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-rw-r--r--sysdeps/ia64/fpu/s_expm1.S2142
1 files changed, 629 insertions, 1513 deletions
diff --git a/sysdeps/ia64/fpu/s_expm1.S b/sysdeps/ia64/fpu/s_expm1.S
index 19a237990c..41b9954ee8 100644
--- a/sysdeps/ia64/fpu/s_expm1.S
+++ b/sysdeps/ia64/fpu/s_expm1.S
@@ -1,10 +1,10 @@
.file "exp_m1.s"
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2002, 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
@@ -20,1694 +20,819 @@
// * 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.
-//
-// 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.
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
-// 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
+// Intel Corporation is the author of this code, and requests that all
+// problem reports or change requests be submitted to it directly at
+// http://www.intel.com/software/products/opensource/libraries/num.htm.
+//
+// History
+//==============================================================
+// 02/02/00 Initial Version
+// 04/04/00 Unwind support added
+// 08/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
+// 07/07/01 Improved speed of all paths
+// 05/20/02 Cleaned up namespace and sf0 syntax
+// 11/20/02 Improved speed, algorithm based on exp
+
+// API
+//==============================================================
+// double expm1(double)
+
+// Overview of operation
+//==============================================================
+// 1. Inputs of Nan, Inf, Zero, NatVal handled with special paths
+//
+// 2. |x| < 2^-60
+// Result = x, computed by x + x*x to handle appropriate flags and rounding
//
-// *********************************************************************
-//
-// Function: Combined exp(x) and expm1(x), where
-// x
-// exp(x) = e , for double precision x values
-// x
-// expm1(x) = e - 1 for double precision x values
-//
-// *********************************************************************
-//
-// Accuracy: Within .7 ulps for 80-bit floating point values
-// Very accurate for double precision values
-//
-// *********************************************************************
-//
-// Resources Used:
-//
-// Floating-Point Registers: f8 (Input and Return Value)
-// f9,f32-f61, f99-f102
-//
-// General Purpose Registers:
-// r32-r61
-// r62-r65 (Used to pass arguments to error handling routine)
-//
-// Predicate Registers: p6-p15
-//
-// *********************************************************************
-//
-// IEEE Special Conditions:
-//
-// Denormal fault raised on denormal inputs
-// Overflow exceptions raised when appropriate for exp and expm1
-// Underflow exceptions raised when appropriate for exp and expm1
-// (Error Handling Routine called for overflow and Underflow)
-// Inexact raised when appropriate by algorithm
-//
-// exp(inf) = inf
-// exp(-inf) = +0
-// exp(SNaN) = QNaN
-// exp(QNaN) = QNaN
-// exp(0) = 1
-// exp(EM_special Values) = QNaN
-// exp(inf) = inf
-// expm1(-inf) = -1
-// expm1(SNaN) = QNaN
-// expm1(QNaN) = QNaN
-// expm1(0) = 0
-// expm1(EM_special Values) = QNaN
-//
-// *********************************************************************
-//
-// Implementation and Algorithm Notes:
-//
-// ker_exp_64( in_FR : X,
-// in_GR : Flag,
-// in_GR : Expo_Range
-// out_FR : Y_hi,
-// out_FR : Y_lo,
-// out_FR : scale,
-// out_PR : Safe )
-//
-// On input, X is in register format and
-// Flag = 0 for exp,
-// Flag = 1 for expm1,
-//
-// On output, provided X and X_cor are real numbers, then
-//
-// scale*(Y_hi + Y_lo) approximates exp(X) if Flag is 0
-// scale*(Y_hi + Y_lo) approximates exp(X)-1 if Flag is 1
-//
-// The accuracy is sufficient for a highly accurate 64 sig.
-// bit implementation. Safe is set if there is no danger of
-// overflow/underflow when the result is composed from scale,
-// Y_hi and Y_lo. Thus, we can have a fast return if Safe is set.
-// Otherwise, one must prepare to handle the possible exception
-// appropriately. Note that SAFE not set (false) does not mean
-// that overflow/underflow will occur; only the setting of SAFE
-// guarantees the opposite.
-//
-// **** High Level Overview ****
-//
-// The method consists of three cases.
-//
-// If |X| < Tiny use case exp_tiny;
-// else if |X| < 2^(-6) use case exp_small;
-// else use case exp_regular;
-//
-// Case exp_tiny:
-//
-// 1 + X can be used to approximate exp(X) or exp(X+X_cor);
-// X + X^2/2 can be used to approximate exp(X) - 1
-//
-// Case exp_small:
-//
-// Here, exp(X), exp(X+X_cor), and exp(X) - 1 can all be
-// appproximated by a relatively simple polynomial.
-//
-// This polynomial resembles the truncated Taylor series
-//
-// exp(w) = 1 + w + w^2/2! + w^3/3! + ... + w^n/n!
-//
-// Case exp_regular:
-//
-// Here we use a table lookup method. The basic idea is that in
-// order to compute exp(X), we accurately decompose X into
-//
-// X = N * log(2)/(2^12) + r, |r| <= log(2)/2^13.
-//
-// Hence
-//
-// exp(X) = 2^( N / 2^12 ) * exp(r).
-//
-// The value 2^( N / 2^12 ) is obtained by simple combinations
-// of values calculated beforehand and stored in table; exp(r)
-// is approximated by a short polynomial because |r| is small.
-//
-// We elaborate this method in 4 steps.
-//
-// Step 1: Reduction
-//
-// The value 2^12/log(2) is stored as a double-extended number
-// L_Inv.
-//
-// N := round_to_nearest_integer( X * L_Inv )
-//
-// The value log(2)/2^12 is stored as two numbers L_hi and L_lo so
-// that r can be computed accurately via
-//
-// r := (X - N*L_hi) - N*L_lo
-//
-// We pick L_hi such that N*L_hi is representable in 64 sig. bits
-// and thus the FMA X - N*L_hi is error free. So r is the
-// 1 rounding error from an exact reduction with respect to
-//
-// L_hi + L_lo.
-//
-// In particular, L_hi has 30 significant bit and can be stored
-// as a double-precision number; L_lo has 64 significant bits and
-// stored as a double-extended number.
-//
-// In the case Flag = 2, we further modify r by
-//
-// r := r + X_cor.
-//
-// Step 2: Approximation
-//
-// exp(r) - 1 is approximated by a short polynomial of the form
-//
-// r + A_1 r^2 + A_2 r^3 + A_3 r^4 .
-//
-// Step 3: Composition from Table Values
-//
-// The value 2^( N / 2^12 ) can be composed from a couple of tables
-// of precalculated values. First, express N as three integers
-// K, M_1, and M_2 as
-//
-// N = K * 2^12 + M_1 * 2^6 + M_2
-//
-// Where 0 <= M_1, M_2 < 2^6; and K can be positive or negative.
-// When N is represented in 2's complement, M_2 is simply the 6
-// lsb's, M_1 is the next 6, and K is simply N shifted right
-// arithmetically (sign extended) by 12 bits.
-//
-// Now, 2^( N / 2^12 ) is simply
-//
-// 2^K * 2^( M_1 / 2^6 ) * 2^( M_2 / 2^12 )
-//
-// Clearly, 2^K needs no tabulation. The other two values are less
-// trivial because if we store each accurately to more than working
-// precision, than its product is too expensive to calculate. We
-// use the following method.
-//
-// Define two mathematical values, delta_1 and delta_2, implicitly
-// such that
-//
-// T_1 = exp( [M_1 log(2)/2^6] - delta_1 )
-// T_2 = exp( [M_2 log(2)/2^12] - delta_2 )
-//
-// are representable as 24 significant bits. To illustrate the idea,
-// we show how we define delta_1:
-//
-// T_1 := round_to_24_bits( exp( M_1 log(2)/2^6 ) )
-// delta_1 = (M_1 log(2)/2^6) - log( T_1 )
-//
-// The last equality means mathematical equality. We then tabulate
-//
-// W_1 := exp(delta_1) - 1
-// W_2 := exp(delta_2) - 1
-//
-// Both in double precision.
-//
-// From the tabulated values T_1, T_2, W_1, W_2, we compose the values
-// T and W via
+// 3. 2^-60 <= |x| < 2^-2
+// Result determined by 13th order Taylor series polynomial
+// expm1f(x) = x + Q2*x^2 + ... + Q13*x^13
//
-// T := T_1 * T_2 ...exactly
-// W := W_1 + (1 + W_1)*W_2
+// 4. x < -48.0
+// Here we know result is essentially -1 + eps, where eps only affects
+// rounded result. Set I.
//
-// W approximates exp( delta ) - 1 where delta = delta_1 + delta_2.
-// The mathematical product of T and (W+1) is an accurate representation
-// of 2^(M_1/2^6) * 2^(M_2/2^12).
+// 5. x >= 709.7827
+// Result overflows. Set I, O, and call error support
//
-// Step 4. Reconstruction
-//
-// Finally, we can reconstruct exp(X), exp(X) - 1.
