE4ECA86E64A683 // 236
-data8 0x3FE503C43CD8EB68 // 237
-data8 0x3FE513356667FC57 // 238
-data8 0x3FE522AE0738A3D7 // 239
-data8 0x3FE5322E26867857 // 240
-data8 0x3FE541B5CB979809 // 241
-data8 0x3FE55144FDBCBD62 // 242
-data8 0x3FE560DBC45153C6 // 243
-data8 0x3FE5707A26BB8C66 // 244
-data8 0x3FE587F60ED5B8FF // 245
-data8 0x3FE597A7977C8F31 // 246
-data8 0x3FE5A760D634BB8A // 247
-data8 0x3FE5B721D295F10E // 248
-data8 0x3FE5C6EA94431EF9 // 249
-data8 0x3FE5D6BB22EA86F5 // 250
-data8 0x3FE5E6938645D38F // 251
-data8 0x3FE5F673C61A2ED1 // 252
-data8 0x3FE6065BEA385926 // 253
-data8 0x3FE6164BFA7CC06B // 254
-data8 0x3FE62643FECF9742 // 255
-//
-// two parts of ln(2)
-data8 0x3FE62E42FEF00000,0x3DD473DE6AF278ED
-//
-// lo parts of ln(1/frcpa(1+i/256)), i=0...255
-data4 0x20E70672 // 0
-data4 0x1F60A5D0 // 1
-data4 0x218EABA0 // 2
-data4 0x21403104 // 3
-data4 0x20E9B54E // 4
-data4 0x21EE1382 // 5
-data4 0x226014E3 // 6
-data4 0x2095E5C9 // 7
-data4 0x228BA9D4 // 8
-data4 0x22932B86 // 9
-data4 0x22608A57 // 10
-data4 0x220209F3 // 11
-data4 0x212882CC // 12
-data4 0x220D46E2 // 13
-data4 0x21FA4C28 // 14
-data4 0x229E5BD9 // 15
-data4 0x228C9838 // 16
-data4 0x2311F954 // 17
-data4 0x221365DF // 18
-data4 0x22BD0CB3 // 19
-data4 0x223D4BB7 // 20
-data4 0x22A71BBE // 21
-data4 0x237DB2FA // 22
-data4 0x23194C9D // 23
-data4 0x22EC639E // 24
-data4 0x2367E669 // 25
-data4 0x232E1D5F // 26
-data4 0x234A639B // 27
-data4 0x2365C0E0 // 28
-data4 0x234646C1 // 29
-data4 0x220CBF9C // 30
-data4 0x22A00FD4 // 31
-data4 0x2306A3F2 // 32
-data4 0x23745A9B // 33
-data4 0x2398D756 // 34
-data4 0x23DD0B6A // 35
-data4 0x23DE338B // 36
-data4 0x23A222DF // 37
-data4 0x223164F8 // 38
-data4 0x23B4E87B // 39
-data4 0x23D6CCB8 // 40
-data4 0x220C2099 // 41
-data4 0x21B86B67 // 42
-data4 0x236D14F1 // 43
-data4 0x225A923F // 44
-data4 0x22748723 // 45
-data4 0x22200D13 // 46
-data4 0x23C296EA // 47
-data4 0x2302AC38 // 48
-data4 0x234B1996 // 49
-data4 0x2385E298 // 50
-data4 0x23175BE5 // 51
-data4 0x2193F482 // 52
-data4 0x23BFEA90 // 53
-data4 0x23D70A0C // 54
-data4 0x231CF30A // 55
-data4 0x235D9E90 // 56
-data4 0x221AD0CB // 57
-data4 0x22FAA08B // 58
-data4 0x23D29A87 // 59
-data4 0x20C4B2FE // 60
-data4 0x2381B8B7 // 61
-data4 0x23F8D9FC // 62
-data4 0x23EAAE7B // 63
-data4 0x2329E8AA // 64
-data4 0x23EC0322 // 65
-data4 0x2357FDCB // 66
-data4 0x2392A9AD // 67
-data4 0x22113B02 // 68
-data4 0x22DEE901 // 69
-data4 0x236A6D14 // 70
-data4 0x2371D33E // 71
-data4 0x2146F005 // 72
-data4 0x23230B06 // 73
-data4 0x22F1C77D // 74
-data4 0x23A89FA3 // 75
-data4 0x231D1241 // 76
-data4 0x244DA96C // 77
-data4 0x23ECBB7D // 78
-data4 0x223E42B4 // 79
-data4 0x23801BC9 // 80
-data4 0x23573263 // 81
-data4 0x227C1158 // 82
-data4 0x237BD749 // 83
-data4 0x21DDBAE9 // 84
-data4 0x23401735 // 85
-data4 0x241D9DEE // 86
-data4 0x23BC88CB // 87
-data4 0x2396D5F1 // 88
-data4 0x23FC89CF // 89
-data4 0x2414F9A2 // 90
-data4 0x2474A0F5 // 91
-data4 0x24354B60 // 92
-data4 0x23C1EB40 // 93
-data4 0x2306DD92 // 94
-data4 0x24353B6B // 95
-data4 0x23CD1701 // 96
-data4 0x237C7A1C // 97
-data4 0x245793AA // 98
-data4 0x24563695 // 99
-data4 0x23C51467 // 100
-data4 0x24476B68 // 101
-data4 0x212585A9 // 102
-data4 0x247B8293 // 103
-data4 0x2446848A // 104
-data4 0x246A53F8 // 105
-data4 0x246E496D // 106
-data4 0x23ED1D36 // 107
-data4 0x2314C258 // 108
-data4 0x233244A7 // 109
-data4 0x245B7AF0 // 110
-data4 0x24247130 // 111
-data4 0x22D67B38 // 112
-data4 0x2449F620 // 113
-data4 0x23BBC8B8 // 114
-data4 0x237D3BA0 // 115
-data4 0x245E8F13 // 116
-data4 0x2435573F // 117
-data4 0x242DE666 // 118
-data4 0x2463BC10 // 119
-data4 0x2466587D // 120
-data4 0x2408144B // 121
-data4 0x2405F0E5 // 122
-data4 0x22381CFF // 123
-data4 0x24154F9B // 124
-data4 0x23A4E96E // 125
-data4 0x24052967 // 126
-data4 0x2406963F // 127
-data4 0x23F7D3CB // 128
-data4 0x2448AFF4 // 129
-data4 0x24657A21 // 130
