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Diffstat (limited to 'sysdeps/ia64/fpu/s_expm1l.S')
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diff --git a/sysdeps/ia64/fpu/s_expm1l.S b/sysdeps/ia64/fpu/s_expm1l.S deleted file mode 100644 index a3a6e401e8..0000000000 --- a/sysdeps/ia64/fpu/s_expm1l.S +++ /dev/null @@ -1,1431 +0,0 @@ -.file "expl_m1.s" - - -// Copyright (c) 2000 - 2003, Intel Corporation -// All rights reserved. -// -// 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 -// 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://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 -// 02/10/03 Reordered header: .section, .global, .proc, .align; -// used data8 for long double table values -// 03/11/03 Improved accuracy and performance, corrected missing inexact flags -// 04/17/03 Eliminated misplaced and unused data label -// 12/15/03 Eliminated call to error support on expm1l underflow -// -//********************************************************************* -// -// Function: Combined expl(x) and expm1l(x), where -// x -// expl(x) = e , for double-extended precision x values -// x -// expm1l(x) = e - 1 for double-extended precision x values -// -//********************************************************************* -// -// Resources Used: -// -// Floating-Point Registers: f8 (Input and Return Value) -// f9-f15,f32-f77 -// -// General Purpose Registers: -// r14-r38 -// r35-r38 (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, -// out_FR : Y_hi, -// out_FR : Y_lo, -// out_FR : scale, -// out_PR : Safe ) -// -// On input, X is in register format -// p6 for exp, -// p7 for expm1, -// -// On output, -// -// scale*(Y_hi + Y_lo) approximates exp(X) if exp -// scale*(Y_hi + Y_lo) approximates exp(X)-1 if expm1 -// -// 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^(-m) use case exp_small; m=12 for exp, m=7 for expm1 -// else use case exp_regular; -// -// Case exp_tiny: -// -// 1 + X can be used to approximate exp(X) -// X + X^2/2 can be used to approximate exp(X) - 1 -// -// Case exp_small: -// -// Here, exp(X) and exp(X) - 1 can all be -// approximated 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. -// -// 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 -// -// T := T_1 * T_2 ...exactly -// W := W_1 + (1 + W_1)*W_2 -// -// 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). -// -// 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 expm1 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 exp ...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 -// Y_hi := 1.0 -// Scale := 1.0 -// -// Else ...i.e. exp( argument ) - 1 -// -// rsq := r * r -// r4 := rsq * rsq -// poly_lo := Q_7 + r*(Q_8 + r*Q_9)) -// poly_med:= Q_3 + r*Q_4 + rsq*(Q_5 + r*Q_6) -// poly_med:= poly_med + r4*poly_lo -// poly_hi := Q_1 + r*Q_2 -// Y_lo := rsq*(poly_hi + rsq*poly_lo) -// 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 -// -//======================================================= -// General Purpose Registers -// -GR_ad_Arg = r14 -GR_ad_A = r15 -GR_sig_inv_ln2 = r15 -GR_rshf_2to51 = r16 -GR_ad_PQ = r16 -GR_ad_Q = r16 -GR_signexp_x = r17 -GR_exp_x = r17 -GR_small_exp = r18 -GR_rshf = r18 -GR_exp_mask = r19 -GR_ad_W1 = r20 -GR_exp_2tom51 = r20 -GR_ad_W2 = r21 -GR_exp_underflow = r21 -GR_M2 = r22 -GR_huge_exp = r22 -GR_M1 = r23 -GR_huge_signif = r23 -GR_K = r24 -GR_one = r24 -GR_minus_one = r24 -GR_exp_bias = r25 -GR_ad_Limits = r26 -GR_N_fix = r26 -GR_exp_2_mk = r26 -GR_ad_P = r27 -GR_exp_2_k = r27 -GR_big_expo_neg = r28 -GR_very_small_exp = r29 -GR_exp_half = r29 -GR_ad_T1 = r30 -GR_ad_T2 = r31 - -GR_SAVE_PFS = r32 -GR_SAVE_B0 = r33 -GR_SAVE_GP = r34 -GR_Parameter_X = r35 -GR_Parameter_Y = r36 -GR_Parameter_RESULT = r37 -GR_Parameter_TAG = r38 - -// Floating Point Registers -// -FR_norm_x = f9 -FR_RSHF_2TO51 = f10 -FR_INV_LN2_2TO63 = f11 -FR_W_2TO51_RSH = f12 -FR_2TOM51 = f13 -FR_RSHF = f14 -FR_Y_hi = f34 -FR_Y_lo = f35 -FR_scale = f36 -FR_tmp = f37 -FR_float_N = f38 -FR_N_signif = f39 -FR_L_hi = f40 -FR_L_lo = f41 -FR_r = f42 -FR_W1 = f43 -FR_T1 = f44 -FR_W2 = f45 -FR_T2 = f46 -FR_W1_p1 = f47 -FR_rsq = f48 -FR_A2 = f49 -FR_r4 = f50 -FR_A3 = f51 -FR_poly = f52 -FR_T = f53 -FR_W = f54 -FR_Wp1 = f55 -FR_p21 = f59 -FR_p210 = f59 -FR_p65 = f60 -FR_p654 = f60 -FR_p6543 = f60 -FR_2_mk = f61 -FR_P4Q7 = f61 -FR_P4 = f61 -FR_Q7 = f61 -FR_P3Q6 = f62 -FR_P3 = f62 -FR_Q6 = f62 -FR_q65 = f62 -FR_q6543 = f62 -FR_P2Q5 = f63 -FR_P2 = f63 -FR_Q5 = f63 -FR_P1Q4 = f64 -FR_P1 = f64 -FR_Q4 = f64 -FR_q43 = f64 -FR_Q3 = f65 -FR_Q2 = f66 -FR_q21 = f66 -FR_Q1 = f67 -FR_A1 = f68 -FR_P6Q9 = f68 -FR_P6 = f68 -FR_Q9 = f68 -FR_P5Q8 = f69 -FR_P5 = f69 -FR_Q8 = f69 -FR_q987 = f69 -FR_q98 = f69 -FR_q9876543 = f69 -FR_min_oflow_x = f70 -FR_huge_exp = f70 -FR_zero_uflow_x = f71 -FR_huge_signif = f71 -FR_huge = f72 -FR_small = f72 -FR_half = f73 -FR_T_scale = f74 -FR_result_lo = f75 -FR_W_T_scale = f76 -FR_Wp1_T_scale = f77 -FR_ftz = f77 -FR_half_x = f77 -// - -FR_X = f9 -FR_Y = f0 -FR_RESULT = f15 - -// ************* 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 2^12/ln(2) is needed for the computation of N. This is also -// obtained by scaling the computations. -// -// Two shifting constants are loaded directly with movl and setf.d. -// 1. RSHF_2TO51 = 1.1000..00 * 2^(63-12) -// This constant is added to x*1/ln2 to shift the integer part of -// x*2^12/ln2 into the rightmost bits of the significand. -// The result of this fma is N_signif. -// 2. RSHF = 1.1000..00 * 2^(63) -// This constant is subtracted from N_signif * 2^(-51) to give -// the integer part of N, N_fix, as a floating-point number. -// The result of this fms is float_N. - -RODATA -.align 64 -LOCAL_OBJECT_START(Constants_exp_64_Arg) -//data8 0xB8AA3B295C17F0BC,0x0000400B // Inv_L = 2^12/log(2) -data8 0xB17217F400000000,0x00003FF2 // L_hi = hi part log(2)/2^12 -data8 0xF473DE6AF278ECE6,0x00003FD4 // L_lo = lo part log(2)/2^12 -LOCAL_OBJECT_END(Constants_exp_64_Arg) - -LOCAL_OBJECT_START(Constants_exp_64_Limits) -data8 0xb17217f7d1cf79ac,0x0000400c // Smallest long dbl oflow x -data8 0xb220000000000000,0x0000c00c // Small long dbl uflow zero x -LOCAL_OBJECT_END(Constants_exp_64_Limits) - -LOCAL_OBJECT_START(Constants_exp_64_A) -data8 0xAAAAAAABB1B736A0,0x00003FFA // A3 -data8 0xAAAAAAAB90CD6327,0x00003FFC // A2 -data8 0xFFFFFFFFFFFFFFFF,0x00003FFD // A1 -LOCAL_OBJECT_END(Constants_exp_64_A) - -LOCAL_OBJECT_START(Constants_exp_64_P) -data8 0xD00D6C8143914A8A,0x00003FF2 // P6 -data8 0xB60BC4AC30304B30,0x00003FF5 // P5 -data8 0x888888887474C518,0x00003FF8 // P4 -data8 0xAAAAAAAA8DAE729D,0x00003FFA // P3 -data8 0xAAAAAAAAAAAAAF61,0x00003FFC // P2 -data8 0x80000000000004C7,0x00003FFE // P1 -LOCAL_OBJECT_END(Constants_exp_64_P) - -LOCAL_OBJECT_START(Constants_exp_64_Q) -data8 0x93F2AC5F7471F32E, 0x00003FE9 // Q9 -data8 0xB8DA0F3550B3E764, 0x00003FEC // Q8 -data8 0xD00D00D0028E89C4, 0x00003FEF // Q7 -data8 0xD00D00DAEB8C4E91, 0x00003FF2 // Q6 -data8 0xB60B60B60B60B6F5, 0x00003FF5 // Q5 -data8 0x888888888886CC23, 0x00003FF8 // Q4 -data8 0xAAAAAAAAAAAAAAAB, 0x00003FFA // Q3 -data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // Q2 -data8 0x8000000000000000, 0x00003FFE // Q1 -LOCAL_OBJECT_END(Constants_exp_64_Q) - -LOCAL_OBJECT_START(Constants_exp_64_T1) -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 -LOCAL_OBJECT_END(Constants_exp_64_T1) - -LOCAL_OBJECT_START(Constants_exp_64_T2) -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 -LOCAL_OBJECT_END(Constants_exp_64_T2) - -LOCAL_OBJECT_START(Constants_exp_64_W1) -data8 0x0000000000000000, 0xBE384454171EC4B4 -data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8 -data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36 -data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE -data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F -data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329 -data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5 -data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F -data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF -data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F -data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92 -data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E -data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D -data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29 -data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A -data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA -data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6 -data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF -data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC -data8 0xBE51C2141AA42614, 0xBE48D087C37293F4 -data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38 -data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962 -data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788 -data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7 -data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2 -data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4 -data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA -data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B -data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A -data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719 -data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D -data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707 -LOCAL_OBJECT_END(Constants_exp_64_W1) - -LOCAL_OBJECT_START(Constants_exp_64_W2) -data8 0x0000000000000000, 0xBE641F2537A3D7A2 -data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6 -data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE -data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3 -data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4 -data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B -data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7 -data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA -data8 0xBE56856B49BFF529, 0x3E66DD3300508651 -data8 0x3E51165FC114BC13, 0x3E53333DC453290F -data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696 -data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93 -data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE -data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22 -data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97 -data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8 -data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC -data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1 -data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7 -data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D -data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C -data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5 -data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9 -data8 0xBE559725ADE45917, 0xBE68C29C042FC476 -data8 0xBE67593B01E511FA, 0xBE4A4313398801ED -data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E -data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D -data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F -data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1 -data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795 -data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E -data8 0x3E68BF5C17365712, 0x3E3956F9B3785569 -LOCAL_OBJECT_END(Constants_exp_64_W2) - - -.section .text - -GLOBAL_IEEE754_ENTRY(expm1l) - -// -// Set p7 true for expm1, p6 false -// - -{ .mlx - getf.exp GR_signexp_x = f8 // Get sign and exponent of x, redo if unorm - movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 -} -{ .mlx - addl GR_ad_Arg = @ltoff(Constants_exp_64_Arg#),gp - movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51) -} -;; - -{ .mfi - ld8 GR_ad_Arg = [GR_ad_Arg] // Point to Arg table - fclass.m p8, p0 = f8, 0x1E7 // Test x for natval, nan, inf, zero - cmp.eq p7, p6 = r0, r0 -} -{ .mfb - mov GR_exp_half = 0x0FFFE // Exponent of 0.5, for very small path - fnorm.s1 FR_norm_x = f8 // Normalize x - br.cond.sptk exp_continue -} -;; - -GLOBAL_IEEE754_END(expm1l) - - -GLOBAL_IEEE754_ENTRY(expl) -// -// Set p7 false for exp, p6 true -// -{ .mlx - getf.exp GR_signexp_x = f8 // Get sign and exponent of x, redo if unorm - movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 -} -{ .mlx - addl GR_ad_Arg = @ltoff(Constants_exp_64_Arg#),gp - movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51) -} -;; - -{ .mfi - ld8 GR_ad_Arg = [GR_ad_Arg] // Point to Arg table - fclass.m p8, p0 = f8, 0x1E7 // Test x for natval, nan, inf, zero - cmp.eq p6, p7 = r0, r0 -} -{ .mfi - mov GR_exp_half = 0x0FFFE // Exponent of 0.5, for very small path - fnorm.s1 FR_norm_x = f8 // Normalize x - nop.i 999 -} -;; - -exp_continue: -// Form two constants we need -// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128 -// 1.1000..000 * 2^(63+63-12) to right shift int(N) into the significand - -{ .mfi - setf.sig FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63 - fclass.nm.unc p9, p0 = f8, 0x1FF // Test x for unsupported - mov GR_exp_2tom51 = 0xffff-51 -} -{ .mlx - setf.d FR_RSHF_2TO51 = GR_rshf_2to51 // Form const 1.1000 * 2^(63+51) - movl GR_rshf = 0x43e8000000000000 // 1.10000 2^63 for right shift -} -;; - -{ .mfi - setf.exp FR_half = GR_exp_half // Form 0.5 for very small path - fma.s1 FR_scale = f1,f1,f0 // Scale = 1.0 - mov GR_exp_bias = 0x0FFFF // Set exponent bias -} -{ .mib - add GR_ad_Limits = 0x20, GR_ad_Arg // Point to Limits table - mov GR_exp_mask = 0x1FFFF // Form exponent mask -(p8) br.cond.spnt EXP_64_SPECIAL // Branch if natval, nan, inf, zero -} -;; - -{ .mfi - setf.exp FR_2TOM51 = GR_exp_2tom51 // Form 2^-51 for scaling float_N - nop.f 999 - add GR_ad_A = 0x40, GR_ad_Arg // Point to A table -} -{ .mib - setf.d FR_RSHF = GR_rshf // Form right shift const 1.1000 * 2^63 - add GR_ad_T1 = 0x160, GR_ad_Arg // Point to T1 table -(p9) br.cond.spnt EXP_64_UNSUPPORTED // Branch if unsupported -} -;; - -.pred.rel "mutex",p6,p7 -{ .mfi - ldfe FR_L_hi = [GR_ad_Arg],16 // Get L_hi - fcmp.eq.s0 p9,p0 = f8, f0 // Dummy op to flag denormals -(p6) add GR_ad_PQ = 0x30, GR_ad_A // Point to P table for exp -} -{ .mfi - ldfe FR_min_oflow_x = [GR_ad_Limits],16 // Get min x to cause overflow - fmpy.s1 FR_rsq = f8, f8 // rsq = x * x for small path -(p7) add GR_ad_PQ = 0x90, GR_ad_A // Point to Q table for expm1 -};; - -{ .mmi - ldfe FR_L_lo = [GR_ad_Arg],16 // Get L_lo - ldfe FR_zero_uflow_x = [GR_ad_Limits],16 // Get x for zero uflow result - add GR_ad_W1 = 0x200, GR_ad_T1 // Point to W1 table -} -;; - -{ .mfi - ldfe FR_P6Q9 = [GR_ad_PQ],16 // P6(exp) or Q9(expm1) for small path - mov FR_r = FR_norm_x // r = X for small path - mov GR_very_small_exp = -60 // Exponent of x for very small path -} -{ .mfi - add GR_ad_W2 = 0x400, GR_ad_T1 // Point to W2 table - nop.f 999 -(p7) mov GR_small_exp = -7 // Exponent of x for small path expm1 -} -;; - -{ .mmi - ldfe FR_P5Q8 = [GR_ad_PQ],16 // P5(exp) or Q8(expm1) for small path - and GR_exp_x = GR_signexp_x, GR_exp_mask -(p6) mov GR_small_exp = -12 // Exponent of x for small path exp -} -;; - -// N_signif = X * Inv_log2_by_2^12 -// By adding 1.10...0*2^63 we shift and get round_int(N_signif) in significand. -// We actually add 1.10...0*2^51 to X * Inv_log2 to do the same thing. -{ .mfi - ldfe FR_P4Q7 = [GR_ad_PQ],16 // P4(exp) or Q7(expm1) for small path - fma.s1 FR_N_signif = FR_norm_x, FR_INV_LN2_2TO63, FR_RSHF_2TO51 - nop.i 999 -} -{ .mfi - sub GR_exp_x = GR_exp_x, GR_exp_bias // Get exponent - fmpy.s1 FR_r4 = FR_rsq, FR_rsq // Form r4 for small path - cmp.eq.unc p15, p0 = r0, r0 // Set Safe as default -} -;; - -{ .mmi - ldfe FR_P3Q6 = [GR_ad_PQ],16 // P3(exp) or Q6(expm1) for small path - cmp.lt p14, p0 = GR_exp_x, GR_very_small_exp // Is |x| < 2^-60? - nop.i 999 -} -;; - -{ .mfi - ldfe FR_P2Q5 = [GR_ad_PQ],16 // P2(exp) or Q5(expm1) for small path - fmpy.s1 FR_half_x = FR_half, FR_norm_x // 0.5 * x for very small path - cmp.lt p13, p0 = GR_exp_x, GR_small_exp // Is |x| < 2^-m? -} -{ .mib - nop.m 999 - nop.i 999 -(p14) br.cond.spnt EXP_VERY_SMALL // Branch if |x| < 2^-60 -} -;; - -{ .mfi - ldfe FR_A3 = [GR_ad_A],16 // Get A3 for normal path - fcmp.ge.s1 p10,p0 = FR_norm_x, FR_min_oflow_x // Will result overflow? - mov GR_big_expo_neg = -16381 // -0x3ffd -} -{ .mfb - ldfe FR_P1Q4 = [GR_ad_PQ],16 // P1(exp) or Q4(expm1) for small path - nop.f 999 -(p13) br.cond.spnt EXP_SMALL // Branch if |x| < 2^-m - // m=12 for exp, m=7 for expm1 -} -;; - -// Now we are on the main path for |x| >= 2^-m, m=12 for exp, m=7 for expm1 -// -// float_N = round_int(N_signif) -// The signficand of N_signif contains the rounded integer part of X * 2^12/ln2, -// as a twos complement number in the lower bits (that is, it may be negative). -// That twos complement number (called N) is put into GR_N. - -// Since N_signif is scaled by 2^51, it must be multiplied by 2^-51 -// before the shift constant 1.10000 * 2^63 is subtracted to yield float_N. -// Thus, float_N contains the floating point version of N - - -{ .mfi - ldfe FR_A2 = [GR_ad_A],16 // Get A2 for main path - fcmp.lt.s1 p11,p0 = FR_norm_x, FR_zero_uflow_x // Certain zero, uflow? - add GR_ad_T2 = 0x100, GR_ad_T1 // Point to T2 table -} -{ .mfi - nop.m 999 - fms.s1 FR_float_N = FR_N_signif, FR_2TOM51, FR_RSHF // Form float_N - nop.i 999 -} -;; - -{ .mbb - getf.sig GR_N_fix = FR_N_signif // Get N from significand -(p10) br.cond.spnt EXP_OVERFLOW // Branch if result will overflow -(p11) br.cond.spnt EXP_CERTAIN_UNDERFLOW_ZERO // Branch if certain zero, uflow -} -;; - -{ .mfi - ldfe FR_A1 = [GR_ad_A],16 // Get A1 for main path - fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_norm_x // r = -L_hi * float_N + x - extr.u GR_M1 = GR_N_fix, 6, 6 // Extract index M_1 -} -{ .mfi - and GR_M2 = 0x3f, GR_N_fix // Extract index M_2 - nop.f 999 - nop.i 999 -} -;; - -// N_fix is only correct up to 50 bits because of our right shift technique. -// Actually in the normal path we will have restricted K to about 14 bits. -// Somewhat arbitrarily we extract 32 bits. -{ .mfi - shladd GR_ad_W1 = GR_M1,3,GR_ad_W1 // Point to W1 - nop.f 999 - extr GR_K = GR_N_fix, 12, 32 // Extract limited range K -} -{ .mfi - shladd GR_ad_T1 = GR_M1,2,GR_ad_T1 // Point to T1 - nop.f 999 - shladd GR_ad_T2 = GR_M2,2,GR_ad_T2 // Point to T2 -} -;; - -{ .mmi - ldfs FR_T1 = [GR_ad_T1],0 // Get T1 - ldfd FR_W1 = [GR_ad_W1],0 // Get W1 - add GR_exp_2_k = GR_exp_bias, GR_K // Form exponent of 2^k -} -;; - -{ .mmi - ldfs FR_T2 = [GR_ad_T2],0 // Get T2 - shladd GR_ad_W2 = GR_M2,3,GR_ad_W2 // Point to W2 - sub GR_exp_2_mk = GR_exp_bias, GR_K // Form exponent of 2^-k -} -;; - -{ .mmf - ldfd FR_W2 = [GR_ad_W2],0 // Get W2 - setf.exp FR_scale = GR_exp_2_k // Set scale = 2^k - fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r // r = -L_lo * float_N + r -} -;; - -{ .mfi - setf.exp FR_2_mk = GR_exp_2_mk // Form 2^-k - fma.s1 FR_poly = FR_r, FR_A3, FR_A2 // poly = r * A3 + A2 - cmp.lt p8,p15 = GR_K,GR_big_expo_neg // Set Safe if K > big_expo_neg -} -{ .mfi - nop.m 999 - fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s1 FR_T = FR_T1, FR_T2 // T = T1 * T2 - nop.i 999 -} -{ .mfi - nop.m 999 - fadd.s1 FR_W1_p1 = FR_W1, f1 // W1_p1 = W1 + 1.0 - nop.i 999 -} -;; - -{ .mfi -(p7) cmp.lt.unc p8, p9 = 10, GR_K // If expm1, set p8 if K > 10 - fma.s1 FR_poly = FR_r, FR_poly, FR_A1 // poly = r * poly + A1 - nop.i 999 -} -;; - -{ .mfi -(p7) cmp.eq p15, p0 = r0, r0 // If expm1, set Safe flag - fma.s1 FR_T_scale = FR_T, FR_scale, f0 // T_scale = T * scale -(p9) cmp.gt.unc p9, p10 = -10, GR_K // If expm1, set p9 if K < -10 - // If expm1, set p10 if -10<=K<=10 -} -{ .mfi - nop.m 999 - fma.s1 FR_W = FR_W2, FR_W1_p1, FR_W1 // W = W2 * (W1+1.0) + W1 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - mov FR_Y_hi = FR_T // Assume Y_hi = T - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 