-// Because
-//
-// X = K * log(2) + (M_1*log(2)/2^6 - delta_1)
-// + (M_2*log(2)/2^12 - delta_2)
-// + delta_1 + delta_2 + r ...accurately
-// We have
-//
-// exp(X) ~=~ 2^K * ( T + T*[exp(delta_1+delta_2+r) - 1] )
-// ~=~ 2^K * ( T + T*[exp(delta + r) - 1] )
-// ~=~ 2^K * ( T + T*[(exp(delta)-1)
-// + exp(delta)*(exp(r)-1)] )
-// ~=~ 2^K * ( T + T*( W + (1+W)*poly(r) ) )
-// ~=~ 2^K * ( Y_hi + Y_lo )
-//
-// where Y_hi = T and Y_lo = T*(W + (1+W)*poly(r))
-//
-// For exp(X)-1, we have
-//
-// exp(X)-1 ~=~ 2^K * ( Y_hi + Y_lo ) - 1
-// ~=~ 2^K * ( Y_hi + Y_lo - 2^(-K) )
-//
-// and we combine Y_hi + Y_lo - 2^(-N) into the form of two
-// numbers Y_hi + Y_lo carefully.
-//
-// **** Algorithm Details ****
-//
-// A careful algorithm must be used to realize the mathematical ideas
-// accurately. We describe each of the three cases. We assume SAFE
-// is preset to be TRUE.
-//
-// Case exp_tiny:
-//
-// The important points are to ensure an accurate result under
-// different rounding directions and a correct setting of the SAFE
-// flag.
-//
-// If Flag is 1, then
-// SAFE := False ...possibility of underflow
-// Scale := 1.0
-// Y_hi := X
-// Y_lo := 2^(-17000)
-// Else
-// Scale := 1.0
-// Y_hi := 1.0
-// Y_lo := X ...for different rounding modes
-// Endif
-//
-// Case exp_small:
-//
-// Here we compute a simple polynomial. To exploit parallelism, we split
-// the polynomial into several portions.
-//
-// Let r = X
-//
-// If Flag is not 1 ...i.e. exp( argument )
-//
-// rsq := r * r;
-// r4 := rsq*rsq
-// poly_lo := P_3 + r*(P_4 + r*(P_5 + r*P_6))
-// poly_hi := r + rsq*(P_1 + r*P_2)
-// Y_lo := poly_hi + r4 * poly_lo
-// set lsb(Y_lo) to 1
-// Y_hi := 1.0
-// Scale := 1.0
-//
-// Else ...i.e. exp( argument ) - 1
-//
-// rsq := r * r
-// r4 := rsq * rsq
-// r6 := rsq * r4
-// poly_lo := r6*(Q_5 + r*(Q_6 + r*Q_7))
-// poly_hi := Q_1 + r*(Q_2 + r*(Q_3 + r*Q_4))
-// Y_lo := rsq*poly_hi + poly_lo
-// set lsb(Y_lo) to 1
-// Y_hi := X
-// Scale := 1.0
-//
-// Endif
-//
-// Case exp_regular:
-//
-// The previous description contain enough information except the
-// computation of poly and the final Y_hi and Y_lo in the case for
-// exp(X)-1.
-//
-// The computation of poly for Step 2:
-//
-// rsq := r*r
-// poly := r + rsq*(A_1 + r*(A_2 + r*A_3))
-//
-// For the case exp(X) - 1, we need to incorporate 2^(-K) into
-// Y_hi and Y_lo at the end of Step 4.
-//
-// If K > 10 then
-// Y_lo := Y_lo - 2^(-K)
-// Else
-// If K < -10 then
-// Y_lo := Y_hi + Y_lo
-// Y_hi := -2^(-K)
-// Else
-// Y_hi := Y_hi - 2^(-K)
-// End If
-// End If
-//
-
-#include "libm_support.h"
-
-GR_SAVE_PFS = r59
-GR_SAVE_B0 = r60
-GR_SAVE_GP = r61
-
-GR_Parameter_X = r62
-GR_Parameter_Y = r63
-GR_Parameter_RESULT = r64
-
-FR_X = f9
-FR_Y = f1
-FR_RESULT = f99
-
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
-
-.align 64
-Constants_exp_64_Arg:
-ASM_TYPE_DIRECTIVE(Constants_exp_64_Arg,@object)
-data4 0x5C17F0BC,0xB8AA3B29,0x0000400B,0x00000000
-data4 0x00000000,0xB17217F4,0x00003FF2,0x00000000
-data4 0xF278ECE6,0xF473DE6A,0x00003FD4,0x00000000
-// /* Inv_L, L_hi, L_lo */
-ASM_SIZE_DIRECTIVE(Constants_exp_64_Arg)
-
-.align 64
-Constants_exp_64_Exponents:
-ASM_TYPE_DIRECTIVE(Constants_exp_64_Exponents,@object)
-data4 0x0000007E,0x00000000,0xFFFFFF83,0xFFFFFFFF
-data4 0x000003FE,0x00000000,0xFFFFFC03,0xFFFFFFFF
-data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF
-data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF
-data4 0xFFFFFFE2,0xFFFFFFFF,0xFFFFFFC4,0xFFFFFFFF
-data4 0xFFFFFFBA,0xFFFFFFFF,0xFFFFFFBA,0xFFFFFFFF
-ASM_SIZE_DIRECTIVE(Constants_exp_64_Exponents)
-
-.align 64
-Constants_exp_64_A:
-ASM_TYPE_DIRECTIVE(Constants_exp_64_A,@object)
-data4 0xB1B736A0,0xAAAAAAAB,0x00003FFA,0x00000000
-data4 0x90CD6327,0xAAAAAAAB,0x00003FFC,0x00000000
-data4 0xFFFFFFFF,0xFFFFFFFF,0x00003FFD,0x00000000
-// /* Reversed */
-ASM_SIZE_DIRECTIVE(Constants_exp_64_A)
-
-.align 64
-Constants_exp_64_P:
-ASM_TYPE_DIRECTIVE(Constants_exp_64_P,@object)
-data4 0x43914A8A,0xD00D6C81,0x00003FF2,0x00000000
-data4 0x30304B30,0xB60BC4AC,0x00003FF5,0x00000000
-data4 0x7474C518,0x88888888,0x00003FF8,0x00000000
-data4 0x8DAE729D,0xAAAAAAAA,0x00003FFA,0x00000000
-data4 0xAAAAAF61,0xAAAAAAAA,0x00003FFC,0x00000000
-data4 0x000004C7,0x80000000,0x00003FFE,0x00000000
-// /* Reversed */
-ASM_SIZE_DIRECTIVE(Constants_exp_64_P)
-
-.align 64
-Constants_exp_64_Q:
-ASM_TYPE_DIRECTIVE(Constants_exp_64_Q,@object)
-data4 0xA49EF6CA,0xD00D56F7,0x00003FEF,0x00000000
-data4 0x1C63493D,0xD00D59AB,0x00003FF2,0x00000000
-data4 0xFB50CDD2,0xB60B60B5,0x00003FF5,0x00000000
-data4 0x7BA68DC8,0x88888888,0x00003FF8,0x00000000
-data4 0xAAAAAC8D,0xAAAAAAAA,0x00003FFA,0x00000000
-data4 0xAAAAACCA,0xAAAAAAAA,0x00003FFC,0x00000000
-data4 0x00000000,0x80000000,0x00003FFE,0x00000000
-// /* Reversed */
-ASM_SIZE_DIRECTIVE(Constants_exp_64_Q)
-
-.align 64
-Constants_exp_64_T1:
-ASM_TYPE_DIRECTIVE(Constants_exp_64_T1,@object)
-data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29
-data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5
-data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC
-data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D
-data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA
-data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516
-data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A
-data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4
-data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B
-data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD
-data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15
-data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B
-data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5
-data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A
-data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177
-data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C
-ASM_SIZE_DIRECTIVE(Constants_exp_64_T1)
-
-.align 64
-Constants_exp_64_T2:
-ASM_TYPE_DIRECTIVE(Constants_exp_64_T2,@object)