-data4 0x22FBC230 // 131
-data4 0x243C8DEA // 132
-data4 0x225DC4B7 // 133
-data4 0x23496EBF // 134
-data4 0x237C2B2B // 135
-data4 0x23A4A5B1 // 136
-data4 0x2394E9D1 // 137
-data4 0x244BC950 // 138
-data4 0x23C7448F // 139
-data4 0x2404A1AD // 140
-data4 0x246511D5 // 141
-data4 0x24246526 // 142
-data4 0x23111F57 // 143
-data4 0x22868951 // 144
-data4 0x243EB77F // 145
-data4 0x239F3DFF // 146
-data4 0x23089666 // 147
-data4 0x23EBFA6A // 148
-data4 0x23C51312 // 149
-data4 0x23E1DD5E // 150
-data4 0x232C0944 // 151
-data4 0x246A741F // 152
-data4 0x2414DF8D // 153
-data4 0x247B5546 // 154
-data4 0x2415C980 // 155
-data4 0x24324ABD // 156
-data4 0x234EB5E5 // 157
-data4 0x2465E43E // 158
-data4 0x242840D1 // 159
-data4 0x24444057 // 160
-data4 0x245E56F0 // 161
-data4 0x21AE30F8 // 162
-data4 0x23FB3283 // 163
-data4 0x247A4D07 // 164
-data4 0x22AE314D // 165
-data4 0x246B7727 // 166
-data4 0x24EAD526 // 167
-data4 0x24B41DC9 // 168
-data4 0x24EE8062 // 169
-data4 0x24A0C7C4 // 170
-data4 0x24E8DA67 // 171
-data4 0x231120F7 // 172
-data4 0x24401FFB // 173
-data4 0x2412DD09 // 174
-data4 0x248C131A // 175
-data4 0x24C0A7CE // 176
-data4 0x243DD4C8 // 177
-data4 0x24457FEB // 178
-data4 0x24DEEFBB // 179
-data4 0x243C70AE // 180
-data4 0x23E7A6FA // 181
-data4 0x24C2D311 // 182
-data4 0x23026255 // 183
-data4 0x2437C9B9 // 184
-data4 0x246BA847 // 185
-data4 0x2420B448 // 186
-data4 0x24C4CF5A // 187
-data4 0x242C4981 // 188
-data4 0x24DE1525 // 189
-data4 0x24F5CC33 // 190
-data4 0x235A85DA // 191
-data4 0x24A0B64F // 192
-data4 0x244BA0A4 // 193
-data4 0x24AAF30A // 194
-data4 0x244C86F9 // 195
-data4 0x246D5B82 // 196
-data4 0x24529347 // 197
-data4 0x240DD008 // 198
-data4 0x24E98790 // 199
-data4 0x2489B0CE // 200
-data4 0x22BC29AC // 201
-data4 0x23F37C7A // 202
-data4 0x24987FE8 // 203
-data4 0x22AFE20B // 204
-data4 0x24C8D7C2 // 205
-data4 0x24B28B7D // 206
-data4 0x23B6B271 // 207
-data4 0x24C77CB6 // 208
-data4 0x24EF1DCA // 209
-data4 0x24A4F0AC // 210
-data4 0x24CF113E // 211
-data4 0x2496BBAB // 212
-data4 0x23C7CC8A // 213
-data4 0x23AE3961 // 214
-data4 0x2410A895 // 215
-data4 0x23CE3114 // 216
-data4 0x2308247D // 217
-data4 0x240045E9 // 218
-data4 0x24974F60 // 219
-data4 0x242CB39F // 220
-data4 0x24AB8D69 // 221
-data4 0x23436788 // 222
-data4 0x24305E9E // 223
-data4 0x243E71A9 // 224
-data4 0x23C2A6B3 // 225
-data4 0x23FFE6CF // 226
-data4 0x2322D801 // 227
-data4 0x24515F21 // 228
-data4 0x2412A0D6 // 229
-data4 0x24E60D44 // 230
-data4 0x240D9251 // 231
-data4 0x247076E2 // 232
-data4 0x229B101B // 233
-data4 0x247B12DE // 234
-data4 0x244B9127 // 235
-data4 0x2499EC42 // 236
-data4 0x21FC3963 // 237
-data4 0x23E53266 // 238
-data4 0x24CE102D // 239
-data4 0x23CC45D2 // 240
-data4 0x2333171D // 241
-data4 0x246B3533 // 242
-data4 0x24931129 // 243
-data4 0x24405FFA // 244
-data4 0x24CF464D // 245
-data4 0x237095CD // 246
-data4 0x24F86CBD // 247
-data4 0x24E2D84B // 248
-data4 0x21ACBB44 // 249
-data4 0x24F43A8C // 250
-data4 0x249DB931 // 251
-data4 0x24A385EF // 252
-data4 0x238B1279 // 253
-data4 0x2436213E // 254
-data4 0x24F18A3B // 255
-LOCAL_OBJECT_END(log_data)
-
-
-// Code
-//==============================================================
.section .text
-GLOBAL_IEEE754_ENTRY(log1p)
+.proc log1p#
+.global log1p#
+.align 64
+log1p:
+#ifdef _LIBC
+.global __log1p
+__log1p:
+#endif
+
{ .mfi
- getf.exp GR_signexp_x = f8 // if x is unorm then must recompute
- fadd.s1 FR_Xp1 = f8, f1 // Form 1+x
- mov GR_05 = 0xfffe
+alloc r32 = ar.pfs,0,22,4,0
+(p0) fsub.s1 FR_Neg_One = f0,f1
+(p0) cmp.eq.unc p7, p0 = r0, r0
}
-{ .mlx
- addl GR_ad_1 = @ltoff(log_data),gp
- movl GR_A3 = 0x3fd5555555555557 // double precision memory
- // representation of A3
+
+{ .mfi
+(p0) cmp.ne.unc p14, p0 = r0, r0
+(p0) fnorm.s1 FR_X_Prime = FR_Input_X
+(p0) cmp.eq.unc p15, p0 = r0, r0 ;;
}
-;;
{ .mfi
- ld8 GR_ad_1 = [GR_ad_1]
- fclass.m p8,p0 = f8,0xb // Is x unorm?
