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glibc/sysdeps/ia64/fpu/s_log1pl.S

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.file "log1pl.s"
// Copyright (C) 2000, 2001, 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.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * 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
// 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
// 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.
//
// 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.
//
// *********************************************************************
//
// History:
// 2/02/00 hand-optimized
// 4/04/00 Unwind support added
// 8/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
//
// *********************************************************************
//
// *********************************************************************
//
// 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)
// 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
//
// 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
// log1pl(-1) = -inf
// log1pl(SNaN) = QNaN
// log1pl(QNaN) = QNaN
// log1pl(EM_special Values) = QNaN
// log10l(inf) = inf
// log10l(-inf) = QNaN
// log10l(+/-0) = -inf
// log10l(SNaN) = QNaN
// log10l(QNaN) = QNaN
// log10l(EM_special Values) = QNaN
//
// *********************************************************************
//
// Computation is based on the following kernel.
//
// ker_log_64( in_FR : X,
// in_FR : E,
// in_FR : Em1,
// in_GR : Expo_Range,
// out_FR : Y_hi,
// out_FR : Y_lo,
// out_FR : Scale,
// out_PR : Safe )
//
// Overview
//
// The method consists of three cases.
//
// If |X+Em1| < 2^(-80) use case log1pl_small;
// elseif |X+Em1| < 2^(-7) use case log_near1;
// else use case log_regular;
//
// Case log1pl_small:
//
// logl( 1 + (X+Em1) ) can be approximated by (X+Em1).
//
// Case log_near1:
//
// 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) 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))
//
// 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 logl( 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
//
//
// logl(1 + r) is approximated by a short polynomial poly(r).
//
// Step 3: Reconstruction
//
//
// Finally, logl( E + X ) is given by
//
// 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 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 + 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.
//
//
// 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 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 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.
//
//
// 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 ].
//
// 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.
//
// 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 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.
//
// Compute G := G_1 * G_2 * G_3.
//
// This is done exactly since each of G_j only has 21 sig. bits.
//
// Compute
//
// 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.
//
//
// Step 2. Approximation
// ---------------------
//
// This step computes an approximation to logl( 1 + r ) where r is the
// 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
//
//
// Step 3. Reconstruction
// ----------------------
//
// This step computes the desired result of logl(X+E):
//
// 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 )
//
// is computable exactly in double-extended precision (64 sig. bits).
// Finally
//
// Y_hi := N*log2_hi + SUM ( log1byGj_hi )
// Y_lo := poly_hi + [ poly_lo +
// ( SUM ( log1byGj_lo ) + N*log2_lo ) ]
// set lsb(Y_lo) to be 1
//
#include "libm_support.h"
#ifdef _LIBC
.rodata
