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-rw-r--r--sysdeps/ia64/fpu/s_log1pl.S2068
1 files changed, 1272 insertions, 796 deletions
diff --git a/sysdeps/ia64/fpu/s_log1pl.S b/sysdeps/ia64/fpu/s_log1pl.S
index 9654265004..7cd3f7834c 100644
--- a/sysdeps/ia64/fpu/s_log1pl.S
+++ b/sysdeps/ia64/fpu/s_log1pl.S
@@ -1,10 +1,10 @@
.file "log1pl.s"
-
-// Copyright (c) 2000 - 2003, Intel Corporation
+// Copyright (C) 2000, 2001, Intel Corporation
// All rights reserved.
-//
-// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
+// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
@@ -20,7 +20,7 @@
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
-
+//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
@@ -35,49 +35,55 @@
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
-// http://www.intel.com/software/products/opensource/libraries/num.htm.
+// http://developer.intel.com/opensource.
//
-//*********************************************************************
+// *********************************************************************
//
// History:
-// 02/02/00 Initial version
-// 04/04/00 Unwind support added
-// 08/15/00 Bundle added after call to __libm_error_support to properly
+// 2/02/00 hand-optimized
+// 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.
-// 05/21/01 Removed logl and log10l, putting them in a separate file
-// 06/29/01 Improved speed of all paths
-// 05/20/02 Cleaned up namespace and sf0 syntax
-// 02/10/03 Reordered header: .section, .global, .proc, .align;
-// used data8 for long double table values
//
-//*********************************************************************
+// *********************************************************************
//
-//*********************************************************************
+// *********************************************************************
//
-// Function: log1pl(x) = ln(x+1), for double-extended precision x values
+// Function: Combined logl(x), log1pl(x), and log10l(x) where
+// logl(x) = ln(x), for double-extended precision x values
+// log1pl(x) = ln(x+1), for double-extended precision x values
+// log10l(x) = log (x), for double-extended precision x values
+// 10
//
-//*********************************************************************
+// *********************************************************************
//
// Resources Used:
//
// Floating-Point Registers: f8 (Input and Return Value)
-// f34-f82
+// f9,f33-f55,f99
//
// General Purpose Registers:
-// r32-r56
-// r53-r56 (Used to pass arguments to error handling routine)
+// r32-r53
+// r54-r57 (Used to pass arguments to error handling routine)
//
-// Predicate Registers: p6-p13
+// Predicate Registers: p6-p15
//
-//*********************************************************************
+// *********************************************************************
//
// IEEE Special Conditions:
//
-// Denormal fault raised on denormal inputs
+// 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
//
+// logl(inf) = inf
+// logl(-inf) = QNaN
+// logl(+/-0) = -inf
+// logl(SNaN) = QNaN
+// logl(QNaN) = QNaN
+// logl(EM_special Values) = QNaN
// log1pl(inf) = inf
// log1pl(-inf) = QNaN
// log1pl(+/-0) = +/-0
@@ -85,37 +91,54 @@
// log1pl(SNaN) = QNaN
// log1pl(QNaN) = QNaN
// log1pl(EM_special Values) = QNaN
-//
-//*********************************************************************
-//
+// log10l(inf) = inf
+// log10l(-inf) = QNaN
+// log10l(+/-0) = -inf
+// log10l(SNaN) = QNaN
+// log10l(QNaN) = QNaN
+// log10l(EM_special Values) = QNaN
+//
+// *********************************************************************
+//
+// Computation is based on the following kernel.
+//
+// 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
//
// The method consists of three cases.
//
-// If |X| < 2^(-80) use case log1p_small;
-// else |X| < 2^(-7) use case log_near1;
-// else use case log_regular;
+// If |X+Em1| < 2^(-80) use case log1pl_small;
+// elseif |X+Em1| < 2^(-7) use case log_near1;
+// else use case log_regular;
//
-// Case log1p_small:
+// Case log1pl_small:
//
-// log1pl( X ) = logl( X+1 ) can be approximated by X
+// logl( 1 + (X+Em1) ) can be approximated by (X+Em1).
//
// Case log_near1:
//
-// log1pl( X ) = log( X+1 ) can be approximated by a simple polynomial
-// in W = X. This polynomial resembles the truncated Taylor
+// logl( 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:
//
// Here we use a table lookup method. The basic idea is that in
-// order to compute logl(Arg) = log1pl (Arg-1) for an argument Arg in [1,2),
-// we construct a value G such that G*Arg is close to 1 and that
+// order to compute logl(Arg) for an argument Arg in [1,2), we
+// construct a value G such that G*Arg is close to 1 and that
// logl(1/G) is obtainable easily from a table of values calculated
// beforehand. Thus
//
-// logl(Arg) = logl(1/G) + logl(G*Arg)
-// = logl(1/G) + logl(1 + (G*Arg - 1))
+// logl(Arg) = logl(1/G) + logl(G*Arg)
+// = logl(1/G) + logl(1 + (G*Arg - 1))
//
// Because |G*Arg - 1| is small, the second term on the right hand
// side can be approximated by a short polynomial. We elaborate
@@ -123,9 +146,9 @@
//
// Step 0: Initialization
//
-// We need to calculate logl( X+1 ). Obtain N, S_hi such that
+// We need to calculate logl( E + X ). Obtain N, S_hi, S_lo such that
//
-// X+1 = 2^N * ( S_hi + S_lo ) exactly
+// E + X = 2^N * ( S_hi + S_lo ) exactly
//
// where S_hi in [1,2) and S_lo is a correction to S_hi in the sense
// that |S_lo| <= ulp(S_hi).
@@ -134,8 +157,8 @@
//
// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate
//
-// G := G_1 * G_2 * G_3
-// r := (G * S_hi - 1) + G * S_lo
+// 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.
@@ -148,34 +171,61 @@
// Step 3: Reconstruction
//
//
-// Finally, log1pl( X ) = logl( X+1 ) is given by
+// Finally, logl( E + X ) is given by
//
-// logl( X+1 ) = logl( 2^N * (S_hi + S_lo) )
+// logl( E + X ) = logl( 2^N * (S_hi + S_lo) )
// ~=~ N*logl(2) + logl(1/G) + logl(1 + r)
// ~=~ N*logl(2) + logl(1/G) + poly(r).