-data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4
-data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7
-data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E
-data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349
-data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987
-data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA
-data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610
-data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A
-data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8
-data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA
-data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50
-data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA
-data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07
-data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269
-data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE
-data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37
-ASM_SIZE_DIRECTIVE(Constants_exp_64_T2)
-
-.align 64
-Constants_exp_64_W1:
-ASM_TYPE_DIRECTIVE(Constants_exp_64_W1,@object)
-data4 0x00000000,0x00000000,0x171EC4B4,0xBE384454
-data4 0x4AA72766,0xBE694741,0xD42518F8,0xBE5D32B6
-data4 0x3A319149,0x3E68D96D,0x62415F36,0xBE68F4DA
-data4 0xC9C86A3B,0xBE6DDA2F,0xF49228FE,0x3E6B2E50
-data4 0x1188B886,0xBE49C0C2,0x1A4C2F1F,0x3E64BFC2
-data4 0x2CB98B54,0xBE6A2FBB,0x9A55D329,0x3E5DC5DE
-data4 0x39A7AACE,0x3E696490,0x5C66DBA5,0x3E54728B
-data4 0xBA1C7D7D,0xBE62B0DB,0x09F1AF5F,0x3E576E04
-data4 0x1A0DD6A1,0x3E612500,0x795FBDEF,0xBE66A419
-data4 0xE1BD41FC,0xBE5CDE8C,0xEA54964F,0xBE621376
-data4 0x476E76EE,0x3E6370BE,0x3427EB92,0x3E390D1A
-data4 0x2BF82BF8,0x3E1336DE,0xD0F7BD9E,0xBE5FF1CB
-data4 0x0CEB09DD,0xBE60A355,0x0980F30D,0xBE5CA37E
-data4 0x4C082D25,0xBE5C541B,0x3B467D29,0xBE5BBECA
-data4 0xB9D946C5,0xBE400D8A,0x07ED374A,0xBE5E2A08
-data4 0x365C8B0A,0xBE66CB28,0xD3403BCA,0x3E3AAD5B
-data4 0xC7EA21E0,0x3E526055,0xE72880D6,0xBE442C75
-data4 0x85222A43,0x3E58B2BB,0x522C42BF,0xBE5AAB79
-data4 0x469DC2BC,0xBE605CB4,0xA48C40DC,0xBE589FA7
-data4 0x1AA42614,0xBE51C214,0xC37293F4,0xBE48D087
-data4 0xA2D673E0,0x3E367A1C,0x114F7A38,0xBE51BEBB
-data4 0x661A4B48,0xBE6348E5,0x1D3B9962,0xBDF52643
-data4 0x35A78A53,0x3E3A3B5E,0x1CECD788,0xBE46C46C
-data4 0x7857D689,0xBE60B7EC,0xD14F1AD7,0xBE594D3D
-data4 0x4C9A8F60,0xBE4F9C30,0x02DFF9D2,0xBE521873
-data4 0x55E6D68F,0xBE5E4C88,0x667F3DC4,0xBE62140F
-data4 0x3BF88747,0xBE36961B,0xC96EC6AA,0x3E602861
-data4 0xD57FD718,0xBE3B5151,0xFC4A627B,0x3E561CD0
-data4 0xCA913FEA,0xBE3A5217,0x9A5D193A,0x3E40A3CC
-data4 0x10A9C312,0xBE5AB713,0xC5F57719,0x3E4FDADB
-data4 0xDBDF59D5,0x3E361428,0x61B4180D,0x3E5DB5DB
-data4 0x7408D856,0xBE42AD5F,0x31B2B707,0x3E2A3148
-ASM_SIZE_DIRECTIVE(Constants_exp_64_W1)
-
-.align 64
-Constants_exp_64_W2:
-ASM_TYPE_DIRECTIVE(Constants_exp_64_W2,@object)
-data4 0x00000000,0x00000000,0x37A3D7A2,0xBE641F25
-data4 0xAD028C40,0xBE68DD57,0xF212B1B6,0xBE5C77D8
-data4 0x1BA5B070,0x3E57878F,0x2ECAE6FE,0xBE55A36A
-data4 0x569DFA3B,0xBE620608,0xA6D300A3,0xBE53B50E
-data4 0x223F8F2C,0x3E5B5EF2,0xD6DE0DF4,0xBE56A0D9
-data4 0xEAE28F51,0xBE64EEF3,0x367EA80B,0xBE5E5AE2
-data4 0x5FCBC02D,0x3E47CB1A,0x9BDAFEB7,0xBE656BA0
-data4 0x805AFEE7,0x3E6E70C6,0xA3415EBA,0xBE6E0509
-data4 0x49BFF529,0xBE56856B,0x00508651,0x3E66DD33
-data4 0xC114BC13,0x3E51165F,0xC453290F,0x3E53333D
-data4 0x05539FDA,0x3E6A072B,0x7C0A7696,0xBE47CD87
-data4 0xEB05C6D9,0xBE668BF4,0x6AE86C93,0xBE67C3E3
-data4 0xD0B3E84B,0xBE533904,0x556B53CE,0x3E63E8D9
-data4 0x63A98DC8,0x3E212C89,0x032A7A22,0xBE33138F
-data4 0xBC584008,0x3E530FA9,0xCCB93C97,0xBE6ADF82
-data4 0x8370EA39,0x3E5F9113,0xFB6A05D8,0x3E5443A4
-data4 0x181FEE7A,0x3E63DACD,0xF0F67DEC,0xBE62B29D
-data4 0x3DDE6307,0x3E65C483,0xD40A24C1,0x3E5BF030
-data4 0x14E437BE,0x3E658B8F,0xED98B6C7,0xBE631C29
-data4 0x04CF7C71,0x3E6335D2,0xE954A79D,0x3E529EED
-data4 0xF64A2FB8,0x3E5D9257,0x854ED06C,0xBE6BED1B
-data4 0xD71405CB,0x3E5096F6,0xACB9FDF5,0xBE3D4893
-data4 0x01B68349,0xBDFEB158,0xC6A463B9,0x3E628D35
-data4 0xADE45917,0xBE559725,0x042FC476,0xBE68C29C
-data4 0x01E511FA,0xBE67593B,0x398801ED,0xBE4A4313
-data4 0xDA7C3300,0x3E699571,0x08062A9E,0x3E5349BE
-data4 0x755BB28E,0x3E5229C4,0x77A1F80D,0x3E67E426
-data4 0x6B69C352,0xBE52B33F,0x084DA57F,0xBE6B3550
-data4 0xD1D09A20,0xBE6DB03F,0x2161B2C1,0xBE60CBC4
-data4 0x78A2B771,0x3E56ED9C,0x9D0FA795,0xBE508E31
-data4 0xFD1A54E9,0xBE59482A,0xB07FD23E,0xBE2A17CE
-data4 0x17365712,0x3E68BF5C,0xB3785569,0x3E3956F9
-ASM_SIZE_DIRECTIVE(Constants_exp_64_W2)
+// 6. 2^-2 <= x < 709.7827 or -48.0 <= x < -2^-2
+// This is the main path. The algorithm is described below:
-.section .text
-.proc expm1#
-.global expm1#
-.align 64
-
-expm1:
-#ifdef _LIBC
-.global __expm1#
-__expm1:
-#endif
-
-
-{ .mii
- alloc r32 = ar.pfs,0,30,4,0
-(p0) add r33 = 1, r0
-(p0) cmp.eq.unc p7, p0 = r0, r0
-}
-;;
-
-
-//
-// Set p7 true for expm1
-// Set Flag = r33 = 1 for expm1
-// These are really no longer necesary, but are a remnant
-// when this file had multiple entry points.
-// They should be carefully removed
+// Take the input x. w is "how many log2/128 in x?"
+// w = x * 128/log2
+// n = int(w)
+// x = n log2/128 + r + delta
+
+// n = 128M + index_1 + 2^4 index_2
+// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta
+
+// exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta)
+// Construct 2^M
+// Get 2^(index_1/128) from table_1;
+// Get 2^(index_2/8) from table_2;
+// Calculate exp(r) by series by 5th order polynomial
+// r = x - n (log2/128)_high
+// delta = - n (log2/128)_low
+// Calculate exp(delta) as 1 + delta
+
+
+// Special values
+//==============================================================
+// expm1(+0) = +0.0
+// expm1(-0) = -0.0
+
+// expm1(+qnan) = +qnan
+// expm1(-qnan) = -qnan
+// expm1(+snan) = +qnan
+// expm1(-snan) = -qnan
+
+// expm1(-inf) = -1.0
+// expm1(+inf) = +inf
+
+// Overflow and Underflow
+//=======================
+// expm1(x) = largest double normal when
+// x = 709.7827 = 40862e42fefa39ef
+//
+// Underflow is handled as described in case 2 above.
