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Diffstat (limited to 'sysdeps/ia64/fpu/s_log1p.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_log1p.S | 2312 |
1 files changed, 893 insertions, 1419 deletions
diff --git a/sysdeps/ia64/fpu/s_log1p.S b/sysdeps/ia64/fpu/s_log1p.S index 0d96c14a55..cd3551984a 100644 --- a/sysdeps/ia64/fpu/s_log1p.S +++ b/sysdeps/ia64/fpu/s_log1p.S @@ -1,10 +1,10 @@ -.file "log1p.s" +.file "log1p.s" -// Copyright (C) 2000, 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 @@ -20,1608 +20,1082 @@ // * The name of Intel Corporation may not be used to endorse or promote // products derived from this software without specific prior written // permission. -// -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR -// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING -// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS -// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -// +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// // Intel Corporation is the author of this code, and requests that all -// problem reports or change requests be submitted to it directly at -// http://developer.intel.com/opensource. +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. // // History //============================================================== -// 2/02/00 Initial version -// 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. +// 06/29/01 Improved speed of all paths +// 05/20/02 Cleaned up namespace and sf0 syntax +// 10/02/02 Improved performance by basing on log algorithm +// 02/10/03 Reordered header: .section, .global, .proc, .align +// 04/18/03 Eliminate possible WAW dependency warning // -// ********************************************************************* -// -// Function: log1p(x) = ln(x+1), for double precision x values -// -// ********************************************************************* -// -// Accuracy: Very accurate for double precision values -// -// ********************************************************************* -// -// Resources Used: -// -// Floating-Point Registers: f8 (Input and Return Value) -// f9,f33-f55,f99 -// -// General Purpose Registers: -// r32-r53 -// r54-r57 (Used to pass arguments to error handling routine) -// -// Predicate Registers: p6-p15 -// -// ********************************************************************* -// -// IEEE Special Conditions: -// -// Denormal fault raised on denormal inputs -// Overflow exceptions cannot occur -// Underflow exceptions raised when appropriate for log1p -// (Error Handling Routine called for underflow) -// Inexact raised when appropriate by algorithm -// -// log1p(inf) = inf -// log1p(-inf) = QNaN -// log1p(+/-0) = +/-0 -// log1p(-1) = -inf -// log1p(SNaN) = QNaN -// log1p(QNaN) = QNaN -// log1p(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 log1p_small; -// elseif |X+Em1| < 2^(-7) use case log_near1; -// else use case log_regular; -// -// Case log1p_small: -// -// log( 1 + (X+Em1) ) can be approximated by (X+Em1). -// -// Case log_near1: -// -// log( 1 + (X+Em1) ) can be approximated by a simple polynomial -// in W = X+Em1. This polynomial resembles the truncated Taylor -// series W - W^/2 + W^3/3 - ... -// -// Case log_regular: -// -// Here we use a table lookup method. The basic idea is that in -// order to compute log(Arg) for an argument Arg in [1,2), we -// construct a value G such that G*Arg is close to 1 and that -// log(1/G) is obtainable easily from a table of values calculated -// beforehand. Thus -// -// log(Arg) = log(1/G) + log(G*Arg) -// = log(1/G) + log(1 + (G*Arg - 1)) -// -// Because |G*Arg - 1| is small, the second term on the right hand -// side can be approximated by a short polynomial. We elaborate -// this method in four steps. -// -// Step 0: Initialization -// -// We need to calculate log( E + X ). Obtain N, S_hi, S_lo such that -// -// 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). -// -// Step 1: Argument Reduction -// -// 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 -// -// These G_j's have the property that the product is exactly -// representable and that |r| < 2^(-12) as a result. -// -// Step 2: Approximation -// -// -// log(1 + r) is approximated by a short polynomial poly(r). -// -// Step 3: Reconstruction -// -// -// Finally, log( E + X ) is given by -// -// log( E + X ) = log( 2^N * (S_hi + S_lo) ) -// ~=~ N*log(2) + log(1/G) + log(1 + r) -// ~=~ N*log(2) + log(1/G) + poly(r). -// -// **** Algorithm **** -// -// Case log1p_small: -// -// Although log(1 + (X+Em1)) is basically X+Em1, we would like to -// preserve the inexactness nature as well as consistent behavior -// under different rounding modes. Note that this case can only be -// taken if E is set to be 1.0. In this case, Em1 is zero, and that -// X can be very tiny and thus the final result can possibly underflow. -// Thus, we compare X against a threshold that is dependent on the -// input Expo_Range. If |X| is smaller than this threshold, we set -// SAFE to be FALSE. -// -// The result is returned as Y_hi, Y_lo, and in the case of SAFE -// is FALSE, an additional value Scale is also returned. -// -// W := X + Em1 -// Threshold := Threshold_Table( Expo_Range ) -// Tiny := Tiny_Table( Expo_Range ) -// -// If ( |W| > Threshold ) then -// Y_hi := W -// Y_lo := -W*W -// Else -// Y_hi := W -// Y_lo := -Tiny -// Scale := 2^(-100) -// Safe := FALSE -// EndIf -// -// -// One may think that Y_lo should be -W*W/2; however, it does not matter -// as Y_lo will be rounded off completely except for the correct effect in -// directed rounding. Clearly -W*W is simplier to compute. Moreover, -// because of the difference in exponent value, Y_hi + Y_lo or -// Y_hi + Scale*Y_lo is always inexact. -// -// Case log_near1: -// -// Here we compute a simple polynomial. To exploit parallelism, we split -// the polynomial into two portions. -// -// W := X + Em1 -// Wsq := W * W -// W4 := Wsq*Wsq -// W6 := W4*Wsq -// Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4)) -// Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8))) -// set lsb(Y_lo) to be 1 -// -// Case log_regular: -// -// We present the algorithm in four steps. -// -// Step 0. Initialization -// ---------------------- -// -// Z := X + E -// N := unbaised exponent of Z -// S_hi := 