//
// **** Algorithm ****
//
-// Case log1p_small:
-//
-// Although log1pl(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
-//
-// log1pl(X) = X - X*X
-//
+// Case log1pl_small:
+//
+// Although logl(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
-// 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)))
+// 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:
//
@@ -184,87 +234,89 @@
// Step 0. Initialization
// ----------------------
//
-// Z := X + 1
+// Z := X + E
// N := unbaised exponent of Z
// S_hi := 2^(-N) * Z
-// S_lo := 2^(-N) * { (max(X,1)-Z) + min(X,1) }
+// 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
+// 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 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 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 ].
+// 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 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.
+// 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.
+// 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 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 ].
+// 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 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.
+// 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.
+// 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 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 ].
+// 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.
+// Fetch G_3 := (1/A_3) truncated to 21 sig. bits.
+// floating pt. Fetch is done using index_3.
//
-// Compute G := G_1 * G_2 * G_3.
+// Compute G := G_1 * G_2 * G_3.
//
-// This is done exactly since each of G_j only has 21 sig. bits.
+// This is done exactly since each of G_j only has 21 sig. bits.
//
-// Compute
+// Compute
//
-// r := (G*S_hi - 1) + G*S_lo using 2 FMA operations.
+// 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.
+// thus, r approximates G*(S_hi+S_lo) - 1 to within a couple of
+// rounding errors.
//
//
// Step 2. Approximation
@@ -274,879 +326,1258 @@
// reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13);
// thus logl(1+r) can be approximated by a short polynomial:
//
-// logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5
+// logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5
//
//
// Step 3. Reconstruction
// ----------------------
//
-// This step computes the desired result of logl(X+1):
+// This step computes the desired result of logl(X+E):
//
-// logl(X+1) = logl( 2^N * (S_hi + S_lo) )
-// = N*logl(2) + logl( S_hi + S_lo) )
-// = N*logl(2) + logl(1/G) +
-// logl(1 + G * ( S_hi + S_lo ) - 1 )
+// logl(X+E) = logl( 2^N * (S_hi + S_lo) )
+// = N*logl(2) + logl( S_hi + S_lo )
+// = N*logl(2) + logl(1/G) +
+// logl(1 + C*(S_hi+S_lo) - 1 )
//
// logl(2), logl(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 )
+// 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 ) ]
+// 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
//
-RODATA
-.align 64
-
-// ************* DO NOT CHANGE THE ORDER OF THESE TABLES *************
+#include "libm_support.h"
-// P_8, P_7, P_6, P_5, P_4, P_3, P_2, and P_1
+#ifdef _LIBC
+.rodata
+#else
+.data
+#endif
-LOCAL_OBJECT_START(Constants_P)
-//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
-data8 0xE3936754EFD62B15,0x00003FFB
-data8 0x8003B271A5E56381,0x0000BFFC
-data8 0x9249248C73282DB0,0x00003FFC
-data8 0xAAAAAA9F47305052,0x0000BFFC
-data8 0xCCCCCCCCCCD17FC9,0x00003FFC
-data8 0x8000000000067ED5,0x0000BFFD
-data8 0xAAAAAAAAAAAAAAAA,0x00003FFD
-data8 0xFFFFFFFFFFFFFFFE,0x0000BFFD
-LOCAL_OBJECT_END(Constants_P)
+// P_7, P_6, P_5, P_4, P_3, P_2, and P_1
+.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
-LOCAL_OBJECT_START(Constants_Q)
-//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
-data8 0xB172180000000000,0x00003FFE
-data8 0x82E308654361C4C6,0x0000BFE2
-data8 0xCCCCCAF2328833CB,0x00003FFC
-data8 0x80000077A9D4BAFB,0x0000BFFD
-data8 0xAAAAAAAAAAABE3D2,0x00003FFD
-data8 0xFFFFFFFFFFFFDAB7,0x0000BFFD
-LOCAL_OBJECT_END(Constants_Q)
-
-// 1/ln10_hi, 1/ln10_lo
-
-LOCAL_OBJECT_START(Constants_1_by_LN10)
-//data4 0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000
-//data4 0xACCF70C8,0xD56EAABE,0x00003FBB,0x00000000
-data8 0xDE5BD8A937287195,0x00003FFD
-data8 0xD56EAABEACCF70C8,0x00003FBB
-LOCAL_OBJECT_END(Constants_1_by_LN10)
-
-
-// Z1 - 16 bit fixed
+.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)
-LOCAL_OBJECT_START(Constants_Z_1)
-data4 0x00008000