#else
.data
#endif
// 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
.align 64
Constants_Q:
ASM_TYPE_DIRECTIVE(Constants_Q,@object)
data4 0x00000000,0xB1721800,0x00003FFE,0x00000000
data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000
data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000
data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000
data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000
ASM_SIZE_DIRECTIVE(Constants_Q)
// Z1 - 16 bit fixed, G1 and H1 - IEEE single
.align 64
Constants_Z_G_H_h1:
ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h1,@object)
data4 0x00008000,0x3F800000,0x00000000,0x00000000,0x00000000,0x00000000
data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000,0x617D741C,0x3DA163A6
data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000,0xCBD3D5BB,0x3E2C55E6
data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000,0xD86EA5E7,0xBE3EB0BF
data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000,0x86B12760,0x3E2E6A8C
data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000,0x5C0739BA,0x3E47574C
data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000,0x13E8AF2F,0x3E20E30F
data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000,0xF2C630BD,0xBE42885B
data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000,0x97E577C6,0x3E497F34
data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000,0xA6B0A5AB,0x3E3E6A6E
data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000,0xD328D9BE,0xBDF43E3C
data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000,0x0ADB090A,0x3E4094C3
data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000,0xFC1FE510,0xBE28FBB2
data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000,0x10FDE3FA,0x3E3A7895
data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000,0x7CC8C98F,0x3E508CE5
data4 0x00004211,0x3F042108,0x3F29516A,0x00000000,0xA223106C,0xBE534874
ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h1)
// Z2 - 16 bit fixed, G2 and H2 - IEEE single
.align 64
Constants_Z_G_H_h2:
ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h2,@object)
data4 0x00008000,0x3F800000,0x00000000,0x00000000,0x00000000,0x00000000
data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000,0x22C42273,0x3DB5A116
data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000,0x21F86ED3,0x3DE620CF
data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000,0x484F34ED,0xBDAFA07E
data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000,0x3860BCF6,0xBDFE07F0
data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000,0xA78093D6,0x3DEA370F
data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000,0x72A753D0,0x3DFF5791
data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000,0xA7EF896B,0x3DFEBE6C
data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000,0x409ECB43,0x3E0CF156
data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000,0xFFEF71DF,0xBE0B6F97
data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000,0x5D59EEE8,0xBE080483
data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000,0xA9192A74,0x3E1F91E9
data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000,0xBF72A8CD,0xBE139A06
data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000,0xF8FBA6CF,0x3E1D9202
data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000,0xBA796223,0xBE1DCCC4
data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000,0xB6B7C239,0xBE049391
ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h2)
// G3 and H3 - IEEE single and h3 -IEEE double
.align 64
Constants_Z_G_H_h3:
ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h3,@object)
data4 0x3F7FFC00,0x38800100,0x562224CD,0x3D355595