+
+
+// Registers used
+//==============================================================
+// Floating Point registers used:
+// f8, input
+// f9 -> f15, f32 -> f75
+
+// General registers used:
+// r14 -> r40
+
+// Predicate registers used:
+// p6 -> p15
+
+// Assembly macros
+//==============================================================
+
+rRshf = r14
+rAD_TB1 = r15
+rAD_T1 = r15
+rAD_TB2 = r16
+rAD_T2 = r16
+rAD_Ln2_lo = r17
+rAD_P = r17
+
+rN = r18
+rIndex_1 = r19
+rIndex_2_16 = r20
+
+rM = r21
+rBiased_M = r21
+rIndex_1_16 = r22
+rSignexp_x = r23
+rExp_x = r24
+rSig_inv_ln2 = r25
+
+rAD_Q1 = r26
+rAD_Q2 = r27
+rTmp = r27
+rExp_bias = r28
+rExp_mask = r29
+rRshf_2to56 = r30
+
+rGt_ln = r31
+rExp_2tom56 = r31
+
+
+GR_SAVE_B0 = r33
+GR_SAVE_PFS = r34
+GR_SAVE_GP = r35
+GR_SAVE_SP = r36
+
+GR_Parameter_X = r37
+GR_Parameter_Y = r38
+GR_Parameter_RESULT = r39
+GR_Parameter_TAG = r40
+
+
+FR_X = f10
+FR_Y = f1
+FR_RESULT = f8
+
+fRSHF_2TO56 = f6
+fINV_LN2_2TO63 = f7
+fW_2TO56_RSH = f9
+f2TOM56 = f11
+fP5 = f12
+fP54 = f50
+fP5432 = f50
+fP4 = f13
+fP3 = f14
+fP32 = f14
+fP2 = f15
+
+fLn2_by_128_hi = f33
+fLn2_by_128_lo = f34
+
+fRSHF = f35
+fNfloat = f36
+fW = f37
+fR = f38
+fF = f39
+
+fRsq = f40
+fRcube = f41
+
+f2M = f42
+fS1 = f43
+fT1 = f44
+
+fMIN_DBL_OFLOW_ARG = f45
+fMAX_DBL_MINUS_1_ARG = f46
+fMAX_DBL_NORM_ARG = f47
+fP_lo = f51
+fP_hi = f52
+fP = f53
+fS = f54
+
+fNormX = f56
+
+fWre_urm_f8 = f57
+
+fGt_pln = f58
+fTmp = f58
+
+fS2 = f59
+fT2 = f60
+fSm1 = f61
+
+fXsq = f62
+fX6 = f63
+fX4 = f63
+fQ7 = f64
+fQ76 = f64
+fQ7654 = f64
+fQ765432 = f64
+fQ6 = f65
+fQ5 = f66
+fQ54 = f66
+fQ4 = f67
+fQ3 = f68
+fQ32 = f68
+fQ2 = f69
+fQD = f70
+fQDC = f70
+fQDCBA = f70
+fQDCBA98 = f70
+fQDCBA98765432 = f70
+fQC = f71
+fQB = f72
+fQBA = f72
+fQA = f73
+fQ9 = f74
+fQ98 = f74
+fQ8 = f75
+
+// Data tables
+//==============================================================
+
+RODATA
+.align 16
+
+// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
+
+// double-extended 1/ln(2)
+// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
+// 3fff b8aa 3b29 5c17 f0bc
+// For speed the significand will be loaded directly with a movl and setf.sig
+// and the exponent will be bias+63 instead of bias+0. Thus subsequent
+// computations need to scale appropriately.
+// The constant 128/ln(2) is needed for the computation of w. This is also
+// obtained by scaling the computations.
+//
+// Two shifting constants are loaded directly with movl and setf.d.
+// 1. fRSHF_2TO56 = 1.1000..00 * 2^(63-7)
+// This constant is added to x*1/ln2 to shift the integer part of
+// x*128/ln2 into the rightmost bits of the significand.
+// The result of this fma is fW_2TO56_RSH.
+// 2. fRSHF = 1.1000..00 * 2^(63)
+// This constant is subtracted from fW_2TO56_RSH * 2^(-56) to give
+// the integer part of w, n, as a floating-point number.
+// The result of this fms is fNfloat.
+
+
+LOCAL_OBJECT_START(exp_Table_1)
+data8 0x40862e42fefa39f0 // smallest dbl overflow arg
+data8 0xc048000000000000 // approx largest arg for minus one result
+data8 0x40862e42fefa39ef // largest dbl arg to give normal dbl result
+data8 0x0 // pad
+data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
+data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
+//
+// Table 1 is 2^(index_1/128) where
+// index_1 goes from 0 to 15
+//
+data8 0x8000000000000000 , 0x00003FFF
+data8 0x80B1ED4FD999AB6C , 0x00003FFF
+data8 0x8164D1F3BC030773 , 0x00003FFF
+data8 0x8218AF4373FC25EC , 0x00003FFF
+data8 0x82CD8698AC2BA1D7 , 0x00003FFF
+data8 0x8383594EEFB6EE37 , 0x00003FFF
+data8 0x843A28C3ACDE4046 , 0x00003FFF
+data8 0x84F1F656379C1A29 , 0x00003FFF
+data8 0x85AAC367CC487B15 , 0x00003FFF
+data8 0x8664915B923FBA04 , 0x00003FFF
+data8 0x871F61969E8D1010 , 0x00003FFF
+data8 0x87DB357FF698D792 , 0x00003FFF
+data8 0x88980E8092DA8527 , 0x00003FFF
+data8 0x8955EE03618E5FDD , 0x00003FFF
+data8 0x8A14D575496EFD9A , 0x00003FFF
+data8 0x8AD4C6452C728924 , 0x00003FFF
+LOCAL_OBJECT_END(exp_Table_1)
+
+// Table 2 is 2^(index_1/8) where
+// index_2 goes from 0 to 7
+LOCAL_OBJECT_START(exp_Table_2)
+data8 0x8000000000000000 , 0x00003FFF
+data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
+data8 0x9837F0518DB8A96F , 0x00003FFF
+data8 0xA5FED6A9B15138EA , 0x00003FFF
+data8 0xB504F333F9DE6484 , 0x00003FFF
+data8 0xC5672A115506DADD , 0x00003FFF
+data8 0xD744FCCAD69D6AF4 , 0x00003FFF
+data8 0xEAC0C6E7DD24392F , 0x00003FFF
+LOCAL_OBJECT_END(exp_Table_2)
+
+
+LOCAL_OBJECT_START(exp_p_table)
+data8 0x3f8111116da21757 //P5
+data8 0x3fa55555d787761c //P4
+data8 0x3fc5555555555414 //P3
+data8 0x3fdffffffffffd6a //P2
+LOCAL_OBJECT_END(exp_p_table)
+
+LOCAL_OBJECT_START(exp_Q1_table)
+data8 0x3de6124613a86d09 // QD = 1/13!
+data8 0x3e21eed8eff8d898 // QC = 1/12!
+data8 0x3ec71de3a556c734 // Q9 = 1/9!
+data8 0x3efa01a01a01a01a // Q8 = 1/8!
+data8 0x8888888888888889,0x3ff8 // Q5 = 1/5!
+data8 0xaaaaaaaaaaaaaaab,0x3ffc // Q3 = 1/3!
+data8 0x0,0x0 // Pad to avoid bank conflicts
+LOCAL_OBJECT_END(exp_Q1_table)
+
+LOCAL_OBJECT_START(exp_Q2_table)
+data8 0x3e5ae64567f544e4 // QB = 1/11!
+data8 0x3e927e4fb7789f5c // QA = 1/10!
+data8 0x3f2a01a01a01a01a // Q7 = 1/7!
+data8 0x3f56c16c16c16c17 // Q6 = 1/6!
+data8 0xaaaaaaaaaaaaaaab,0x3ffa // Q4 = 1/4!
+data8 0x8000000000000000,0x3ffe // Q2 = 1/2!
+LOCAL_OBJECT_END(exp_Q2_table)
+.section .text
+GLOBAL_IEEE754_ENTRY(expm1)
-{ .mfi
-(p0) add r32 = 1,r0
-(p0) fnorm.s1 f9 = f8
- nop.i 999
+{ .mlx
+ getf.exp rSignexp_x = f8 // Must recompute if x unorm
+ movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // signif of 1/ln2
}
-
-
-{ .mfi
- nop.m 999
-(p0) fclass.m.unc p6, p8 = f8, 0x1E7
- nop.i 999
+{ .mlx
+ addl rAD_TB1 = @ltoff(exp_Table_1), gp
+ movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56)
}
+;;
+// We do this fnorm right at the beginning to normalize
+// any input unnormals so that SWA is not taken.
{ .mfi
- nop.m 999
-(p0) fclass.nm.unc p9, p0 = f8, 0x1FF
- nop.i 999
+ ld8 rAD_TB1 = [rAD_TB1]
+ fclass.m p6,p0 = f8,0x0b // Test for x=unorm
+ mov rExp_mask = 0x1ffff
}
-
{ .mfi
- nop.m 999
-(p0) mov f36 = f1
- nop.i 999 ;;
-}
-
-//
-// Identify NatVals, NaNs, Infs, and Zeros.
-// Identify EM unsupporteds.