-data4 0x00007879
-data4 0x000071C8
-data4 0x00006BCB
-data4 0x00006667
-data4 0x00006187
-data4 0x00005D18
-data4 0x0000590C
-data4 0x00005556
-data4 0x000051EC
-data4 0x00004EC5
-data4 0x00004BDB
-data4 0x00004925
-data4 0x0000469F
-data4 0x00004445
-data4 0x00004211
-LOCAL_OBJECT_END(Constants_Z_1)
-
-// G1 and H1 - IEEE single and h1 - IEEE double
-
-LOCAL_OBJECT_START(Constants_G_H_h1)
-data4 0x3F800000,0x00000000
-data8 0x0000000000000000
-data4 0x3F70F0F0,0x3D785196
-data8 0x3DA163A6617D741C
-data4 0x3F638E38,0x3DF13843
-data8 0x3E2C55E6CBD3D5BB
-data4 0x3F579430,0x3E2FF9A0
-data8 0xBE3EB0BFD86EA5E7
-data4 0x3F4CCCC8,0x3E647FD6
-data8 0x3E2E6A8C86B12760
-data4 0x3F430C30,0x3E8B3AE7
-data8 0x3E47574C5C0739BA
-data4 0x3F3A2E88,0x3EA30C68
-data8 0x3E20E30F13E8AF2F
-data4 0x3F321640,0x3EB9CEC8
-data8 0xBE42885BF2C630BD
-data4 0x3F2AAAA8,0x3ECF9927
-data8 0x3E497F3497E577C6
-data4 0x3F23D708,0x3EE47FC5
-data8 0x3E3E6A6EA6B0A5AB
-data4 0x3F1D89D8,0x3EF8947D
-data8 0xBDF43E3CD328D9BE
-data4 0x3F17B420,0x3F05F3A1
-data8 0x3E4094C30ADB090A
-data4 0x3F124920,0x3F0F4303
-data8 0xBE28FBB2FC1FE510
-data4 0x3F0D3DC8,0x3F183EBF
-data8 0x3E3A789510FDE3FA
-data4 0x3F088888,0x3F20EC80
-data8 0x3E508CE57CC8C98F
-data4 0x3F042108,0x3F29516A
-data8 0xBE534874A223106C
-LOCAL_OBJECT_END(Constants_G_H_h1)
-
-// Z2 - 16 bit fixed
-
-LOCAL_OBJECT_START(Constants_Z_2)
-data4 0x00008000
-data4 0x00007F81
-data4 0x00007F02
-data4 0x00007E85
-data4 0x00007E08
-data4 0x00007D8D
-data4 0x00007D12
-data4 0x00007C98
-data4 0x00007C20
-data4 0x00007BA8
-data4 0x00007B31
-data4 0x00007ABB
-data4 0x00007A45
-data4 0x000079D1
-data4 0x0000795D
-data4 0x000078EB
-LOCAL_OBJECT_END(Constants_Z_2)
-
-// G2 and H2 - IEEE single and h2 - IEEE double
-
-LOCAL_OBJECT_START(Constants_G_H_h2)
-data4 0x3F800000,0x00000000
-data8 0x0000000000000000
-data4 0x3F7F00F8,0x3B7F875D
-data8 0x3DB5A11622C42273
-data4 0x3F7E03F8,0x3BFF015B
-data8 0x3DE620CF21F86ED3
-data4 0x3F7D08E0,0x3C3EE393
-data8 0xBDAFA07E484F34ED
-data4 0x3F7C0FC0,0x3C7E0586
-data8 0xBDFE07F03860BCF6
-data4 0x3F7B1880,0x3C9E75D2
-data8 0x3DEA370FA78093D6
-data4 0x3F7A2328,0x3CBDC97A
-data8 0x3DFF579172A753D0
-data4 0x3F792FB0,0x3CDCFE47
-data8 0x3DFEBE6CA7EF896B
-data4 0x3F783E08,0x3CFC15D0
-data8 0x3E0CF156409ECB43
-data4 0x3F774E38,0x3D0D874D
-data8 0xBE0B6F97FFEF71DF
-data4 0x3F766038,0x3D1CF49B
-data8 0xBE0804835D59EEE8
-data4 0x3F757400,0x3D2C531D
-data8 0x3E1F91E9A9192A74
-data4 0x3F748988,0x3D3BA322
-data8 0xBE139A06BF72A8CD
-data4 0x3F73A0D0,0x3D4AE46F
-data8 0x3E1D9202F8FBA6CF
-data4 0x3F72B9D0,0x3D5A1756
-data8 0xBE1DCCC4BA796223
-data4 0x3F71D488,0x3D693B9D
-data8 0xBE049391B6B7C239
-LOCAL_OBJECT_END(Constants_G_H_h2)
-
-// G3 and H3 - IEEE single and h3 - IEEE double
-
-LOCAL_OBJECT_START(Constants_G_H_h3)
-data4 0x3F7FFC00,0x38800100
-data8 0x3D355595562224CD
-data4 0x3F7FF400,0x39400480
-data8 0x3D8200A206136FF6
-data4 0x3F7FEC00,0x39A00640
-data8 0x3DA4D68DE8DE9AF0
-data4 0x3F7FE400,0x39E00C41
-data8 0xBD8B4291B10238DC
-data4 0x3F7FDC00,0x3A100A21
-data8 0xBD89CCB83B1952CA
-data4 0x3F7FD400,0x3A300F22
-data8 0xBDB107071DC46826
-data4 0x3F7FCC08,0x3A4FF51C
-data8 0x3DB6FCB9F43307DB
-data4 0x3F7FC408,0x3A6FFC1D
-data8 0xBD9B7C4762DC7872
-data4 0x3F7FBC10,0x3A87F20B
-data8 0xBDC3725E3F89154A
-data4 0x3F7FB410,0x3A97F68B
-data8 0xBD93519D62B9D392
-data4 0x3F7FAC18,0x3AA7EB86
-data8 0x3DC184410F21BD9D
-data4 0x3F7FA420,0x3AB7E101
-data8 0xBDA64B952245E0A6
-data4 0x3F7F9C20,0x3AC7E701
-data8 0x3DB4B0ECAABB34B8
-data4 0x3F7F9428,0x3AD7DD7B
-data8 0x3D9923376DC40A7E
-data4 0x3F7F8C30,0x3AE7D474
-data8 0x3DC6E17B4F2083D3
-data4 0x3F7F8438,0x3AF7CBED
-data8 0x3DAE314B811D4394
-data4 0x3F7F7C40,0x3B03E1F3
-data8 0xBDD46F21B08F2DB1
-data4 0x3F7F7448,0x3B0BDE2F
-data8 0xBDDC30A46D34522B
-data4 0x3F7F6C50,0x3B13DAAA
-data8 0x3DCB0070B1F473DB
-data4 0x3F7F6458,0x3B1BD766
-data8 0xBDD65DDC6AD282FD
-data4 0x3F7F5C68,0x3B23CC5C
-data8 0xBDCDAB83F153761A
-data4 0x3F7F5470,0x3B2BC997
-data8 0xBDDADA40341D0F8F
-data4 0x3F7F4C78,0x3B33C711
-data8 0x3DCD1BD7EBC394E8
-data4 0x3F7F4488,0x3B3BBCC6
-data8 0xBDC3532B52E3E695
-data4 0x3F7F3C90,0x3B43BAC0
-data8 0xBDA3961EE846B3DE
-data4 0x3F7F34A0,0x3B4BB0F4
-data8 0xBDDADF06785778D4
-data4 0x3F7F2CA8,0x3B53AF6D
-data8 0x3DCC3ED1E55CE212
-data4 0x3F7F24B8,0x3B5BA620
-data8 0xBDBA31039E382C15
-data4 0x3F7F1CC8,0x3B639D12
-data8 0x3D635A0B5C5AF197
-data4 0x3F7F14D8,0x3B6B9444
-data8 0xBDDCCB1971D34EFC
-data4 0x3F7F0CE0,0x3B7393BC