data4 0x3F7FF400,0x39400480,0x06136FF6,0x3D8200A2
data4 0x3F7FEC00,0x39A00640,0xE8DE9AF0,0x3DA4D68D
data4 0x3F7FE400,0x39E00C41,0xB10238DC,0xBD8B4291
data4 0x3F7FDC00,0x3A100A21,0x3B1952CA,0xBD89CCB8
data4 0x3F7FD400,0x3A300F22,0x1DC46826,0xBDB10707
data4 0x3F7FCC08,0x3A4FF51C,0xF43307DB,0x3DB6FCB9
data4 0x3F7FC408,0x3A6FFC1D,0x62DC7872,0xBD9B7C47
data4 0x3F7FBC10,0x3A87F20B,0x3F89154A,0xBDC3725E
data4 0x3F7FB410,0x3A97F68B,0x62B9D392,0xBD93519D
data4 0x3F7FAC18,0x3AA7EB86,0x0F21BD9D,0x3DC18441
data4 0x3F7FA420,0x3AB7E101,0x2245E0A6,0xBDA64B95
data4 0x3F7F9C20,0x3AC7E701,0xAABB34B8,0x3DB4B0EC
data4 0x3F7F9428,0x3AD7DD7B,0x6DC40A7E,0x3D992337
data4 0x3F7F8C30,0x3AE7D474,0x4F2083D3,0x3DC6E17B
data4 0x3F7F8438,0x3AF7CBED,0x811D4394,0x3DAE314B
data4 0x3F7F7C40,0x3B03E1F3,0xB08F2DB1,0xBDD46F21
data4 0x3F7F7448,0x3B0BDE2F,0x6D34522B,0xBDDC30A4
data4 0x3F7F6C50,0x3B13DAAA,0xB1F473DB,0x3DCB0070
data4 0x3F7F6458,0x3B1BD766,0x6AD282FD,0xBDD65DDC
data4 0x3F7F5C68,0x3B23CC5C,0xF153761A,0xBDCDAB83
data4 0x3F7F5470,0x3B2BC997,0x341D0F8F,0xBDDADA40
data4 0x3F7F4C78,0x3B33C711,0xEBC394E8,0x3DCD1BD7
data4 0x3F7F4488,0x3B3BBCC6,0x52E3E695,0xBDC3532B
data4 0x3F7F3C90,0x3B43BAC0,0xE846B3DE,0xBDA3961E
data4 0x3F7F34A0,0x3B4BB0F4,0x785778D4,0xBDDADF06
data4 0x3F7F2CA8,0x3B53AF6D,0xE55CE212,0x3DCC3ED1
data4 0x3F7F24B8,0x3B5BA620,0x9E382C15,0xBDBA3103
data4 0x3F7F1CC8,0x3B639D12,0x5C5AF197,0x3D635A0B
data4 0x3F7F14D8,0x3B6B9444,0x71D34EFC,0xBDDCCB19
data4 0x3F7F0CE0,0x3B7393BC,0x52CD7ADA,0x3DC74502
data4 0x3F7F04F0,0x3B7B8B6D,0x7D7F2A42,0xBDB68F17
ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h3)
//
// 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,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
//
// Added for unwind support
//
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 = f99
.section .text
.proc logl#
.global logl#
.align 64
logl:
#ifdef _LIBC
.global __ieee754_logl
__ieee754_logl:
#endif
{ .mfi
alloc r32 = ar.pfs,0,22,4,0
(p0) fnorm.s1 FR_X_Prime = FR_Input_X
(p0) cmp.eq.unc p7, p0 = r0, r0
}
{ .mfi
(p0) cmp.ne.unc p14, p0 = r0, r0
(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
(p0) cmp.ne.unc p15, p0 = r0, r0 ;;
}
{ .mfi
nop.m 0
(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
nop.i 0
}
{ .mfi
nop.m 999
(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, f0
nop.i 0
}
{ .mfi
nop.m 999
(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, f0
nop.i 0
}
{ .mfi
nop.m 999
(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f1
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p0) fsub.s1 FR_Em1 = f0,f1
nop.i 999
}
{ .mfb
nop.m 999
(p0) fadd FR_E = f0,f0
//
// Create E = 0 and Em1 = -1
// Check for X == 1, meaning logl(1)
// Check for X < 0, meaning logl(negative)
// Check for X == 0, meaning logl(0)
// Identify NatVals, NaNs, Infs.
// Identify EM unsupporteds.
// Identify Negative values - us S1 so as
// not to raise denormal operand exception
// Set p15 to false for log
// Set p14 to false for log
// Set p7 true for log and log1p
//
(p0) br.cond.sptk L(LOGL_BEGIN) ;;
}
.endp logl
ASM_SIZE_DIRECTIVE(logl)
.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) ;;
}
.endp log10l
ASM_SIZE_DIRECTIVE(log10l)
.section .text
.proc log1pl#
.global log1pl#
.align 64
log1pl:
#ifdef _LIBC
.global __log1pl
__log1pl:
#endif
{ .mfi
alloc r32 = ar.pfs,0,22,4,0
(p0) fsub.s1 FR_Neg_One = f0,f1
(p0) cmp.eq.unc p7, p0 = r0, r0
}
{ .mfi
(p0) cmp.ne.unc p14, p0 = r0, r0
(p0) fnorm.s1 FR_X_Prime = FR_Input_X
(p0) cmp.eq.unc p15, p0 = r0, r0 ;;
}
{ .mfi
nop.m 0
(p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
nop.i 0
}
{ .mfi
nop.m 999
(p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