- mov GR_exp_mask = 0x1ffff
+ nop.m 999
+(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 0
- fnorm.s1 FR_NormX = f8 // Normalize x
- mov GR_exp_bias = 0xffff
+ nop.m 999
+(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
+ nop.i 999
}
;;
{ .mfi
- setf.exp FR_A2 = GR_05 // create A2 = 0.5
- fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf?
- nop.i 0
+ nop.m 999
+(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f0
+ nop.i 999
}
-{ .mib
- setf.d FR_A3 = GR_A3 // create A3
- add GR_ad_2 = 16,GR_ad_1 // address of A5,A4
-(p8) br.cond.spnt log1p_unorm // Branch if x=unorm
+
+{ .mfi
+ nop.m 999
+(p0) fadd FR_Em1 = f0,f0
+ nop.i 999 ;;
}
-;;
-log1p_common:
{ .mfi
- nop.m 0
- frcpa.s1 FR_RcpX,p0 = f1,FR_Xp1
- nop.i 0
+ nop.m 999
+(p0) fadd FR_E = f0,f1
+ nop.i 999 ;;
}
-{ .mfb
- nop.m 0
-(p9) fma.d.s0 f8 = f8,f1,f0 // set V-flag
-(p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf
+
+{ .mfi
+ nop.m 999
+(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, FR_Neg_One
+ nop.i 999
}
-;;
{ .mfi
- getf.exp GR_Exp = FR_Xp1 // signexp of x+1
- fclass.m p10,p0 = FR_Xp1,0x3A // is 1+x < 0?
- and GR_exp_x = GR_exp_mask, GR_signexp_x // biased exponent of x
+ nop.m 999
+(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, FR_Neg_One
+ nop.i 999
}
+
+
+L(LOG_BEGIN):
+
{ .mfi
- ldfpd FR_A7,FR_A6 = [GR_ad_1]
- nop.f 0
- nop.i 0
+ nop.m 999
+(p0) fadd.s1 FR_Z = FR_X_Prime, FR_E
+ nop.i 999
+}
+
+{ .mlx
+ nop.m 999
+(p0) movl GR_Table_Scale = 0x0000000000000018 ;;
+}
+
+{ .mmi
+ nop.m 999
+//
+// Create E = 1 and Em1 = 0
+// Check for X == 0, meaning log(1+0)
+// Check for X < -1, meaning log(negative)
+// Check for X == -1, meaning log(0)
+// Normalize x
+// Identify NatVals, NaNs, Infs.
+// Identify EM unsupporteds.
+// Identify Negative values - us S1 so as
+// not to raise denormal operand exception
+// Set p15 to true for log1p
+// Set p14 to false for log1p
+// Set p7 true for log and log1p
+//
+(p0) addl GR_Table_Base = @ltoff(Constants_Z_G_H_h1#),gp
+ nop.i 999
}
-;;
{ .mfi
- getf.sig GR_Sig = FR_Xp1 // get significand to calculate index
- // for Thi,Tlo if |x| >= 2^-8
- fcmp.eq.s1 p12,p0 = f8,f0 // is x equal to 0?
- sub GR_exp_x = GR_exp_x, GR_exp_bias // true exponent of x
+ nop.m 999
+(p0) fmax.s1 FR_AA = FR_X_Prime, FR_E
+ nop.i 999 ;;
}
-;;
{ .mfi
- sub GR_N = GR_Exp,GR_exp_bias // true exponent of x+1
- fcmp.eq.s1 p11,p0 = FR_Xp1,f0 // is x = -1?