-data8 0x3DC7450252CD7ADA
-data4 0x3F7F04F0,0x3B7B8B6D
-data8 0xBDB68F177D7F2A42
-LOCAL_OBJECT_END(Constants_G_H_h3)
-
-
-// Floating Point Registers
-
-FR_Input_X = f8
-
-FR_Y_hi = f34
-FR_Y_lo = f35
-
-FR_Scale = f36
-FR_X_Prime = f37
-FR_S_hi = f38
-FR_W = f39
-FR_G = f40
-
-FR_H = f41
-FR_wsq = f42
-FR_w4 = f43
-FR_h = f44
-FR_w6 = f45
-
-FR_G2 = f46
-FR_H2 = f47
-FR_poly_lo = f48
-FR_P8 = f49
-FR_poly_hi = f50
-
-FR_P7 = f51
-FR_h2 = f52
-FR_rsq = f53
-FR_P6 = f54
-FR_r = f55
-
-FR_log2_hi = f56
-FR_log2_lo = f57
-FR_p87 = f58
-FR_p876 = f58
-FR_p8765 = f58
-FR_float_N = f59
-FR_Q4 = f60
+// 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_p43 = f61
-FR_p432 = f61
-FR_p4321 = f61
-FR_P4 = f62
-FR_G3 = f63
-FR_H3 = f64
-FR_h3 = f65
+.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_Q3 = f66
-FR_P3 = f67
-FR_Q2 = f68
-FR_P2 = f69
-FR_1LN10_hi = f70
+.align 64
+Constants_1_by_LN10:
+ASM_TYPE_DIRECTIVE(Constants_1_by_LN10,@object)
+data4 0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000
+data4 0xACCF70C8,0xD56EAABE,0x00003FBB,0x00000000
+ASM_SIZE_DIRECTIVE(Constants_1_by_LN10)
+
+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
+
+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_Q1 = f71
-FR_P1 = f72
-FR_1LN10_lo = f73
-FR_P5 = f74
-FR_rcub = f75
+//
+// Added for unwind support
+//
-FR_Output_X_tmp = f76
-FR_Neg_One = f77
-FR_Z = f78
-FR_AA = f79
-FR_BB = f80
-FR_S_lo = f81
-FR_2_to_minus_N = f82
+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
FR_X = f8
FR_Y = f0
-FR_RESULT = f76
-
+FR_RESULT = f99
-// General Purpose Registers
+.section .text
+.proc logl#
+.global logl#
+.align 64
+logl:
+#ifdef _LIBC
+.global __ieee754_logl
+__ieee754_logl:
+#endif
+{ .mfi
+alloc r32 = ar.pfs,0,22,4,0
+(p0) fnorm.s1 FR_X_Prime = FR_Input_X
+(p0) cmp.eq.unc p7, p0 = r0, r0
+}
+{ .mfi
+(p0) cmp.ne.unc p14, p0 = r0, r0
+(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
+(p0) cmp.ne.unc p15, p0 = r0, r0 ;;
+}
+{ .mfi
+ nop.m 0
+(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
+ nop.i 0
+}
+{ .mfi
+nop.m 999
+(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, f0
+ nop.i 0
+}
+{ .mfi
+ nop.m 999
+(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, f0
+ nop.i 0
+}
+{ .mfi
+ nop.m 999
+(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f1
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
+(p0) fsub.s1 FR_Em1 = f0,f1
+ nop.i 999
+}
+{ .mfb
+ nop.m 999
+(p0) fadd FR_E = f0,f0
+//
+// Create E = 0 and Em1 = -1
+// Check for X == 1, meaning logl(1)
+// Check for X < 0, meaning logl(negative)
+// Check for X == 0, meaning logl(0)
+// Identify NatVals, NaNs, Infs.
+// Identify EM unsupporteds.
+// Identify Negative values - us S1 so as
+// not to raise denormal operand exception
+// Set p15 to false for log
+// Set p14 to false for log
+// Set p7 true for log and log1p
+//
+(p0) br.cond.sptk L(LOGL_BEGIN) ;;
+}
-GR_ad_p = r33
-GR_Index1 = r34
-GR_Index2 = r35
-GR_signif = r36
-GR_X_0 = r37
-GR_X_1 = r38
-GR_X_2 = r39
-GR_minus_N = r39
-GR_Z_1 = r40
-GR_Z_2 = r41
-GR_N = r42
-GR_Bias = r43
-GR_M = r44
-GR_Index3 = r45
-GR_exp_2tom80 = r45
-GR_ad_p2 = r46
-GR_exp_mask = r47
-GR_exp_2tom7 = r48
-GR_ad_ln10 = r49
-GR_ad_tbl_1 = r50
-GR_ad_tbl_2 = r51
-GR_ad_tbl_3 = r52
-GR_ad_q = r53
-GR_ad_z_1 = r54
-GR_ad_z_2 = r55
-GR_ad_z_3 = r56
-GR_minus_N = r39
+.endp logl
+ASM_SIZE_DIRECTIVE(logl)
-//
-// Added for unwind support
-//
+.section .text
+.proc log10l#
+.global log10l#
+.align 64
+log10l:
+#ifdef _LIBC
+.global __ieee754_log10l
+__ieee754_log10l:
+#endif
+{ .mfi
+alloc r32 = ar.pfs,0,22,4,0
+(p0) fadd FR_E = f0,f0
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+(p0) fsub.s1 FR_Em1 = f0,f1
+ nop.i 0
+}
+{ .mfi
+(p0) cmp.ne.unc p15, p0 = r0, r0
+(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f1
+ nop.i 0
+}
+{ .mfi
+(p0) cmp.eq.unc p14, p0 = r0, r0
+(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, f0
+(p0) cmp.ne.unc p7, p0 = r0, r0 ;;
+}
+{ .mfi
+ nop.m 999
+(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, f0
+ nop.i 999
+}
+{ .mfi
+ nop.m 999
+(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
+ nop.i 999 ;;
+}
+{ .mfi
+ nop.m 999
+(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
+ nop.i 999
+}
+{ .mfb
+ nop.m 999
+(p0) fnorm.s1 FR_X_Prime = FR_Input_X
+//
+// Create E = 0 and Em1 = -1
+// Check for X == 1, meaning logl(1)
+// Check for X < 0, meaning logl(negative)
+// Check for X == 0, meaning logl(0)
+// Identify NatVals, NaNs, Infs.