-// Save special input registers
-//
-// Create FR_X_cor = 0.0
-// GR_Flag = 0
-// GR_Expo_Range = 1
-// FR_Scale = 1.0
-//
-
-{ .mfb
- nop.m 999
-(p0) mov f32 = f0
-(p6) br.cond.spnt EXP_64_SPECIAL ;;
-}
-
-{ .mib
- nop.m 999
- nop.i 999
-(p9) br.cond.spnt EXP_64_UNSUPPORTED ;;
-}
-
-//
-// Branch out for special input values
-//
-
-{ .mfi
-(p0) cmp.ne.unc p12, p13 = 0x01, r33
-(p0) fcmp.lt.unc.s0 p9,p0 = f8, f0
-(p0) cmp.eq.unc p15, p0 = r0, r0
-}
-
-//
-// Raise possible denormal operand exception
-// Normalize x
-//
-// This function computes exp( x + x_cor)
-// Input FR 1: FR_X
-// Input FR 2: FR_X_cor
-// Input GR 1: GR_Flag
-// Input GR 2: GR_Expo_Range
-// Output FR 3: FR_Y_hi
-// Output FR 4: FR_Y_lo
-// Output FR 5: FR_Scale
-// Output PR 1: PR_Safe
-
-//
-// Prepare to load constants
-// Set Safe = True
-//
-
-{ .mmi
-(p0) addl r34 = @ltoff(Constants_exp_64_Arg#), gp
-(p0) addl r40 = @ltoff(Constants_exp_64_W1#), gp
-(p0) addl r41 = @ltoff(Constants_exp_64_W2#), gp
-}
-;;
-
-{ .mmi
- ld8 r34 = [r34]
- ld8 r40 = [r40]
-(p0) addl r50 = @ltoff(Constants_exp_64_T1#), gp
-}
-;;
-
-
-{ .mmi
- ld8 r41 = [r41]
-(p0) ldfe f37 = [r34],16
-(p0) addl r51 = @ltoff(Constants_exp_64_T2#), gp
-}
-;;
-
-//
-// N = fcvt.fx(float_N)
-// Set p14 if -6 > expo_X
-//
-
-
-//
-// Bias = 0x0FFFF
-// expo_X = expo_X and Mask
-//
-
-//
-// Load L_lo
-// Set p10 if 14 < expo_X
-//
-
-{ .mmi
- ld8 r50 = [r50]
-(p0) ldfe f40 = [r34],16
- nop.i 999
+ mov rExp_bias = 0xffff
+ fnorm.s1 fNormX = f8
+ mov rExp_2tom56 = 0xffff-56
}
;;
-{ .mlx
- nop.m 999
-(p0) movl r58 = 0x0FFFF
-}
-;;
-
-//
-// Load W2_ptr
-// Branch to SMALL is expo_X < -6
-//
+// Form two constants we need
+// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
+// 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand
-//
-// float_N = X * L_Inv
-// expo_X = exponent of X
-// Mask = 0x1FFFF
-//
-
-{ .mmi
- ld8 r51 = [r51]
-(p0) ldfe f41 = [r34],16
+{ .mfi
+ setf.sig fINV_LN2_2TO63 = rSig_inv_ln2 // form 1/ln2 * 2^63
+ fclass.m p8,p0 = f8,0x07 // Test for x=0
+ nop.i 0
}
-;;
-
{ .mlx
-(p0) addl r34 = @ltoff(Constants_exp_64_Exponents#), gp
-(p0) movl r39 = 0x1FFFF
-}
-;;
-
-{ .mmi
- ld8 r34 = [r34]
-(p0) getf.exp r37 = f9
- nop.i 999
+ setf.d fRSHF_2TO56 = rRshf_2to56 // Form 1.100 * 2^(63+56)
+ movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for rshift
}
;;
-{ .mii
- nop.m 999
- nop.i 999
-(p0) and r37 = r37, r39 ;;
-}
-
-{ .mmi
-(p0) sub r37 = r37, r58 ;;
-(p0) cmp.gt.unc p14, p0 = -6, r37
-(p0) cmp.lt.unc p10, p0 = 14, r37 ;;
-}
-
{ .mfi
- nop.m 999
-//
-// Load L_inv
-// Set p12 true for Flag = 0 (exp)
-// Set p13 true for Flag = 1 (expm1)
-//
-(p0) fmpy.s1 f38 = f9, f37
- nop.i 999 ;;
+ setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat
+ fclass.m p9,p0 = f8,0x22 // Test for x=-inf
+ add rAD_TB2 = 0x140, rAD_TB1 // Point to Table 2
}
-
-{ .mfb
- nop.m 999
-//
-// Load L_hi
-// expo_X = expo_X - Bias
-// get W1_ptr
-//
-(p0) fcvt.fx.s1 f39 = f38
-(p14) br.cond.spnt EXP_SMALL ;;
-}
-
{ .mib
- nop.m 999
- nop.i 999
-(p10) br.cond.spnt EXP_HUGE ;;
-}
-
-{ .mmi
-(p0) shladd r34 = r32,4,r34
-(p0) addl r35 = @ltoff(Constants_exp_64_A#), gp
- nop.i 999
+ add rAD_Q1 = 0x1e0, rAD_TB1 // Point to Q table for small path
+ add rAD_Ln2_lo = 0x30, rAD_TB1 // Point to ln2_by_128_lo
+(p6) br.cond.spnt EXPM1_UNORM // Branch if x unorm
}
;;
-{ .mmi
- ld8 r35 = [r35]
- nop.m 999
- nop.i 999
-}
-;;
-
-//
-// Load T_1,T_2
-//
-
-{ .mmb
-(p0) ldfe f51 = [r35],16
-(p0) ld8 r45 = [r34],8
- nop.b 999 ;;
-}
-//
-// Set Safe = True if k >= big_expo_neg
-// Set Safe = False if k < big_expo_neg
-//
-
-{ .mmb
-(p0) ldfe f49 = [r35],16
-(p0) ld8 r48 = [r34],0
- nop.b 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Branch to HUGE is expo_X > 14
-//
-(p0) fcvt.xf f38 = f39
- nop.i 999 ;;
-}
-
+EXPM1_COMMON:
{ .mfi
-(p0) getf.sig r52 = f39
- nop.f 999
- nop.i 999 ;;
-}
-
-{ .mii
- nop.m 999
-(p0) extr.u r43 = r52, 6, 6 ;;
-//
-// r = r - float_N * L_lo
-// K = extr(N_fix,12,52)
-//
-(p0) shladd r40 = r43,3,r40 ;;
-}
-
-{ .mfi
-(p0) shladd r50 = r43,2,r50
-(p0) fnma.s1 f42 = f40, f38, f9
-//
-// float_N = float(N)
-// N_fix = signficand N
-//
-(p0) extr.u r42 = r52, 0, 6
-}
-
-{ .mmi
-(p0) ldfd f43 = [r40],0 ;;
-(p0) shladd r41 = r42,3,r41
-(p0) shladd r51 = r42,2,r51
-}
-//
-// W_1_p1 = 1 + W_1
-//
-
-{ .mmi
-(p0) ldfs f44 = [r50],0 ;;
-(p0) ldfd f45 = [r41],0
-//
-// M_2 = extr(N_fix,0,6)
-// M_1 = extr(N_fix,6,6)
-// r = X - float_N * L_hi
-//
-(p0) extr r44 = r52, 12, 52
-}
-
-{ .mmi
-(p0) ldfs f46 = [r51],0 ;;
-(p0) sub r46 = r58, r44
-(p0) cmp.gt.unc p8, p15 = r44, r45
-}
-//
-// W = W_1 + W_1_p1*W_2
-// Load A_2
-// Bias_m_K = Bias - K
-//
-
-{ .mii
-(p0) ldfe f40 = [r35],16
-//
-// load A_1
-// poly = A_2 + r*A_3
-// rsq = r * r
-// neg_2_mK = exponent of Bias_m_k
-//
-(p0) add r47 = r58, r44 ;;
-//
-// Set Safe = True if k <= big_expo_pos
-// Set Safe = False if k > big_expo_pos
-// Load A_3
-//
-(p15) cmp.lt p8,p15 = r44,r48 ;;
-}
-
-{ .mmf
-(p0) setf.exp f61 = r46
-//
-// Bias_p + K = Bias + K
-// T = T_1 * T_2
-//
-(p0) setf.exp f36 = r47
-(p0) fnma.s1 f42 = f41, f38, f42 ;;
+ ldfpd fMIN_DBL_OFLOW_ARG, fMAX_DBL_MINUS_1_ARG = [rAD_TB1],16
+ fclass.m p10,p0 = f8,0x1e1 // Test for x=+inf, NaN, NaT
+ add rAD_Q2 = 0x50, rAD_Q1 // Point to Q table for small path
}
-
-{ .mfi
- nop.m 999
-//
-// Load W_1,W_2
-// Load big_exp_pos, load big_exp_neg
-//
-(p0) fadd.s1 f47 = f43, f1
- nop.i 999 ;;
+{ .mfb
+ nop.m 0
+ nop.f 0
+(p8) br.ret.spnt b0 // Exit for x=0, return x
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 f52 = f42, f51, f49
- nop.i 999
+ ldfd fMAX_DBL_NORM_ARG = [rAD_TB1],16
+ nop.f 0
+ and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x
}
-
-{ .mfi
- nop.m 999
-(p0) fmpy.s1 f48 = f42, f42
- nop.i 999 ;;
+{ .mfb
+ setf.d fRSHF = rRshf // Form right shift const 1.100 * 2^63
+(p9) fms.d.s0 f8 = f0,f0,f1 // quick exit for x=-inf
+(p9) br.ret.spnt b0
}
+;;
{ .mfi
- nop.m 999
-(p0) fmpy.s1 f53 = f44, f46
- nop.i 999 ;;
+ ldfpd fQD, fQC = [rAD_Q1], 16 // Load coeff for small path
+ nop.f 0
+ sub rExp_x = rExp_x, rExp_bias // True exponent of x
}
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 f54 = f45, f47, f43
- nop.i 999
+{ .mfb
+ ldfpd fQB, fQA = [rAD_Q2], 16 // Load coeff for small path
+(p10) fma.d.s0 f8 = f8, f1, f0 // For x=+inf, NaN, NaT
+(p10) br.ret.spnt b0 // Exit for x=+inf, NaN, NaT
}
+;;
{ .mfi
- nop.m 999
-(p0) fneg f61 = f61
- nop.i 999 ;;
+ ldfpd fQ9, fQ8 = [rAD_Q1], 16 // Load coeff for small path
+ fma.s1 fXsq = fNormX, fNormX, f0 // x*x for small path
+ cmp.gt p7, p8 = -2, rExp_x // Test |x| < 2^(-2)
}
-
{ .mfi
- nop.m 999
-(p0) fma.s1 f52 = f42, f52, f40
- nop.i 999 ;;
+ ldfpd fQ7, fQ6 = [rAD_Q2], 16 // Load coeff for small path
+ nop.f 0
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fadd.s1 f55 = f54, f1
- nop.i 999
+ ldfe fQ5 = [rAD_Q1], 16 // Load coeff for small path
+ nop.f 0
+ nop.i 0
}
-
-{ .mfi
- nop.m 999
-//
-// W + Wp1 * poly
-//
-(p0) mov f34 = f53
- nop.i 999 ;;
+{ .mib
+ ldfe fQ4 = [rAD_Q2], 16 // Load coeff for small path
+(p7) cmp.gt.unc p6, p7 = -60, rExp_x // Test |x| < 2^(-60)
+(p7) br.cond.spnt EXPM1_SMALL // Branch if 2^-60 <= |x| < 2^-2
}
+;;
-{ .mfi
- nop.m 999
-//
-// A_1 + r * poly
-// Scale = setf_exp(Bias_p_k)
-//
-(p0) fma.s1 f52 = f48, f52, f42
- nop.i 999 ;;
-}
+// W = X * Inv_log2_by_128
+// By adding 1.10...0*2^63 we shift and get round_int(W) in significand.