- cmp.gt p6,p7 = -8, GR_exp_x // Is |x| < 2^-8
+ ld8 GR_Table_Base = [GR_Table_Base]
+(p0) fmin.s1 FR_BB = FR_X_Prime, FR_E
+ nop.i 999
}
+
{ .mfb
- ldfpd FR_A5,FR_A4 = [GR_ad_2],16
- nop.f 0
-(p10) br.cond.spnt log1p_lt_minus_1 // jump if x < -1
+ nop.m 999
+(p0) fadd.s1 FR_W = FR_X_Prime, FR_Em1
+//
+// Begin load of constants base
+// FR_Z = Z = |x| + E
+// FR_W = W = |x| + Em1
+// AA = fmax(|x|,E)
+// BB = fmin(|x|,E)
+//
+(p6) br.cond.spnt L(LOG_64_special) ;;
+}
+
+{ .mib
+ nop.m 999
+ nop.i 999
+(p10) br.cond.spnt L(LOG_64_unsupported) ;;
+}
+
+{ .mib
+ nop.m 999
+ nop.i 999
+(p13) br.cond.spnt L(LOG_64_negative) ;;
+}
+
+{ .mib
+(p0) getf.sig GR_signif = FR_Z
+ nop.i 999
+(p9) br.cond.spnt L(LOG_64_one) ;;
+}
+
+{ .mib
+ nop.m 999
+ nop.i 999
+(p8) br.cond.spnt L(LOG_64_zero) ;;
}
-;;
-// p6 is true if |x| < 1/256
-// p7 is true if |x| >= 1/256
-.pred.rel "mutex",p6,p7
{ .mfi
-(p7) add GR_ad_1 = 0x820,GR_ad_1 // address of log(2) parts
-(p6) fms.s1 FR_r = f8,f1,f0 // range reduction for |x|<1/256
-(p6) cmp.gt.unc p10,p0 = -80, GR_exp_x // Is |x| < 2^-80
+(p0) getf.exp GR_N = FR_Z
+//
+// Raise possible denormal operand exception
+// Create Bias
+//
+// This function computes ln( x + e )
+// Input FR 1: FR_X = FR_Input_X
+// Input FR 2: FR_E = FR_E
+// Input FR 3: FR_Em1 = FR_Em1
+// Input GR 1: GR_Expo_Range = GR_Expo_Range = 1
+// Output FR 4: FR_Y_hi
+// Output FR 5: FR_Y_lo
+// Output FR 6: FR_Scale
+// Output PR 7: PR_Safe
+//
+(p0) fsub.s1 FR_S_lo = FR_AA, FR_Z
+//
+// signif = getf.sig(Z)
+// abs_W = fabs(w)
+//
+(p0) extr.u GR_Table_ptr = GR_signif, 59, 4 ;;
}
-{ .mfb
-(p7) setf.sig FR_N = GR_N // copy unbiased exponent of x to the
- // significand field of FR_N
-(p7) fms.s1 FR_r = FR_RcpX,FR_Xp1,f1 // range reduction for |x|>=1/256
-(p12) br.ret.spnt b0 // exit for x=0, return x
+
+{ .mfi
+ nop.m 999
+(p0) fmerge.se FR_S_hi = f1,FR_Z
+(p0) extr.u GR_X_0 = GR_signif, 49, 15
+}
+
+{ .mmi
+ nop.m 999
+(p0) addl GR_Table_Base1 = @ltoff(Constants_Z_G_H_h2#),gp
+ nop.i 999
}
;;
+{ .mlx
+ ld8 GR_Table_Base1 = [GR_Table_Base1]
+(p0) movl GR_Bias = 0x000000000000FFFF ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fabs FR_abs_W = FR_W
+(p0) pmpyshr2.u GR_Table_ptr = GR_Table_ptr,GR_Table_Scale,0
+}
+
+{ .mfi
+ nop.m 999
+//
+// Branch out for special input values
+//
+(p0) fcmp.lt.unc.s0 p8, p0 = FR_Input_X, f0
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+//
+// X_0 = extr.u(signif,49,15)
+// Index1 = extr.u(signif,59,4)
+//
+(p0) fadd.s1 FR_S_lo = FR_S_lo, FR_BB
+ nop.i 999 ;;
+}
+
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+//
+// Offset_to_Z1 = 24 * Index1
+// For performance, don't use result
+// for 3 or 4 cycles.
+//
+(p0) add GR_Table_ptr = GR_Table_ptr, GR_Table_Base ;;
+}
+//
+// Add Base to Offset for Z1
+// Create Bias
+
+{ .mmi
+(p0) ld4 GR_Z_1 = [GR_Table_ptr],4 ;;
+(p0) ldfs FR_G = [GR_Table_ptr],4
+ nop.i 999 ;;
+}
+
+{ .mmi
+(p0) ldfs FR_H = [GR_Table_ptr],8 ;;
+(p0) ldfd FR_h = [GR_Table_ptr],0
+(p0) pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15
+}
+//
+// Load Z_1
+// Get Base of Table2
+//
+
+{ .mfi
+(p0) getf.exp GR_M = FR_abs_W
+ nop.f 999
+ nop.i 999 ;;
+}
+
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+//
+// M = getf.exp(abs_W)
+// S_lo = AA - Z
+// X_1 = pmpyshr2(X_0,Z_1,15)
+//
+(p0) sub GR_M = GR_M, GR_Bias ;;
+}
+//
+// M = M - Bias
+// Load G1
+// N = getf.exp(Z)
+//
+
+{ .mii
+(p0) cmp.gt.unc p11, p0 = -80, GR_M