+// Identify EM unsupporteds.
+// Identify Negative values - us S1 so as
+// Identify Negative values - us S1 so as
+// not to raise denormal operand exception
+// Set p15 to false for log10
+// Set p14 to true for log10
+// Set p7 to false for log10
+//
+(p0) br.cond.sptk L(LOGL_BEGIN) ;;
+}
-GR_SAVE_PFS = r50
-GR_SAVE_B0 = r51
-GR_SAVE_GP = r52
-GR_Parameter_X = r53
-GR_Parameter_Y = r54
-GR_Parameter_RESULT = r55
-GR_Parameter_TAG = r56
+.endp log10l
+ASM_SIZE_DIRECTIVE(log10l)
.section .text
-GLOBAL_IEEE754_ENTRY(log1pl)
+.proc log1pl#
+.global log1pl#
+.align 64
+log1pl:
+#ifdef _LIBC
+.global __log1pl
+__log1pl:
+#endif
{ .mfi
- alloc r32 = ar.pfs,0,21,4,0
- fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf
- nop.i 999
+alloc r32 = ar.pfs,0,22,4,0
+(p0) fsub.s1 FR_Neg_One = f0,f1
+(p0) cmp.eq.unc p7, p0 = r0, r0
}
{ .mfi
- addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp
- fma.s1 FR_Z = FR_Input_X, f1, f1 // x+1
- nop.i 999
+(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
+ nop.m 0
+(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
+ nop.i 0
}
-;;
-
{ .mfi
nop.m 999
- fmerge.ns FR_Neg_One = f1, f1 // Form -1.0
- nop.i 999
+(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
+ nop.i 0
}
{ .mfi
nop.m 999
- fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x
- nop.i 999
+(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f0
+ nop.i 0
}
-;;
-
{ .mfi
- ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1
- nop.f 999
- mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7
+ nop.m 999
+(p0) fadd FR_Em1 = f0,f0
+ nop.i 999 ;;
}
-;;
-
-{ .mfb
- getf.sig GR_signif = FR_Z // Get significand of x+1
- fcmp.eq.s1 p9, p0 = FR_Input_X, f0 // Test for x=0
-(p6) br.cond.spnt LOG1P_special // Branch for nan, inf, natval
+{ .mfi
+ nop.m 999
+(p0) fadd FR_E = f0,f1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1
- fcmp.lt.s1 p13, p0 = FR_X_Prime, FR_Neg_One // Test for x<-1
- add GR_ad_p = -0x100, GR_ad_z_1 // Point to Constants_P
+ nop.m 999
+(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, FR_Neg_One
+ nop.i 999
}
{ .mfi
- add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2
- nop.f 999
- add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2
+ nop.m 999
+(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, FR_Neg_One
+ nop.i 999
}
-;;
-
+L(LOGL_BEGIN):
{ .mfi
- add GR_ad_q = 0x080, GR_ad_p // Point to Constants_Q
- fcmp.eq.s1 p8, p0 = FR_X_Prime, FR_Neg_One // Test for x=-1
- extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif
+ nop.m 999
+(p0) fadd.s1 FR_Z = FR_X_Prime, FR_E
+ nop.i 999
}
-{ .mfb
- add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3
- nop.f 999
-(p9) br.ret.spnt b0 // Exit if x=0, return input
+{ .mlx
+ nop.m 999
+(p0) movl GR_Table_Scale = 0x0000000000000018 ;;
}
-;;
-
-{ .mfi
- shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1
- fclass.nm p10, p0 = FR_Input_X, 0x1FF // Test for unsupported
- extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of significand
+{ .mmi
+ nop.m 999
+ nop.m 999
+//
+// Create E = 1 and Em1 = 0
+// Check for X == 0, meaning logl(1+0)
+// Check for X < -1, meaning logl(negative)
+// Check for X == -1, meaning logl(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
}
{ .mfi
- ldfe FR_P8 = [GR_ad_p],16 // Load P_8 for near1 path
- fsub.s1 FR_W = FR_X_Prime, f0 // W = x
- add GR_ad_ln10 = 0x060, GR_ad_q // Point to Constants_1_by_LN10
+ nop.m 999
+(p0) fmax.s1 FR_AA = FR_X_Prime, FR_E
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1
- fmax.s1 FR_AA = FR_X_Prime, f1 // For S_lo, form AA = max(X,1.0)
- mov GR_exp_mask = 0x1FFFF // Create exponent mask
+ ld8 GR_Table_Base = [GR_Table_Base]
+(p0) fmin.s1 FR_BB = FR_X_Prime, FR_E
+ nop.i 999
+}
+{ .mfb
+ 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(LOGL_64_special) ;;
}
{ .mib
- shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1
- mov GR_Bias = 0x0FFFF // Create exponent bias
-(p13) br.cond.spnt LOG1P_LT_Minus_1 // Branch if x<-1
+ nop.m 999
+ nop.i 999
+(p10) br.cond.spnt L(LOGL_64_unsupported) ;;
}
-;;
-
-{ .mfb
- 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|
-(p8) br.cond.spnt LOG1P_EQ_Minus_1 // Branch if x=-1
+{ .mib
+ nop.m 999
+ nop.i 999
+(p13) br.cond.spnt L(LOGL_64_negative) ;;
}
-;;
-
-{ .mmb
- getf.exp GR_N = FR_Z // Get N = exponent of x+1
- ldfd FR_h = [GR_ad_tbl_1] // Load h_1
-(p10) br.cond.spnt LOG1P_unsupported // Branch for unsupported type
+{ .mib
+(p0) getf.sig GR_signif = FR_Z
+ nop.i 999
+(p9) br.cond.spnt L(LOGL_64_one) ;;
}
-;;
-
-{ .mfi
- ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi
- fcmp.eq.s0 p8, p0 = FR_Input_X, f0 // Dummy op to flag denormals
- pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1
+{ .mib
+ nop.m 999
+ nop.i 999
+(p8) br.cond.spnt L(LOGL_64_zero) ;;
}
-;;
-
+{ .mfi
+(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
//
-// For performance, don't use result of pmpyshr2.u for 4 cycles.