nop.i 0
}
{ .mfi
nop.m 999
(p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f0
nop.i 0
}
{ .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 ;;
}
{ .mfi
nop.m 999
(p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, FR_Neg_One
nop.i 999
}
{ .mfi
nop.m 999
(p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, FR_Neg_One
nop.i 999
}
L(LOGL_BEGIN):
{ .mfi
nop.m 999
(p0) fadd.s1 FR_Z = FR_X_Prime, FR_E
nop.i 999
}
{ .mlx
nop.m 999
(p0) movl GR_Table_Scale = 0x0000000000000018 ;;
}
{ .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
nop.m 999
(p0) fmax.s1 FR_AA = FR_X_Prime, FR_E
nop.i 999 ;;
}
{ .mfi
ld8 GR_Table_Base = [GR_Table_Base]
(p0) fmin.s1 FR_BB = FR_X_Prime, FR_E
nop.i 999
}
{ .mfb
nop.m 999
(p0) fadd.s1 FR_W = FR_X_Prime, FR_Em1
//
// Begin load of constants base
// FR_Z = Z = |x| + E
// FR_W = W = |x| + Em1
// AA = fmax(|x|,E)
// BB = fmin(|x|,E)
//
(p6) br.cond.spnt L(LOGL_64_special) ;;
}
{ .mib
nop.m 999
nop.i 999
(p10) br.cond.spnt L(LOGL_64_unsupported) ;;
}
{ .mib
nop.m 999
nop.i 999
(p13) br.cond.spnt L(LOGL_64_negative) ;;
}
{ .mib
(p0) getf.sig GR_signif = FR_Z
nop.i 999
(p9) br.cond.spnt L(LOGL_64_one) ;;
}
{ .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
//
(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
nop.m 999
nop.m 999
(p0) addl GR_Table_Base1 = @ltoff(Constants_Z_G_H_h2#),gp ;;
}
{ .mlx
ld8 GR_Table_Base1 = [GR_Table_Base1]
(p0) movl GR_Bias = 0x000000000000FFFF ;;
}
{ .mfi
nop.m 999
(p0) fabs FR_abs_W = FR_W
(p0) pmpyshr2.u GR_Table_ptr = GR_Table_ptr,GR_Table_Scale,0
}
{ .mfi
nop.m 999
//
// Branch out for special input values
//
(p0) fcmp.lt.unc.s0 p8, p0 = FR_Input_X, f0
nop.i 999 ;;
}
{ .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
(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
}
//
// 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
(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
(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
}
{ .mmi
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
//
// 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 LOGL_main ;;
}
L(log1pl_near):
{ .mmi
nop.m 999
nop.m 999
// /*******************************************************/
// /*********** Branch log1pl_near ************************/
// /*******************************************************/
(p0) addl GR_Table_Base = @ltoff(Constants_P#),gp ;;
}
{ .mmi
nop.m 999
ld8 GR_Table_Base = [GR_Table_Base]
nop.i 999
};;
//
// Load base address of poly. coeff.
//
{ .mmb
(p0) add GR_Table_ptr = 0x40,GR_Table_Base
//
// Address tables with separate pointers
//
(p0) ldfe FR_P8 = [GR_Table_Base],16
nop.b 999 ;;
}
{ .mmb
(p0) ldfe FR_P4 = [GR_Table_ptr],16
//
// Load P4
// Load P8
//
(p0) ldfe FR_P7 = [GR_Table_Base],16
nop.b 999 ;;
}
{ .mmf
(p0) ldfe FR_P3 = [GR_Table_ptr],16
//
// Load P3
// Load P7
//
(p0) ldfe FR_P6 = [GR_Table_Base],16
(p0) fmpy.s1 FR_wsq = FR_W, FR_W ;;
}
{ .mfi
(p0) ldfe FR_P2 = [GR_Table_ptr],16
nop.f 999
nop.i 999 ;;
}
{ .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 ;;
}
{ .mfi
nop.m 999
(p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P2
nop.i 999
}
{ .mfi
nop.m 999
(p0) fma.s1 FR_Y_lo = FR_W, FR_Y_lo, FR_P6
(p0) add GR_Perturb = 0x1, r0 ;;
}
{ .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 ;;
}
{ .mfi
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
(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
(p0) fma.s1 FR_dummy = FR_wsq,FR_Y_hi, f0
nop.i 999
}
{ .mfi
nop.m 999
(p0) fma.s1 FR_Y_hi = FR_W,f1,f0
nop.i 999
};;
{ .mfb
nop.m 999
//
// Y_hi = w
// Y_lo = y_lo * w + p5
//
(p0) fma.s1 FR_Y_lo = FR_w6, FR_Y_lo,FR_dummy
//
// Y_lo = y_lo * w6 + y_high order part.
