diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_log1pl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_log1pl.S | 2068 |
1 files changed, 1272 insertions, 796 deletions
diff --git a/sysdeps/ia64/fpu/s_log1pl.S b/sysdeps/ia64/fpu/s_log1pl.S index 9654265004..7cd3f7834c 100644 --- a/sysdeps/ia64/fpu/s_log1pl.S +++ b/sysdeps/ia64/fpu/s_log1pl.S @@ -1,10 +1,10 @@ .file "log1pl.s" - -// Copyright (c) 2000 - 2003, Intel Corporation +// Copyright (C) 2000, 2001, Intel Corporation // All rights reserved. -// -// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// +// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, +// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are @@ -20,7 +20,7 @@ // * The name of Intel Corporation may not be used to endorse or promote // products derived from this software without specific prior written // permission. - +// // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR @@ -35,49 +35,55 @@ // // Intel Corporation is the author of this code, and requests that all // problem reports or change requests be submitted to it directly at -// http://www.intel.com/software/products/opensource/libraries/num.htm. +// http://developer.intel.com/opensource. // -//********************************************************************* +// ********************************************************************* // // History: -// 02/02/00 Initial version -// 04/04/00 Unwind support added -// 08/15/00 Bundle added after call to __libm_error_support to properly +// 2/02/00 hand-optimized +// 4/04/00 Unwind support added +// 8/15/00 Bundle added after call to __libm_error_support to properly // set [the previously overwritten] GR_Parameter_RESULT. -// 05/21/01 Removed logl and log10l, putting them in a separate file -// 06/29/01 Improved speed of all paths -// 05/20/02 Cleaned up namespace and sf0 syntax -// 02/10/03 Reordered header: .section, .global, .proc, .align; -// used data8 for long double table values // -//********************************************************************* +// ********************************************************************* // -//********************************************************************* +// ********************************************************************* // -// Function: log1pl(x) = ln(x+1), for double-extended precision x values +// Function: Combined logl(x), log1pl(x), and log10l(x) where +// logl(x) = ln(x), for double-extended precision x values +// log1pl(x) = ln(x+1), for double-extended precision x values +// log10l(x) = log (x), for double-extended precision x values +// 10 // -//********************************************************************* +// ********************************************************************* // // Resources Used: // // Floating-Point Registers: f8 (Input and Return Value) -// f34-f82 +// f9,f33-f55,f99 // // General Purpose Registers: -// r32-r56 -// r53-r56 (Used to pass arguments to error handling routine) +// r32-r53 +// r54-r57 (Used to pass arguments to error handling routine) // -// Predicate Registers: p6-p13 +// Predicate Registers: p6-p15 // -//********************************************************************* +// ********************************************************************* // // IEEE Special Conditions: // -// Denormal fault raised on denormal inputs +// Denormal fault raised on denormal inputs // Overflow exceptions cannot occur // Underflow exceptions raised when appropriate for log1p +// (Error Handling Routine called for underflow) // Inexact raised when appropriate by algorithm // +// logl(inf) = inf +// logl(-inf) = QNaN +// logl(+/-0) = -inf +// logl(SNaN) = QNaN +// logl(QNaN) = QNaN +// logl(EM_special Values) = QNaN // log1pl(inf) = inf // log1pl(-inf) = QNaN // log1pl(+/-0) = +/-0 @@ -85,37 +91,54 @@ // log1pl(SNaN) = QNaN // log1pl(QNaN) = QNaN // log1pl(EM_special Values) = QNaN -// -//********************************************************************* -// +// log10l(inf) = inf +// log10l(-inf) = QNaN +// log10l(+/-0) = -inf +// log10l(SNaN) = QNaN +// log10l(QNaN) = QNaN +// log10l(EM_special Values) = QNaN +// +// ********************************************************************* +// +// Computation is based on the following kernel. +// +// ker_log_64( in_FR : X, +// in_FR : E, +// in_FR : Em1, +// in_GR : Expo_Range, +// out_FR : Y_hi, +// out_FR : Y_lo, +// out_FR : Scale, +// out_PR : Safe ) +// // Overview // // The method consists of three cases. // -// If |X| < 2^(-80) use case log1p_small; -// else |X| < 2^(-7) use case log_near1; -// else use case log_regular; +// If |X+Em1| < 2^(-80) use case log1pl_small; +// elseif |X+Em1| < 2^(-7) use case log_near1; +// else use case log_regular; // -// Case log1p_small: +// Case log1pl_small: // -// log1pl( X ) = logl( X+1 ) can be approximated by X +// logl( 1 + (X+Em1) ) can be approximated by (X+Em1). // // Case log_near1: // -// log1pl( X ) = log( X+1 ) can be approximated by a simple polynomial -// in W = X. This polynomial resembles the truncated Taylor +// logl( 1 + (X+Em1) ) can be approximated by a simple polynomial +// in W = X+Em1. This polynomial resembles the truncated Taylor // series W - W^/2 + W^3/3 - ... // // Case log_regular: // // Here we use a table lookup method. The basic idea is that in -// order to compute logl(Arg) = log1pl (Arg-1) for an argument Arg in [1,2), -// we construct a value G such that G*Arg is close to 1 and that +// order to compute logl(Arg) for an argument Arg in [1,2), we +// construct a value G such that G*Arg is close to 1 and that // logl(1/G) is obtainable easily from a table of values calculated // beforehand. Thus // -// logl(Arg) = logl(1/G) + logl(G*Arg) -// = logl(1/G) + logl(1 + (G*Arg - 1)) +// logl(Arg) = logl(1/G) + logl(G*Arg) +// = logl(1/G) + logl(1 + (G*Arg - 1)) // // Because |G*Arg - 1| is small, the second term on the right hand // side can be approximated by a short polynomial. We elaborate @@ -123,9 +146,9 @@ // // Step 0: Initialization // -// We need to calculate logl( X+1 ). Obtain N, S_hi such that +// We need to calculate logl( E + X ). Obtain N, S_hi, S_lo such that // -// X+1 = 2^N * ( S_hi + S_lo ) exactly +// E + X = 2^N * ( S_hi + S_lo ) exactly // // where S_hi in [1,2) and S_lo is a correction to S_hi in the sense // that |S_lo| <= ulp(S_hi). @@ -134,8 +157,8 @@ // // Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate // -// G := G_1 * G_2 * G_3 -// r := (G * S_hi - 1) + G * S_lo +// G := G_1 * G_2 * G_3 +// r := (G * S_hi - 1) + G * S_lo // // These G_j's have the property that the product is exactly // representable and that |r| < 2^(-12) as a result. @@ -148,34 +171,61 @@ // Step 3: Reconstruction // // -// Finally, log1pl( X ) = logl( X+1 ) is given by +// Finally, logl( E + X ) is given by // -// logl( X+1 ) = logl( 2^N * (S_hi + S_lo) ) +// logl( E + X ) = logl( 2^N * (S_hi + S_lo) ) // ~=~ N*logl(2) + logl(1/G) + logl(1 + r) // ~=~ N*logl(2) + logl(1/G) + poly(r). // // **** Algorithm **** // -// Case log1p_small: -// -// Although log1pl(X) is basically X, we would like to preserve the inexactness -// nature as well as consistent behavior under different rounding modes. -// We can do this by computing the result as -// -// log1pl(X) = X - X*X -// +// Case log1pl_small: +// +// Although logl(1 + (X+Em1)) is basically X+Em1, we would like to +// preserve the inexactness nature as well as consistent behavior +// under different rounding modes. Note that this case can only be +// taken if E is set to be 1.0. In this case, Em1 is zero, and