+(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 ;;
+}
+{ .mfi
+ nop.m 999
+(p0) fmerge.se FR_S_hi = f1,FR_Z
+(p0) extr.u GR_X_0 = GR_signif, 49, 15
+}
{ .mmi
- ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo
- sub GR_N = GR_N, GR_Bias
- mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80
+ nop.m 999
+ nop.m 999
+(p0) addl GR_Table_Base1 = @ltoff(Constants_Z_G_H_h2#),gp ;;
+}
+{ .mlx
+ ld8 GR_Table_Base1 = [GR_Table_Base1]
+(p0) movl GR_Bias = 0x000000000000FFFF ;;
}
-;;
-
{ .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)
+ nop.m 999
+(p0) fabs FR_abs_W = FR_W
+(p0) pmpyshr2.u GR_Table_ptr = GR_Table_ptr,GR_Table_Scale,0
}
-;;
-
-{ .mmf
- ldfe FR_Q3 = [GR_ad_q],16 // Load Q3
- setf.sig FR_float_N = GR_N // Put integer N into rightmost significand
- fmin.s1 FR_BB = FR_X_Prime, f1 // For S_lo, form BB = min(X,1.0)
+{ .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
- getf.exp GR_M = FR_W // Get signexp of w = x
- ldfe FR_Q2 = [GR_ad_q],16 // Load Q2
- extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
+(p0) ld4 GR_Z_1 = [GR_Table_ptr],4 ;;
+(p0) ldfs FR_G = [GR_Table_ptr],4
+ nop.i 999 ;;
}
-;;
-
{ .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
- add GR_ad_p2 = 0x30,GR_ad_p // Point to P_4
+(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(log1pl_small) ;;
+}
+{ .mib
+ nop.m 999
+ nop.i 999
+(p12) br.cond.spnt L(log1pl_near) ;;
+}
+{ .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
- 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
- and GR_M = GR_exp_mask, GR_M // Get exponent of w = x
+(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
+(p0) ld4 GR_Z_2 = [GR_Index2],4
+(p0) 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
- ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2
- cmp.lt p8, p9 = GR_M, GR_exp_2tom7 // Test |x| < 2^-7
- cmp.lt p7, p0 = GR_M, GR_exp_2tom80 // Test |x| < 2^-80
+(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 ;;
}
-;;
-
-// Small path is separate code
-// p7 is for the small path: |x| < 2^-80
-// near1 and regular paths are merged.
-// p8 is for the near1 path: |x| < 2^-7
-// p9 is for regular path: |x| >= 2^-7
-
+//
+// Load H_2
+// two_negN = setf.exp(scaleN)
+// G = G_1 * G_2
+//
{ .mfi
- ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2
- nop.f 999
- nop.i 999
+(p0) ldfd FR_h_tmp = [GR_Index2],0
+ nop.f 999
+(p0) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 ;;
}
-{ .mfb
-(p9) setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N)
-(p7) fnma.s0 f8 = FR_X_Prime, FR_X_Prime, FR_X_Prime // Result x - x*x
-(p7) br.ret.spnt b0 // Branch if |x| < 2^-80
+{ .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
-(p8) ldfe FR_P7 = [GR_ad_p],16 // Load P_7 for near1 path
-(p8) ldfe FR_P4 = [GR_ad_p2],16 // Load P_4 for near1 path
-(p9) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2
+ nop.m 999
+ nop.m 999
+//
+// float_N = fcvt.xf(float_N)
+// load G3
+//
+(p0) addl GR_Table_Base = @ltoff(Constants_Q#),gp ;;
}
-;;
+{ .mmi
+ nop.m 999
+ ld8 GR_Table_Base = [GR_Table_Base]
+ 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
//
-// For performance, don't use result of pmpyshr2.u for 4 cycles.