+// We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing.
{ .mfi
- nop.m 999
-//
-// poly = r + rsq(A_1 + r*poly)
-// Wp1 = 1 + W
-// neg_2_mK = -neg_2_mK
-//
-(p0) fma.s1 f35 = f55, f52, f54
- nop.i 999 ;;
+ ldfe fLn2_by_128_hi = [rAD_TB1],32
+ fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56
+ nop.i 0
}
-
{ .mfb
- nop.m 999
-(p0) fmpy.s1 f35 = f35, f53
-//
-// Y_hi = T
-// Y_lo = T * (W + Wp1*poly)
-//
-(p12) br.cond.sptk EXP_MAIN ;;
+ ldfe fLn2_by_128_lo = [rAD_Ln2_lo]
+(p6) fma.d.s0 f8 = f8, f8, f8 // If x < 2^-60, result=x+x*x
+(p6) br.ret.spnt b0 // Exit if x < 2^-60
}
-//
-// Branch if exp(x)
-// Continue for exp(x-1)
-//
+;;
-{ .mii
-(p0) cmp.lt.unc p12, p13 = 10, r44
- nop.i 999 ;;
-//
-// Set p12 if 10 < K, Else p13
-//
-(p13) cmp.gt.unc p13, p14 = -10, r44 ;;
-}
+// Divide arguments into the following categories:
+// Certain minus one p11 - -inf < x <= MAX_DBL_MINUS_1_ARG
+// Possible Overflow p14 - MAX_DBL_NORM_ARG < x < MIN_DBL_OFLOW_ARG
+// Certain Overflow p15 - MIN_DBL_OFLOW_ARG <= x < +inf
//
-// K > 10: Y_lo = Y_lo + neg_2_mK
-// K <=10: Set p13 if -10 > K, Else set p14
+// If the input is really a double arg, then there will never be "Possible
+// Overflow" arguments.
//
-{ .mfi
-(p13) cmp.eq p15, p0 = r0, r0
-(p14) fadd.s1 f34 = f61, f34
- nop.i 999 ;;
-}
+// After that last load, rAD_TB1 points to the beginning of table 1
{ .mfi
- nop.m 999
-(p12) fadd.s1 f35 = f35, f61
- nop.i 999 ;;
+ nop.m 0
+ fcmp.ge.s1 p15,p14 = fNormX,fMIN_DBL_OFLOW_ARG
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p13) fadd.s1 f35 = f35, f34
- nop.i 999
+ add rAD_P = 0x80, rAD_TB2
+ fcmp.le.s1 p11,p0 = fNormX,fMAX_DBL_MINUS_1_ARG
+ nop.i 0
}
+;;
{ .mfb
- nop.m 999
-//
-// K <= 10 and K < -10, Set Safe = True
-// K <= 10 and K < 10, Y_lo = Y_hi + Y_lo
-// K <= 10 and K > =-10, Y_hi = Y_hi + neg_2_mk
-//
-(p13) mov f34 = f61
-(p0) br.cond.sptk EXP_MAIN ;;
-}
-EXP_SMALL:
-
-{ .mmi
-(p12) addl r35 = @ltoff(Constants_exp_64_P#), gp
-(p0) addl r34 = @ltoff(Constants_exp_64_Exponents#), gp
- nop.i 999
+ ldfpd fP5, fP4 = [rAD_P] ,16
+(p14) fcmp.gt.unc.s1 p14,p0 = fNormX,fMAX_DBL_NORM_ARG
+(p15) br.cond.spnt EXPM1_CERTAIN_OVERFLOW
}
;;
-{ .mmi
-(p12) ld8 r35 = [r35]
- ld8 r34 = [r34]
- nop.i 999
-}
-;;
+// Nfloat = round_int(W)
+// The signficand of fW_2TO56_RSH contains the rounded integer part of W,
+// as a twos complement number in the lower bits (that is, it may be negative).
+// That twos complement number (called N) is put into rN.
+// Since fW_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
+// before the shift constant 1.10000 * 2^63 is subtracted to yield fNfloat.
+// Thus, fNfloat contains the floating point version of N
-{ .mmi
-(p13) addl r35 = @ltoff(Constants_exp_64_Q#), gp
- nop.m 999
- nop.i 999
+{ .mfb
+ ldfpd fP3, fP2 = [rAD_P]
+ fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF
+(p11) br.cond.spnt EXPM1_CERTAIN_MINUS_ONE
}
;;
-
-//
-// Return
-// K <= 10 and K < 10, Y_hi = neg_2_mk
-//
-// /*******************************************************/
-// /*********** Branch EXP_SMALL *************************/
-// /*******************************************************/
-
{ .mfi
-(p13) ld8 r35 = [r35]
-(p0) mov f42 = f9
-(p0) add r34 = 0x48,r34
+ getf.sig rN = fW_2TO56_RSH
+ nop.f 0
+ nop.i 0
}
;;
-//
-// Flag = 0
-// r4 = rsq * rsq
-//
+// rIndex_1 has index_1
+// rIndex_2_16 has index_2 * 16
+// rBiased_M has M
+// rIndex_1_16 has index_1 * 16
+// r = x - Nfloat * ln2_by_128_hi
+// f = 1 - Nfloat * ln2_by_128_lo
{ .mfi
-(p0) ld8 r49 =[r34],0
- nop.f 999
- nop.i 999 ;;
-}
-
-{ .mii
- nop.m 999
- nop.i 999 ;;
-//
-// Flag = 1
-//
-(p0) cmp.lt.unc p14, p0 = r37, r49 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// r = X
-//
-(p0) fmpy.s1 f48 = f42, f42
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-//
-// rsq = r * r
-//
-(p0) fmpy.s1 f50 = f48, f48
-//
-// Is input very small?
