summaryrefslogtreecommitdiff
path: root/sysdeps/ia64/fpu/s_log1pl.S
diff options
context:
space:
mode:
Diffstat (limited to 'sysdeps/ia64/fpu/s_log1pl.S')
-rw-r--r--sysdeps/ia64/fpu/s_log1pl.S2068
1 files changed, 796 insertions, 1272 deletions
diff --git a/sysdeps/ia64/fpu/s_log1pl.S b/sysdeps/ia64/fpu/s_log1pl.S
index 7cd3f7834c..9654265004 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, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2003, Intel Corporation
// All rights reserved.
-//
-// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
-// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
+//
+// Contributed 2000 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
@@ -20,7 +20,7 @@
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
-//
+
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
@@ -35,55 +35,49 @@
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
-// http://developer.intel.com/opensource.
+// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
-// *********************************************************************
+//*********************************************************************
//
// History:
-// 2/02/00 hand-optimized
-// 4/04/00 Unwind support added
-// 8/15/00 Bundle added after call to __libm_error_support to properly
+// 02/02/00 Initial version
+// 04/04/00 Unwind support added
+// 08/15/00 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: 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
+// Function: log1pl(x) = ln(x+1), for double-extended precision x values
//
-// *********************************************************************
+//*********************************************************************
//
// Resources Used:
//
// Floating-Point Registers: f8 (Input and Return Value)
-// f9,f33-f55,f99
+// f34-f82
//
// General Purpose Registers:
-// r32-r53
-// r54-r57 (Used to pass arguments to error handling routine)
+// r32-r56
+// r53-r56 (Used to pass arguments to error handling routine)
//
-// Predicate Registers: p6-p15
+// Predicate Registers: p6-p13
//
-// *********************************************************************
+//*********************************************************************
//
// 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
@@ -91,54 +85,37 @@
// 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+Em1| < 2^(-80) use case log1pl_small;
-// elseif |X+Em1| < 2^(-7) use case log_near1;
-// else use case log_regular;
+// If |X| < 2^(-80) use case log1p_small;
+// else |X| < 2^(-7) use case log_near1;
+// else use case log_regular;
//
-// Case log1pl_small:
+// Case log1p_small:
//
-// logl( 1 + (X+Em1) ) can be approximated by (X+Em1).
+// log1pl( X ) = logl( X+1 ) can be approximated by X
//
// Case log_near1:
//
-// logl( 1 + (X+Em1) ) can be approximated by a simple polynomial
-// in W = X+Em1. This polynomial resembles the truncated Taylor
+// log1pl( X ) = log( X+1 ) can be approximated by a simple polynomial
+// in W = X. 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) 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) = 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
// 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
@@ -146,9 +123,9 @@
//
// Step 0: Initialization
//
-// We need to calculate logl( E + X ). Obtain N, S_hi, S_lo such that
+// We need to calculate logl( X+1 ). Obtain N, S_hi such that
//
-// E + X = 2^N * ( S_hi + S_lo ) exactly
+// X+1 = 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).
@@ -157,8 +134,8 @@
//
// 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.
@@ -171,61 +148,34 @@
// Step 3: Reconstruction
//
//
-// Finally, logl( E + X ) is given by
+// Finally, log1pl( X ) = logl( X+1 ) is given by
//
-// logl( E + X ) = logl( 2^N * (S_hi + S_lo) )
+// logl( X+1 ) = 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 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 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 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
+// 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)))
//
// Case log_regular:
//
@@ -234,89 +184,87 @@
// Step 0. Initialization
// ----------------------
//
-// Z := X + E
+// Z := X + 1
// 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.