+// 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
-(p8) ldfe FR_P6 = [GR_ad_p],16 // Load P_6 for near1 path
-(p8) ldfe FR_P3 = [GR_ad_p2],16 // Load P_3 for near1 path
-(p9) fma.s1 FR_S_lo = FR_S_lo, f1, FR_BB // S_lo = S_lo + BB
+(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
+(p0) ldfe FR_Q3 = [GR_Table_Base],16
+(p0) fadd.s1 FR_H = FR_H, FR_H_tmp
+ nop.i 999 ;;
}
-;;
-
{ .mmf
-(p8) ldfe FR_P5 = [GR_ad_p],16 // Load P_5 for near1 path
-(p8) ldfe FR_P2 = [GR_ad_p2],16 // Load P_2 for near1 path
-(p8) fmpy.s1 FR_wsq = FR_W, FR_W // wsq = w * w for near1 path
+(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 ;;
}
-;;
-
-{ .mmi
-(p8) ldfe FR_P1 = [GR_ad_p2],16 ;; // Load P_1 for near1 path
- nop.m 999
-(p9) extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
+//
+// 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
-(p9) shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3
-(p9) fcvt.xf FR_float_N = FR_float_N
- nop.i 999
+ nop.m 999
+(p0) fmpy.s1 FR_G = FR_G, FR_G_tmp
+ nop.i 999 ;;
}
-;;
-
{ .mfi
-(p9) ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3
- nop.f 999
- nop.i 999
+ nop.m 999
+(p0) fadd.s1 FR_H = FR_H, FR_H_tmp
+ nop.i 999 ;;
}
-;;
-
{ .mfi
-(p9) ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
-(p9) fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
- nop.i 999
+ nop.m 999
+(p0) fms.s1 FR_r = FR_G, FR_S_hi, f1
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p9) fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
- nop.i 999
+ nop.m 999
+(p0) fadd.s1 FR_h = FR_h, FR_h_tmp
+ nop.i 999 ;;
}
-;;
-
-{ .mmf
- nop.m 999
- nop.m 999
-(p9) fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
+{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
-(p8) fmpy.s1 FR_w4 = FR_wsq, FR_wsq // w4 = w^4 for near1 path
- nop.i 999
+ 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 999
-(p8) fma.s1 FR_p87 = FR_W, FR_P8, FR_P7 // p87 = w * P8 + P7
- nop.i 999
+ 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 999
-(p9) fma.s1 FR_S_lo = FR_S_lo, FR_2_to_minus_N, f0 // S_lo = S_lo * 2^(-N)
- nop.i 999
+ 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 999
-(p8) fma.s1 FR_p43 = FR_W, FR_P4, FR_P3 // p43 = w * P4 + P3
- nop.i 999
+(p0) setf.sig FR_dummy = GR_Perturb
+(p0) fmpy.s1 FR_rsq = FR_r, FR_r
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
-(p9) fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
- nop.i 999
+ 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
-(p9) fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
-(p9) fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
- nop.i 999
+ 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 ;;
}
{ .mfi
+ nop.m 999
+(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_rsq, FR_h
+ nop.i 999 ;;
+}
+{ .mfb
+ 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 LOGL_main ;;
+}
+L(log1pl_near):
+{ .mmi
+ nop.m 999
+ nop.m 999
+// /*******************************************************/
+// /*********** Branch log1pl_near ************************/
+// /*******************************************************/
+(p0) addl GR_Table_Base = @ltoff(Constants_P#),gp ;;
+}
+{ .mmi
nop.m 999
-(p8) fmpy.s1 FR_w6 = FR_w4, FR_wsq // w6 = w^6 for near1 path
+ ld8 GR_Table_Base = [GR_Table_Base]
nop.i 999
+};;
+//
+// Load base address of poly. coeff.
+//
+{ .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
- nop.m 999
-(p8) fma.s1 FR_p432 = FR_W, FR_p43, FR_P2 // p432 = w * p43 + P2
- nop.i 999
+(p0) ldfe FR_P2 = [GR_Table_ptr],16
+ nop.f 999
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p8) fma.s1 FR_p876 = FR_W, FR_p87, FR_P6 // p876 = w * p87 + P6
- nop.i 999
+ 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
- nop.m 999
-(p9) fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1
- nop.i 999
+(p0) ldfe FR_P5 = [GR_Table_Base],16
+(p0) fma.s1 FR_Y_lo = FR_W, FR_P8, FR_P7
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p9) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi = N * log2_hi + H
- nop.i 999
+(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
-(p9) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N * log2_lo + h
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P2
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
-(p9) fma.s1 FR_r = FR_G, FR_S_lo, FR_r // r = G * S_lo + (G * S_hi - 1)
- nop.i 999
+ 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
-(p8) fma.s1 FR_p4321 = FR_W, FR_p432, FR_P1 // p4321 = w * p432 + P1
- nop.i 999
+ 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
-(p8) fma.s1 FR_p8765 = FR_W, FR_p876, FR_P5 // p8765 = w * p876 + P5
- nop.i 999
+ 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
- nop.m 999
-(p9) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3
- nop.i 999
+(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
-(p9) fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_dummy = FR_wsq,FR_Y_hi, f0
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
-(p8) fma.s1 FR_Y_lo = FR_wsq, FR_p4321, f0 // Y_lo = wsq * p4321
- nop.i 999
+ nop.m 999
+(p0) fma.s1 FR_Y_hi = FR_W,f1,f0
+ nop.i 999
+};;
+{ .mfb
+ nop.m 999
+//
+// Y_hi = w
+// Y_lo = y_lo * w + p5
+//
+(p0) fma.s1 FR_Y_lo = FR_w6, FR_Y_lo,FR_dummy
+//
+// Y_lo = y_lo * w6 + y_high order part.
+//
+// performance
+//
+(p0) br.cond.sptk LOGL_main ;;
+}
+L(log1pl_small):
+{ .mmi
+ nop.m 999
+// /*******************************************************/
+// /*********** Branch log1pl_small ***********************/
+// /*******************************************************/
+(p0) addl GR_Table_Base = @ltoff(Constants_Threshold#),gp
}
{ .mfi
nop.m 999
-(p8) fma.s1 FR_Y_hi = FR_W, f1, f0 // Y_hi = w for near1 path
- nop.i 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 = 0x0000000000000004 ;;
+}
+//
+// 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
- nop.m 999
-(p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo = poly_lo * r + Q2
- nop.i 999
+(p0) ldfe FR_Tiny = [GR_Table_Base],0
+ nop.f 999
+ nop.i 999 ;;
}
{ .mfi
- nop.m 999
-(p9) fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
- nop.i 999
+ nop.m 999
+(p0) fcmp.gt.unc.s1 p13, p12 = FR_abs_W, FR_Threshold
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
-(p8) fma.s1 FR_Y_lo = FR_w6, FR_p8765,FR_Y_lo // Y_lo = w6 * p8765 + w2 * p4321
- nop.i 999
+ nop.m 999
+(p13) fnmpy.s1 FR_Y_lo = FR_W, FR_W
+ nop.i 999
}
-;;
-
{ .mfi
- nop.m 999
-(p9) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1 * rsq + r
- nop.i 999
+ nop.m 999
+(p13) fadd FR_SCALE = f0, f1
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 999
-(p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h // poly_lo = poly_lo*r^3 + h
- nop.i 999
+ nop.m 999
+(p12) fsub.s1 FR_Y_lo = f0, FR_Tiny
+(p12) cmp.ne.unc p7, p0 = r0, r0
}
-;;
-
{ .mfi
- nop.m 999
-(p9) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo = poly_hi + poly_lo
- nop.i 999
+(p12) setf.exp FR_SCALE = GR_Bias
+ nop.f 999
+ nop.i 999 ;;
}
-;;
-
-// Remainder of code is common for near1 and regular paths
{ .mfb
- nop.m 999
- fadd.s0 f8 = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi
- br.ret.sptk b0 // Common exit for 2^-80 < x < inf
+ nop.m 999
+//
+// Set p7 to SAFE = FALSE
+// Set Scale = 2^-100
+//
+(p0) fma.s0 f8 = FR_Y_lo,FR_SCALE,FR_Y_hi
+(p0) br.ret.sptk b0 ;;
}
-;;
-
-
-// Here if x=-1
-LOG1P_EQ_Minus_1:
+L(LOGL_64_one):
+{ .mfb
+ nop.m 999
+(p0) fmpy.s0 f8 = FR_Input_X, f0
+(p0) br.ret.sptk b0 ;;
+}
+//
+// Raise divide by zero for +/-0 input.