-//
-(p14) br.cond.spnt EXP_VERY_SMALL ;;
-}
-//
-// Flag_not1: Y_hi = 1.0
-// Flag is 1: r6 = rsq * r4
-//
-
-{ .mfi
-(p12) ldfe f52 = [r35],16
-(p12) mov f34 = f1
-(p0) add r53 = 0x1,r0 ;;
-}
-
-{ .mfi
-(p13) ldfe f51 = [r35],16
-//
-// Flag_not_1: Y_lo = poly_hi + r4 * poly_lo
-//
-(p13) mov f34 = f9
- nop.i 999 ;;
-}
-
-{ .mmf
-(p12) ldfe f53 = [r35],16
-//
-// For Flag_not_1, Y_hi = X
-// Scale = 1
-// Create 0x000...01
-//
-(p0) setf.sig f37 = r53
-(p0) mov f36 = f1 ;;
-}
-
-{ .mmi
-(p13) ldfe f52 = [r35],16 ;;
-(p12) ldfe f54 = [r35],16
- nop.i 999 ;;
+ and rIndex_1 = 0x0f, rN
+ fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX
+ shr rM = rN, 0x7
}
-
{ .mfi
-(p13) ldfe f53 = [r35],16
-(p13) fmpy.s1 f58 = f48, f50
- nop.i 999 ;;
+ and rIndex_2_16 = 0x70, rN
+ fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1
+ nop.i 0
}
-//
-// Flag_not1: poly_lo = P_5 + r*P_6
-// Flag_1: poly_lo = Q_6 + r*Q_7
-//
+;;
-{ .mmi
-(p13) ldfe f54 = [r35],16 ;;
-(p12) ldfe f55 = [r35],16
- nop.i 999 ;;
-}
+// rAD_T1 has address of T1
+// rAD_T2 has address if T2
{ .mmi
-(p12) ldfe f56 = [r35],16 ;;
-(p13) ldfe f55 = [r35],16
- nop.i 999 ;;
+ add rBiased_M = rExp_bias, rM
+ add rAD_T2 = rAD_TB2, rIndex_2_16
+ shladd rAD_T1 = rIndex_1, 4, rAD_TB1
}
+;;
+// Create Scale = 2^M
+// Load T1 and T2
{ .mmi
-(p12) ldfe f57 = [r35],0 ;;
-(p13) ldfe f56 = [r35],16
- nop.i 999 ;;
-}
-
-{ .mfi
-(p13) ldfe f57 = [r35],0
- nop.f 999
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// For Flag_not_1, load p5,p6,p1,p2
-// Else load p5,p6,p1,p2
-//
-(p12) fma.s1 f60 = f52, f42, f53
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p13) fma.s1 f60 = f51, f42, f52
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p12) fma.s1 f60 = f60, f42, f54
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p12) fma.s1 f59 = f56, f42, f57
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p13) fma.s1 f60 = f42, f60, f53
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p12) fma.s1 f59 = f59, f48, f42
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Flag_1: poly_lo = Q_5 + r*(Q_6 + r*Q_7)
-// Flag_not1: poly_lo = P_4 + r*(P_5 + r*P_6)
-// Flag_not1: poly_hi = (P_1 + r*P_2)
-//
-(p13) fmpy.s1 f60 = f60, f58
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p12) fma.s1 f60 = f60, f42, f55
- nop.i 999 ;;
+ setf.exp f2M = rBiased_M
+ ldfe fT2 = [rAD_T2]
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-//
-// Flag_1: poly_lo = r6 *(Q_5 + ....)
-// Flag_not1: poly_hi = r + rsq *(P_1 + r*P_2)
-//
-(p12) fma.s1 f35 = f60, f50, f59
- nop.i 999
+ ldfe fT1 = [rAD_T1]
+ fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p13) fma.s1 f59 = f54, f42, f55
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fP54 = fR, fP5, fP4
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-//
-// Flag_not1: Y_lo = rsq* poly_hi + poly_lo
-// Flag_1: poly_lo = rsq* poly_hi + poly_lo
-//
-(p13) fma.s1 f59 = f59, f42, f56
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Flag_not_1: (P_1 + r*P_2)
-//
-(p13) fma.s1 f59 = f59, f42, f57
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fP32 = fR, fP3, fP2
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-//
-// Flag_not_1: poly_hi = r + rsq * (P_1 + r*P_2)
-//
-(p13) fma.s1 f35 = f59, f48, f60
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fRsq = fR, fR, f0
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-//
-// Create 0.000...01
-//
-(p0) for f37 = f35, f37
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-//
-// Set lsb of Y_lo to 1
-//
-(p0) fmerge.se f35 = f35,f37
-(p0) br.cond.sptk EXP_MAIN ;;
-}
-EXP_VERY_SMALL:
-
-{ .mmi
- nop.m 999
-(p13) addl r34 = @ltoff(Constants_exp_64_Exponents#),gp
- nop.i 999;;
+ nop.m 0
+ fma.s1 fP5432 = fRsq, fP54, fP32
+ nop.i 0
}
+;;
{ .mfi
-(p13) ld8 r34 = [r34];
-(p12) mov f35 = f9
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-(p12) mov f34 = f1
-(p12) br.cond.sptk EXP_MAIN ;;
-}
-
-{ .mlx
-(p13) add r34 = 8,r34
-(p13) movl r39 = 0x0FFFE ;;
+ nop.m 0
+ fma.s1 fS2 = fF,fT2,f0
+ nop.i 0
}
-//
-// Load big_exp_neg
-// Create 1/2's exponent
-//
-
-{ .mii
-(p13) setf.exp f56 = r39
-(p13) shladd r34 = r32,4,r34 ;;
- nop.i 999
-}
-//
-// Negative exponents are stored after positive
-//
-
{ .mfi
-(p13) ld8 r45 = [r34],0
-//
-// Y_hi = x
-// Scale = 1
-//
-(p13) fmpy.s1 f35 = f9, f9
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fS1 = f2M,fT1,f0
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-//
-// Reset Safe if necessary
-// Create 1/2
-//
-(p13) mov f34 = f9
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fP = fRsq, fP5432, fR
+ nop.i 0
}
+;;
{ .mfi
-(p13) cmp.lt.unc p0, p15 = r37, r45
-(p13) mov f36 = f1
- nop.i 999 ;;
+ nop.m 0
+ fms.s1 fSm1 = fS1,fS2,f1 // S - 1.0
+ nop.i 0
}
-
{ .mfb
- nop.m 999
-//
-// Y_lo = x * x
-//
-(p13) fmpy.s1 f35 = f35, f56
-//
-// Y_lo = x*x/2
-//
-(p13) br.cond.sptk EXP_MAIN ;;
-}
-EXP_HUGE:
-
-{ .mfi
- nop.m 999
-(p0) fcmp.gt.unc.s1 p14, p0 = f9, f0
- nop.i 999
-}
-
-{ .mlx
- nop.m 999
-(p0) movl r39 = 0x15DC0 ;;
-}
-
-{ .mfi
-(p14) setf.exp f34 = r39
-(p14) mov f35 = f1
-(p14) cmp.eq p0, p15 = r0, r0 ;;
+ nop.m 0
+ fma.s1 fS = fS1,fS2,f0
+(p14) br.cond.spnt EXPM1_POSSIBLE_OVERFLOW
}
+;;
{ .mfb
- nop.m 999
-(p14) mov f36 = f34
-//
-// If x > 0, Set Safe = False
-// If x > 0, Y_hi = 2**(24,000)
-// If x > 0, Y_lo = 1.0
-// If x > 0, Scale = 2**(24,000)
-//
-(p14) br.cond.sptk EXP_MAIN ;;
-}
-
-{ .mlx
- nop.m 999
-(p12) movl r39 = 0xA240
-}
-
-{ .mlx
- nop.m 999
-(p12) movl r38 = 0xA1DC ;;
-}
-
-{ .mmb
-(p13) cmp.eq p15, p14 = r0, r0
-(p12) setf.exp f34 = r39
- nop.b 999 ;;
-}
-
-{ .mlx
-(p12) setf.exp f35 = r38
-(p13) movl r39 = 0xFF9C
+ nop.m 0
+ fma.d.s0 f8 = fS, fP, fSm1
+ br.ret.sptk b0 // Normal path exit
}
+;;
-{ .mfi
- nop.m 999
-(p13) fsub.s1 f34 = f0, f1
- nop.i 999 ;;
+// Here if 2^-60 <= |x| <2^-2
+// Compute 13th order polynomial
+EXPM1_SMALL:
+{ .mmf
+ ldfe fQ3 = [rAD_Q1], 16
+ ldfe fQ2 = [rAD_Q2], 16
+ fma.s1 fX4 = fXsq, fXsq, f0
}
+;;
{ .mfi
- nop.m 999
-(p12) mov f36 = f34
-(p12) cmp.eq p0, p15 = r0, r0 ;;
+ nop.m 0
+ fma.s1 fQDC = fQD, fNormX, fQC
+ nop.i 0
}
-
{ .mfi
-(p13) setf.exp f35 = r39
-(p13) mov f36 = f1
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fQBA = fQB, fNormX, fQA
+ nop.i 0
}
-EXP_MAIN:
+;;
{ .mfi
-(p0) cmp.ne.unc p12, p0 = 0x01, r33
-(p0) fmpy.s1 f101 = f36, f35
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fQ98 = fQ9, fNormX, fQ8
+ nop.i 0
}
-
-{ .mfb
- nop.m 999
-(p0) fma.d.s0 f99 = f34, f36, f101
-(p15) br.cond.sptk EXP_64_RETURN;;
-}
-
{ .mfi
- nop.m 999
-(p0) fsetc.s3 0x7F,0x01
- nop.i 999
-}
-
-{ .mlx
- nop.m 999
-(p0) movl r50 = 0x000000000103FF ;;
-}
-//
-// S0 user supplied status
-// S2 user supplied status + WRE + TD (Overflows)
-// S3 user supplied status + RZ + TD (Underflows)
-//
-//
-// If (Safe) is true, then
-// Compute result using user supplied status field.