//
// performance
//
(p0) br.cond.sptk LOGL_main ;;
}
L(log1pl_small):
{ .mmi
nop.m 999
// /*******************************************************/
// /*********** Branch log1pl_small ***********************/
// /*******************************************************/
(p0) addl GR_Table_Base = @ltoff(Constants_Threshold#),gp
}
{ .mfi
nop.m 999
(p0) mov FR_Em1 = FR_W
(p0) cmp.eq.unc p7, p0 = r0, r0 ;;
}
{ .mlx
ld8 GR_Table_Base = [GR_Table_Base]
(p0) movl GR_Expo_Range = 0x0000000000000004 ;;
}
//
// Set Safe to true
// Set Expo_Range = 0 for single
// Set Expo_Range = 2 for double
// Set Expo_Range = 4 for double-extended
//
{ .mmi
(p0) shladd GR_Table_Base = GR_Expo_Range,4,GR_Table_Base ;;
(p0) ldfe FR_Threshold = [GR_Table_Base],16
nop.i 999
}
{ .mlx
nop.m 999
(p0) movl GR_Bias = 0x000000000000FF9B ;;
}
{ .mfi
(p0) ldfe FR_Tiny = [GR_Table_Base],0
nop.f 999
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p0) fcmp.gt.unc.s1 p13, p12 = FR_abs_W, FR_Threshold
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p13) fnmpy.s1 FR_Y_lo = FR_W, FR_W
nop.i 999
}
{ .mfi
nop.m 999
(p13) fadd FR_SCALE = f0, f1
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p12) fsub.s1 FR_Y_lo = f0, FR_Tiny
(p12) cmp.ne.unc p7, p0 = r0, r0
}
{ .mfi
(p12) setf.exp FR_SCALE = GR_Bias
nop.f 999
nop.i 999 ;;
}
{ .mfb
nop.m 999
//
// Set p7 to SAFE = FALSE
// Set Scale = 2^-100
//
(p0) fma.s0 f8 = FR_Y_lo,FR_SCALE,FR_Y_hi
(p0) br.ret.sptk b0 ;;
}
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 we have logl(1), log10l(1) or log1pl(0), return 0.
//
(p0) fsub.s0 FR_Output_X_tmp = f0, f1
nop.i 999 ;;
}
{ .mii
(p14) mov GR_Parameter_TAG = 6
nop.i 999 ;;
(p15) mov GR_Parameter_TAG = 138 ;;
}
{ .mfb
nop.m 999
(p0) frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0
(p0) br.cond.sptk __libm_error_region ;;
}
{ .mfb
nop.m 999
//
// Report that logl(0) computed
// { .mfb
(p0) mov FR_Input_X = FR_Output_X_tmp
(p0) br.ret.sptk b0 ;;
}
L(LOGL_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 ;;
}
{ .mfb
nop.m 999
//
// Check for Natval, QNan, SNaN, +Inf
//
(p7) fmpy.s0 f8 = FR_Input_X, f1
//
// For SNaN raise invalid and return QNaN.
// For QNaN raise invalid and return QNaN.
// For +Inf return +Inf.
//
(p7) br.ret.sptk b0 ;;
}
//
// For -Inf raise invalid and return QNaN.
//
{ .mii
(p0) mov GR_Parameter_TAG = 1
nop.i 999 ;;
(p14) mov GR_Parameter_TAG = 7 ;;
}
{ .mfi
(p15) mov GR_Parameter_TAG = 139
nop.f 999
nop.i 999 ;;
}
{ .mfb
nop.m 999
(p0) fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0
(p0) br.cond.sptk __libm_error_region ;;
}
//
// 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 .
//
(p0) fmpy.s0 f8 = FR_Input_X, f0
(p0) br.ret.sptk b0 ;;
}
L(LOGL_64_negative):
{ .mfi
nop.m 999
//
// Deal with x < 0 in a special way
//
(p0) frcpa.s0 FR_Output_X_tmp, p8 = f0, f0
//
// Deal with x < 0 in a special way - raise
// invalid and produce QNaN indefinite.
//
(p0) mov GR_Parameter_TAG = 1 ;;
}
{ .mii
(p14) mov GR_Parameter_TAG = 7
nop.i 999 ;;
(p15) mov GR_Parameter_TAG = 139
}
.endp log1pl
ASM_SIZE_DIRECTIVE(log1pl)
.proc __libm_error_region
__libm_error_region:
.prologue
{ .mfi
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
}
{ .mfi
.fframe 64
add sp=-64,sp // Create new stack
nop.f 0
mov GR_SAVE_GP=gp // Save gp
};;
{ .mmi
stfe [GR_Parameter_Y] = FR_Y,16 // Save 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
};;
.body
{ .mib
stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y
nop.b 0 // Parameter 3 address
}
{ .mib
stfe [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
};;
{ .mmi
nop.m 0
nop.m 0
add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
ldfe 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
};;
{ .mib
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 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#
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