+(p0) cmp.gt.unc p12, p0 = -7, GR_M ;;
+(p0) extr.u GR_Index2 = GR_X_1, 6, 4 ;;
+}
+
+{ .mib
+ nop.m 999
+//
+// if -80 > M, set p11
+// Index2 = extr.u(X_1,6,4)
+// if -7 > M, set p12
+// Load H1
+//
+(p0) pmpyshr2.u GR_Index2 = GR_Index2,GR_Table_Scale,0
+(p11) br.cond.spnt L(log1p_small) ;;
+}
+
{ .mib
-(p7) ldfpd FR_Ln2hi,FR_Ln2lo = [GR_ad_1],16
-(p7) extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index
-(p11) br.cond.spnt log1p_eq_minus_1 // jump if x = -1
+ nop.m 999
+ nop.i 999
+(p12) br.cond.spnt L(log1p_near) ;;
}
-;;
-{ .mmf
-(p7) shladd GR_ad_2 = GR_Ind,3,GR_ad_2 // address of Thi
-(p7) shladd GR_ad_1 = GR_Ind,2,GR_ad_1 // address of Tlo
-(p10) fnma.d.s0 f8 = f8,f8,f8 // If |x| very small, result=x-x*x
+{ .mii
+(p0) sub GR_N = GR_N, GR_Bias
+//
+// poly_lo = r * poly_lo
+//
+(p0) add GR_Perturb = 0x1, r0 ;;
+(p0) sub GR_ScaleN = GR_Bias, GR_N
}
-;;
+
+{ .mii
+(p0) setf.sig FR_float_N = GR_N
+ nop.i 999 ;;
+//
+// Prepare Index2 - pmpyshr2.u(X_1,Z_2,15)
+// Load h1
+// S_lo = S_lo + BB
+// Branch for -80 > M
+//
+(p0) add GR_Index2 = GR_Index2, GR_Table_Base1
+}
+
+{ .mmi
+(p0) setf.exp FR_two_negN = GR_ScaleN
+ nop.m 999
+(p0) addl GR_Table_Base = @ltoff(Constants_Z_G_H_h3#),gp
+};;
+
+//
+// Index2 points to Z2
+// Branch for -7 > M
+//
{ .mmb
-(p7) ldfd FR_Thi = [GR_ad_2]
-(p7) ldfs FR_Tlo = [GR_ad_1]
-(p10) br.ret.spnt b0 // Exit if |x| < 2^(-80)
+(p0) ld4 GR_Z_2 = [GR_Index2],4
+ ld8 GR_Table_Base = [GR_Table_Base]
+ nop.b 999 ;;
}
-;;
+(p0) nop.i 999
+//
+// Load Z_2
+// N = N - Bias
+// Tablebase points to Table3
+//
+
+{ .mmi
+(p0) ldfs FR_G_tmp = [GR_Index2],4 ;;
+//
+// Load G_2
+// pmpyshr2 X_2= (X_1,Z_2,15)
+// float_N = setf.sig(N)
+// ScaleN = Bias - N
+//
+(p0) ldfs FR_H_tmp = [GR_Index2],8
+ nop.i 999 ;;
+}
+//
+// Load H_2
+// two_negN = setf.exp(scaleN)
+// G = G_1 * G_2
+//
{ .mfi
- nop.m 0
- fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2
- nop.i 0
+(p0) ldfd FR_h_tmp = [GR_Index2],0
+ nop.f 999
+(p0) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 ;;
+}
+
+{ .mii
+ nop.m 999
+(p0) extr.u GR_Index3 = GR_X_2, 1, 5 ;;
+//
+// Load h_2
+// H = H_1 + H_2
+// h = h_1 + h_2
+// Index3 = extr.u(X_2,1,5)
+//
+(p0) shladd GR_Index3 = GR_Index3,4,GR_Table_Base
+}
+
+{ .mmi
+ nop.m 999
+ nop.m 999
+//
+// float_N = fcvt.xf(float_N)
+// load G3
+//
+(p0) addl GR_Table_Base = @ltoff(Constants_Q#),gp ;;
}
+
{ .mfi
- nop.m 0
- fms.s1 FR_A2 = FR_A3,FR_r,FR_A2 // A3*r+A2
- nop.i 0
+ld8 GR_Table_Base = [GR_Table_Base]
+nop.f 999
+nop.i 999
+} ;;
+
+{ .mfi
+(p0) ldfe FR_log2_hi = [GR_Table_Base],16
+(p0) fmpy.s1 FR_S_lo = FR_S_lo, FR_two_negN
+ nop.i 999 ;;
+}
+
+{ .mmf
+ nop.m 999
+//
+// G = G3 * G
+// Load h3
+// Load log2_hi
+// H = H + H3
+//
+(p0) ldfe FR_log2_lo = [GR_Table_Base],16
+(p0) fmpy.s1 FR_G = FR_G, FR_G_tmp ;;
+}
+
+{ .mmf
+(p0) ldfs FR_G_tmp = [GR_Index3],4
+//
+// h = h + h3
+// r = G * S_hi + 1
+// Load log2_lo
+//
+(p0) ldfe FR_Q4 = [GR_Table_Base],16
+(p0) fadd.s1 FR_h = FR_h, FR_h_tmp ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 FR_A6 = FR_A7,FR_r,FR_A6 // A7*r+A6
- nop.i 0
+(p0) ldfe FR_Q3 = [GR_Table_Base],16
+(p0) fadd.s1 FR_H = FR_H, FR_H_tmp
+ nop.i 999 ;;
}
+
+{ .mmf
+(p0) ldfs FR_H_tmp = [GR_Index3],4
+(p0) ldfe FR_Q2 = [GR_Table_Base],16
+//
+// Comput Index for Table3
+// S_lo = S_lo * two_negN
+//
+(p0) fcvt.xf FR_float_N = FR_float_N ;;
+}
+//
+// If S_lo == 0, set p8 false
+// Load H3
+// Load ptr to table of polynomial coeff.