-// No overflow or underflow here, but perhaps inexact.
-// Return
-// Else
-// Determine if overflow or underflow was raised.
-// Fetch +/- overflow threshold for IEEE single, double,
-// double extended
-//
-
-{ .mfi
-(p0) setf.exp f60 = r50
-(p0) fma.d.s3 f102 = f34, f36, f101
- nop.i 999
+ nop.m 0
+ fma.s1 fQ76= fQ7, fNormX, fQ6
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fsetc.s3 0x7F,0x40
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fQ54 = fQ5, fNormX, fQ4
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-//
-// For Safe, no need to check for over/under.
-// For expm1, handle errors like exp.
-//
-(p0) fsetc.s2 0x7F,0x42
- nop.i 999;;
+ nop.m 0
+ fma.s1 fX6 = fX4, fXsq, f0
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fma.d.s2 f100 = f34, f36, f101
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fQ32= fQ3, fNormX, fQ2
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fsetc.s2 0x7F,0x40
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fQDCBA = fQDC, fXsq, fQBA
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p7) fclass.m.unc p12, p0 = f102, 0x00F
- nop.i 999
+ nop.m 0
+ fma.s1 fQ7654 = fQ76, fXsq, fQ54
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fclass.m.unc p11, p0 = f102, 0x00F
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fQDCBA98 = fQDCBA, fXsq, fQ98
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p7) fcmp.ge.unc.s1 p10, p0 = f100, f60
- nop.i 999
+ nop.m 0
+ fma.s1 fQ765432 = fQ7654, fXsq, fQ32
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-//
-// Create largest double exponent + 1.
-// Create smallest double exponent - 1.
-//
-(p0) fcmp.ge.unc.s1 p8, p0 = f100, f60
- nop.i 999 ;;
-}
-//
-// fcmp: resultS2 >= + overflow threshold -> set (a) if true
-// fcmp: resultS2 <= - overflow threshold -> set (b) if true
-// fclass: resultS3 is denorm/unorm/0 -> set (d) if true
-//
-
-{ .mib
-(p10) mov r65 = 41
- nop.i 999
-(p10) br.cond.sptk __libm_error_region ;;
-}
-
-{ .mib
-(p8) mov r65 = 14
- nop.i 999
-(p8) br.cond.sptk __libm_error_region ;;
+ nop.m 0
+ fma.s1 fQDCBA98765432 = fQDCBA98, fX6, fQ765432
+ nop.i 0
}
-//
-// Report that exp overflowed
-//
+;;
-{ .mib
-(p12) mov r65 = 42
- nop.i 999
-(p12) br.cond.sptk __libm_error_region ;;
+{ .mfb
+ nop.m 0
+ fma.d.s0 f8 = fQDCBA98765432, fXsq, fNormX
+ br.ret.sptk b0 // Exit small branch
}
+;;
-{ .mib
-(p11) mov r65 = 15
- nop.i 999
-(p11) br.cond.sptk __libm_error_region ;;
-}
-{ .mib
- nop.m 999
- nop.i 999
-//
-// Report that exp underflowed
-//
-(p0) br.cond.sptk EXP_64_RETURN;;
-}
-EXP_64_SPECIAL:
+EXPM1_POSSIBLE_OVERFLOW:
-{ .mfi
- nop.m 999
-(p0) fclass.m.unc p6, p0 = f8, 0x0c3
- nop.i 999
-}
+// Here if fMAX_DBL_NORM_ARG < x < fMIN_DBL_OFLOW_ARG
+// This cannot happen if input is a double, only if input higher precision.
+// Overflow is a possibility, not a certainty.
-{ .mfi
- nop.m 999
-(p0) fclass.m.unc p13, p8 = f8, 0x007
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p7) fclass.m.unc p14, p0 = f8, 0x007
- nop.i 999
-}
+// Recompute result using status field 2 with user's rounding mode,
+// and wre set. If result is larger than largest double, then we have
+// overflow
{ .mfi
- nop.m 999
-(p0) fclass.m.unc p12, p9 = f8, 0x021
- nop.i 999 ;;
+ mov rGt_ln = 0x103ff // Exponent for largest dbl + 1 ulp
+ fsetc.s2 0x7F,0x42 // Get user's round mode, set wre
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fclass.m.unc p11, p0 = f8, 0x022
- nop.i 999
+ setf.exp fGt_pln = rGt_ln // Create largest double + 1 ulp
+ fma.d.s2 fWre_urm_f8 = fS, fP, fSm1 // Result with wre set
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p7) fclass.m.unc p10, p0 = f8, 0x022
- nop.i 999 ;;
+ nop.m 0
+ fsetc.s2 0x7F,0x40 // Turn off wre in sf2
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-//
-// Identify +/- 0, Inf, or -Inf
-// Generate the right kind of NaN.
-//
-(p13) fadd.d.s0 f99 = f0, f1
- nop.i 999 ;;
+ nop.m 0
+ fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow
+ nop.i 0
}
+;;
-{ .mfi
- nop.m 999
-(p14) mov f99 = f8
- nop.i 999 ;;
+{ .mfb
+ nop.m 0
+ nop.f 0
+(p6) br.cond.spnt EXPM1_CERTAIN_OVERFLOW // Branch if overflow
}
+;;
{ .mfb
- nop.m 999
-(p6) fadd.d.s0 f99 = f8, f1
-//
-// exp(+/-0) = 1
-// expm1(+/-0) = +/-0
-// No exceptions raised
-//
-(p6) br.cond.sptk EXP_64_RETURN;;
+ nop.m 0
+ fma.d.s0 f8 = fS, fP, fSm1
+ br.ret.sptk b0 // Exit if really no overflow
}
+;;
-{ .mib
- nop.m 999
- nop.i 999
-(p14) br.cond.sptk EXP_64_RETURN;;
+EXPM1_CERTAIN_OVERFLOW:
+{ .mmi
+ sub rTmp = rExp_mask, r0, 1
+;;
+ setf.exp fTmp = rTmp
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p11) mov f99 = f0
- nop.i 999 ;;
+ alloc r32=ar.pfs,1,4,4,0
+ fmerge.s FR_X = f8,f8
+ nop.i 0
}
-
{ .mfb
- nop.m 999
-(p10) fsub.d.s1 f99 = f0, f1
-//
-// exp(-Inf) = 0
-// expm1(-Inf) = -1
-// No exceptions raised.
-//
-(p10) br.cond.sptk EXP_64_RETURN;;
+ mov GR_Parameter_TAG = 41
+ fma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result
+ br.cond.sptk __libm_error_region
}
+;;
+// Here if x unorm
+EXPM1_UNORM:
{ .mfb
- nop.m 999
-(p12) fmpy.d.s1 f99 = f8, f1
-//
-// exp(+Inf) = Inf
-// No exceptions raised.
-//
-(p0) br.cond.sptk EXP_64_RETURN;;
+ getf.exp rSignexp_x = fNormX // Must recompute if x unorm
+ fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag
+ br.cond.sptk EXPM1_COMMON
}
+;;
-
-EXP_64_UNSUPPORTED:
-
-{ .mfb
- nop.m 999
-(p0) fmpy.d.s0 f99 = f8, f0
- nop.b 0;;
+// here if result will be -1 and inexact, x <= -48.0
+EXPM1_CERTAIN_MINUS_ONE:
+{ .mmi
+ mov rTmp = 1
+;;
+ setf.exp fTmp = rTmp
+ nop.i 0
}
+;;
-EXP_64_RETURN:
{ .mfb
- nop.m 999
-(p0) mov f8 = f99
-(p0) br.ret.sptk b0
+ nop.m 0
+ fms.d.s0 FR_RESULT = fTmp, fTmp, f1 // Set I, rounded -1+eps result
+ br.ret.sptk b0
}
-.endp expm1
-ASM_SIZE_DIRECTIVE(expm1)
+;;
-.proc __libm_error_region
-__libm_error_region:
+GLOBAL_IEEE754_END(expm1)
+
+LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
-// (1)
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
@@ -1716,38 +841,32 @@ __libm_error_region:
}
{ .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] = FR_Y,16 // STORE Parameter 2 on stack
- add GR_Parameter_X = 16,sp // Parameter 1 address
+ 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_X // STORE Parameter 1 on stack
+ 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
+ nop.b 0
}
{ .mib
- stfd [GR_Parameter_Y] = FR_RESULT // 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 f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
@@ -1760,9 +879,6 @@ __libm_error_region:
br.ret.sptk b0 // Return
};;
-.endp __libm_error_region
-ASM_SIZE_DIRECTIVE(__libm_error_region)
-
-
+LOCAL_LIBM_END(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#