2^(-N) * Z -// S_lo := 2^(-N) * { (max(X,E)-Z) + min(X,E) } -// -// Note that S_lo is always 0 for the case E = 0. -// -// Step 1. Argument Reduction -// -------------------------- -// -// Let -// -// Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63 -// -// We obtain G_1, G_2, G_3 by the following steps. -// +// API +//============================================================== +// double log1p(double) // -// Define X_0 := 1.d_1 d_2 ... d_14. This is extracted -// from S_hi. +// log1p(x) = log(x+1) // -// Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated -// to lsb = 2^(-4). +// Overview of operation +//============================================================== +// Background +// ---------- // -// Define index_1 := [ d_1 d_2 d_3 d_4 ]. +// This algorithm is based on fact that +// log1p(x) = log(1+x) and +// log(a b) = log(a) + log(b). +// In our case we have 1+x = 2^N f, where 1 <= f < 2. +// So +// log(1+x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f) // -// 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. +// To calculate log(f) we do following +// log(f) = log(f * frcpa(f) / frcpa(f)) = +// = log(f * frcpa(f)) + log(1/frcpa(f)) // -// 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. +// According to definition of IA-64's frcpa instruction it's a +// floating point that approximates 1/f using a lookup on the +// top of 8 bits of the input number's + 1 significand with relative +// error < 2^(-8.886). So we have following // -// 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. +// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256 // +// and // -// 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. +// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) = +// = log(1 + r) + T // -// Define index_2 := [ d_5 d_6 d_7 d_8 ]. +// The first value can be computed by polynomial P(r) approximating +// log(1 + r) on |r| < 1/256 and the second is precomputed tabular +// value defined by top 8 bit of f. // -// 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 +// Finally we have that log(1+x) ~ (N*log(2) + T) + P(r) // -// Fetch G_2 := (1/A_2) truncated to 21 sig. bits. -// floating pt. +// Note that if input argument is close to 0.0 (in our case it means +// that |x| < 1/256) we can use just polynomial approximation +// because 1+x = 2^0 * f = f = 1 + r and +// log(1+x) = log(1 + r) ~ P(r) // -// 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. // +// Implementation +// -------------- // -// 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). +// 1. |x| >= 2^(-8), and x > -1 +// InvX = frcpa(x+1) +// r = InvX*(x+1) - 1 +// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)), +// all coefficients are calcutated in quad and rounded to double +// precision. A7,A6,A5,A4 are stored in memory whereas A3 and A2 +// created with setf. // -// Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ]. +// N = float(n) where n is true unbiased exponent of x // -// Fetch G_3 := (1/A_3) truncated to 21 sig. bits. -// floating pt. Fetch is done using index_3. +// T is tabular value of log(1/frcpa(x)) calculated in quad precision +// and represented by two floating-point numbers 64-bit Thi and 32-bit Tlo. +// To load Thi,Tlo we get bits from 55 to 62 of register format significand +// as index and calculate two addresses +// ad_Thi = Thi_table_base_addr + 8 * index +// ad_Tlo = Tlo_table_base_addr + 4 * index // -// Compute G := G_1 * G_2 * G_3. +// L1 (log(2)) is calculated in quad +// precision and represented by two floating-point 64-bit numbers L1hi,L1lo +// stored in memory. // -// This is done exactly since each of G_j only has 21 sig. bits. +// And final result = ((L1hi*N + Thi) + (N*L1lo + Tlo)) + P(r) // -// Compute // -// r := (G*S_hi - 1) + G*S_lo using 2 FMA operations. +// 2. 2^(-80) <= |x| < 2^(-8) +// r = x +// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)), +// A7,A6,A5,A4,A3,A2 are the same as in case |x| >= 1/256 // -// thus, r approximates G*(S_hi+S_lo) - 1 to within a couple of -// rounding errors. +// And final results +// log(1+x) = P(r) // +// 3. 0 < |x| < 2^(-80) +// Although log1p(x) is basically x, we would like to preserve the inexactness +// nature as well as consistent behavior under different rounding modes. +// We can do this by computing the result as // -// Step 2. Approximation -// --------------------- +// log1p(x) = x - x*x // -// This step computes an approximation to log( 1 + r ) where r is the -// reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13); -// thus log(1+r) can be approximated by a short polynomial: // -// log(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5 +// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are +// filtered and processed on special branches. // + // -// Step 3. Reconstruction -// ---------------------- +// Special values +//============================================================== // -// This step computes the desired result of log(X+E): +// log1p(-1) = -inf // Call error support // -// log(X+E) = log( 2^N * (S_hi + S_lo) ) -// = N*log(2) + log( S_hi + S_lo ) -// = N*log(2) + log(1/G) + -// log(1 + C*(S_hi+S_lo) - 1 ) +// log1p(+qnan) = +qnan +// log1p(-qnan) = -qnan +// log1p(+snan) = +qnan +// log1p(-snan) = -qnan // -// log(2), log(1/G_j) are stored as pairs of (single,double) numbers: -// log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are -// single-precision numbers and the low parts are double precision -// numbers. These have the property that +// log1p(x),x<-1= QNAN Indefinite // Call error support +// log1p(-inf) = QNAN Indefinite +// log1p(+inf) = +inf +// log1p(+/-0) = +/-0 // -// N*log2_hi + SUM ( log1byGj_hi ) // -// is computable exactly in double-extended precision (64 sig. bits). -// Finally +// Registers used +//============================================================== +// Floating Point registers used: +// f8, input +// f7 -> f15, f32 -> f40 // -// 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 +// General registers used: +// r8 -> r11 +// r14 -> r20 // +// Predicate registers used: +// p6 -> p12 -#include "libm_support.h" - -#ifdef _LIBC -.rodata -#else -.data -#endif +// Assembly macros +//============================================================== +GR_TAG = r8 +GR_ad_1 = r8 +GR_ad_2 = r9 +GR_Exp = r10 +GR_N = r11 -// P_7, P_6, P_5, P_4, P_3, P_2, and P_1 +GR_signexp_x = r14 +GR_exp_mask = r15 +GR_exp_bias = r16 +GR_05 = r17 +GR_A3 = r18 +GR_Sig = r19 +GR_Ind = r19 +GR_exp_x = r20 -.