+//
+
+{ .mmf
+(p0) ldfd FR_h_tmp = [GR_Index3],0
+(p0) ldfe FR_Q1 = [GR_Table_Base],0
+(p0) fcmp.eq.unc.s1 p0, p8 = FR_S_lo, f0 ;;
+}
+
{ .mfi
- nop.m 0
- fma.s1 FR_A4 = FR_A5,FR_r,FR_A4 // A5*r+A4
- nop.i 0
+ nop.m 999
+(p0) fmpy.s1 FR_G = FR_G, FR_G_tmp
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
-(p7) fcvt.xf FR_N = FR_N
- nop.i 0
+ nop.m 999
+(p0) fadd.s1 FR_H = FR_H, FR_H_tmp
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 FR_r4 = FR_r2,FR_r2,f0 // r^4
- nop.i 0
+ nop.m 999
+(p0) fms.s1 FR_r = FR_G, FR_S_hi, f1
+ nop.i 999
}
+
{ .mfi
- nop.m 0
- // (A3*r+A2)*r^2+r
- fma.s1 FR_A2 = FR_A2,FR_r2,FR_r
- nop.i 0
+ nop.m 999
+(p0) fadd.s1 FR_h = FR_h, FR_h_tmp
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- // (A7*r+A6)*r^2+(A5*r+A4)
- fma.s1 FR_A4 = FR_A6,FR_r2,FR_A4
- nop.i 0
+ nop.m 999
+(p0) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- // N*Ln2hi+Thi
-(p7) fma.s1 FR_NxLn2hipThi = FR_N,FR_Ln2hi,FR_Thi
- nop.i 0
+ nop.m 999
+//
+// Load Q4
+// Load Q3
+// Load Q2
+// Load Q1
+//
+(p8) fma.s1 FR_r = FR_G, FR_S_lo, FR_r
+ nop.i 999
}
+
{ .mfi
- nop.m 0
- // N*Ln2lo+Tlo
-(p7) fma.s1 FR_NxLn2lopTlo = FR_N,FR_Ln2lo,FR_Tlo
- nop.i 0
+ nop.m 999
+//
+// poly_lo = r * Q4 + Q3
+// rsq = r* r
+//
+(p0) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
-(p7) fma.s1 f8 = FR_A4,FR_r4,FR_A2 // P(r) if |x| >= 1/256
- nop.i 0
+ nop.m 999
+//
+// If (S_lo!=0) r = s_lo * G + r
+//
+(p0) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3
+ nop.i 999
}
+//
+// Create a 0x00000....01
+// poly_lo = poly_lo * rsq + h
+//
+
{ .mfi
- nop.m 0
- // (N*Ln2hi+Thi) + (N*Ln2lo+Tlo)
-(p7) fma.s1 FR_NxLn2pT = FR_NxLn2hipThi,f1,FR_NxLn2lopTlo
- nop.i 0
+(p0) setf.sig FR_dummy = GR_Perturb
+(p0) fmpy.s1 FR_rsq = FR_r, FR_r
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+//
+// h = N * log2_lo + h
+// Y_hi = n * log2_hi + H
+//
+(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2
+ nop.i 999
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+//
+// poly_lo = r * poly_o + Q2
+// poly_hi = Q1 * rsq + r
+//
+(p0) fmpy.s1 FR_poly_lo = FR_poly_lo, FR_r
+ nop.i 999 ;;
}
-;;
-.pred.rel "mutex",p6,p7
{ .mfi
- nop.m 0
-(p6) fma.d.s0 f8 = FR_A4,FR_r4,FR_A2 // result if 2^(-80) <= |x| < 1/256
- nop.i 0
+ nop.m 999
+(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_rsq, FR_h
+ nop.i 999 ;;
}
+
{ .mfb
- nop.m 0
-(p7) fma.d.s0 f8 = f8,f1,FR_NxLn2pT // result if |x| >= 1/256
- br.ret.sptk b0 // Exit if |x| >= 2^(-80)
+ nop.m 999
+(p0) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo
+//
+// Create the FR for a binary "or"
+// Y_lo = poly_hi + poly_lo
+//
+// (p0) for FR_dummy = FR_Y_lo,FR_dummy ;;
+//
+// Turn the lsb of Y_lo ON
+//
+// (p0) fmerge.se FR_Y_lo = FR_Y_lo,FR_dummy ;;
+//
+// Merge the new lsb into Y_lo, for alone doesn't
+//
+(p0) br.cond.sptk L(LOG_main) ;;
+}
+
+
+L(log1p_near):
+
+{ .mmi
+ nop.m 999
+ nop.m 999
+// /*******************************************************/
+// /*********** Branch log1p_near ************************/
+// /*******************************************************/
+(p0) addl GR_Table_Base = @ltoff(Constants_P#),gp ;;
+}
+//
+// Load base address of poly. coeff.
+//
+{.mmi
+ nop.m 999
+ ld8 GR_Table_Base = [GR_Table_Base]
+ nop.i 999
+};;
+
+{ .mmb
+(p0) add GR_Table_ptr = 0x40,GR_Table_Base
+//
+// Address tables with separate pointers
+//
+(p0) ldfe FR_P8 = [GR_Table_Base],16
+ nop.b 999 ;;
+}
+
+{ .mmb
+(p0) ldfe FR_P4 = [GR_Table_ptr],16
+//
+// Load P4
+// Load P8
+//
+(p0) ldfe FR_P7 = [GR_Table_Base],16
+ nop.b 999 ;;
+}
+
+{ .mmf
+(p0) ldfe FR_P3 = [GR_Table_ptr],16
+//
+// Load P3
+// Load P7
+//
+(p0) ldfe FR_P6 = [GR_Table_Base],16
+(p0) fmpy.s1 FR_wsq = FR_W, FR_W ;;
+}
+
+{ .mfi
+(p0) ldfe FR_P2 = [GR_Table_ptr],16
+ nop.f 999
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_Y_hi = FR_W, FR_P4, FR_P3
+ nop.i 999
+}
+//
+// Load P2
+// Load P6
+// Wsq = w * w
+// Y_hi = p4 * w + p3
+//
+
+{ .mfi
+(p0) ldfe FR_P5 = [GR_Table_Base],16