that +// X can be very tiny and thus the final result can possibly underflow. +// Thus, we compare X against a threshold that is dependent on the +// input Expo_Range. If |X| is smaller than this threshold, we set +// SAFE to be FALSE. +// +// The result is returned as Y_hi, Y_lo, and in the case of SAFE +// is FALSE, an additional value Scale is also returned. +// +// W := X + Em1 +// Threshold := Threshold_Table( Expo_Range ) +// Tiny := Tiny_Table( Expo_Range ) +// +// If ( |W| > Threshold ) then +// Y_hi := W +// Y_lo := -W*W +// Else +// Y_hi := W +// Y_lo := -Tiny +// Scale := 2^(-100) +// Safe := FALSE +// EndIf +// +// +// One may think that Y_lo should be -W*W/2; however, it does not matter +// as Y_lo will be rounded off completely except for the correct effect in +// directed rounding. Clearly -W*W is simplier to compute. Moreover, +// because of the difference in exponent value, Y_hi + Y_lo or +// Y_hi + Scale*Y_lo is always inexact. // // Case log_near1: // // Here we compute a simple polynomial. To exploit parallelism, we split // the polynomial into two portions. // -// W := X -// Wsq := W * W -// W4 := Wsq*Wsq -// W6 := W4*Wsq -// Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4)) -// Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8))) +// W := X + Em1 +// Wsq := W * W +// W4 := Wsq*Wsq +// W6 := W4*Wsq +// Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4)) +// Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8))) +// set lsb(Y_lo) to be 1 // // Case log_regular: // @@ -184,87 +234,89 @@ // Step 0. Initialization // ---------------------- // -// Z := X + 1 +// Z := X + E // N := unbaised exponent of Z // S_hi := 2^(-N) * Z -// S_lo := 2^(-N) * { (max(X,1)-Z) + min(X,1) } +// S_lo := 2^(-N) * { (max(X,E)-Z) + min(X,E) } +// +// Note that S_lo is always 0 for the case E = 0. // // Step 1. Argument Reduction // -------------------------- // // Let // -// Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63 +// Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63 // // We obtain G_1, G_2, G_3 by the following steps. // // -// Define X_0 := 1.d_1 d_2 ... d_14. This is extracted -// from S_hi. +// Define X_0 := 1.d_1 d_2 ... d_14. This is extracted +// from S_hi. // -// Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated -// to lsb = 2^(-4). +// Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated +// to lsb = 2^(-4). // -// Define index_1 := [ d_1 d_2 d_3 d_4 ]. +// Define index_1 := [ d_1 d_2 d_3 d_4 ]. // -// Fetch Z_1 := (1/A_1) rounded UP in fixed point with -// fixed point lsb = 2^(-15). -// Z_1 looks like z_0.z_1 z_2 ... z_15 -// Note that the fetching is done using index_1. -// A_1 is actually not needed in the implementation -// and is used here only to explain how is the value -// Z_1 defined. +// Fetch Z_1 := (1/A_1) rounded UP in fixed point with +// fixed point lsb = 2^(-15). +// Z_1 looks like z_0.z_1 z_2 ... z_15 +// Note that the fetching is done using index_1. +// A_1 is actually not needed in the implementation +// and is used here only to explain how is the value +// Z_1 defined. // -// Fetch G_1 := (1/A_1) truncated to 21 sig. bits. -// floating pt. Again, fetching is done using index_1. A_1 -// explains how G_1 is defined. +// Fetch G_1 := (1/A_1) truncated to 21 sig. bits. +// floating pt. Again, fetching is done using index_1. A_1 +// explains how G_1 is defined. // -// Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14) -// = 1.0 0 0 0 d_5 ... d_14 -// This is accomplised by integer multiplication. -// It is proved that X_1 indeed always begin -// with 1.0000 in fixed point. +// Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14) +// = 1.0 0 0 0 d_5 ... d_14 +// This is accomplised by integer multiplication. +// It is proved that X_1 indeed always begin +// with 1.0000 in fixed point. // // -// Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1 -// truncated to lsb = 2^(-8). Similar to A_1, -// A_2 is not needed in actual implementation. It -// helps explain how some of the values are defined. +// Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1 +// truncated to lsb = 2^(-8). Similar to A_1, +// A_2 is not needed in actual implementation. It +// helps explain how some of the values are defined. // -// Define index_2 := [ d_5 d_6 d_7 d_8 ]. +// Define index_2 := [ d_5 d_6 d_7 d_8 ]. // -// Fetch Z_2 := (1/A_2) rounded UP in fixed point with -// fixed point lsb = 2^(-15). Fetch done using index_2. -// Z_2 looks like z_0.z_1 z_2 ... z_15 +// Fetch Z_2 := (1/A_2) rounded UP in fixed point with +// fixed point lsb = 2^(-15). Fetch done using index_2. +// Z_2 looks like z_0.z_1 z_2 ... z_15 // -// Fetch G_2 := (1/A_2) truncated to 21 sig. bits. -// floating pt. +// Fetch G_2 := (1/A_2) truncated to 21 sig. bits. +// floating pt. // -// Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14) -// = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14 -// This is accomplised by integer multiplication. -// It is proved that X_2 indeed always begin -// with 1.00000000 in fixed point. +// Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14) +// = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14 +// This is accomplised by integer multiplication. +// It is proved that X_2 indeed always begin +// with 1.00000000 in fixed point. // // -// Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1. -// This is 2^(-14) + X_2 truncated to lsb = 2^(-13). +// Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1. +// This is 2^(-14) + X_2 truncated to lsb = 2^(-13). // -// Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ]. +// Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ]. // -// Fetch G_3 := (1/A_3) truncated to 21 sig. bits. -// floating pt. Fetch is done using index_3. +// Fetch G_3 := (1/A_3) truncated to 21 sig. bits. +// floating pt. Fetch is done using index_3. // -// Compute G := G_1 * G_2 * G_3. +// Compute G := G_1 * G_2 * G_3. // -// This is done exactly since each of G_j only has 21 sig. bits. +// This is done exactly since each of G_j only has 21 sig. bits. // -// Compute +// Compute // -// r := (G*S_hi - 1) + G*S_lo using 2 FMA operations. +// r := (G*S_hi - 1) + G*S_lo using 2 FMA operations. // -// Thus r approximates G*(S_hi + S_lo) - 1 to within a couple of -// rounding errors. +// thus, r approximates G*(S_hi+S_lo) - 1 to within a couple of +// rounding errors. // // // Step 2. Approximation @@ -274,879 +326,1258 @@ // reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13); // thus logl(1+r) can be approximated by a short polynomial: // -// logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5 +// logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5 // // // Step 3. Reconstruction // ---------------------- // -// This step computes the desired result of logl(X+1): +// This step computes the desired result of logl(X+E): // -// logl(X+1) = logl( 2^N * (S_hi + S_lo) ) -// = N*logl(2) + logl( S_hi + S_lo) ) -// = N*logl(2) + logl(1/G) + -// logl(1 + G * ( S_hi + S_lo ) - 1 ) +// logl(X+E) = logl( 2^N * (S_hi + S_lo) ) +// = N*logl(2) + logl( S_hi + S_lo ) +// = N*logl(2) + logl(1/G) + +// logl(1 + C*(S_hi+S_lo) - 1 ) // // logl(2), logl(1/G_j) are stored as pairs of (single,double) numbers: // log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are // single-precision numbers and the low parts are double precision // numbers. These have the property that // -// N*log2_hi + SUM ( log1byGj_hi ) +// N*log2_hi + SUM ( log1byGj_hi ) // // is computable exactly in double-extended precision (64 sig. bits). // Finally // -// Y_hi := N*log2_hi + SUM ( log1byGj_hi ) -// Y_lo := poly_hi + [ poly_lo + -// ( SUM ( log1byGj_lo ) + N*log2_lo ) ] +// Y_hi := N*log2_hi + SUM ( log1byGj_hi ) +// Y_lo := poly_hi + [ poly_lo + +// ( SUM ( log1byGj_lo ) + N*log2_lo ) ] +// set lsb(Y_lo) to be 1 // -RODATA -.align 64 - -// ************* DO NOT CHANGE THE ORDER OF THESE TABLES ************* +#include "libm_support.h" -// P_8, P_7, P_6, P_5, P_4, P_3, P_2, and P_1 +#ifdef _LIBC +.rodata +#else +.data +#endif -LOCAL_OBJECT_START(Constants_P) -//data4 0xEFD62B15,0xE3936754,0x00003FFB,0x00000000 -//data4 0xA5E56381,0x8003B271,0x0000BFFC,0x00000000 -//data4 0x73282DB0,0x9249248C,0x00003FFC,0x00000000 -//data4 0x47305052,0xAAAAAA9F,0x0000BFFC,0x00000000 -//data4 0xCCD17FC9,0xCCCCCCCC,0x00003FFC,0x00000000 -//data4 0x00067ED5,0x80000000,0x0000BFFD,0x00000000 -//data4 0xAAAAAAAA,0xAAAAAAAA,0x00003FFD,0x00000000 -//data4 0xFFFFFFFE,0xFFFFFFFF,0x0000BFFD,0x00000000 -data8 0xE3936754EFD62B15,0x00003FFB -data8 0x8003B271A5E56381,0x0000BFFC -data8 0x9249248C73282DB0,0x00003FFC -data8 0xAAAAAA9F47305052,0x0000BFFC -data8 0xCCCCCCCCCCD17FC9,0x00003FFC -data8 0x8000000000067ED5,0x0000BFFD -data8 0xAAAAAAAAAAAAAAAA,0x00003FFD -data8 0xFFFFFFFFFFFFFFFE,0x0000BFFD -LOCAL_OBJECT_END(Constants_P) +// P_7, P_6, P_5, P_4, P_3, P_2, and P_1 +.align 64 +Constants_P: +ASM_TYPE_DIRECTIVE(Constants_P,@object) +data4 0xEFD62B15,0xE3936754,0x00003FFB,0x00000000 +data4 0xA5E56381,0x8003B271,0x0000BFFC,0x00000000 +data4 0x73282DB0,0x9249248C,0x00003FFC,0x00000000 +data4 0x47305052,0xAAAAAA9F,0x0000BFFC,0x00000000 +data4 0xCCD17FC9,0xCCCCCCCC,0x00003FFC,0x00000000 +data4 0x00067ED5,0x80000000,0x0000BFFD,0x00000000 +data4 0xAAAAAAAA,0xAAAAAAAA,0x00003FFD,0x00000000 +data4 0xFFFFFFFE,0xFFFFFFFF,0x0000BFFD,0x00000000 +ASM_SIZE_DIRECTIVE(Constants_P) + // log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1 -LOCAL_OBJECT_START(Constants_Q) -//data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 -//data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 -//data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 -//data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 -//data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 -//data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 -data8 0xB172180000000000,0x00003FFE -data8 0x82E308654361C4C6,0x0000BFE2 -data8 0xCCCCCAF2328833CB,0x00003FFC -data8 0x80000077A9D4BAFB,0x0000BFFD -data8 0xAAAAAAAAAAABE3D2,0x00003FFD -data8 0xFFFFFFFFFFFFDAB7,0x0000BFFD -LOCAL_OBJECT_END(Constants_Q) - -// 1/ln10_hi, 1/ln10_lo - -LOCAL_OBJECT_START(Constants_1_by_LN10) -//data4 0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000 -//data4 0xACCF70C8,0xD56EAABE,0x00003FBB,0x00000000 -data8 0xDE5BD8A937287195,0x00003FFD -data8 0xD56EAABEACCF70C8,0x00003FBB -LOCAL_OBJECT_END(Constants_1_by_LN10) - - -// Z1 - 16 bit fixed +.align 64 +Constants_Q: +ASM_TYPE_DIRECTIVE(Constants_Q,@object) +data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 +data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 +data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 +data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 +data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 +data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 +ASM_SIZE_DIRECTIVE(Constants_Q) -LOCAL_OBJECT_START(Constants_Z_1) -data4 0x00008000 -data4 0x00007879 -data4 0x000071C8 -data4 0x00006BCB -data4 0x00006667 -data4 0x00006187 -data4 0x00005D18 -data4 0x0000590C -data4 0x00005556 -data4 0x000051EC -data4 0x00004EC5 -data4 0x00004BDB -data4 0x00004925 -data4 0x0000469F -data4 0x00004445 -data4 0x00004211 -LOCAL_OBJECT_END(Constants_Z_1) - -// G1 and H1 - IEEE single and h1 - IEEE double - -LOCAL_OBJECT_START(Constants_G_H_h1) -data4 0x3F800000,0x00000000 -data8 0x0000000000000000 -data4 0x3F70F0F0,0x3D785196 -data8 0x3DA163A6617D741C -data4 0x3F638E38,0x3DF13843 -data8 0x3E2C55E6CBD3D5BB -data4 0x3F579430,0x3E2FF9A0 -data8 0xBE3EB0BFD86EA5E7 -data4 0x3F4CCCC8,0x3E647FD6 -data8 0x3E2E6A8C86B12760 -data4 0x3F430C30,0x3E8B3AE7 -data8 0x3E47574C5C0739BA -data4 0x3F3A2E88,0x3EA30C68 -data8 0x3E20E30F13E8AF2F -data4 0x3F321640,0x3EB9CEC8 -data8 0xBE42885BF2C630BD -data4 0x3F2AAAA8,0x3ECF9927 -data8 0x3E497F3497E577C6 -data4 0x3F23D708,0x3EE47FC5 -data8 0x3E3E6A6EA6B0A5AB -data4 0x3F1D89D8,0x3EF8947D -data8 0xBDF43E3CD328D9BE -data4 0x3F17B420,0x3F05F3A1 -data8 0x3E4094C30ADB090A -data4 0x3F124920,0x3F0F4303 -data8 0xBE28FBB2FC1FE510 -data4 0x3F0D3DC8,0x3F183EBF -data8 0x3E3A789510FDE3FA -data4 0x3F088888,0x3F20EC80 -data8 0x3E508CE57CC8C98F -data4 0x3F042108,0x3F29516A -data8 0xBE534874A223106C -LOCAL_OBJECT_END(Constants_G_H_h1) - -// Z2 - 16 bit fixed - -LOCAL_OBJECT_START(Constants_Z_2) -data4 0x00008000 -data4 0x00007F81 -data4 0x00007F02 -data4 0x00007E85 -data4 0x00007E08 -data4 0x00007D8D -data4 0x00007D12 -data4 0x00007C98 -data4 0x00007C20 -data4 0x00007BA8 -data4 0x00007B31 -data4 0x00007ABB -data4 0x00007A45 -data4 0x000079D1 -data4 0x0000795D -data4 0x000078EB -LOCAL_OBJECT_END(Constants_Z_2) - -// G2 and H2 - IEEE single and h2 - IEEE double - -LOCAL_OBJECT_START(Constants_G_H_h2) -data4 0x3F800000,0x00000000 -data8 0x0000000000000000 -data4 0x3F7F00F8,0x3B7F875D -data8 0x3DB5A11622C42273 -data4 0x3F7E03F8,0x3BFF015B -data8 0x3DE620CF21F86ED3 -data4 0x3F7D08E0,0x3C3EE393 -data8 0xBDAFA07E484F34ED -data4 0x3F7C0FC0,0x3C7E0586 -data8 0xBDFE07F03860BCF6 -data4 0x3F7B1880,0x3C9E75D2 -data8 0x3DEA370FA78093D6 -data4 0x3F7A2328,0x3CBDC97A -data8 0x3DFF579172A753D0 -data4 0x3F792FB0,0x3CDCFE47 -data8 0x3DFEBE6CA7EF896B -data4 0x3F783E08,0x3CFC15D0 -data8 0x3E0CF156409ECB43 -data4 0x3F774E38,0x3D0D874D -data8 0xBE0B6F97FFEF71DF -data4 0x3F766038,0x3D1CF49B -data8 0xBE0804835D59EEE8 -data4 0x3F757400,0x3D2C531D -data8 0x3E1F91E9A9192A74 -data4 0x3F748988,0x3D3BA322 -data8 0xBE139A06BF72A8CD -data4 0x3F73A0D0,0x3D4AE46F -data8 0x3E1D9202F8FBA6CF -data4 0x3F72B9D0,0x3D5A1756 -data8 0xBE1DCCC4BA796223 -data4 0x3F71D488,0x3D693B9D -data8 0xBE049391B6B7C239 -LOCAL_OBJECT_END(Constants_G_H_h2) - -// G3 and H3 - IEEE single and h3 - IEEE double - -LOCAL_OBJECT_START(Constants_G_H_h3) -data4 0x3F7FFC00,0x38800100 -data8 0x3D355595562224CD -data4 0x3F7FF400,0x39400480 -data8 0x3D8200A206136FF6 -data4 0x3F7FEC00,0x39A00640 -data8 0x3DA4D68DE8DE9AF0 -data4 0x3F7FE400,0x39E00C41 -data8 0xBD8B4291B10238DC -data4 0x3F7FDC00,0x3A100A21 -data8 0xBD89CCB83B1952CA -data4 0x3F7FD400,0x3A300F22 -data8 0xBDB107071DC46826 -data4 0x3F7FCC08,0x3A4FF51C -data8 0x3DB6FCB9F43307DB -data4 0x3F7FC408,0x3A6FFC1D -data8 0xBD9B7C4762DC7872 -data4 0x3F7FBC10,0x3A87F20B -data8 0xBDC3725E3F89154A -data4 0x3F7FB410,0x3A97F68B -data8 0xBD93519D62B9D392 -data4 0x3F7FAC18,0x3AA7EB86 -data8 0x3DC184410F21BD9D -data4 0x3F7FA420,0x3AB7E101 -data8 0xBDA64B952245E0A6 -data4 0x3F7F9C20,0x3AC7E701 -data8 0x3DB4B0ECAABB34B8 -data4 0x3F7F9428,0x3AD7DD7B -data8 0x3D9923376DC40A7E -data4 0x3F7F8C30,0x3AE7D474 -data8 0x3DC6E17B4F2083D3 -data4 0x3F7F8438,0x3AF7CBED -data8 0x3DAE314B811D4394 -data4 0x3F7F7C40,0x3B03E1F3 -data8 0xBDD46F21B08F2DB1 -data4 0x3F7F7448,0x3B0BDE2F -data8 0xBDDC30A46D34522B -data4 0x3F7F6C50,0x3B13DAAA -data8 0x3DCB0070B1F473DB -data4 0x3F7F6458,0x3B1BD766 -data8 0xBDD65DDC6AD282FD -data4 0x3F7F5C68,0x3B23CC5C -data8 0xBDCDAB83F153761A -data4 0x3F7F5470,0x3B2BC997 -data8 0xBDDADA40341D0F8F -data4 0x3F7F4C78,0x3B33C711 -data8 0x3DCD1BD7EBC394E8 -data4 0x3F7F4488,0x3B3BBCC6 -data8 0xBDC3532B52E3E695 -data4 0x3F7F3C90,0x3B43BAC0 -data8 0xBDA3961EE846B3DE -data4 0x3F7F34A0,0x3B4BB0F4 -data8 0xBDDADF06785778D4 -data4 0x3F7F2CA8,0x3B53AF6D -data8 0x3DCC3ED1E55CE212 -data4 0x3F7F24B8,0x3B5BA620 -data8 0xBDBA31039E382C15 -data4 0x3F7F1CC8,0x3B639D12 -data8 0x3D635A0B5C5AF197 -data4 0x3F7F14D8,0x3B6B9444 -data8 0xBDDCCB1971D34EFC -data4 0x3F7F0CE0,0x3B7393BC -data8 0x3DC7450252CD7ADA -data4 0x3F7F04F0,0x3B7B8B6D -data8 0xBDB68F177D7F2A42 -LOCAL_OBJECT_END(Constants_G_H_h3) - - -// Floating Point Registers - -FR_Input_X = f8 - -FR_Y_hi = f34 -FR_Y_lo = f35 - -FR_Scale = f36 -FR_X_Prime = f37 -FR_S_hi = f38 -FR_W = f39 -FR_G = f40 - -FR_H = f41 -FR_wsq = f42 -FR_w4 = f43 -FR_h = f44 -FR_w6 = f45 - -FR_G2 = f46 -FR_H2 = f47 -FR_poly_lo = f48 -FR_P8 = f49 -FR_poly_hi = f50 - -FR_P7 = f51 -FR_h2 = f52 -FR_rsq = f53 -FR_P6 = f54 -FR_r = f55 - -FR_log2_hi = f56 -FR_log2_lo = f57 -FR_p87 = f58 -FR_p876 = f58 -FR_p8765 = f58 -FR_float_N = f59 -FR_Q4 = f60 +// Z1 - 16 bit fixed, G1 and H1 - IEEE single + +.align 64 +Constants_Z_G_H_h1: +ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h1,@object) +data4 0x00008000,0x3F800000,0x00000000,0x00000000,0x00000000,0x00000000 +data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000,0x617D741C,0x3DA163A6 +data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000,0xCBD3D5BB,0x3E2C55E6 +data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000,0xD86EA5E7,0xBE3EB0BF +data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000,0x86B12760,0x3E2E6A8C +data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000,0x5C0739BA,0x3E47574C +data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000,0x13E8AF2F,0x3E20E30F +data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000,0xF2C630BD,0xBE42885B +data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000,0x97E577C6,0x3E497F34 +data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000,0xA6B0A5AB,0x3E3E6A6E +data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000,0xD328D9BE,0xBDF43E3C +data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000,0x0ADB090A,0x3E4094C3 +data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000,0xFC1FE510,0xBE28FBB2 +data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000,0x10FDE3FA,0x3E3A7895 +data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000,0x7CC8C98F,0x3E508CE5 +data4 0x00004211,0x3F042108,0x3F29516A,0x00000000,0xA223106C,0xBE534874 +ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h1) + +// Z2 - 16 bit fixed, G2 and H2 - IEEE single + +.align 64 +Constants_Z_G_H_h2: +ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h2,@object) +data4 0x00008000,0x3F800000,0x00000000,0x00000000,0x00000000,0x00000000 +data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000,0x22C42273,0x3DB5A116 +data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000,0x21F86ED3,0x3DE620CF +data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000,0x484F34ED,0xBDAFA07E +data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000,0x3860BCF6,0xBDFE07F0 +data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000,0xA78093D6,0x3DEA370F +data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000,0x72A753D0,0x3DFF5791 +data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000,0xA7EF896B,0x3DFEBE6C +data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000,0x409ECB43,0x3E0CF156 +data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000,0xFFEF71DF,0xBE0B6F97 +data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000,0x5D59EEE8,0xBE080483 +data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000,0xA9192A74,0x3E1F91E9 +data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000,0xBF72A8CD,0xBE139A06 +data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000,0xF8FBA6CF,0x3E1D9202 +data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000,0xBA796223,0xBE1DCCC4 +data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000,0xB6B7C239,0xBE049391 +ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h2) + +// G3 and H3 - IEEE single and h3 -IEEE double + +.align 64 +Constants_Z_G_H_h3: +ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h3,@object) +data4 0x3F7FFC00,0x38800100,0x562224CD,0x3D355595 +data4 0x3F7FF400,0x39400480,0x06136FF6,0x3D8200A2 +data4 0x3F7FEC00,0x39A00640,0xE8DE9AF0,0x3DA4D68D +data4 0x3F7FE400,0x39E00C41,0xB10238DC,0xBD8B4291 +data4 0x3F7FDC00,0x3A100A21,0x3B1952CA,0xBD89CCB8 +data4 0x3F7FD400,0x3A300F22,0x1DC46826,0xBDB10707 +data4 0x3F7FCC08,0x3A4FF51C,0xF43307DB,0x3DB6FCB9 +data4 0x3F7FC408,0x3A6FFC1D,0x62DC7872,0xBD9B7C47 +data4 0x3F7FBC10,0x3A87F20B,0x3F89154A,0xBDC3725E +data4 0x3F7FB410,0x3A97F68B,0x62B9D392,0xBD93519D +data4 0x3F7FAC18,0x3AA7EB86,0x0F21BD9D,0x3DC18441 +data4 0x3F7FA420,0x3AB7E101,0x2245E0A6,0xBDA64B95 +data4 0x3F7F9C20,0x3AC7E701,0xAABB34B8,0x3DB4B0EC +data4 0x3F7F9428,0x3AD7DD7B,0x6DC40A7E,0x3D992337 +data4 0x3F7F8C30,0x3AE7D474,0x4F2083D3,0x3DC6E17B +data4 0x3F7F8438,0x3AF7CBED,0x811D4394,0x3DAE314B +data4 0x3F7F7C40,0x3B03E1F3,0xB08F2DB1,0xBDD46F21 +data4 0x3F7F7448,0x3B0BDE2F,0x6D34522B,0xBDDC30A4 +data4 0x3F7F6C50,0x3B13DAAA,0xB1F473DB,0x3DCB0070 +data4 0x3F7F6458,0x3B1BD766,0x6AD282FD,0xBDD65DDC +data4 0x3F7F5C68,0x3B23CC5C,0xF153761A,0xBDCDAB83 +data4 0x3F7F5470,0x3B2BC997,0x341D0F8F,0xBDDADA40 +data4 0x3F7F4C78,0x3B33C711,0xEBC394E8,0x3DCD1BD7 +data4 0x3F7F4488,0x3B3BBCC6,0x52E3E695,0xBDC3532B +data4 0x3F7F3C90,0x3B43BAC0,0xE846B3DE,0xBDA3961E +data4 0x3F7F34A0,0x3B4BB0F4,0x785778D4,0xBDDADF06 +data4 0x3F7F2CA8,0x3B53AF6D,0xE55CE212,0x3DCC3ED1 +data4 0x3F7F24B8,0x3B5BA620,0x9E382C15,0xBDBA3103 +data4 0x3F7F1CC8,0x3B639D12,0x5C5AF197,0x3D635A0B +data4 0x3F7F14D8,0x3B6B9444,0x71D34EFC,0xBDDCCB19 +data4 0x3F7F0CE0,0x3B7393BC,0x52CD7ADA,0x3DC74502 +data4 0x3F7F04F0,0x3B7B8B6D,0x7D7F2A42,0xBDB68F17 +ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h3) + +// +// Exponent Thresholds and Tiny Thresholds +// for 8, 11, 15, and 17 bit exponents +// +// Expo_Range Value +// +// 0 (8 bits) 2^(-126) +// 1 (11 bits) 2^(-1022) +// 2 (15 bits) 2^(-16382) +// 3 (17 bits) 2^(-16382) +// +// Tiny_Table +// ---------- +// Expo_Range Value +// +// 0 (8 bits) 2^(-16382) +// 1 (11 bits) 2^(-16382) +// 2 (15 bits) 2^(-16382) +// 3 (17 bits) 2^(-16382) +// -FR_p43 = f61 -FR_p432 = f61 -FR_p4321 = f61 -FR_P4 = f62 -FR_G3 = f63 -FR_H3 = f64 -FR_h3 = f65 +.align 64 +Constants_Threshold: +ASM_TYPE_DIRECTIVE(Constants_Threshold,@object) +data4 0x00000000,0x80000000,0x00003F81,0x00000000 +data4 0x00000000,0x80000000,0x00000001,0x00000000 +data4 0x00000000,0x80000000,0x00003C01,0x00000000 +data4 0x00000000,0x80000000,0x00000001,0x00000000 +data4 0x00000000,0x80000000,0x00000001,0x00000000 +data4 0x00000000,0x80000000,0x00000001,0x00000000 +data4 0x00000000,0x80000000,0x00000001,0x00000000 +data4 0x00000000,0x80000000,0x00000001,0x00000000 +ASM_SIZE_DIRECTIVE(Constants_Threshold) -FR_Q3 = f66 -FR_P3 = f67 -FR_Q2 = f68 -FR_P2 = f69 -FR_1LN10_hi = f70 +.align 64 +Constants_1_by_LN10: +ASM_TYPE_DIRECTIVE(Constants_1_by_LN10,@object) +data4 0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000 +data4 0xACCF70C8,0xD56EAABE,0x00003FBB,0x00000000 +ASM_SIZE_DIRECTIVE(Constants_1_by_LN10) + +FR_Input_X = f8 +FR_Neg_One = f9 +FR_E = f33 +FR_Em1 = f34 +FR_Y_hi = f34 +// Shared with Em1 +FR_Y_lo = f35 +FR_Scale = f36 +FR_X_Prime = f37 +FR_Z = f38 +FR_S_hi = f38 +// Shared with Z +FR_W = f39 +FR_G = f40 +FR_wsq = f40 +// Shared with G +FR_H = f41 +FR_w4 = f41 +// Shared with H +FR_h = f42 +FR_w6 = f42 +// Shared with h +FR_G_tmp = f43 +FR_poly_lo = f43 +// Shared with G_tmp +FR_P8 = f43 +// Shared with G_tmp +FR_H_tmp = f44 +FR_poly_hi = f44 + // Shared with H_tmp +FR_P7 = f44 +// Shared with H_tmp +FR_h_tmp = f45 +FR_rsq = f45 +// Shared with h_tmp +FR_P6 = f45 +// Shared with h_tmp +FR_abs_W = f46 +FR_r = f46 +// Shared with abs_W +FR_AA = f47 +FR_log2_hi = f47 +// Shared with AA +FR_BB = f48 +FR_log2_lo = f48 +// Shared with BB +FR_S_lo = f49 +FR_two_negN = f50 +FR_float_N = f51 +FR_Q4 = f52 +FR_dummy = f52 +// Shared with Q4 +FR_P4 = f52 +// Shared with Q4 +FR_Threshold = f52 +// Shared with Q4 +FR_Q3 = f53 +FR_P3 = f53 +// Shared with Q3 +FR_Tiny = f53 +// Shared with Q3 +FR_Q2 = f54 +FR_P2 = f54 +// Shared with Q2 +FR_1LN10_hi = f54 +// Shared with Q2 +FR_Q1 = f55 +FR_P1 = f55 +// Shared with Q1 +FR_1LN10_lo = f55 +// Shared with Q1 +FR_P5 = f98 +FR_SCALE = f98 +FR_Output_X_tmp = f99 + +GR_Expo_Range = r32 +GR_Table_Base = r34 +GR_Table_Base1 = r35 +GR_Table_ptr = r36 +GR_Index2 = r37 +GR_signif = r38 +GR_X_0 = r39 +GR_X_1 = r40 +GR_X_2 = r41 +GR_Z_1 = r42 +GR_Z_2 = r43 +GR_N = r44 +GR_Bias = r45 +GR_M = r46 +GR_ScaleN = r47 +GR_Index3 = r48 +GR_Perturb = r49 +GR_Table_Scale = r50 -FR_Q1 = f71 -FR_P1 = f72 -FR_1LN10_lo = f73 -FR_P5 = f74 -FR_rcub = f75 +// +// Added for unwind support +// -FR_Output_X_tmp = f76 -FR_Neg_One = f77 -FR_Z = f78 -FR_AA = f79 -FR_BB = f80 -FR_S_lo = f81 -FR_2_to_minus_N = f82 +GR_SAVE_PFS = r51 +GR_SAVE_B0 = r52 +GR_SAVE_GP = r53 +GR_Parameter_X = r54 +GR_Parameter_Y = r55 +GR_Parameter_RESULT = r56 +GR_Parameter_TAG = r57 FR_X = f8 FR_Y = f0 -FR_RESULT = f76 - +FR_RESULT = f99 -// General Purpose Registers +.section .text +.proc logl# +.global logl# +.align 64 +logl: +#ifdef _LIBC +.global __ieee754_logl +__ieee754_logl: +#endif +{ .mfi +alloc r32 = ar.pfs,0,22,4,0 +(p0) fnorm.s1 FR_X_Prime = FR_Input_X +(p0) cmp.eq.unc p7, p0 = r0, r0 +} +{ .mfi +(p0) cmp.ne.unc p14, p0 = r0, r0 +(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3 +(p0) cmp.ne.unc p15, p0 = r0, r0 ;; +} +{ .mfi + nop.m 0 +(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF + nop.i 0 +} +{ .mfi +nop.m 999 +(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, f0 + nop.i 0 +} +{ .mfi + nop.m 999 +(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, f0 + nop.i 0 +} +{ .mfi + nop.m 999 +(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f1 + nop.i 999 ;; +} +{ .mfi + nop.m 999 +(p0) fsub.s1 FR_Em1 = f0,f1 + nop.i 999 +} +{ .mfb + nop.m 999 +(p0) fadd FR_E = f0,f0 +// +// Create E = 0 and Em1 = -1 +// Check for X == 1, meaning logl(1) +// Check for X < 0, meaning logl(negative) +// Check for X == 0, meaning logl(0) +// Identify NatVals, NaNs, Infs. +// Identify EM unsupporteds. +// Identify Negative values - us S1 so as +// not to raise denormal operand exception +// Set p15 to false for log +// Set p14 to false for log +// Set p7 true for log and log1p +// +(p0) br.cond.sptk L(LOGL_BEGIN) ;; +} -GR_ad_p = r33 -GR_Index1 = r34 -GR_Index2 = r35 -GR_signif = r36 -GR_X_0 = r37 -GR_X_1 = r38 -GR_X_2 = r39 -GR_minus_N = r39 -GR_Z_1 = r40 -GR_Z_2 = r41 -GR_N = r42 -GR_Bias = r43 -GR_M = r44 -GR_Index3 = r45 -GR_exp_2tom80 = r45 -GR_ad_p2 = r46 -GR_exp_mask = r47 -GR_exp_2tom7 = r48 -GR_ad_ln10 = r49 -GR_ad_tbl_1 = r50 -GR_ad_tbl_2 = r51 -GR_ad_tbl_3 = r52 -GR_ad_q = r53 -GR_ad_z_1 = r54 -GR_ad_z_2 = r55 -GR_ad_z_3 = r56 -GR_minus_N = r39 +.endp logl +ASM_SIZE_DIRECTIVE(logl) -// -// Added for unwind support -// +.section .text +.proc log10l# +.global log10l# +.align 64 +log10l: +#ifdef _LIBC +.global __ieee754_log10l +__ieee754_log10l: +#endif +{ .mfi +alloc r32 = ar.pfs,0,22,4,0 +(p0) fadd FR_E = f0,f0 + nop.i 0 +} +{ .mfi + nop.m 0 +(p0) fsub.s1 FR_Em1 = f0,f1 + nop.i 0 +} +{ .mfi +(p0) cmp.ne.unc p15, p0 = r0, r0 +(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f1 + nop.i 0 +} +{ .mfi +(p0) cmp.eq.unc p14, p0 = r0, r0 +(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, f0 +(p0) cmp.ne.unc p7, p0 = r0, r0 ;; +} +{ .mfi + nop.m 999 +(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, f0 + nop.i 999 +} +{ .mfi + nop.m 999 +(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF + nop.i 999 ;; +} +{ .mfi + nop.m 999 +(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3 + nop.i 999 +} +{ .mfb + nop.m 999 +(p0) fnorm.s1 FR_X_Prime = FR_Input_X +// +// Create E = 0 and Em1 = -1 +// Check for X == 1, meaning logl(1) +// Check for X < 0, meaning logl(negative) +// Check for X == 0, meaning logl(0) +// Identify NatVals, NaNs, Infs. +// Identify EM unsupporteds. +// Identify Negative values - us S1 so as +// Identify Negative values - us S1 so as +// not to raise denormal operand exception +// Set p15 to false for log10 +// Set p14 to true for log10 +// Set p7 to false for log10 +// +(p0) br.cond.sptk L(LOGL_BEGIN) ;; +} -GR_SAVE_PFS = r50 -GR_SAVE_B0 = r51 -GR_SAVE_GP = r52 -GR_Parameter_X = r53 -GR_Parameter_Y = r54 -GR_Parameter_RESULT = r55 -GR_Parameter_TAG = r56 +.endp log10l +ASM_SIZE_DIRECTIVE(log10l) .section .text -GLOBAL_IEEE754_ENTRY(log1pl) +.proc log1pl# +.global log1pl# +.align 64 +log1pl: +#ifdef _LIBC +.global __log1pl +__log1pl: +#endif { .mfi - alloc r32 = ar.pfs,0,21,4,0 - fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf - nop.i 999 +alloc r32 = ar.pfs,0,22,4,0 +(p0) fsub.s1 FR_Neg_One = f0,f1 +(p0) cmp.eq.unc p7, p0 = r0, r0 } { .mfi - addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp - fma.s1 FR_Z = FR_Input_X, f1, f1 // x+1 - nop.i 999 +(p0) cmp.ne.unc p14, p0 = r0, r0 +(p0) fnorm.s1 FR_X_Prime = FR_Input_X +(p0) cmp.eq.unc p15, p0 = r0, r0 ;; +} +{ .mfi + nop.m 0 +(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3 + nop.i 0 } -;; - { .mfi nop.m 999 - fmerge.ns FR_Neg_One = f1, f1 // Form -1.0 - nop.i 999 +(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF + nop.i 0 } { .mfi nop.m 999 - fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x - nop.i 999 +(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f0 + nop.i 0 } -;; - { .mfi - ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1 - nop.f 999 - mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 + nop.m 999 +(p0) fadd FR_Em1 = f0,f0 + nop.i 999 ;; } -;; - -{ .mfb - getf.sig GR_signif = FR_Z // Get significand of x+1 - fcmp.eq.s1 p9, p0 = FR_Input_X, f0 // Test for x=0 -(p6) br.cond.spnt LOG1P_special // Branch for nan, inf, natval +{ .mfi + nop.m 999 +(p0) fadd FR_E = f0,f1 + nop.i 999 ;; } -;; - { .mfi - add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 - fcmp.lt.s1 p13, p0 = FR_X_Prime, FR_Neg_One // Test for x<-1 - add GR_ad_p = -0x100, GR_ad_z_1 // Point to Constants_P + nop.m 999 +(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, FR_Neg_One + nop.i 999 } { .mfi - add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 - nop.f 999 - add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 + nop.m 999 +(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, FR_Neg_One + nop.i 999 } -;; - +L(LOGL_BEGIN): { .mfi - add GR_ad_q = 0x080, GR_ad_p // Point to Constants_Q - fcmp.eq.s1 p8, p0 = FR_X_Prime, FR_Neg_One // Test for x=-1 - extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif + nop.m 999 +(p0) fadd.s1 FR_Z = FR_X_Prime, FR_E + nop.i 999 } -{ .mfb - add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3 - nop.f 999 -(p9) br.ret.spnt b0 // Exit if x=0, return input +{ .mlx + nop.m 999 +(p0) movl GR_Table_Scale = 0x0000000000000018 ;; } -;; - -{ .mfi - shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 - fclass.nm p10, p0 = FR_Input_X, 0x1FF // Test for unsupported - extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of significand +{ .mmi + nop.m 999 + nop.m 999 +// +// Create E = 1 and Em1 = 0 +// Check for X == 0, meaning