+// S_lo := 2^(-N) * { (max(X,1)-Z) + min(X,1) }
//
// 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
@@ -326,1258 +274,879 @@
// 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+E):
+// This step computes the desired result of logl(X+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(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(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 ) ]
-// set lsb(Y_lo) to be 1
+// Y_hi := N*log2_hi + SUM ( log1byGj_hi )
+// Y_lo := poly_hi + [ poly_lo +
+// ( SUM ( log1byGj_lo ) + N*log2_lo ) ]
//
-#include "libm_support.h"
+RODATA
+.align 64
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
+// ************* DO NOT CHANGE THE ORDER OF THESE TABLES *************
-// P_7, P_6, P_5, P_4, P_3, P_2, and P_1
+// P_8, P_7, P_6, P_5, P_4, P_3, P_2, and P_1
+
+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)
-.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
-.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)
+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
-//
-// 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)
-//
+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)
-.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)
+// G1 and H1 - IEEE single and h1 - IEEE double
-.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
+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)
-//
-// Added for unwind support
-//
+// 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)
-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
+
+// 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
+
+FR_p43 = f61
+FR_p432 = f61
+FR_p4321 = f61
+FR_P4 = f62
+FR_G3 = f63
+FR_H3 = f64
+FR_h3 = f65
+
+FR_Q3 = f66
+FR_P3 = f67
+FR_Q2 = f68
+FR_P2 = f69
+FR_1LN10_hi = f70
+
+FR_Q1 = f71
+FR_P1 = f72
+FR_1LN10_lo = f73
+FR_P5 = f74
+FR_rcub = f75
+
+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
FR_X = f8
FR_Y = f0
-FR_RESULT = f99
+FR_RESULT = f76
-.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) ;;
-}
-.endp logl
-ASM_SIZE_DIRECTIVE(logl)
+// General Purpose Registers
-.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_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
+
+//
+// Added for unwind support
+//
-.endp log10l
-ASM_SIZE_DIRECTIVE(log10l)
+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
.section .text
-.proc log1pl#
-.global log1pl#
-.align 64
-log1pl:
-#ifdef _LIBC
-.global __log1pl
-__log1pl:
-#endif
+GLOBAL_IEEE754_ENTRY(log1pl)
{ .mfi
-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
-(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 ;;
+ alloc r32 = ar.pfs,0,21,4,0
+ fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf
+ nop.i 999
}
{ .mfi
- nop.m 0
-(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
- nop.i 0
+ addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp
+ fma.s1 FR_Z = FR_Input_X, f1, f1 // x+1
+ nop.i 999
}
+;;
+
{ .mfi
nop.m 999
-(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
- nop.i 0
+ fmerge.ns FR_Neg_One = f1, f1 // Form -1.0
+ nop.i 999
}
{ .mfi
nop.m 999
-(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f0
- nop.i 0
+ fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p0) fadd FR_Em1 = f0,f0
- nop.i 999 ;;
+ 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
}
-{ .mfi
- nop.m 999
-(p0) fadd FR_E = f0,f1
- 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) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, FR_Neg_One
- nop.i 999
+ 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
}
{ .mfi
- nop.m 999
-(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, FR_Neg_One
- nop.i 999
+ 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
}
-L(LOGL_BEGIN):
+;;
+
{ .mfi
- 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 ;;
+ 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
}
-{ .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
+{ .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
}
+;;
+
{ .mfi
- nop.m 999
-(p0) fmax.s1 FR_AA = FR_X_Prime, FR_E
- nop.i 999 ;;
+ 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
}
{ .mfi
- 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) ;;
+ 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
}
-{ .mib
- nop.m 999
- nop.i 999
-(p10) br.cond.spnt L(LOGL_64_unsupported) ;;
+;;
+
+{ .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
}
{ .mib
- nop.m 999
- nop.i 999
-(p13) br.cond.spnt L(LOGL_64_negative) ;;
+ 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
}
-{ .mib
-(p0) getf.sig GR_signif = FR_Z
- nop.i 999
-(p9) br.cond.spnt L(LOGL_64_one) ;;
+;;
+
+{ .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
-(p8) br.cond.spnt L(LOGL_64_zero) ;;
+;;
+
+{ .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
}
+;;
+
{ .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
-//
-(p0) fsub.s1 FR_S_lo = FR_AA, FR_Z
+ 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
+}
+;;
+
//
-// signif = getf.sig(Z)
-// abs_W = fabs(w)
+// For performance, don't use result of pmpyshr2.u for 4 cycles.
//
-(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
- 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
- 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 ;;
+ ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo
+ sub GR_N = GR_N, GR_Bias
+ mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80
}
+;;
+
{ .mfi
- 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 ;;
+ 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)
}
-{ .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 ;;
+;;
+
+{ .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)
}
-//
-// 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 ;;
+ 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
}
+;;
+
{ .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(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
+ 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
}
+;;
+
{ .mmi
-(p0) setf.exp FR_two_negN = GR_ScaleN
- nop.m 999
-(p0) addl GR_Table_Base = @ltoff(Constants_Z_G_H_h3#),gp ;;
+ 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
}
-//
-// 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
-(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 ;;
+ 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
}
-//
-// Load H_2
-// two_negN = setf.exp(scaleN)
-// G = G_1 * G_2
-//
+;;
+
+// 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
+
{ .mfi
-(p0) ldfd FR_h_tmp = [GR_Index2],0
- nop.f 999
-(p0) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 ;;
+ ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2
+ nop.f 999
+ nop.i 999
}
-{ .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
+{ .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
}
+;;
+
{ .mmi
- nop.m 999
- nop.m 999
-//
-// float_N = fcvt.xf(float_N)
-// load G3
-//
-(p0) addl GR_Table_Base = @ltoff(Constants_Q#),gp ;;
+(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
}
-{ .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
//
-// G = G3 * G
-// Load h3
-// Load log2_hi
-// H = H + H3
+// For performance, don't use result of pmpyshr2.u for 4 cycles.