+(p0) fma.s1 FR_Y_lo = FR_W, FR_P8, FR_P7
+ nop.i 999 ;;
+}
+
+{ .mfi
+(p0) ldfe FR_P1 = [GR_Table_ptr],16
+//
+// Load P1
+// Load P5
+// Y_lo = p8 * w + P7
+//
+(p0) fmpy.s1 FR_w4 = FR_wsq, FR_wsq
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P2
+ nop.i 999
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_Y_lo = FR_W, FR_Y_lo, FR_P6
+(p0) add GR_Perturb = 0x1, r0 ;;
+}
+
+{ .mfi
+ nop.m 999
+//
+// w4 = w2 * w2
+// Y_hi = y_hi * w + p2
+// Y_lo = y_lo * w + p6
+// Create perturbation bit
+//
+(p0) fmpy.s1 FR_w6 = FR_w4, FR_wsq
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P1
+ nop.i 999
+}
+//
+// Y_hi = y_hi * w + p1
+// w6 = w4 * w2
+//
+
+{ .mfi
+(p0) setf.sig FR_Q4 = GR_Perturb
+(p0) fma.s1 FR_Y_lo = FR_W, FR_Y_lo, FR_P5
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_Y_hi = FR_wsq,FR_Y_hi, FR_W
+ nop.i 999
}
-;;
-.align 32
-log1p_unorm:
-// Here if x=unorm
{ .mfb
- getf.exp GR_signexp_x = FR_NormX // recompute biased exponent
- nop.f 0
- br.cond.sptk log1p_common
+ nop.m 999
+//
+// Y_hi = y_hi * wsq + w
+// Y_lo = y_lo * w + p5
+//
+(p0) fmpy.s1 FR_Y_lo = FR_w6, FR_Y_lo
+//
+// Y_lo = y_lo * w6
+//
+// (p0) for FR_dummy = FR_Y_lo,FR_dummy ;;
+//
+// Set lsb on: Taken out to improve performance
+//
+// (p0) fmerge.se FR_Y_lo = FR_Y_lo,FR_dummy ;;
+//
+// Make sure it's on in Y_lo also. Taken out to improve
+// performance
+//
+(p0) br.cond.sptk L(LOG_main) ;;
+}
+
+
+L(log1p_small):
+
+{ .mmi
+ nop.m 999
+ nop.m 999
+// /*******************************************************/
+// /*********** Branch log1p_small ***********************/
+// /*******************************************************/
+(p0) addl GR_Table_Base = @ltoff(Constants_Threshold#),gp
}
-;;
-.align 32
-log1p_eq_minus_1:
-// Here if x=-1
{ .mfi
- nop.m 0
- fmerge.s FR_X = f8,f8 // keep input argument for subsequent
- // call of __libm_error_support#
- nop.i 0
+ nop.m 999
+(p0) mov FR_Em1 = FR_W
+(p0) cmp.eq.unc p7, p0 = r0, r0 ;;
+}
+
+{ .mlx
+ ld8 GR_Table_Base = [GR_Table_Base]
+(p0) movl GR_Expo_Range = 0x0000000000000002 ;;
+}
+//
+// Set Safe to true
+// Set Expo_Range = 0 for single
+// Set Expo_Range = 2 for double
+// Set Expo_Range = 4 for double-extended
+//
+
+{ .mmi
+(p0) shladd GR_Table_Base = GR_Expo_Range,4,GR_Table_Base ;;
+(p0) ldfe FR_Threshold = [GR_Table_Base],16
+ nop.i 999
+}
+
+{ .mlx
+ nop.m 999
+(p0) movl GR_Bias = 0x000000000000FF9B ;;
}
-;;
{ .mfi
- mov GR_TAG = 140 // set libm error in case of log1p(-1).
- frcpa.s0 f8,p0 = f8,f0 // log1p(-1) should be equal to -INF.
- // We can get it using frcpa because it
- // sets result to the IEEE-754 mandated
- // quotient of f8/f0.
- nop.i 0
+(p0) ldfe FR_Tiny = [GR_Table_Base],0
+ nop.f 999
+ nop.i 999 ;;
}
-{ .mib
- nop.m 0
- nop.i 0
- br.cond.sptk log_libm_err
+
+{ .mfi
+ nop.m 999
+(p0) fcmp.gt.unc.s1 p13, p12 = FR_abs_W, FR_Threshold
+ nop.i 999 ;;
}
-;;
-.align 32
-log1p_lt_minus_1:
-// Here if x < -1
{ .mfi
- nop.m 0
- fmerge.s FR_X = f8,f8
- nop.i 0
+ nop.m 999
+(p13) fnmpy.s1 FR_Y_lo = FR_W, FR_W
+ nop.i 999
+}
+
+{ .mfi
+ nop.m 999
+(p13) fadd FR_SCALE = f0, f1
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p12) fsub.s1 FR_Y_lo = f0, FR_Tiny
+(p12) cmp.ne.unc p7, p0 = r0, r0
}
-;;
{ .mfi
- mov GR_TAG = 141 // set libm error in case of x < -1.
- frcpa.s0 f8,p0 = f0,f0 // log1p(x) x < -1 should be equal to NaN.
- // We can get it using frcpa because it
- // sets result to the IEEE-754 mandated
- // quotient of f0/f0 i.e. NaN.
- nop.i 0
+(p12) setf.exp FR_SCALE = GR_Bias
+ nop.f 999
+ nop.i 999 ;;
+}
+
+//
+// Set p7 to SAFE = FALSE
+// Set Scale = 2^-100
+//
+{ .mfb
+ nop.m 999
+(p0) fma.d.s0 FR_Input_X = FR_Y_lo,FR_SCALE,FR_Y_hi
+(p0) br.ret.sptk b0
}
;;
-.align 32
-log_libm_err:
-{ .mmi
- alloc r32 = ar.pfs,1,4,4,0
- mov GR_Parameter_TAG = GR_TAG
- nop.i 0
+L(LOG_64_one):
+
+{ .mfb
+ nop.m 999
+(p0) fmpy.d.s0 FR_Input_X = FR_Input_X, f0
+(p0) br.ret.sptk b0
}
;;
-GLOBAL_IEEE754_END(log1p)
+//
+// Raise divide by zero for +/-0 input.