logl(1+0) +// Check for X < -1, meaning logl(negative) +// Check for X == -1, meaning logl(0) +// Normalize x +// Identify NatVals, NaNs, Infs. +// Identify EM unsupporteds. +// Identify Negative values - us S1 so as +// not to raise denormal operand exception +// Set p15 to true for log1p +// Set p14 to false for log1p +// Set p7 true for log and log1p +// +(p0) addl GR_Table_Base = @ltoff(Constants_Z_G_H_h1#),gp } { .mfi - ldfe FR_P8 = [GR_ad_p],16 // Load P_8 for near1 path - fsub.s1 FR_W = FR_X_Prime, f0 // W = x - add GR_ad_ln10 = 0x060, GR_ad_q // Point to Constants_1_by_LN10 + nop.m 999 +(p0) fmax.s1 FR_AA = FR_X_Prime, FR_E + nop.i 999 ;; } -;; - { .mfi - ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 - fmax.s1 FR_AA = FR_X_Prime, f1 // For S_lo, form AA = max(X,1.0) - mov GR_exp_mask = 0x1FFFF // Create exponent mask + ld8 GR_Table_Base = [GR_Table_Base] +(p0) fmin.s1 FR_BB = FR_X_Prime, FR_E + nop.i 999 +} +{ .mfb + nop.m 999 +(p0) fadd.s1 FR_W = FR_X_Prime, FR_Em1 +// +// Begin load of constants base +// FR_Z = Z = |x| + E +// FR_W = W = |x| + Em1 +// AA = fmax(|x|,E) +// BB = fmin(|x|,E) +// +(p6) br.cond.spnt L(LOGL_64_special) ;; } { .mib - shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 - mov GR_Bias = 0x0FFFF // Create exponent bias -(p13) br.cond.spnt LOG1P_LT_Minus_1 // Branch if x<-1 + nop.m 999 + nop.i 999 +(p10) br.cond.spnt L(LOGL_64_unsupported) ;; } -;; - -{ .mfb - ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 - fmerge.se FR_S_hi = f1,FR_Z // Form |x+1| -(p8) br.cond.spnt LOG1P_EQ_Minus_1 // Branch if x=-1 +{ .mib + nop.m 999 + nop.i 999 +(p13) br.cond.spnt L(LOGL_64_negative) ;; } -;; - -{ .mmb - getf.exp GR_N = FR_Z // Get N = exponent of x+1 - ldfd FR_h = [GR_ad_tbl_1] // Load h_1 -(p10) br.cond.spnt LOG1P_unsupported // Branch for unsupported type +{ .mib +(p0) getf.sig GR_signif = FR_Z + nop.i 999 +(p9) br.cond.spnt L(LOGL_64_one) ;; } -;; - -{ .mfi - ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi - fcmp.eq.s0 p8, p0 = FR_Input_X, f0 // Dummy op to flag denormals - pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1 +{ .mib + nop.m 999 + nop.i 999 +(p8) br.cond.spnt L(LOGL_64_zero) ;; } -;; - +{ .mfi +(p0) getf.exp GR_N = FR_Z +// +// Raise possible denormal operand exception +// Create Bias +// +// This function computes ln( x + e ) +// Input FR 1: FR_X = FR_Input_X +// Input FR 2: FR_E = FR_E +// Input FR 3: FR_Em1 = FR_Em1 +// Input GR 1: GR_Expo_Range = GR_Expo_Range = 1 +// Output FR 4: FR_Y_hi +// Output FR 5: FR_Y_lo +// Output FR 6: FR_Scale +// Output PR 7: PR_Safe // -// For performance, don't use result of pmpyshr2.u for 4 cycles. +(p0) fsub.s1 FR_S_lo = FR_AA, FR_Z // +// signif = getf.sig(Z) +// abs_W = fabs(w) +// +(p0) extr.u GR_Table_ptr = GR_signif, 59, 4 ;; +} +{ .mfi + nop.m 999 +(p0) fmerge.se FR_S_hi = f1,FR_Z +(p0) extr.u GR_X_0 = GR_signif, 49, 15 +} { .mmi - ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo - sub GR_N = GR_N, GR_Bias - mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80 + nop.m 999 + nop.m 999 +(p0) addl GR_Table_Base1 = @ltoff(Constants_Z_G_H_h2#),gp ;; +} +{ .mlx + ld8 GR_Table_Base1 = [GR_Table_Base1] +(p0) movl GR_Bias = 0x000000000000FFFF ;; } -;; - { .mfi - ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 - fms.s1 FR_S_lo = FR_AA, f1, FR_Z // Form S_lo = AA - Z - sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N) + nop.m 999 +(p0) fabs FR_abs_W = FR_W +(p0) pmpyshr2.u GR_Table_ptr = GR_Table_ptr,GR_Table_Scale,0 } -;; - -{ .mmf - ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 - setf.sig FR_float_N = GR_N // Put integer N into rightmost significand - fmin.s1 FR_BB = FR_X_Prime, f1 // For S_lo, form BB = min(X,1.0) +{ .mfi + nop.m 999 +// +// Branch out for special input values +// +(p0) fcmp.lt.unc.s0 p8, p0 = FR_Input_X, f0 + nop.i 999 ;; } -;; - +{ .mfi + nop.m 999 +// +// X_0 = extr.u(signif,49,15) +// Index1 = extr.u(signif,59,4) +// +(p0) fadd.s1 FR_S_lo = FR_S_lo, FR_BB + nop.i 999 ;; +} +{ .mii + nop.m 999 + nop.i 999 ;; +// +// Offset_to_Z1 = 24 * Index1 +// For performance, don't use result +// for 3 or 4 cycles. +// +(p0) add GR_Table_ptr = GR_Table_ptr, GR_Table_Base ;; +} +// +// Add Base to Offset for Z1 +// Create Bias { .mmi - getf.exp GR_M = FR_W // Get signexp of w = x - ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 - extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 +(p0) ld4 GR_Z_1 = [GR_Table_ptr],4 ;; +(p0) ldfs FR_G = [GR_Table_ptr],4 + nop.i 999 ;; } -;; - { .mmi - ldfe FR_Q1 = [GR_ad_q] // Load Q1 - shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 - add GR_ad_p2 = 0x30,GR_ad_p // Point to P_4 +(p0) ldfs FR_H = [GR_Table_ptr],8 ;; +(p0) ldfd FR_h = [GR_Table_ptr],0 +(p0) pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 +} +// +// Load Z_1 +// Get Base of Table2 +// +{ .mfi +(p0) getf.exp GR_M = FR_abs_W + nop.f 999 + nop.i 999 ;; +} +{ .mii + nop.m 999 + nop.i 999 ;; +// +// M = getf.exp(abs_W) +// S_lo = AA - Z +// X_1 = pmpyshr2(X_0,Z_1,15) +// +(p0) sub GR_M = GR_M, GR_Bias ;; +} +// +// M = M - Bias +// Load G1 +// N = getf.exp(Z) +// +{ .mii +(p0) cmp.gt.unc p11, p0 = -80, GR_M +(p0) cmp.gt.unc p12, p0 = -7, GR_M ;; +(p0) extr.u GR_Index2 = GR_X_1, 6, 4 ;; +} +{ .mib + nop.m 999 +// +// if -80 > M, set p11 +// Index2 = extr.u(X_1,6,4) +// if -7 > M, set p12 +// Load H1 +// +(p0) pmpyshr2.u GR_Index2 = GR_Index2,GR_Table_Scale,0 +(p11) br.cond.spnt L(log1pl_small) ;; +} +{ .mib + nop.m 999 + nop.i 999 +(p12) br.cond.spnt L(log1pl_near) ;; +} +{ .mii +(p0) sub GR_N = GR_N, GR_Bias +// +// poly_lo = r * poly_lo +// +(p0) add GR_Perturb = 0x1, r0 ;; +(p0) sub GR_ScaleN = GR_Bias, GR_N +} +{ .mii +(p0) setf.sig FR_float_N = GR_N + nop.i 999 ;; +// +// Prepare Index2 - pmpyshr2.u(X_1,Z_2,15) +// Load h1 +// S_lo = S_lo + BB +// Branch for -80 > M +// +(p0) add GR_Index2 = GR_Index2, GR_Table_Base1 } -;; - { .mmi - ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 - shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2 - and GR_M = GR_exp_mask, GR_M // Get exponent of w = x +(p0) setf.exp FR_two_negN = GR_ScaleN + nop.m 999 +(p0) addl GR_Table_Base = @ltoff(Constants_Z_G_H_h3#),gp ;; } -;; - +// +// Index2 points to Z2 +// Branch for -7 > M +// +{ .mmb +(p0) ld4 GR_Z_2 = [GR_Index2],4 +(p0) ld8 GR_Table_Base = [GR_Table_Base] + nop.b 999 ;; +} +(p0) nop.i 999 +// +// Load Z_2 +// N = N - Bias +// Tablebase points to Table3 +// { .mmi - ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 - cmp.lt p8, p9 = GR_M, GR_exp_2tom7 // Test |x| < 2^-7 - cmp.lt p7, p0 = GR_M, GR_exp_2tom80 // Test |x| < 2^-80 +(p0) ldfs FR_G_tmp = [GR_Index2],4 ;; +// +// Load G_2 +// pmpyshr2 X_2= (X_1,Z_2,15) +// float_N = setf.sig(N) +// ScaleN = Bias - N +// +(p0) ldfs FR_H_tmp = [GR_Index2],8 + nop.i 999 ;; } -;; - -// Small path is separate code -// p7 is for the small path: |x| < 2^-80 -// near1 and regular paths are merged. -// p8 is for the near1 path: |x| < 2^-7 -// p9 is for regular path: |x| >= 2^-7 - +// +// Load H_2 +// two_negN = setf.exp(scaleN) +// G = G_1 * G_2 +// { .mfi - ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 - nop.f 999 - nop.i 999 +(p0) ldfd FR_h_tmp = [GR_Index2],0 + nop.f 999 +(p0) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 ;; } -{ .mfb -(p9) setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N) -(p7) fnma.s0 f8 = FR_X_Prime, FR_X_Prime, FR_X_Prime // Result x - x*x -(p7) br.ret.spnt b0 // Branch if |x| < 2^-80 +{ .mii + nop.m 999 +(p0) extr.u GR_Index3 = GR_X_2, 1, 5 ;; +// +// Load h_2 +// H = H_1 + H_2 +// h = h_1 + h_2 +// Index3 = extr.u(X_2,1,5) +// +(p0) shladd GR_Index3 = GR_Index3,4,GR_Table_Base } -;; - { .mmi -(p8) ldfe FR_P7 = [GR_ad_p],16 // Load P_7 for near1 path -(p8) ldfe FR_P4 = [GR_ad_p2],16 // Load P_4 for near1 path -(p9) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2 + nop.m 999 + nop.m 999 +// +// float_N = fcvt.xf(float_N) +// load G3 +// +(p0) addl GR_Table_Base = @ltoff(Constants_Q#),gp ;; } -;; +{ .mmi + nop.m 999 + ld8 GR_Table_Base = [GR_Table_Base] + nop.i 999 +};; +{ .mfi +(p0) ldfe FR_log2_hi = [GR_Table_Base],16 +(p0) fmpy.s1 FR_S_lo = FR_S_lo, FR_two_negN + nop.i 999 ;; +} +{ .mmf + nop.m 999 // -// For performance, don't use result of pmpyshr2.u for 4 cycles. +// G = G3 * G +// Load h3 +// Load log2_hi +// H = H + H3 // +(p0) ldfe FR_log2_lo = [GR_Table_Base],16 +(p0) fmpy.s1 FR_G = FR_G, FR_G_tmp ;; +} { .mmf -(p8) ldfe FR_P6 = [GR_ad_p],16 // Load P_6 for near1 path -(p8) ldfe FR_P3 = [GR_ad_p2],16 // Load P_3 for near1 path -(p9) fma.s1 FR_S_lo = FR_S_lo, f1, FR_BB // S_lo = S_lo + BB +(p0) ldfs FR_G_tmp = [GR_Index3],4 +// +// h = h + h3 +// r = G * S_hi + 1 +// Load log2_lo +// +(p0) ldfe FR_Q4 = [GR_Table_Base],16 +(p0) fadd.s1 FR_h = FR_h, FR_h_tmp ;; +} +{ .mfi +(p0) ldfe FR_Q3 = [GR_Table_Base],16 +(p0) fadd.s1 FR_H = FR_H, FR_H_tmp + nop.i 999 ;; } -;; - { .mmf -(p8) ldfe FR_P5 = [GR_ad_p],16 // Load P_5 for near1 path -(p8) ldfe FR_P2 = [GR_ad_p2],16 // Load P_2 for near1 path -(p8) fmpy.s1 FR_wsq = FR_W, FR_W // wsq = w * w for near1 path +(p0) ldfs FR_H_tmp = [GR_Index3],4 +(p0) ldfe FR_Q2 = [GR_Table_Base],16 +// +// Comput Index for Table3 +// S_lo = S_lo * two_negN +// +(p0) fcvt.xf FR_float_N = FR_float_N ;; } -;; - -{ .mmi -(p8) ldfe FR_P1 = [GR_ad_p2],16 ;; // Load P_1 for near1 path - nop.m 999 -(p9) extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 +// +// If S_lo == 0, set p8 false +// Load H3 +// Load ptr to table of polynomial coeff. +// +{ .mmf +(p0) ldfd FR_h_tmp = [GR_Index3],0 +(p0) ldfe FR_Q1 = [GR_Table_Base],0 +(p0) fcmp.eq.unc.s1 p0, p8 = FR_S_lo, f0 ;; } -;; - { .mfi -(p9) shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3 -(p9) fcvt.xf FR_float_N = FR_float_N - nop.i 999 + nop.m 999 +(p0) fmpy.s1 FR_G = FR_G, FR_G_tmp + nop.i 999 ;; } -;; - { .mfi -(p9) ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 - nop.f 999 - nop.i 999 + nop.m 999 +(p0) fadd.s1 FR_H = FR_H, FR_H_tmp + nop.i 999 ;; } -;; - { .mfi -(p9) ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 -(p9) fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 - nop.i 999 + nop.m 999 +(p0) fms.s1 FR_r = FR_G, FR_S_hi, f1 + nop.i 999 } { .mfi - nop.m 999 -(p9) fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 - nop.i 999 + nop.m 999 +(p0) fadd.s1 FR_h = FR_h, FR_h_tmp + nop.i 999 ;; } -;; - -{ .mmf - nop.m 999 - nop.m 999 -(p9) fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 +{ .mfi + nop.m 999 +(p0) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p8) fmpy.s1 FR_w4 = FR_wsq, FR_wsq // w4 = w^4 for near1 path - nop.i 999 + nop.m 999 +// +// Load Q4 +// Load Q3 +// Load Q2 +// Load Q1 +// +(p8) fma.s1 FR_r = FR_G, FR_S_lo, FR_r + nop.i 999 } { .mfi - nop.m 999 -(p8) fma.s1 FR_p87 = FR_W, FR_P8, FR_P7 // p87 = w * P8 + P7 - nop.i 999 + nop.m 999 +// +// poly_lo = r * Q4 + Q3 +// rsq = r* r +// +(p0) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p9) fma.s1 FR_S_lo = FR_S_lo, FR_2_to_minus_N, f0 // S_lo = S_lo * 2^(-N) - nop.i 999 + nop.m 999 +// +// If (S_lo!=0) r = s_lo * G + r +// +(p0) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 + nop.i 999 } +// +// Create a 0x00000....01 +// poly_lo = poly_lo * rsq + h +// { .mfi - nop.m 999 -(p8) fma.s1 FR_p43 = FR_W, FR_P4, FR_P3 // p43 = w * P4 + P3 - nop.i 999 +(p0) setf.sig FR_dummy = GR_Perturb +(p0) fmpy.s1 FR_rsq = FR_r, FR_r + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p9) fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 - nop.i 999 + nop.m 999 +// +// h = N * log2_lo + h +// Y_hi = n * log2_hi + H +// +(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 + nop.i 999 } { .mfi - nop.m 999 -(p9) fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p9) fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 - nop.i 999 + nop.m 999 +// +// poly_lo = r * poly_o + Q2 +// poly_hi = Q1 * rsq + r +// +(p0) fmpy.s1 FR_poly_lo = FR_poly_lo, FR_r + nop.i 999 ;; } { .mfi + nop.m 999 +(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_rsq, FR_h + nop.i 999 ;; +} +{ .mfb + nop.m 999 +(p0) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo +// +// Create the FR for a binary "or" +// Y_lo = poly_hi + poly_lo +// +// (p0) for FR_dummy = FR_Y_lo,FR_dummy ;; +// +// Turn the lsb of Y_lo ON +// +// (p0) fmerge.se FR_Y_lo = FR_Y_lo,FR_dummy ;; +// +// Merge the new lsb into Y_lo, for alone doesn't +// +(p0) br.cond.sptk LOGL_main ;; +} +L(log1pl_near): +{ .mmi + nop.m 999 + nop.m 999 +// /*******************************************************/ +// /*********** Branch log1pl_near ************************/ +// /*******************************************************/ +(p0) addl GR_Table_Base = @ltoff(Constants_P#),gp ;; +} +{ .mmi nop.m 999 -(p8) fmpy.s1 FR_w6 = FR_w4, FR_wsq // w6 = w^6 for near1 path + ld8 GR_Table_Base = [GR_Table_Base] nop.i 999 +};; +// +// Load base address of poly. coeff. +// +{ .mmb +(p0) add GR_Table_ptr = 0x40,GR_Table_Base +// +// Address tables with separate pointers +// +(p0) ldfe FR_P8 = [GR_Table_Base],16 + nop.b 999 ;; +} +{ .mmb +(p0) ldfe FR_P4 = [GR_Table_ptr],16 +// +// Load P4 +// Load P8 +// +(p0) ldfe FR_P7 = [GR_Table_Base],16 + nop.b 999 ;; +} +{ .mmf +(p0) ldfe FR_P3 = [GR_Table_ptr],16 +// +// Load P3 +// Load P7 +// +(p0) ldfe FR_P6 = [GR_Table_Base],16 +(p0) fmpy.s1 FR_wsq = FR_W, FR_W ;; } -;; - { .mfi - nop.m 999 -(p8) fma.s1 FR_p432 = FR_W, FR_p43, FR_P2 // p432 = w * p43 + P2 - nop.i 999 +(p0) ldfe FR_P2 = [GR_Table_ptr],16 + nop.f 999 + nop.i 999 ;; } { .mfi - nop.m 999 -(p8) fma.s1 FR_p876 = FR_W, FR_p87, FR_P6 // p876 = w * p87 + P6 - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_Y_hi = FR_W, FR_P4, FR_P3 + nop.i 999 } -;; - +// +// Load P2 +// Load P6 +// Wsq = w * w +// Y_hi = p4 * w + p3 +// { .mfi - nop.m 999 -(p9) fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1 - nop.i 999 +(p0) ldfe FR_P5 = [GR_Table_Base],16 +(p0) fma.s1 FR_Y_lo = FR_W, FR_P8, FR_P7 + nop.i 999 ;; } { .mfi - nop.m 999 -(p9) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi = N * log2_hi + H - nop.i 999 +(p0) ldfe FR_P1 = [GR_Table_ptr],16 +// +// Load P1 +// Load P5 +// Y_lo = p8 * w + P7 +// +(p0) fmpy.s1 FR_w4 = FR_wsq, FR_wsq + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p9) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N * log2_lo + h - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P2 + nop.i 999 } -;; - { .mfi - nop.m 999 -(p9) fma.s1 FR_r = FR_G, FR_S_lo, FR_r // r = G * S_lo + (G * S_hi - 1) - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_Y_lo = FR_W, FR_Y_lo, FR_P6 +(p0) add GR_Perturb = 0x1, r0 ;; } -;; - { .mfi - nop.m 999 -(p8) fma.s1 FR_p4321 = FR_W, FR_p432, FR_P1 // p4321 = w * p432 + P1 - nop.i 999 + nop.m 999 +// +// w4 = w2 * w2 +// Y_hi = y_hi * w + p2 +// Y_lo = y_lo * w + p6 +// Create perturbation bit +// +(p0) fmpy.s1 FR_w6 = FR_w4, FR_wsq + nop.i 999 ;; } { .mfi - nop.m 999 -(p8) fma.s1 FR_p8765 = FR_W, FR_p876, FR_P5 // p8765 = w * p876 + P5 - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P1 + nop.i 999 } -;; - +// +// Y_hi = y_hi * w + p1 +// w6 = w4 * w2 +// { .mfi - nop.m 999 -(p9) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3 - nop.i 999 +(p0) setf.sig FR_Q4 = GR_Perturb +(p0) fma.s1 FR_Y_lo = FR_W, FR_Y_lo, FR_P5 + nop.i 999 ;; } { .mfi - nop.m 999 -(p9) fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_dummy = FR_wsq,FR_Y_hi, f0 + nop.i 999 } -;; - { .mfi - nop.m 999 -(p8) fma.s1 FR_Y_lo = FR_wsq, FR_p4321, f0 // Y_lo = wsq * p4321 - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_Y_hi = FR_W,f1,f0 + nop.i 999 +};; +{ .mfb + nop.m 999 +// +// Y_hi = w +// Y_lo = y_lo * w + p5 +// +(p0) fma.s1 FR_Y_lo = FR_w6, FR_Y_lo,FR_dummy +// +// Y_lo = y_lo * w6 + y_high order part. +// +// performance +// +(p0) br.cond.sptk LOGL_main ;; +} +L(log1pl_small): +{ .mmi + nop.m 999 +// /*******************************************************/ +// /*********** Branch log1pl_small ***********************/ +// /*******************************************************/ +(p0) addl GR_Table_Base = @ltoff(Constants_Threshold#),gp } { .mfi nop.m 999 -(p8) fma.s1 FR_Y_hi = FR_W, f1, f0 // Y_hi = w for near1 path - nop.i 999 +(p0) mov FR_Em1 = FR_W +(p0) cmp.eq.unc p7, p0 = r0, r0 ;; +} +{ .mlx + ld8 GR_Table_Base = [GR_Table_Base] +(p0) movl GR_Expo_Range = 0x0000000000000004 ;; +} +// +// Set Safe to true +// Set Expo_Range = 0 for single +// Set Expo_Range = 2 for double +// Set Expo_Range = 4 for double-extended +// +{ .mmi +(p0) shladd GR_Table_Base = GR_Expo_Range,4,GR_Table_Base ;; +(p0) ldfe FR_Threshold = [GR_Table_Base],16 + nop.i 999 +} +{ .mlx + nop.m 999 +(p0) movl GR_Bias = 0x000000000000FF9B ;; } -;; - { .mfi - nop.m 999 -(p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo = poly_lo * r + Q2 - nop.i 999 +(p0) ldfe FR_Tiny = [GR_Table_Base],0 + nop.f 999 + nop.i 999 ;; } { .mfi - nop.m 999 -(p9) fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 - nop.i 999 + nop.m 999 +(p0) fcmp.gt.unc.s1 p13, p12 = FR_abs_W, FR_Threshold + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p8) fma.s1 FR_Y_lo = FR_w6, FR_p8765,FR_Y_lo // Y_lo = w6 * p8765 + w2 * p4321 - nop.i 999 + nop.m 999 +(p13) fnmpy.s1 FR_Y_lo = FR_W, FR_W + nop.i 999 } -;; - { .mfi - nop.m 999 -(p9) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1 * rsq + r - nop.i 999 + nop.m 999 +(p13) fadd FR_SCALE = f0, f1 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h // poly_lo = poly_lo*r^3 + h - nop.i 999 + nop.m 999 +(p12) fsub.s1 FR_Y_lo = f0, FR_Tiny +(p12) cmp.ne.unc p7, p0 = r0, r0 } -;; - { .mfi - nop.m 999 -(p9) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo = poly_hi + poly_lo - nop.i 999 +(p12) setf.exp FR_SCALE = GR_Bias + nop.f 999 + nop.i 999 ;; } -;; - -// Remainder of code is common for near1 and regular paths { .mfb - nop.m 999 - fadd.s0 f8 = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi - br.ret.sptk b0 // Common exit for 2^-80 < x < inf + nop.m 999 +// +// Set p7 to SAFE = FALSE +// Set Scale = 2^-100 +// +(p0) fma.s0 f8 = FR_Y_lo,FR_SCALE,FR_Y_hi +(p0) br.ret.sptk b0 ;; } -;; - - -// Here if x=-1 -LOG1P_EQ_Minus_1: +L(LOGL_64_one): +{ .mfb + nop.m 999 +(p0) fmpy.s0 f8 = FR_Input_X, f0 +(p0) br.ret.sptk b0 ;; +} +// +// Raise divide by zero for +/-0 input. +// +L(LOGL_64_zero): +{ .mfi +(p0) mov GR_Parameter_TAG = 0 // -// If x=-1 raise divide by zero and return -inf +// If we have logl(1), log10l(1) or log1pl(0), return 0. // -{ .mfi - mov GR_Parameter_TAG = 138 - fsub.s1 FR_Output_X_tmp = f0, f1 - nop.i 999 +(p0) fsub.s0 FR_Output_X_tmp = f0, f1 + nop.i 999 ;; +} +{ .mii +(p14) mov GR_Parameter_TAG = 6 + nop.i 999 ;; +(p15) mov GR_Parameter_TAG = 138 ;; } -;; - { .mfb - nop.m 999 - frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0 - br.cond.sptk __libm_error_region + nop.m 999 +(p0) frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0 +(p0) br.cond.sptk __libm_error_region ;; +} +{ .mfb + nop.m 999 +// +// Report that logl(0) computed +// { .mfb +(p0) mov FR_Input_X = FR_Output_X_tmp +(p0) br.ret.sptk b0 ;; } -;; -LOG1P_special: +L(LOGL_64_special): { .mfi - nop.m 999 - fclass.m.unc p8, p0 = FR_Input_X, 0x1E1 // Test for natval, nan, +inf - nop.i 999 + nop.m 999 +// +// Return -Inf or value from handler. +// +(p0) fclass.m.unc p7, p0 = FR_Input_X, 0x1E1 + nop.i 999 ;; } -;; - +{ .mfb + nop.m 999 +// +// Check for Natval, QNan, SNaN, +Inf +// +(p7) fmpy.s0 f8 = FR_Input_X, f1 // // For SNaN raise invalid and return QNaN. // For QNaN raise invalid and return QNaN. // For +Inf return +Inf. // -{ .mfb - nop.m 999 -(p8) fmpy.s0 f8 = FR_Input_X, f1 -(p8) br.ret.sptk b0 // Return for natval, nan, +inf +(p7) br.ret.sptk b0 ;; } -;; - // // For -Inf raise invalid and return QNaN. // +{ .mii +(p0) mov GR_Parameter_TAG = 1 + nop.i 999 ;; +(p14) mov GR_Parameter_TAG = 7 ;; +} +{ .mfi +(p15) mov GR_Parameter_TAG = 139 + nop.f 999 + nop.i 999 ;; +} { .mfb - mov GR_Parameter_TAG = 139 - fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0 - br.cond.sptk __libm_error_region + nop.m 999 +(p0) fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0 +(p0) br.cond.sptk __libm_error_region ;; } -;; - - -LOG1P_unsupported: +// +// Report that logl(-Inf) computed +// Report that log10l(-Inf) computed +// Report that log1p(-Inf) computed +// +{ .mfb + nop.m 0 +(p0) mov FR_Input_X = FR_Output_X_tmp +(p0) br.ret.sptk b0 ;; +} +L(LOGL_64_unsupported): +{ .mfb + nop.m 999 // -// Return generated NaN or other value. +// Return generated NaN or other value . // -{ .mfb - nop.m 999 - fmpy.s0 f8 = FR_Input_X, f0 - br.ret.sptk b0 +(p0) fmpy.s0 f8 = FR_Input_X, f0 +(p0) br.ret.sptk b0 ;; } -;; - -// Here if -inf < x < -1 -LOG1P_LT_Minus_1: +L(LOGL_64_negative): +{ .mfi + nop.m 999 +// +// Deal with x < 0 in a special way +// +(p0) frcpa.s0 FR_Output_X_tmp, p8 = f0, f0 // -// Deal with x < -1 in a special way - raise +// Deal with x < 0 in a special way - raise // invalid and produce QNaN indefinite. // -{ .mfb - mov GR_Parameter_TAG = 139 - frcpa.s0 FR_Output_X_tmp, p8 = f0, f0 - br.cond.sptk __libm_error_region +(p0) mov GR_Parameter_TAG = 1 ;; } -;; - - -GLOBAL_IEEE754_END(log1pl) +{ .mii +(p14) mov GR_Parameter_TAG = 7 + nop.i 999 ;; +(p15) mov GR_Parameter_TAG = 139 +} +.endp log1pl +ASM_SIZE_DIRECTIVE(log1pl) -LOCAL_LIBM_ENTRY(__libm_error_region) +.proc __libm_error_region +__libm_error_region: .prologue { .mfi add GR_Parameter_Y=-32,sp // Parameter 2 value @@ -1178,8 +1609,8 @@ LOCAL_LIBM_ENTRY(__libm_error_region) br.call.sptk b0=__libm_error_support# // Call error handling function };; { .mmi - nop.m 999 - nop.m 999 + nop.m 0 + nop.m 0 add GR_Parameter_RESULT = 48,sp };; { .mmi @@ -1194,7 +1625,52 @@ LOCAL_LIBM_ENTRY(__libm_error_region) br.ret.sptk b0 // Return };; -LOCAL_LIBM_END(__libm_error_region#) +.endp __libm_error_region +ASM_SIZE_DIRECTIVE(__libm_error_region) + +.proc LOGL_main +LOGL_main: +{ .mfi + nop.m 999 +// +// kernel_log_64 computes ln(X + E) +// +(p7) fadd.s0 FR_Input_X = FR_Y_lo,FR_Y_hi + nop.i 0 +} +{ .mmi + nop.m 999 + nop.m 999 +(p14) addl GR_Table_Base = @ltoff(Constants_1_by_LN10#),gp ;; +} +{ .mmi + nop.m 999 +(p14) ld8 GR_Table_Base = [GR_Table_Base] + nop.i 999 +};; + +{ .mmi +(p14) ldfe FR_1LN10_hi = [GR_Table_Base],16 ;; +(p14) ldfe FR_1LN10_lo = [GR_Table_Base] + nop.i 999 ;; +} +{ .mfi + nop.m 999 +(p14) fmpy.s1 FR_Output_X_tmp = FR_Y_lo,FR_1LN10_hi + nop.i 999 ;; +} +{ .mfi + nop.m 999 +(p14) fma.s1 FR_Output_X_tmp = FR_Y_hi,FR_1LN10_lo,FR_Output_X_tmp + nop.i 999 ;; +} +{ .mfb + nop.m 999 +(p14) fma.s0 FR_Input_X = FR_Y_hi,FR_1LN10_hi,FR_Output_X_tmp +(p0) br.ret.sptk b0 ;; +} +.endp LOGL_main +ASM_SIZE_DIRECTIVE(LOGL_main) .type __libm_error_support#,@function .global __libm_error_support# |