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 +GR_SAVE_B0 = r33 +GR_SAVE_PFS = r34 +GR_SAVE_GP = r35 +GR_SAVE_SP = r36 -.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 +GR_Parameter_X = r37 +GR_Parameter_Y = r38 +GR_Parameter_RESULT = r39 +GR_Parameter_TAG = r40 -.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) -// -.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) -.align 64 -Constants_1_by_LN10: -ASM_TYPE_DIRECTIVE(Constants_1_by_LN10,@object) -data4 0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000 -data4 0xACCF70C8,0xD56EAABE,0x00003FBD,0x00000000 -ASM_SIZE_DIRECTIVE(Constants_1_by_LN10) +FR_NormX = f7 +FR_RcpX = f9 +FR_r = f10 +FR_r2 = f11 +FR_r4 = f12 +FR_N = f13 +FR_Ln2hi = f14 +FR_Ln2lo = f15 -FR_Input_X = f8 -FR_Neg_One = f9 -FR_E = f33 -FR_Em1 = f34 -FR_Y_hi = f34 -// Shared with Em1 -FR_Y_lo = f35 -FR_Scale = f36 -FR_X_Prime = f37 -FR_Z = f38 -FR_S_hi = f38 -// Shared with Z -FR_W = f39 -FR_G = f40 -FR_wsq = f40 -// Shared with G -FR_H = f41 -FR_w4 = f41 -// Shared with H -FR_h = f42 -FR_w6 = f42 -// Shared with h -FR_G_tmp = f43 -FR_poly_lo = f43 -// Shared with G_tmp -FR_P8 = f43 -// Shared with G_tmp -FR_H_tmp = f44 -FR_poly_hi = f44 - // Shared with H_tmp -FR_P7 = f44 -// Shared with H_tmp -FR_h_tmp = f45 -FR_rsq = f45 -// Shared with h_tmp -FR_P6 = f45 -// Shared with h_tmp -FR_abs_W = f46 -FR_r = f46 -// Shared with abs_W -FR_AA = f47 -FR_log2_hi = f47 -// Shared with AA -FR_BB = f48 -FR_log2_lo = f48 -// Shared with BB -FR_S_lo = f49 -FR_two_negN = f50 -FR_float_N = f51 -FR_Q4 = f52 -FR_dummy = f52 -// Shared with Q4 -FR_P4 = f52 -// Shared with Q4 -FR_Threshold = f52 -// Shared with Q4 -FR_Q3 = f53 -FR_P3 = f53 -// Shared with Q3 -FR_Tiny = f53 -// Shared with Q3 -FR_Q2 = f54 -FR_P2 = f54 -// Shared with Q2 -FR_1LN10_hi = f54 -// Shared with Q2 -FR_Q1 = f55 -FR_P1 = f55 -// Shared with Q1 -FR_1LN10_lo = f55 -// Shared with Q1 -FR_P5 = f98 -FR_SCALE = f98 -FR_Output_X_tmp = f99 +FR_A7 = f32 +FR_A6 = f33 +FR_A5 = f34 +FR_A4 = f35 +FR_A3 = f36 +FR_A2 = f37 -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_Thi = f38 +FR_NxLn2hipThi = f38 +FR_NxLn2pT = f38 +FR_Tlo = f39 +FR_NxLn2lopTlo = f39 +FR_Xp1 = f40 -GR_SAVE_PFS = r51 -GR_SAVE_B0 = r52 -GR_SAVE_GP = r53 -GR_Parameter_X = r54 -GR_Parameter_Y = r55 -GR_Parameter_RESULT = r56 +FR_Y = f1 +FR_X = f10 +FR_RESULT = f8 -GR_Parameter_TAG = r57 +// Data +//============================================================== +RODATA +.align 16 + +LOCAL_OBJECT_START(log_data) +// coefficients of polynomial approximation +data8 0x3FC2494104381A8E // A7 +data8 0xBFC5556D556BBB69 // A6 +data8 0x3FC999999988B5E9 // A5 +data8 0xBFCFFFFFFFF6FFF5 // A4 +// +// hi parts of ln(1/frcpa(1+i/256)), i=0...255 +data8 0x3F60040155D5889D // 0 +data8 0x3F78121214586B54 // 1 +data8 0x3F841929F96832EF // 2 +data8 0x3F8C317384C75F06 // 3 +data8 0x3F91A6B91AC73386 // 4 +data8 0x3F95BA9A5D9AC039 // 5 +data8 0x3F99D2A8074325F3 // 6 +data8 0x3F9D6B2725979802 // 7 +data8 0x3FA0C58FA19DFAA9 // 8 +data8 0x3FA2954C78CBCE1A // 9 +data8 0x3FA4A94D2DA96C56 // 10 +data8 0x3FA67C94F2D4BB58 // 11 +data8 0x3FA85188B630F068 // 12 +data8 0x3FAA6B8ABE73AF4C // 13 +data8 0x3FAC441E06F72A9E // 14 +data8 0x3FAE1E6713606D06 // 15 +data8 0x3FAFFA6911AB9300 // 16 +data8 0x3FB0EC139C5DA600 // 17 +data8 0x3FB1DBD2643D190B // 18 +data8 0x3FB2CC7284FE5F1C // 19 +data8 0x3FB3BDF5A7D1EE64 // 20 +data8 0x3FB4B05D7AA012E0 // 21 +data8 0x3FB580DB7CEB5701 // 22 +data8 0x3FB674F089365A79 // 23 +data8 0x3FB769EF2C6B568D // 24 +data8 0x3FB85FD927506A47 // 25 +data8 0x3FB9335E5D594988 // 26 +data8 0x3FBA2B0220C8E5F4 // 27 +data8 0x3FBB0004AC1A86AB // 28 +data8 0x3FBBF968769FCA10 // 29 +data8 0x3FBCCFEDBFEE13A8 // 30 +data8 0x3FBDA727638446A2 // 31 +data8 0x3FBEA3257FE10F79 // 32 +data8 0x3FBF7BE9FEDBFDE5 // 33 +data8 0x3FC02AB352FF25F3 // 34 +data8 0x3FC097CE579D204C // 35 +data8 0x3FC1178E8227E47B // 36 +data8 0x3FC185747DBECF33 // 37 +data8 0x3FC1F3B925F25D41 // 38 +data8 0x3FC2625D1E6DDF56 // 39 +data8 0x3FC2D1610C868139 // 40 +data8 0x3FC340C59741142E // 41 +data8 0x3FC3B08B6757F2A9 // 42 +data8 0x3FC40DFB08378003 // 43 +data8 0x3FC47E74E8CA5F7C // 44 +data8 0x3FC4EF51F6466DE4 // 45 +data8 0x3FC56092E02BA516 // 46 +data8 0x3FC5D23857CD74D4 // 47 +data8 0x3FC6313A37335D76 // 48 +data8 0x3FC6A399DABBD383 // 49 +data8 0x3FC70337DD3CE41A // 50 +data8 0x3FC77654128F6127 // 51 +data8 0x3FC7E9D82A0B022D // 52 +data8 0x3FC84A6B759F512E // 53 +data8 0x3FC8AB47D5F5A30F // 54 +data8 0x3FC91FE49096581B // 55 +data8 0x3FC981634011AA75 // 56 +data8 0x3FC9F6C407089664 // 57 +data8 0x3FCA58E729348F43 // 58 +data8 0x3FCABB55C31693AC // 59 +data8 0x3FCB1E104919EFD0 // 60 +data8 0x3FCB94EE93E367CA // 61 +data8 0x3FCBF851C067555E // 62 +data8 0x3FCC5C0254BF23A5 // 63 +data8 0x3FCCC000C9DB3C52 // 64 +data8 0x3FCD244D99C85673 // 65 +data8 0x3FCD88E93FB2F450 // 66 +data8 0x3FCDEDD437EAEF00 // 67 +data8 0x3FCE530EFFE71012 // 68 +data8 0x3FCEB89A1648B971 // 69 +data8 0x3FCF1E75FADF9BDE // 70 +data8 0x3FCF84A32EAD7C35 // 71 +data8 0x3FCFEB2233EA07CD // 72 +data8 0x3FD028F9C7035C1C // 73 +data8 0x3FD05C8BE0D9635A // 74 +data8 0x3FD085EB8F8AE797 // 75 +data8 0x3FD0B9C8E32D1911 // 76 +data8 0x3FD0EDD060B78080 // 77 +data8 0x3FD122024CF0063F // 78 +data8 0x3FD14BE2927AECD4 // 79 +data8 0x3FD180618EF18ADF // 80 +data8 0x3FD1B50BBE2FC63B // 81 +data8 0x3FD1DF4CC7CF242D // 82 +data8 0x3FD214456D0EB8D4 // 83 +data8 0x3FD23EC5991EBA49 // 84 +data8 0x3FD2740D9F870AFB // 85 +data8 0x3FD29ECDABCDFA03 // 86 +data8 0x3FD2D46602ADCCEE // 87 +data8 0x3FD2FF66B04EA9D4 // 88 +data8 0x3FD335504B355A37 // 89 +data8 0x3FD360925EC44F5C // 90 +data8 0x3FD38BF1C3337E74 // 91 +data8 0x3FD3C25277333183 // 92 +data8 0x3FD3EDF463C1683E // 93 +data8 0x3FD419B423D5E8C7 // 94 +data8 0x3FD44591E0539F48 // 95 +data8 0x3FD47C9175B6F0AD // 96 +data8 0x3FD4A8B341552B09 // 97 +data8 0x3FD4D4F39089019F // 98 +data8 0x3FD501528DA1F967 // 99 +data8 0x3FD52DD06347D4F6 // 100 +data8 0x3FD55A6D3C7B8A89 // 101 +data8 0x3FD5925D2B112A59 // 102 +data8 0x3FD5BF406B543DB1 // 103 +data8 0x3FD5EC433D5C35AD // 104 +data8 0x3FD61965CDB02C1E // 105 +data8 0x3FD646A84935B2A1 // 106 +data8 0x3FD6740ADD31DE94 // 107 +data8 0x3FD6A18DB74A58C5 // 108 +data8 0x3FD6CF31058670EC // 109 +data8 0x3FD6F180E852F0B9 // 110 +data8 0x3FD71F5D71B894EF // 111 +data8 0x3FD74D5AEFD66D5C // 112 +data8 0x3FD77B79922BD37D // 113 +data8 0x3FD7A9B9889F19E2 // 114 +data8 0x3FD7D81B037EB6A6 // 115 +data8 0x3FD8069E33827230 // 116 +data8 0x3FD82996D3EF8BCA // 117 +data8 0x3FD85855776DCBFA // 118 +data8 0x3FD8873658327CCE // 119 +data8 0x3FD8AA75973AB8CE // 120 +data8 0x3FD8D992DC8824E4 // 121 +data8 0x3FD908D2EA7D9511 // 122 +data8 0x3FD92C59E79C0E56 // 123 +data8 0x3FD95BD750EE3ED2 // 124 +data8 0x3FD98B7811A3EE5B // 125 +data8 0x3FD9AF47F33D406B // 126 +data8 0x3FD9DF270C1914A7 // 127 +data8 0x3FDA0325ED14FDA4 // 128 +data8 0x3FDA33440224FA78 // 129 +data8 0x3FDA57725E80C382 // 130 +data8 0x3FDA87D0165DD199 // 131 +data8 0x3FDAAC2E6C03F895 // 132 +data8 0x3FDADCCC6FDF6A81 // 133 +data8 0x3FDB015B3EB1E790 // 134 +data8 0x3FDB323A3A635948 // 135 +data8 0x3FDB56FA04462909 // 136 +data8 0x3FDB881AA659BC93 // 137 +data8 0x3FDBAD0BEF3DB164 // 138 +data8 0x3FDBD21297781C2F // 139 +data8 0x3FDC039236F08818 // 140 +data8 0x3FDC28CB1E4D32FC // 141 +data8 0x3FDC4E19B84723C1 // 142 +data8 0x3FDC7FF9C74554C9 // 143 +data8 0x3FDCA57B64E9DB05 // 144 +data8 0x3FDCCB130A5CEBAF // 145 +data8 0x3FDCF0C0D18F326F // 146 +data8 0x3FDD232075B5A201 // 147 +data8 0x3FDD490246DEFA6B // 148 +data8 0x3FDD6EFA918D25CD // 149 +data8 0x3FDD9509707AE52F // 150 +data8 0x3FDDBB2EFE92C554 // 151 +data8 0x3FDDEE2F3445E4AE // 152 +data8 0x3FDE148A1A2726CD // 153 +data8 0x3FDE3AFC0A49FF3F // 154 +data8 0x3FDE6185206D516D // 155 +data8 0x3FDE882578823D51 // 156 +data8 0x3FDEAEDD2EAC990C // 157 +data8 0x3FDED5AC5F436BE2 // 158 +data8 0x3FDEFC9326D16AB8 // 159 +data8 0x3FDF2391A21575FF // 160 +data8 0x3FDF4AA7EE03192C // 161 +data8 0x3FDF71D627C30BB0 // 162 +data8 0x3FDF991C6CB3B379 // 163 +data8 0x3FDFC07ADA69A90F // 164 +data8 0x3FDFE7F18EB03D3E // 165 +data8 0x3FE007C053C5002E // 166 +data8 0x3FE01B942198A5A0 // 167 +data8 0x3FE02F74400C64EA // 168 +data8 0x3FE04360BE7603AC // 169 +data8 0x3FE05759AC47FE33 // 170 +data8 0x3FE06B5F1911CF51 // 171 +data8 0x3FE078BF0533C568 // 172 +data8 0x3FE08CD9687E7B0E // 173 +data8 0x3FE0A10074CF9019 // 174 +data8 0x3FE0B5343A234476 // 175 +data8 0x3FE0C974C89431CD // 176 +data8 0x3FE0DDC2305B9886 // 177 +data8 0x3FE0EB524BAFC918 // 178 +data8 0x3FE0FFB54213A475 // 179 +data8 0x3FE114253DA97D9F // 180 +data8 0x3FE128A24F1D9AFF // 181 +data8 0x3FE1365252BF0864 // 182 +data8 0x3FE14AE558B4A92D // 183 +data8 0x3FE15F85A19C765B // 184 +data8 0x3FE16D4D38C119FA // 185 +data8 0x3FE18203C20DD133 // 186 +data8 0x3FE196C7BC4B1F3A // 187 +data8 0x3FE1A4A738B7A33C // 188 +data8 0x3FE1B981C0C9653C // 189 +data8 0x3FE1CE69E8BB106A // 190 +data8 0x3FE1DC619DE06944 // 191 +data8 0x3FE1F160A2AD0DA3 // 192 +data8 0x3FE2066D7740737E // 193 +data8 0x3FE2147DBA47A393 // 194 +data8 0x3FE229A1BC5EBAC3 // 195 +data8 0x3FE237C1841A502E // 196 +data8 0x3FE24CFCE6F80D9A // 197 +data8 0x3FE25B2C55CD5762 // 198 +data8 0x3FE2707F4D5F7C40 // 199 +data8 0x3FE285E0842CA383 // 200 +data8 0x3FE294294708B773 // 201 +data8 0x3FE2A9A2670AFF0C // 202 +data8 0x3FE2B7FB2C8D1CC0 // 203 +data8 0x3FE2C65A6395F5F5 // 204 +data8 0x3FE2DBF557B0DF42 // 205 +data8 0x3FE2EA64C3F97654 // 206 +data8 0x3FE3001823684D73 // 207 +data8 0x3FE30E97E9A8B5CC // 208 +data8 0x3FE32463EBDD34E9 // 209 +data8 0x3FE332F4314AD795 // 210 +data8 0x3FE348D90E7464CF // 211 +data8 0x3FE35779F8C43D6D // 212 +data8 0x3FE36621961A6A99 // 213 +data8 0x3FE37C299F3C366A // 214 +data8 0x3FE38AE2171976E7 // 215 +data8 0x3FE399A157A603E7 // 216 +data8 0x3FE3AFCCFE77B9D1 // 217 +data8 0x3FE3BE9D503533B5 // 218 +data8 0x3FE3CD7480B4A8A2 // 219 +data8 0x3FE3E3C43918F76C // 220 +data8 0x3FE3F2ACB27ED6C6 // 221 +data8 0x3FE4019C2125CA93 // 222 +data8 0x3FE4181061389722 // 223 +data8 0x3FE42711518DF545 // 224 +data8 0x3FE436194E12B6BF // 225 +data8 0x3FE445285D68EA69 // 226 +data8 0x3FE45BCC464C893A // 227 +data8 0x3FE46AED21F117FC // 228 +data8 0x3FE47A1527E8A2D3 // 229 +data8 0x3FE489445EFFFCCB // 230 +data8 0x3FE4A018BCB69835 // 231 +data8 0x3FE4AF5A0C9D65D7 // 232 +data8 0x3FE4BEA2A5BDBE87 // 233 +data8 0x3FE4CDF28F10AC46 // 234 +data8 0x3FE4DD49CF994058 // 235 +data8 0x3FE4ECA86E64A683 // 236 +data8 0x3FE503C43CD8EB68 // 237 +data8 0x3FE513356667FC57 // 238 +data8 0x3FE522AE0738A3D7 // 239 +data8 0x3FE5322E26867857 // 240 +data8 0x3FE541B5CB979809 // 241 +data8 0x3FE55144FDBCBD62 // 242 +data8 0x3FE560DBC45153C6 // 243 +data8 0x3FE5707A26BB8C66 // 244 +data8 0x3FE587F60ED5B8FF // 245 +data8 0x3FE597A7977C8F31 // 246 +data8 0x3FE5A760D634BB8A // 247 +data8 0x3FE5B721D295F10E // 248 +data8 0x3FE5C6EA94431EF9 // 249 +data8 0x3FE5D6BB22EA86F5 // 250 +data8 0x3FE5E6938645D38F // 251 +data8 0x3FE5F673C61A2ED1 // 252 +data8 0x3FE6065BEA385926 // 253 +data8 0x3FE6164BFA7CC06B // 254 +data8 0x3FE62643FECF9742 // 255 +// +// two parts of ln(2) +data8 0x3FE62E42FEF00000,0x3DD473DE6AF278ED +// +// lo parts of ln(1/frcpa(1+i/256)), i=0...255 +data4 0x20E70672 // 0 +data4 0x1F60A5D0 // 1 +data4 0x218EABA0 // 2 +data4 0x21403104 // 3 +data4 0x20E9B54E // 4 +data4 0x21EE1382 // 5 +data4 0x226014E3 // 6 +data4 0x2095E5C9 // 7 +data4 0x228BA9D4 // 8 +data4 0x22932B86 // 9 +data4 0x22608A57 // 10 +data4 0x220209F3 // 11 +data4 0x212882CC // 12 +data4 0x220D46E2 // 13 +data4 0x21FA4C28 // 14 +data4 0x229E5BD9 // 15 +data4 0x228C9838 // 16 +data4 0x2311F954 // 17 +data4 0x221365DF // 18 +data4 0x22BD0CB3 // 19 +data4 0x223D4BB7 // 20 +data4 0x22A71BBE // 21 +data4 0x237DB2FA // 22 +data4 0x23194C9D // 23 +data4 0x22EC639E // 24 +data4 0x2367E669 // 25 +data4 0x232E1D5F // 26 +data4 0x234A639B // 27 +data4 0x2365C0E0 // 28 +data4 0x234646C1 // 29 +data4 0x220CBF9C // 30 +data4 0x22A00FD4 // 31 +data4 0x2306A3F2 // 32 +data4 0x23745A9B // 33 +data4 0x2398D756 // 34 +data4 0x23DD0B6A // 35 +data4 0x23DE338B // 36 +data4 0x23A222DF // 37 +data4 0x223164F8 // 38 +data4 0x23B4E87B // 39 +data4 0x23D6CCB8 // 40 +data4 0x220C2099 // 41 +data4 0x21B86B67 // 42 +data4 0x236D14F1 // 43 +data4 0x225A923F // 44 +data4 0x22748723 // 45 +data4 0x22200D13 // 46 +data4 0x23C296EA // 47 +data4 0x2302AC38 // 48 +data4 0x234B1996 // 49 +data4 0x2385E298 // 50 +data4 0x23175BE5 // 51 +data4 0x2193F482 // 52 +data4 0x23BFEA90 // 53 +data4 0x23D70A0C // 54 +data4 0x231CF30A // 55 +data4 0x235D9E90 // 56 +data4 0x221AD0CB // 57 +data4 0x22FAA08B // 58 +data4 0x23D29A87 // 59 +data4 0x20C4B2FE // 60 +data4 0x2381B8B7 // 61 +data4 0x23F8D9FC // 62 +data4 0x23EAAE7B // 63 +data4 0x2329E8AA // 64 +data4 0x23EC0322 // 65 +data4 0x2357FDCB // 66 +data4 0x2392A9AD // 67 +data4 0x22113B02 // 68 +data4 0x22DEE901 // 69 +data4 0x236A6D14 // 70 +data4 0x2371D33E // 71 +data4 0x2146F005 // 72 +data4 0x23230B06 // 73 +data4 0x22F1C77D // 74 +data4 0x23A89FA3 // 75 +data4 0x231D1241 // 76 +data4 0x244DA96C // 77 +data4 0x23ECBB7D // 78 +data4 0x223E42B4 // 79 +data4 0x23801BC9 // 80 +data4 0x23573263 // 81 +data4 0x227C1158 // 82 +data4 0x237BD749 // 83 +data4 0x21DDBAE9 // 84 +data4 0x23401735 // 85 +data4 0x241D9DEE // 86 +data4 0x23BC88CB // 87 +data4 0x2396D5F1 // 88 +data4 0x23FC89CF // 89 +data4 0x2414F9A2 // 90 +data4 0x2474A0F5 // 91 +data4 0x24354B60 // 92 +data4 0x23C1EB40 // 93 +data4 0x2306DD92 // 94 +data4 0x24353B6B // 95 +data4 0x23CD1701 // 96 +data4 0x237C7A1C // 97 +data4 0x245793AA // 98 +data4 0x24563695 // 99 +data4 0x23C51467 // 100 +data4 0x24476B68 // 101 +data4 0x212585A9 // 102 +data4 0x247B8293 // 103 +data4 0x2446848A // 104 +data4 0x246A53F8 // 105 +data4 0x246E496D // 106 +data4 0x23ED1D36 // 107 +data4 0x2314C258 // 108 +data4 0x233244A7 // 109 +data4 0x245B7AF0 // 110 +data4 0x24247130 // 111 +data4 0x22D67B38 // 112 +data4 0x2449F620 // 113 +data4 0x23BBC8B8 // 114 +data4 0x237D3BA0 // 115 +data4 0x245E8F13 // 116 +data4 0x2435573F // 117 +data4 0x242DE666 // 118 +data4 0x2463BC10 // 119 +data4 0x2466587D // 120 +data4 0x2408144B // 121 +data4 0x2405F0E5 // 122 +data4 0x22381CFF // 123 +data4 0x24154F9B // 124 +data4 0x23A4E96E // 125 +data4 0x24052967 // 126 +data4 0x2406963F // 127 +data4 0x23F7D3CB // 128 +data4 0x2448AFF4 // 129 +data4 0x24657A21 // 130 +data4 0x22FBC230 // 131 +data4 0x243C8DEA // 132 +data4 0x225DC4B7 // 133 +data4 0x23496EBF // 134 +data4 0x237C2B2B // 135 +data4 0x23A4A5B1 // 136 +data4 0x2394E9D1 // 137 +data4 0x244BC950 // 138 +data4 0x23C7448F // 139 +data4 0x2404A1AD // 140 +data4 0x246511D5 // 141 +data4 0x24246526 // 142 +data4 0x23111F57 // 143 +data4 0x22868951 // 144 +data4 0x243EB77F // 145 +data4 0x239F3DFF // 146 +data4 0x23089666 // 147 +data4 0x23EBFA6A // 148 +data4 0x23C51312 // 149 +data4 0x23E1DD5E // 150 +data4 0x232C0944 // 151 +data4 0x246A741F // 152 +data4 0x2414DF8D // 153 +data4 0x247B5546 // 154 +data4 0x2415C980 // 155 +data4 0x24324ABD // 156 +data4 0x234EB5E5 // 157 +data4 0x2465E43E // 158 +data4 0x242840D1 // 159 +data4 0x24444057 // 160 +data4 0x245E56F0 // 161 +data4 0x21AE30F8 // 162 +data4 0x23FB3283 // 163 +data4 0x247A4D07 // 164 +data4 0x22AE314D // 165 +data4 0x246B7727 // 166 +data4 0x24EAD526 // 167 +data4 0x24B41DC9 // 168 +data4 0x24EE8062 // 169 +data4 0x24A0C7C4 // 170 +data4 0x24E8DA67 // 171 +data4 0x231120F7 // 172 +data4 0x24401FFB // 173 +data4 0x2412DD09 // 174 +data4 0x248C131A // 175 +data4 0x24C0A7CE // 176 +data4 0x243DD4C8 // 177 +data4 0x24457FEB // 178 +data4 0x24DEEFBB // 179 +data4 0x243C70AE // 180 +data4 0x23E7A6FA // 181 +data4 0x24C2D311 // 182 +data4 0x23026255 // 183 +data4 0x2437C9B9 // 184 +data4 0x246BA847 // 185 +data4 0x2420B448 // 186 +data4 0x24C4CF5A // 187 +data4 0x242C4981 // 188 +data4 0x24DE1525 // 189 +data4 0x24F5CC33 // 190 +data4 0x235A85DA // 191 +data4 0x24A0B64F // 192 +data4 0x244BA0A4 // 193 +data4 0x24AAF30A // 194 +data4 0x244C86F9 // 195 +data4 0x246D5B82 // 196 +data4 0x24529347 // 197 +data4 0x240DD008 // 198 +data4 0x24E98790 // 199 +data4 0x2489B0CE // 200 +data4 0x22BC29AC // 201 +data4 0x23F37C7A // 202 +data4 0x24987FE8 // 203 +data4 0x22AFE20B // 204 +data4 0x24C8D7C2 // 205 +data4 0x24B28B7D // 206 +data4 0x23B6B271 // 207 +data4 0x24C77CB6 // 208 +data4 0x24EF1DCA // 209 +data4 0x24A4F0AC // 210 +data4 0x24CF113E // 211 +data4 0x2496BBAB // 212 +data4 0x23C7CC8A // 213 +data4 0x23AE3961 // 214 +data4 0x2410A895 // 215 +data4 0x23CE3114 // 216 +data4 0x2308247D // 217 +data4 0x240045E9 // 218 +data4 0x24974F60 // 219 +data4 0x242CB39F // 220 +data4 0x24AB8D69 // 221 +data4 0x23436788 // 222 +data4 0x24305E9E // 223 +data4 0x243E71A9 // 224 +data4 0x23C2A6B3 // 225 +data4 0x23FFE6CF // 226 +data4 0x2322D801 // 227 +data4 0x24515F21 // 228 +data4 0x2412A0D6 // 229 +data4 0x24E60D44 // 230 +data4 0x240D9251 // 231 +data4 0x247076E2 // 232 +data4 0x229B101B // 233 +data4 0x247B12DE // 234 +data4 0x244B9127 // 235 +data4 0x2499EC42 // 236 +data4 0x21FC3963 // 237 +data4 0x23E53266 // 238 +data4 0x24CE102D // 239 +data4 0x23CC45D2 // 240 +data4 0x2333171D // 241 +data4 0x246B3533 // 242 +data4 0x24931129 // 243 +data4 0x24405FFA // 244 +data4 0x24CF464D // 245 +data4 0x237095CD // 246 +data4 0x24F86CBD // 247 +data4 0x24E2D84B // 248 +data4 0x21ACBB44 // 249 +data4 0x24F43A8C // 250 +data4 0x249DB931 // 251 +data4 0x24A385EF // 252 +data4 0x238B1279 // 253 +data4 0x2436213E // 254 +data4 0x24F18A3B // 255 +LOCAL_OBJECT_END(log_data) + + +// Code +//============================================================== .section .text -.proc log1p# -.global log1p# -.align 64 -log1p: -#ifdef _LIBC -.global __log1p -__log1p: -#endif - +GLOBAL_IEEE754_ENTRY(log1p) { .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 + getf.exp GR_signexp_x = f8 // if x is unorm then must recompute + fadd.s1 FR_Xp1 = f8, f1 // Form 1+x + mov GR_05 = 0xfffe } - -{ .mfi -(p0) cmp.ne.unc p14, p0 = r0, r0 -(p0) fnorm.s1 FR_X_Prime = FR_Input_X -(p0) cmp.eq.unc p15, p0 = r0, r0 ;; -} - -{ .mfi - nop.m 999 -(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF - nop.i 999 +{ .mlx + addl GR_ad_1 = @ltoff(log_data),gp + movl GR_A3 = 0x3fd5555555555557 // double precision memory + // representation of A3 } ;; { .mfi - nop.m 999 -(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f0 - nop.i 999 -} - -{ .mfi - nop.m 999 -(p0) fadd FR_Em1 = f0,f0 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) fadd FR_E = f0,f1 - nop.i 999 ;; + ld8 GR_ad_1 = [GR_ad_1] + fclass.m p8,p0 = f8,0xb // Is x unorm? + mov GR_exp_mask = 0x1ffff } - { .mfi - nop.m 999 -(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, FR_Neg_One - nop.i 999 + nop.m 0 + fnorm.s1 FR_NormX = f8 // Normalize x + mov GR_exp_bias = 0xffff } +;; { .mfi - nop.m 999 -(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, FR_Neg_One - nop.i 999 -} - - -L(LOG_BEGIN): - -{ .mfi - nop.m 999 -(p0) fadd.s1 FR_Z = FR_X_Prime, FR_E - nop.i 999 + setf.exp FR_A2 = GR_05 // create A2 = 0.5 + fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf? + nop.i 0 } - -{ .mlx - nop.m 999 -(p0) movl GR_Table_Scale = 0x0000000000000018 ;; -} - -{ .mmi - nop.m 999 -// -// Create E = 1 and Em1 = 0 -// Check for X == 0, meaning log(1+0) -// Check for X < -1, meaning log(negative) -// Check for X == -1, meaning log(0) -// Normalize x -// Identify NatVals, NaNs, Infs. -// Identify EM unsupporteds. -// Identify Negative values - us S1 so as -// not to raise denormal operand exception -// Set p15 to true for log1p -// Set p14 to false for log1p -// Set p7 true for log and log1p -// -(p0) addl GR_Table_Base = @ltoff(Constants_Z_G_H_h1#),gp - nop.i 999 -} - -{ .mfi - nop.m 999 -(p0) fmax.s1 FR_AA = FR_X_Prime, FR_E - nop.i 999 ;; +{ .mib + setf.d FR_A3 = GR_A3 // create A3 + add GR_ad_2 = 16,GR_ad_1 // address of A5,A4 +(p8) br.cond.spnt log1p_unorm // Branch if x=unorm } +;; +log1p_common: { .mfi - ld8 GR_Table_Base = [GR_Table_Base] -(p0) fmin.s1 FR_BB = FR_X_Prime, FR_E - nop.i 999 + nop.m 0 + frcpa.s1 FR_RcpX,p0 = f1,FR_Xp1 + nop.i 0 } - { .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(LOG_64_special) ;; -} - -{ .mib - nop.m 999 - nop.i 999 -(p10) br.cond.spnt L(LOG_64_unsupported) ;; -} - -{ .mib - nop.m 999 - nop.i 999 -(p13) br.cond.spnt L(LOG_64_negative) ;; -} - -{ .mib -(p0) getf.sig GR_signif = FR_Z - nop.i 999 -(p9) br.cond.spnt L(LOG_64_one) ;; -} - -{ .mib - nop.m 999 - nop.i 999 -(p8) br.cond.spnt L(LOG_64_zero) ;; + nop.m 0 +(p9) fma.d.s0 f8 = f8,f1,f0 // set V-flag +(p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf } +;; { .mfi -(p0) getf.exp GR_N = FR_Z -// -// Raise possible denormal operand exception -// Create Bias -// -// This function computes ln( x + e ) -// Input FR 1: FR_X = FR_Input_X -// Input FR 2: FR_E = FR_E -// Input FR 3: FR_Em1 = FR_Em1 -// Input GR 1: GR_Expo_Range = GR_Expo_Range = 1 -// Output FR 4: FR_Y_hi -// Output FR 5: FR_Y_lo -// Output FR 6: FR_Scale -// Output PR 7: PR_Safe -// -(p0) fsub.s1 FR_S_lo = FR_AA, FR_Z -// -// signif = getf.sig(Z) -// abs_W = fabs(w) -// -(p0) extr.u GR_Table_ptr = GR_signif, 59, 4 ;; + getf.exp GR_Exp = FR_Xp1 // signexp of x+1 + fclass.m p10,p0 = FR_Xp1,0x3A // is 1+x < 0? + and GR_exp_x = GR_exp_mask, GR_signexp_x // biased exponent of x } - { .mfi - nop.m 999 -(p0) fmerge.se FR_S_hi = f1,FR_Z -(p0) extr.u GR_X_0 = GR_signif, 49, 15 -} - -{ .mmi - nop.m 999 -(p0) addl GR_Table_Base1 = @ltoff(Constants_Z_G_H_h2#),gp - nop.i 999 + ldfpd FR_A7,FR_A6 = [GR_ad_1] + nop.f 0 + nop.i 0 } ;; -{ .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 ;; + getf.sig GR_Sig = FR_Xp1 // get significand to calculate index + // for Thi,Tlo if |x| >= 2^-8 + fcmp.eq.s1 p12,p0 = f8,f0 // is x equal to 0? + sub GR_exp_x = GR_exp_x, GR_exp_bias // true exponent of x } +;; { .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 ;; + sub GR_N = GR_Exp,GR_exp_bias // true exponent of x+1 + fcmp.eq.s1 p11,p0 = FR_Xp1,f0 // is x = -1? + cmp.gt p6,p7 = -8, GR_exp_x // Is |x| < 2^-8 } -// -// Add Base to Offset for Z1 -// Create Bias - -{ .mmi -(p0) ld4 GR_Z_1 = [GR_Table_ptr],4 ;; -(p0) ldfs FR_G = [GR_Table_ptr],4 - nop.i 999 ;; -} - -{ .mmi -(p0) ldfs FR_H = [GR_Table_ptr],8 ;; -(p0) ldfd FR_h = [GR_Table_ptr],0 -(p0) pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 +{ .mfb + ldfpd FR_A5,FR_A4 = [GR_ad_2],16 + nop.f 0 +(p10) br.cond.spnt log1p_lt_minus_1 // jump if x < -1 } -// -// Load Z_1 -// Get Base of Table2 -// +;; +// p6 is true if |x| < 1/256 +// p7 is true if |x| >= 1/256 +.pred.rel "mutex",p6,p7 { .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 ;; +(p7) add GR_ad_1 = 0x820,GR_ad_1 // address of log(2) parts +(p6) fms.s1 FR_r = f8,f1,f0 // range reduction for |x|<1/256 +(p6) cmp.gt.unc p10,p0 = -80, GR_exp_x // Is |x| < 2^-80 } -// -// M = M - Bias -// Load G1 -// N = getf.exp(Z) -// - -{ .mii -(p0) cmp.gt.unc p11, p0 = -80, GR_M -(p0) cmp.gt.unc p12, p0 = -7, GR_M ;; -(p0) extr.u GR_Index2 = GR_X_1, 6, 4 ;; -} - -{ .mib - nop.m 999 -// -// if -80 > M, set p11 -// Index2 = extr.u(X_1,6,4) -// if -7 > M, set p12 -// Load H1 -// -(p0) pmpyshr2.u GR_Index2 = GR_Index2,GR_Table_Scale,0 -(p11) br.cond.spnt L(log1p_small) ;; +{ .mfb +(p7) setf.sig FR_N = GR_N // copy unbiased exponent of x to the + // significand field of FR_N +(p7) fms.s1 FR_r = FR_RcpX,FR_Xp1,f1 // range reduction for |x|>=1/256 +(p12) br.ret.spnt b0 // exit for x=0, return x } +;; { .mib - nop.m 999 - nop.i 999 -(p12) br.cond.spnt L(log1p_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 -(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 - ld8 GR_Table_Base = [GR_Table_Base] - nop.b 999 ;; -} -(p0) nop.i 999 -// -// Load Z_2 -// N = N - Bias -// Tablebase points to Table3 -// - -{ .mmi -(p0) ldfs FR_G_tmp = [GR_Index2],4 ;; -// -// Load G_2 -// pmpyshr2 X_2= (X_1,Z_2,15) -// float_N = setf.sig(N) -// ScaleN = Bias - N -// -(p0) ldfs FR_H_tmp = [GR_Index2],8 - nop.i 999 ;; -} -// -// Load H_2 -// two_negN = setf.exp(scaleN) -// G = G_1 * G_2 -// - -{ .mfi -(p0) ldfd FR_h_tmp = [GR_Index2],0 - nop.f 999 -(p0) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 ;; -} - -{ .mii - nop.m 999 -(p0) extr.u GR_Index3 = GR_X_2, 1, 5 ;; -// -// Load h_2 -// H = H_1 + H_2 -// h = h_1 + h_2 -// Index3 = extr.u(X_2,1,5) -// -(p0) shladd GR_Index3 = GR_Index3,4,GR_Table_Base +(p7) ldfpd FR_Ln2hi,FR_Ln2lo = [GR_ad_1],16 +(p7) extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index +(p11) br.cond.spnt log1p_eq_minus_1 // jump if x = -1 } - -{ .mmi - nop.m 999 - nop.m 999 -// -// float_N = fcvt.xf(float_N) -// load G3 -// -(p0) addl GR_Table_Base = @ltoff(Constants_Q#),gp ;; -} - -{ .mfi -ld8 GR_Table_Base = [GR_Table_Base] -nop.f 999 -nop.i 999 -} ;; - -{ .mfi -(p0) ldfe FR_log2_hi = [GR_Table_Base],16 -(p0) fmpy.s1 FR_S_lo = FR_S_lo, FR_two_negN - nop.i 999 ;; -} - -{ .mmf - nop.m 999 -// -// G = G3 * G -// Load h3 -// Load log2_hi -// H = H + H3 -// -(p0) ldfe FR_log2_lo = [GR_Table_Base],16 -(p0) fmpy.s1 FR_G = FR_G, FR_G_tmp ;; -} - -{ .mmf -(p0) ldfs FR_G_tmp = [GR_Index3],4 -// -// h = h + h3 -// r = G * S_hi + 1 -// Load log2_lo -// -(p0) ldfe FR_Q4 = [GR_Table_Base],16 -(p0) fadd.s1 FR_h = FR_h, FR_h_tmp ;; -} - -{ .mfi -(p0) ldfe FR_Q3 = [GR_Table_Base],16 -(p0) fadd.s1 FR_H = FR_H, FR_H_tmp - nop.i 999 ;; -} - -{ .mmf -(p0) ldfs FR_H_tmp = [GR_Index3],4 -(p0) ldfe FR_Q2 = [GR_Table_Base],16 -// -// Comput Index for Table3 -// S_lo = S_lo * two_negN -// -(p0) fcvt.xf FR_float_N = FR_float_N ;; -} -// -// If S_lo == 0, set p8 false -// Load H3 -// Load ptr to table of polynomial coeff. -// +;; { .mmf -(p0) ldfd FR_h_tmp = [GR_Index3],0 -(p0) ldfe FR_Q1 = [GR_Table_Base],0 -(p0) fcmp.eq.unc.s1 p0, p8 = FR_S_lo, f0 ;; -} - -{ .mfi - nop.m 999 -(p0) fmpy.s1 FR_G = FR_G, FR_G_tmp - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) fadd.s1 FR_H = FR_H, FR_H_tmp - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) fms.s1 FR_r = FR_G, FR_S_hi, f1 - nop.i 999 -} - -{ .mfi - nop.m 999 -(p0) fadd.s1 FR_h = FR_h, FR_h_tmp - nop.i 999 ;; -} - -{ .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 -// -// 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 -// -// 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 -// -// 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 -(p0) setf.sig FR_dummy = GR_Perturb -(p0) fmpy.s1 FR_rsq = FR_r, FR_r - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// h = N * log2_lo + h -// Y_hi = n * log2_hi + H -// -(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 - nop.i 999 -} - -{ .mfi - nop.m 999 -(p0) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -// -// poly_lo = r * poly_o + Q2 -// poly_hi = Q1 * rsq + r -// -(p0) fmpy.s1 FR_poly_lo = FR_poly_lo, FR_r - nop.i 999 ;; -} - -{ .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 L(LOG_main) ;; -} - - -L(log1p_near): - -{ .mmi - nop.m 999 - nop.m 999 -// /*******************************************************/ -// /*********** Branch log1p_near ************************/ -// /*******************************************************/ -(p0) addl GR_Table_Base = @ltoff(Constants_P#),gp ;; -} -// -// Load base address of poly. coeff. -// -{.mmi - nop.m 999 - ld8 GR_Table_Base = [GR_Table_Base] - nop.i 999 -};; - -{ .mmb -(p0) add GR_Table_ptr = 0x40,GR_Table_Base -// -// Address tables with separate pointers -// -(p0) ldfe FR_P8 = [GR_Table_Base],16 - nop.b 999 ;; +(p7) shladd GR_ad_2 = GR_Ind,3,GR_ad_2 // address of Thi +(p7) shladd GR_ad_1 = GR_Ind,2,GR_ad_1 // address of Tlo +(p10) fnma.d.s0 f8 = f8,f8,f8 // If |x| very small, result=x-x*x } +;; { .mmb -(p0) ldfe FR_P4 = [GR_Table_ptr],16 -// -// Load P4 -// Load P8 -// -(p0) ldfe FR_P7 = [GR_Table_Base],16 - nop.b 999 ;; -} - -{ .mmf -(p0) ldfe FR_P3 = [GR_Table_ptr],16 -// -// Load P3 -// Load P7 -// -(p0) ldfe FR_P6 = [GR_Table_Base],16 -(p0) fmpy.s1 FR_wsq = FR_W, FR_W ;; -} - -{ .mfi -(p0) ldfe FR_P2 = [GR_Table_ptr],16 - nop.f 999 - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) fma.s1 FR_Y_hi = FR_W, FR_P4, FR_P3 - nop.i 999 -} -// -// Load P2 -// Load P6 -// Wsq = w * w -// Y_hi = p4 * w + p3 -// - -{ .mfi -(p0) ldfe FR_P5 = [GR_Table_Base],16 -(p0) fma.s1 FR_Y_lo = FR_W, FR_P8, FR_P7 - nop.i 999 ;; -} - -{ .mfi -(p0) ldfe FR_P1 = [GR_Table_ptr],16 -// -// Load P1 -// Load P5 -// Y_lo = p8 * w + P7 -// -(p0) fmpy.s1 FR_w4 = FR_wsq, FR_wsq - nop.i 999 ;; +(p7) ldfd FR_Thi = [GR_ad_2] +(p7) ldfs FR_Tlo = [GR_ad_1] +(p10) br.ret.spnt b0 // Exit if |x| < 2^(-80) } +;; { .mfi - nop.m 999 -(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P2 - nop.i 999 + nop.m 0 + fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2 + nop.i 0 } - { .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 0 + fms.s1 FR_A2 = FR_A3,FR_r,FR_A2 // A3*r+A2 + nop.i 0 } +;; { .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 0 + fma.s1 FR_A6 = FR_A7,FR_r,FR_A6 // A7*r+A6 + nop.i 0 } - { .mfi - nop.m 999 -(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P1 - nop.i 999 + nop.m 0 + fma.s1 FR_A4 = FR_A5,FR_r,FR_A4 // A5*r+A4 + nop.i 0 } -// -// 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 0 +(p7) fcvt.xf FR_N = FR_N + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fma.s1 FR_Y_hi = FR_wsq,FR_Y_hi, FR_W - nop.i 999 -} - -{ .mfb - nop.m 999 -// -// Y_hi = y_hi * wsq + w -// Y_lo = y_lo * w + p5 -// -(p0) fmpy.s1 FR_Y_lo = FR_w6, FR_Y_lo -// -// Y_lo = y_lo * w6 -// -// (p0) for FR_dummy = FR_Y_lo,FR_dummy ;; -// -// Set lsb on: Taken out to improve performance -// -// (p0) fmerge.se FR_Y_lo = FR_Y_lo,FR_dummy ;; -// -// Make sure it's on in Y_lo also. Taken out to improve -// performance -// -(p0) br.cond.sptk L(LOG_main) ;; -} - - -L(log1p_small): - -{ .mmi - nop.m 999 - nop.m 999 -// /*******************************************************/ -// /*********** Branch log1p_small ***********************/ -// /*******************************************************/ -(p0) addl GR_Table_Base = @ltoff(Constants_Threshold#),gp + nop.m 0 + fma.s1 FR_r4 = FR_r2,FR_r2,f0 // r^4 + nop.i 0 } - { .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 = 0x0000000000000002 ;; -} -// -// Set Safe to true -// Set Expo_Range = 0 for single -// Set Expo_Range = 2 for double -// Set Expo_Range = 4 for double-extended -// - -{ .mmi -(p0) shladd GR_Table_Base = GR_Expo_Range,4,GR_Table_Base ;; -(p0) ldfe FR_Threshold = [GR_Table_Base],16 - nop.i 999 -} - -{ .mlx - nop.m 999 -(p0) movl GR_Bias = 0x000000000000FF9B ;; + nop.m 0 + // (A3*r+A2)*r^2+r + fma.s1 FR_A2 = FR_A2,FR_r2,FR_r + nop.i 0 } +;; { .mfi -(p0) ldfe FR_Tiny = [GR_Table_Base],0 - nop.f 999 - nop.i 999 ;; + nop.m 0 + // (A7*r+A6)*r^2+(A5*r+A4) + fma.s1 FR_A4 = FR_A6,FR_r2,FR_A4 + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fcmp.gt.unc.s1 p13, p12 = FR_abs_W, FR_Threshold - nop.i 999 ;; + nop.m 0 + // N*Ln2hi+Thi +(p7) fma.s1 FR_NxLn2hipThi = FR_N,FR_Ln2hi,FR_Thi + nop.i 0 } - { .mfi - nop.m 999 -(p13) fnmpy.s1 FR_Y_lo = FR_W, FR_W - nop.i 999 + nop.m 0 + // N*Ln2lo+Tlo +(p7) fma.s1 FR_NxLn2lopTlo = FR_N,FR_Ln2lo,FR_Tlo + nop.i 0 } +;; { .mfi - nop.m 999 -(p13) fadd FR_SCALE = f0, f1 - nop.i 999 ;; + nop.m 0 +(p7) fma.s1 f8 = FR_A4,FR_r4,FR_A2 // P(r) if |x| >= 1/256 + nop.i 0 } - { .mfi - nop.m 999 -(p12) fsub.s1 FR_Y_lo = f0, FR_Tiny -(p12) cmp.ne.unc p7, p0 = r0, r0 + nop.m 0 + // (N*Ln2hi+Thi) + (N*Ln2lo+Tlo) +(p7) fma.s1 FR_NxLn2pT = FR_NxLn2hipThi,f1,FR_NxLn2lopTlo + nop.i 0 } +;; +.pred.rel "mutex",p6,p7 { .mfi -(p12) setf.exp FR_SCALE = GR_Bias - nop.f 999 - nop.i 999 ;; + nop.m 0 +(p6) fma.d.s0 f8 = FR_A4,FR_r4,FR_A2 // result if 2^(-80) <= |x| < 1/256 + nop.i 0 } - -// -// Set p7 to SAFE = FALSE -// Set Scale = 2^-100 -// { .mfb - nop.m 999 -(p0) fma.d.s0 FR_Input_X = FR_Y_lo,FR_SCALE,FR_Y_hi -(p0) br.ret.sptk b0 + nop.m 0 +(p7) fma.d.s0 f8 = f8,f1,FR_NxLn2pT // result if |x| >= 1/256 + br.ret.sptk b0 // Exit if |x| >= 2^(-80) } ;; -L(LOG_64_one): - +.align 32 +log1p_unorm: +// Here if x=unorm { .mfb - nop.m 999 -(p0) fmpy.d.s0 FR_Input_X = FR_Input_X, f0 -(p0) br.ret.sptk b0 + getf.exp GR_signexp_x = FR_NormX // recompute biased exponent + nop.f 0 + br.cond.sptk log1p_common } ;; -// -// Raise divide by zero for +/-0 input. -// -L(LOG_64_zero): - +.align 32 +log1p_eq_minus_1: +// Here if x=-1 { .mfi -(p0) mov GR_Parameter_TAG = 140 -// -// If we have log1p(0), return -Inf. -// -(p0) fsub.s0 FR_Output_X_tmp = f0, f1 - nop.i 999 ;; + nop.m 0 + fmerge.s FR_X = f8,f8 // keep input argument for subsequent + // call of __libm_error_support# + nop.i 0 } -{ .mfb - nop.m 999 -(p0) frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0 -(p0) br.cond.sptk L(LOG_ERROR_Support) ;; -} - -L(LOG_64_special): +;; { .mfi - nop.m 999 -// -// Return -Inf or value from handler. -// -(p0) fclass.m.unc p7, p0 = FR_Input_X, 0x1E1 - nop.i 999 ;; + mov GR_TAG = 140 // set libm error in case of log1p(-1). + frcpa.s0 f8,p0 = f8,f0 // log1p(-1) should be equal to -INF. + // We can get it using frcpa because it + // sets result to the IEEE-754 mandated + // quotient of f8/f0. + nop.i 0 } -{ .mfb - nop.m 999 -// -// Check for Natval, QNan, SNaN, +Inf -// -(p7) fmpy.d.s0 f8 = FR_Input_X, f1 -// -// For SNaN raise invalid and return QNaN. -// For QNaN raise invalid and return QNaN. -// For +Inf return +Inf. -// -(p7) br.ret.sptk b0 +{ .mib + nop.m 0 + nop.i 0 + br.cond.sptk log_libm_err } ;; -// -// For -Inf raise invalid and return QNaN. -// - -{ .mfb -(p0) mov GR_Parameter_TAG = 141 -(p0) fmpy.d.s0 FR_Output_X_tmp = FR_Input_X, f0 -(p0) br.cond.sptk L(LOG_ERROR_Support) ;; +.align 32 +log1p_lt_minus_1: +// Here if x < -1 +{ .mfi + nop.m 0 + fmerge.s FR_X = f8,f8 + nop.i 0 } +;; -// -// Report that log1p(-Inf) computed -// - -L(LOG_64_unsupported): - -// -// Return generated NaN or other value . -// - -{ .mfb - nop.m 999 -(p0) fmpy.d.s0 FR_Input_X = FR_Input_X, f0 -(p0) br.ret.sptk b0 ;; +{ .mfi + mov GR_TAG = 141 // set libm error in case of x < -1. + frcpa.s0 f8,p0 = f0,f0 // log1p(x) x < -1 should be equal to NaN. + // We can get it using frcpa because it + // sets result to the IEEE-754 mandated + // quotient of f0/f0 i.e. NaN. + nop.i 0 } +;; -L(LOG_64_negative): - -{ .mfi - nop.m 999 -// -// Deal with x < 0 in a special way -// -(p0) frcpa.s0 FR_Output_X_tmp, p8 = f0, f0 -// -// Deal with x < 0 in a special way - raise -// invalid and produce QNaN indefinite. -// -(p0) mov GR_Parameter_TAG = 141 +.align 32 +log_libm_err: +{ .mmi + alloc r32 = ar.pfs,1,4,4,0 + mov GR_Parameter_TAG = GR_TAG + nop.i 0 } +;; -.endp log1p# -ASM_SIZE_DIRECTIVE(log1p) +GLOBAL_IEEE754_END(log1p) -.proc __libm_error_region -__libm_error_region: -L(LOG_ERROR_Support): +LOCAL_LIBM_ENTRY(__libm_error_region) .prologue - -// (1) { .mfi - add GR_Parameter_Y=-32,sp // Parameter 2 value + add GR_Parameter_Y = -32,sp // Parameter 2 value nop.f 0 .save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs + mov GR_SAVE_PFS = ar.pfs // Save ar.pfs } { .mfi .fframe 64 - add sp=-64,sp // Create new stack + add sp = -64,sp // Create new stack nop.f 0 - mov GR_SAVE_GP=gp // Save gp + mov GR_SAVE_GP = gp // Save gp };; - - -// (2) { .mmi - stfd [GR_Parameter_Y] = f0,16 // STORE Parameter 2 on stack + stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack add GR_Parameter_X = 16,sp // Parameter 1 address .save b0, GR_SAVE_B0 - mov GR_SAVE_B0=b0 // Save b0 + mov GR_SAVE_B0 = b0 // Save b0 };; - .body -// (3) { .mib - stfd [GR_Parameter_X] =FR_Input_X // STORE Parameter 1 on stack - add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address - nop.b 0 + stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address + nop.b 0 } { .mib - stfd [GR_Parameter_Y] = FR_Output_X_tmp // STORE Parameter 3 on stack + stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack add GR_Parameter_Y = -16,GR_Parameter_Y - br.call.sptk b0=__libm_error_support# // Call error handling function + br.call.sptk b0=__libm_error_support# // Call error handling function };; { .mmi - nop.m 0 - nop.m 0 add GR_Parameter_RESULT = 48,sp + nop.m 0 + nop.i 0 };; - -// (4) { .mmi - ldfd FR_Input_X = [GR_Parameter_RESULT] // Get return result off stack + ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack .restore sp - add sp = 64,sp // Restore stack pointer - mov b0 = GR_SAVE_B0 // Restore return address + add sp = 64,sp // Restore stack pointer + mov b0 = GR_SAVE_B0 // Restore return address };; { .mib - mov gp = GR_SAVE_GP // Restore gp - mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs - br.ret.sptk b0 + mov gp = GR_SAVE_GP // Restore gp + mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs + br.ret.sptk b0 // Return };; - -.endp __libm_error_region -ASM_SIZE_DIRECTIVE(__libm_error_region) - -.proc __libm_LOG_main -__libm_LOG_main: -L(LOG_main): - -// -// kernel_log_64 computes ln(X + E) -// - -{ .mfi - nop.m 999 -(p7) fadd.d.s0 FR_Input_X = FR_Y_lo,FR_Y_hi - nop.i 999 -} - -{ .mmi - nop.m 999 - nop.m 999 -(p14) addl GR_Table_Base = @ltoff(Constants_1_by_LN10#),gp ;; -} - -{ .mmi - nop.m 999 -(p14) ld8 GR_Table_Base = [GR_Table_Base] - nop.i 999 -};; - -{ .mmi -(p14) ldfe FR_1LN10_hi = [GR_Table_Base],16 ;; -(p14) ldfe FR_1LN10_lo = [GR_Table_Base] - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p14) fmpy.s1 FR_Output_X_tmp = FR_Y_lo,FR_1LN10_hi - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p14) fma.s1 FR_Output_X_tmp = FR_Y_hi,FR_1LN10_lo,FR_Output_X_tmp - nop.i 999 ;; -} - -{ .mfb - nop.m 999 -(p14) fma.d.s0 FR_Input_X = FR_Y_hi,FR_1LN10_hi,FR_Output_X_tmp -(p0) br.ret.sptk b0 ;; -} -.endp __libm_LOG_main -ASM_SIZE_DIRECTIVE(__libm_LOG_main) - +LOCAL_LIBM_END(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support# + |