+//
+L(LOG_64_zero):
+{ .mfi
+(p0) mov GR_Parameter_TAG = 140
+//
+// If we have log1p(0), return -Inf.
+//
+(p0) fsub.s0 FR_Output_X_tmp = f0, f1
+ nop.i 999 ;;
+}
+{ .mfb
+ nop.m 999
+(p0) frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0
+(p0) br.cond.sptk L(LOG_ERROR_Support) ;;
+}
+
+L(LOG_64_special):
-LOCAL_LIBM_ENTRY(__libm_error_region)
+{ .mfi
+ nop.m 999
+//
+// Return -Inf or value from handler.
+//
+(p0) fclass.m.unc p7, p0 = FR_Input_X, 0x1E1
+ nop.i 999 ;;
+}
+{ .mfb
+ nop.m 999
+//
+// Check for Natval, QNan, SNaN, +Inf
+//
+(p7) fmpy.d.s0 f8 = FR_Input_X, f1
+//
+// For SNaN raise invalid and return QNaN.
+// For QNaN raise invalid and return QNaN.
+// For +Inf return +Inf.
+//
+(p7) br.ret.sptk b0
+}
+;;
+
+//
+// For -Inf raise invalid and return QNaN.
+//
+
+{ .mfb
+(p0) mov GR_Parameter_TAG = 141
+(p0) fmpy.d.s0 FR_Output_X_tmp = FR_Input_X, f0
+(p0) br.cond.sptk L(LOG_ERROR_Support) ;;
+}
+
+//
+// Report that log1p(-Inf) computed
+//
+
+L(LOG_64_unsupported):
+
+//
+// Return generated NaN or other value .
+//
+
+{ .mfb
+ nop.m 999
+(p0) fmpy.d.s0 FR_Input_X = FR_Input_X, f0
+(p0) br.ret.sptk b0 ;;
+}
+
+L(LOG_64_negative):
+
+{ .mfi
+ nop.m 999
+//
+// Deal with x < 0 in a special way
+//
+(p0) frcpa.s0 FR_Output_X_tmp, p8 = f0, f0
+//
+// Deal with x < 0 in a special way - raise
+// invalid and produce QNaN indefinite.
+//
+(p0) mov GR_Parameter_TAG = 141
+}
+
+.endp log1p#
+ASM_SIZE_DIRECTIVE(log1p)
+
+.proc __libm_error_region
+__libm_error_region:
+L(LOG_ERROR_Support):
.prologue
+
+// (1)
{ .mfi
- add GR_Parameter_Y = -32,sp // Parameter 2 value
+ add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
.save ar.pfs,GR_SAVE_PFS
- mov GR_SAVE_PFS = ar.pfs // Save ar.pfs
+ mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
{ .mfi
.fframe 64
- add sp = -64,sp // Create new stack
+ add sp=-64,sp // Create new stack
nop.f 0
- mov GR_SAVE_GP = gp // Save gp
+ mov GR_SAVE_GP=gp // Save gp
};;
+
+
+// (2)
{ .mmi
- stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
+ stfd [GR_Parameter_Y] = f0,16 // STORE Parameter 2 on stack
add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0, GR_SAVE_B0
- mov GR_SAVE_B0 = b0 // Save b0
+ mov GR_SAVE_B0=b0 // Save b0
};;
+
.body
+// (3)
{ .mib
- stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
- add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
- nop.b 0
+ stfd [GR_Parameter_X] =FR_Input_X // STORE Parameter 1 on stack
+ add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
+ nop.b 0
}
{ .mib
- stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
+ stfd [GR_Parameter_Y] = FR_Output_X_tmp // STORE Parameter 3 on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
- br.call.sptk b0=__libm_error_support# // Call error handling function
+ br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
- add GR_Parameter_RESULT = 48,sp
nop.m 0
- nop.i 0
+ nop.m 0
+ add GR_Parameter_RESULT = 48,sp
};;
+
+// (4)
{ .mmi
- ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
+ ldfd FR_Input_X = [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
+ 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
+ mov gp = GR_SAVE_GP // Restore gp
+ mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
+ br.ret.sptk b0
};;
-LOCAL_LIBM_END(__libm_error_region)
+
+.endp __libm_error_region
+ASM_SIZE_DIRECTIVE(__libm_error_region)
+
+.proc __libm_LOG_main
+__libm_LOG_main:
+L(LOG_main):
+
+//
+// kernel_log_64 computes ln(X + E)
+//
+
+{ .mfi
+ nop.m 999
+(p7) fadd.d.s0 FR_Input_X = FR_Y_lo,FR_Y_hi
+ nop.i 999
+}
+
+{ .mmi
+ nop.m 999
+ nop.m 999
+(p14) addl GR_Table_Base = @ltoff(Constants_1_by_LN10#),gp ;;
+}
+
+{ .mmi
+ nop.m 999
+(p14) ld8 GR_Table_Base = [GR_Table_Base]
+ nop.i 999
+};;
+
+{ .mmi
+(p14) ldfe FR_1LN10_hi = [GR_Table_Base],16 ;;
+(p14) ldfe FR_1LN10_lo = [GR_Table_Base]
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p14) fmpy.s1 FR_Output_X_tmp = FR_Y_lo,FR_1LN10_hi
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p14) fma.s1 FR_Output_X_tmp = FR_Y_hi,FR_1LN10_lo,FR_Output_X_tmp
+ nop.i 999 ;;
+}
+
+{ .mfb
+ nop.m 999
+(p14) fma.d.s0 FR_Input_X = FR_Y_hi,FR_1LN10_hi,FR_Output_X_tmp
+(p0) br.ret.sptk b0 ;;
+}
+.endp __libm_LOG_main
+ASM_SIZE_DIRECTIVE(__libm_LOG_main)
+
.type __libm_error_support#,@function
.global __libm_error_support#
-