FR_poly = FR_rsq, FR_poly, FR_r // poly = rsq * poly + r - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 FR_Wp1_T_scale = FR_W, FR_T_scale, FR_T_scale // (W+1)*T*scale - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 FR_W_T_scale = FR_W, FR_T_scale, f0 // W*T*scale - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fsub.s1 FR_Y_hi = f0, FR_2_mk // If expm1, if K < -10 set Y_hi - nop.i 999 -} -{ .mfi - nop.m 999 -(p10) fsub.s1 FR_Y_hi = FR_T, FR_2_mk // If expm1, if |K|<=10 set Y_hi - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 FR_result_lo = FR_Wp1_T_scale, FR_poly, FR_W_T_scale - nop.i 999 -} -;; - -.pred.rel "mutex",p8,p9 -// If K > 10 adjust result_lo = result_lo - scale * 2^-k -// If |K| <= 10 adjust result_lo = result_lo + scale * T -{ .mfi - nop.m 999 -(p8) fnma.s1 FR_result_lo = FR_scale, FR_2_mk, FR_result_lo // If K > 10 - nop.i 999 -} -{ .mfi - nop.m 999 -(p9) fma.s1 FR_result_lo = FR_T_scale, f1, FR_result_lo // If |K| <= 10 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s0 FR_tmp = FR_A1, FR_A1 // Dummy op to set inexact - nop.i 999 -} -{ .mfb - nop.m 999 -(p15) fma.s0 f8 = FR_Y_hi, FR_scale, FR_result_lo // Safe result -(p15) br.ret.sptk b0 // Safe exit for normal path -} -;; - -// Here if unsafe, will only be here for exp with K < big_expo_neg -{ .mfb - nop.m 999 - fma.s0 FR_RESULT = FR_Y_hi, FR_scale, FR_result_lo // Prelim result - br.cond.sptk EXP_POSSIBLE_UNDERFLOW // Branch to unsafe code -} -;; - - -EXP_SMALL: -// Here if 2^-60 < |x| < 2^-m, m=12 for exp, m=7 for expm1 -{ .mfi -(p7) ldfe FR_Q3 = [GR_ad_Q],16 // Get Q3 for small path, if expm1 -(p6) fma.s1 FR_p65 = FR_P6, FR_r, FR_P5 // If exp, p65 = P6 * r + P5 - nop.i 999 -} -{ .mfi - mov GR_minus_one = -1 -(p7) fma.s1 FR_q98 = FR_Q9, FR_r, FR_Q8 // If expm1, q98 = Q9 * r + Q8 - nop.i 999 -} -;; - -{ .mfi -(p7) ldfe FR_Q2 = [GR_ad_Q],16 // Get Q2 for small path, if expm1 -(p7) fma.s1 FR_q65 = FR_Q6, FR_r, FR_Q5 // If expm1, q65 = Q6 * r + Q5 - nop.i 999 -} -;; - -{ .mfi - setf.sig FR_tmp = GR_minus_one // Create value to force inexact -(p6) fma.s1 FR_p21 = FR_P2, FR_r, FR_P1 // If exp, p21 = P2 * r + P1 - nop.i 999 -} -{ .mfi -(p7) ldfe FR_Q1 = [GR_ad_Q],16 // Get Q1 for small path, if expm1 -(p7) fma.s1 FR_q43 = FR_Q4, FR_r, FR_Q3 // If expm1, q43 = Q4 * r + Q3 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p6) fma.s1 FR_p654 = FR_p65, FR_r, FR_P4 // If exp, p654 = p65 * r + P4 - nop.i 999 -} -{ .mfi - nop.m 999 -(p7) fma.s1 FR_q987 = FR_q98, FR_r, FR_Q7 // If expm1, q987 = q98 * r + Q7 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p7) fma.s1 FR_q21 = FR_Q2, FR_r, FR_Q1 // If expm1, q21 = Q2 * r + Q1 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p6) fma.s1 FR_p210 = FR_p21, FR_rsq, FR_r // If exp, p210 = p21 * r + P0 - nop.i 999 -} -{ .mfi - nop.m 999 -(p7) fma.s1 FR_q6543 = FR_q65, FR_rsq, FR_q43 // If expm1, q6543 = q65*r2+q43 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p6) fma.s1 FR_p6543 = FR_p654, FR_r, FR_P3 // If exp, p6543 = p654 * r + P3 - nop.i 999 -} -{ .mfi - nop.m 999 -(p7) fma.s1 FR_q9876543 = FR_q987, FR_r4, FR_q6543 // If expm1, q9876543 = ... - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p6) fma.s1 FR_Y_lo = FR_p6543, FR_r4, FR_p210 // If exp, form Y_lo - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p7) fma.s1 