diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_log1pl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_log1pl.S | 2068 |
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# |