//
-(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
-(p0) ldfe FR_Q3 = [GR_Table_Base],16
-(p0) fadd.s1 FR_H = FR_H, FR_H_tmp
- nop.i 999 ;;
+(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
}
+;;
+
{ .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 ;;
+(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
}
-//
-// 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 ;;
+;;
+
+{ .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
}
+;;
+
{ .mfi
- nop.m 999
-(p0) fmpy.s1 FR_G = FR_G, FR_G_tmp
- nop.i 999 ;;
+(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
}
+;;
+
{ .mfi
- nop.m 999
-(p0) fadd.s1 FR_H = FR_H, FR_H_tmp
- nop.i 999 ;;
+(p9) ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3
+ nop.f 999
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p0) fms.s1 FR_r = FR_G, FR_S_hi, f1
- nop.i 999
+(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
}
{ .mfi
- nop.m 999
-(p0) fadd.s1 FR_h = FR_h, FR_h_tmp
- nop.i 999 ;;
+ nop.m 999
+(p9) fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
+ nop.i 999
}
-{ .mfi
- nop.m 999
-(p0) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H
- 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
-//
-// Load Q4
-// Load Q3
-// Load Q2
-// Load Q1
-//
-(p8) fma.s1 FR_r = FR_G, FR_S_lo, FR_r
- nop.i 999
+ nop.m 999
+(p8) fmpy.s1 FR_w4 = FR_wsq, FR_wsq // w4 = w^4 for near1 path
+ nop.i 999
}
{ .mfi
- 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 ;;
+ nop.m 999
+(p8) fma.s1 FR_p87 = FR_W, FR_P8, FR_P7 // p87 = w * P8 + P7
+ nop.i 999
}
+;;
+
{ .mfi
- 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
+ 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
}
-//
-// Create a 0x00000....01
-// poly_lo = poly_lo * rsq + h
-//
{ .mfi
-(p0) setf.sig FR_dummy = GR_Perturb
-(p0) fmpy.s1 FR_rsq = FR_r, FR_r
- nop.i 999 ;;
+ nop.m 999
+(p8) fma.s1 FR_p43 = FR_W, FR_P4, FR_P3 // p43 = w * P4 + P3
+ 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
+ nop.m 999
+(p9) fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p0) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
- nop.i 999 ;;
+ nop.m 999
+(p9) fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
+ 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 ;;
+ nop.m 999
+(p9) fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
+ 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
- ld8 GR_Table_Base = [GR_Table_Base]
+(p8) fmpy.s1 FR_w6 = FR_w4, FR_wsq // w6 = w^6 for near1 path
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
-(p0) ldfe FR_P2 = [GR_Table_ptr],16
- nop.f 999
- nop.i 999 ;;
+ nop.m 999
+(p8) fma.s1 FR_p432 = FR_W, FR_p43, FR_P2 // p432 = w * p43 + P2
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p0) fma.s1 FR_Y_hi = FR_W, FR_P4, FR_P3
- nop.i 999
+ nop.m 999
+(p8) fma.s1 FR_p876 = FR_W, FR_p87, FR_P6 // p876 = w * p87 + P6
+ 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 ;;
+ nop.m 999
+(p9) fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1
+ 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 ;;
+ 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
}
+;;
+
{ .mfi
- nop.m 999
-(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P2
- nop.i 999
+ nop.m 999
+(p9) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N * log2_lo + h
+ 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 ;;
+ 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
}
+;;
+
{ .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 ;;
+ nop.m 999
+(p8) fma.s1 FR_p4321 = FR_W, FR_p432, FR_P1 // p4321 = w * p432 + P1
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P1
- nop.i 999
+ nop.m 999
+(p8) fma.s1 FR_p8765 = FR_W, FR_p876, FR_P5 // p8765 = w * p876 + P5
+ 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 ;;
+ nop.m 999
+(p9) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3
+ nop.i 999
}
{ .mfi
- nop.m 999
-(p0) fma.s1 FR_dummy = FR_wsq,FR_Y_hi, f0
- nop.i 999
+ nop.m 999
+(p9) fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
+ nop.i 999
}
+;;
+
{ .mfi
- 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
+ nop.m 999
+(p8) fma.s1 FR_Y_lo = FR_wsq, FR_p4321, f0 // Y_lo = wsq * p4321
+ nop.i 999
}
{ .mfi
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 = 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 ;;
+(p8) fma.s1 FR_Y_hi = FR_W, f1, f0 // Y_hi = w for near1 path
+ nop.i 999
}
+;;
+
{ .mfi
-(p0) ldfe FR_Tiny = [GR_Table_Base],0
- nop.f 999
- nop.i 999 ;;
+ 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
}
{ .mfi
- nop.m 999
-(p0) fcmp.gt.unc.s1 p13, p12 = FR_abs_W, FR_Threshold
- nop.i 999 ;;
+ nop.m 999
+(p9) fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p13) fnmpy.s1 FR_Y_lo = FR_W, FR_W
- nop.i 999
+ 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
}
+;;
+
{ .mfi
- nop.m 999
-(p13) fadd FR_SCALE = f0, f1
- nop.i 999 ;;
+ nop.m 999
+(p9) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1 * rsq + r
+ nop.i 999
}
+;;
+
{ .mfi
- nop.m 999
-(p12) fsub.s1 FR_Y_lo = f0, FR_Tiny
-(p12) cmp.ne.unc p7, p0 = r0, r0
+ 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
}
+;;
+
{ .mfi
-(p12) setf.exp FR_SCALE = GR_Bias
- nop.f 999
- nop.i 999 ;;
-}
-{ .mfb
- 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 ;;
+ nop.m 999
+(p9) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo = poly_hi + poly_lo
+ nop.i 999
}
-L(LOGL_64_one):
+;;
+
+// Remainder of code is common for near1 and regular paths
{ .mfb
- nop.m 999
-(p0) fmpy.s0 f8 = FR_Input_X, f0
-(p0) br.ret.sptk b0 ;;
+ 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
}
-//
-// Raise divide by zero for +/-0 input.