+//
+L(LOGL_64_zero):
+{ .mfi
+(p0) mov GR_Parameter_TAG = 0
//
-// If x=-1 raise divide by zero and return -inf
+// If we have logl(1), log10l(1) or log1pl(0), return 0.
//
-{ .mfi
- mov GR_Parameter_TAG = 138
- fsub.s1 FR_Output_X_tmp = f0, f1
- nop.i 999
+(p0) fsub.s0 FR_Output_X_tmp = f0, f1
+ nop.i 999 ;;
+}
+{ .mii
+(p14) mov GR_Parameter_TAG = 6
+ nop.i 999 ;;
+(p15) mov GR_Parameter_TAG = 138 ;;
}
-;;
-
{ .mfb
- nop.m 999
- frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0
- br.cond.sptk __libm_error_region
+ nop.m 999
+(p0) frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0
+(p0) br.cond.sptk __libm_error_region ;;
+}
+{ .mfb
+ nop.m 999
+//
+// Report that logl(0) computed
+// { .mfb
+(p0) mov FR_Input_X = FR_Output_X_tmp
+(p0) br.ret.sptk b0 ;;
}
-;;
-LOG1P_special:
+L(LOGL_64_special):
{ .mfi
- nop.m 999
- fclass.m.unc p8, p0 = FR_Input_X, 0x1E1 // Test for natval, nan, +inf
- nop.i 999
+ 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.s0 f8 = FR_Input_X, f1
//
// For SNaN raise invalid and return QNaN.
// For QNaN raise invalid and return QNaN.
// For +Inf return +Inf.
//
-{ .mfb
- nop.m 999
-(p8) fmpy.s0 f8 = FR_Input_X, f1
-(p8) br.ret.sptk b0 // Return for natval, nan, +inf
+(p7) br.ret.sptk b0 ;;
}
-;;
-
//
// For -Inf raise invalid and return QNaN.
//
+{ .mii
+(p0) mov GR_Parameter_TAG = 1
+ nop.i 999 ;;
+(p14) mov GR_Parameter_TAG = 7 ;;
+}
+{ .mfi
+(p15) mov GR_Parameter_TAG = 139
+ nop.f 999
+ nop.i 999 ;;
+}
{ .mfb
- mov GR_Parameter_TAG = 139
- fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0
- br.cond.sptk __libm_error_region
+ nop.m 999
+(p0) fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0
+(p0) br.cond.sptk __libm_error_region ;;
}
-;;
-
-
-LOG1P_unsupported:
+//
+// Report that logl(-Inf) computed
+// Report that log10l(-Inf) computed
+// Report that log1p(-Inf) computed
+//
+{ .mfb
+ nop.m 0
+(p0) mov FR_Input_X = FR_Output_X_tmp
+(p0) br.ret.sptk b0 ;;
+}
+L(LOGL_64_unsupported):
+{ .mfb
+ nop.m 999
//
-// Return generated NaN or other value.
+// Return generated NaN or other value .
//
-{ .mfb
- nop.m 999
- fmpy.s0 f8 = FR_Input_X, f0
- br.ret.sptk b0
+(p0) fmpy.s0 f8 = FR_Input_X, f0
+(p0) br.ret.sptk b0 ;;
}
-;;
-
-// Here if -inf < x < -1
-LOG1P_LT_Minus_1:
+L(LOGL_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 < -1 in a special way - raise
+// Deal with x < 0 in a special way - raise
// invalid and produce QNaN indefinite.
//
-{ .mfb
- mov GR_Parameter_TAG = 139
- frcpa.s0 FR_Output_X_tmp, p8 = f0, f0
- br.cond.sptk __libm_error_region
+(p0) mov GR_Parameter_TAG = 1 ;;
}
-;;
-
-
-GLOBAL_IEEE754_END(log1pl)
+{ .mii
+(p14) mov GR_Parameter_TAG = 7
+ nop.i 999 ;;
+(p15) mov GR_Parameter_TAG = 139
+}
+.endp log1pl
+ASM_SIZE_DIRECTIVE(log1pl)
-LOCAL_LIBM_ENTRY(__libm_error_region)
+.proc __libm_error_region
+__libm_error_region:
.prologue
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
@@ -1178,8 +1609,8 @@ LOCAL_LIBM_ENTRY(__libm_error_region)
br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
- nop.m 999
- nop.m 999
+ nop.m 0
+ nop.m 0
add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
@@ -1194,7 +1625,52 @@ LOCAL_LIBM_ENTRY(__libm_error_region)
br.ret.sptk b0 // Return
};;
-LOCAL_LIBM_END(__libm_error_region#)
+.endp __libm_error_region
+ASM_SIZE_DIRECTIVE(__libm_error_region)
+
+.proc LOGL_main
+LOGL_main:
+{ .mfi
+ nop.m 999
+//
+// kernel_log_64 computes ln(X + E)
+//
+(p7) fadd.s0 FR_Input_X = FR_Y_lo,FR_Y_hi
+ nop.i 0
+}
+{ .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.s0 FR_Input_X = FR_Y_hi,FR_1LN10_hi,FR_Output_X_tmp
+(p0) br.ret.sptk b0 ;;
+}
+.endp LOGL_main
+ASM_SIZE_DIRECTIVE(LOGL_main)
.type __libm_error_support#,@function
.global __libm_error_support#