-//
-L(LOGL_64_zero):
-{ .mfi
-(p0) mov GR_Parameter_TAG = 0
+;;
+
+
+// Here if x=-1
+LOG1P_EQ_Minus_1:
//
-// If we have logl(1), log10l(1) or log1pl(0), return 0.
+// If x=-1 raise divide by zero and return -inf
//
-(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
-(p0) frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0
-(p0) br.cond.sptk __libm_error_region ;;
+{ .mfi
+ mov GR_Parameter_TAG = 138
+ fsub.s1 FR_Output_X_tmp = f0, f1
+ nop.i 999
}
+;;
+
{ .mfb
- nop.m 999
-//
-// Report that logl(0) computed
-// { .mfb
-(p0) mov FR_Input_X = FR_Output_X_tmp
-(p0) br.ret.sptk b0 ;;
+ nop.m 999
+ frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0
+ br.cond.sptk __libm_error_region
}
+;;
-L(LOGL_64_special):
+LOG1P_special:
{ .mfi
- nop.m 999
-//
-// Return -Inf or value from handler.
-//
-(p0) fclass.m.unc p7, p0 = FR_Input_X, 0x1E1
- nop.i 999 ;;
+ nop.m 999
+ fclass.m.unc p8, p0 = FR_Input_X, 0x1E1 // Test for natval, nan, +inf
+ 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.
//
-(p7) br.ret.sptk b0 ;;
+{ .mfb
+ nop.m 999
+(p8) fmpy.s0 f8 = FR_Input_X, f1
+(p8) br.ret.sptk b0 // Return for natval, nan, +inf
}
+;;
+
//
// 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
- nop.m 999
-(p0) fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0
-(p0) br.cond.sptk __libm_error_region ;;
+ mov GR_Parameter_TAG = 139
+ fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0
+ br.cond.sptk __libm_error_region
}
-//
-// 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
+;;
+
+
+LOG1P_unsupported:
//
-// Return generated NaN or other value .
+// Return generated NaN or other value.
//
-(p0) fmpy.s0 f8 = FR_Input_X, f0
-(p0) br.ret.sptk b0 ;;
+{ .mfb
+ nop.m 999
+ fmpy.s0 f8 = FR_Input_X, f0
+ br.ret.sptk b0
}
-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
+;;
+
+// Here if -inf < x < -1
+LOG1P_LT_Minus_1:
//
-// Deal with x < 0 in a special way - raise
+// Deal with x < -1 in a special way - raise
// invalid and produce QNaN indefinite.
//
-(p0) mov GR_Parameter_TAG = 1 ;;
-}
-{ .mii
-(p14) mov GR_Parameter_TAG = 7
- nop.i 999 ;;
-(p15) mov GR_Parameter_TAG = 139
+{ .mfb
+ mov GR_Parameter_TAG = 139
+ frcpa.s0 FR_Output_X_tmp, p8 = f0, f0
+ br.cond.sptk __libm_error_region
}
-.endp log1pl
-ASM_SIZE_DIRECTIVE(log1pl)
+;;
+
-.proc __libm_error_region
-__libm_error_region:
+GLOBAL_IEEE754_END(log1pl)
+
+LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
@@ -1609,8 +1178,8 @@ __libm_error_region:
br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
- nop.m 0
- nop.m 0
+ nop.m 999
+ nop.m 999
add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
@@ -1625,52 +1194,7 @@ __libm_error_region:
br.ret.sptk b0 // Return
};;
-.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)
+LOCAL_LIBM_END(__libm_error_region#)
.type __libm_error_support#,@function
.global __libm_error_support#