FR_Y_lo = FR_q9876543, FR_rsq, FR_q21 // If expm1, form Y_lo - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmpy.s0 FR_tmp = FR_tmp, FR_tmp // Dummy op to set inexact - nop.i 999 -} -;; - -.pred.rel "mutex",p6,p7 -{ .mfi - nop.m 999 -(p6) fma.s0 f8 = FR_Y_lo, f1, f1 // If exp, result = 1 + Y_lo - nop.i 999 -} -{ .mfb - nop.m 999 -(p7) fma.s0 f8 = FR_Y_lo, FR_rsq, FR_norm_x // If expm1, result = Y_lo*r2+x - br.ret.sptk b0 // Exit for 2^-60 <= |x| < 2^-m - // m=12 for exp, m=7 for expm1 -} -;; - - -EXP_VERY_SMALL: -// -// Here if 0 < |x| < 2^-60 -// If exp, result = 1.0 + x -// If expm1, result = x +x*x/2, but have to check for possible underflow -// - -{ .mfi -(p7) mov GR_exp_underflow = -16381 // Exponent for possible underflow -(p6) fadd.s0 f8 = f1, FR_norm_x // If exp, result = 1+x - nop.i 999 -} -{ .mfi - nop.m 999 -(p7) fmpy.s1 FR_result_lo = FR_half_x, FR_norm_x // If expm1 result_lo = x*x/2 - nop.i 999 -} -;; - -{ .mfi -(p7) cmp.lt.unc p0, p8 = GR_exp_x, GR_exp_underflow // Unsafe if expm1 x small -(p7) mov FR_Y_hi = FR_norm_x // If expm1, Y_hi = x -(p7) cmp.lt p0, p15 = GR_exp_x, GR_exp_underflow // Unsafe if expm1 x small -} -;; - -{ .mfb - nop.m 999 -(p8) fma.s0 f8 = FR_norm_x, f1, FR_result_lo // If expm1, result=x+x*x/2 -(p15) br.ret.sptk b0 // If Safe, exit -} -;; - -// Here if expm1 and 0 < |x| < 2^-16381; may be possible underflow -{ .mfb - nop.m 999 - fma.s0 FR_RESULT = FR_Y_hi, FR_scale, FR_result_lo // Prelim result - br.cond.sptk EXP_POSSIBLE_UNDERFLOW // Branch to unsafe code -} -;; - -EXP_CERTAIN_UNDERFLOW_ZERO: -// Here if x < zero_uflow_x -// For exp, set result to tiny+0.0 and set I, U, and branch to error handling -// For expm1, set result to tiny-1.0 and set I, and exit -{ .mmi - alloc GR_SAVE_PFS = ar.pfs,0,3,4,0 - nop.m 999 - mov GR_one = 1 -} -;; - -{ .mmi - setf.exp FR_small = GR_one // Form small value - nop.m 999 -(p6) mov GR_Parameter_TAG = 13 // Error tag for exp underflow -} -;; - -{ .mfi - nop.m 999 - fmerge.s FR_X = f8,f8 // Save x for error call - nop.i 999 -} -;; - -.pred.rel "mutex",p6,p7 -{ .mfb - nop.m 999 -(p6) fma.s0 FR_RESULT = FR_small, FR_small, f0 // If exp, set I,U, tiny result -(p6) br.cond.sptk __libm_error_region // If exp, go to error handling -} -{ .mfb - nop.m 999 -(p7) fms.s0 f8 = FR_small, FR_small, f1 // If expm1, set I, result -1.0 -(p7) br.ret.sptk b0 // If expm1, exit -} -;; - - -EXP_OVERFLOW: -// Here if x >= min_oflow_x -{ .mmi - alloc GR_SAVE_PFS = ar.pfs,0,3,4,0 - mov GR_huge_exp = 0x1fffe - nop.i 999 -} -{ .mfi - mov GR_huge_signif = -0x1 - nop.f 999 -(p6) mov GR_Parameter_TAG = 12 // Error tag for exp overflow -} -;; - -{ .mmf - setf.exp FR_huge_exp = GR_huge_exp // Create huge value - setf.sig FR_huge_signif = GR_huge_signif // Create huge value - fmerge.s FR_X = f8,f8 // Save x for error call -} -;; - -{ .mfi - nop.m 999 - fmerge.se FR_huge = FR_huge_exp, FR_huge_signif -(p7) mov GR_Parameter_TAG = 39 // Error tag for expm1 overflow -} -;; - -{ .mfb - nop.m 999 - fma.s0 FR_RESULT = FR_huge, FR_huge, FR_huge // Force I, O, and Inf - br.cond.sptk __libm_error_region // Branch to error handling -} -;; - - - -EXP_POSSIBLE_UNDERFLOW: -// Here if exp and zero_uflow_x < x < about -11356 [where k < -16381] -// Here if expm1 and |x| < 2^-16381 -{ .mfi - alloc GR_SAVE_PFS = ar.pfs,0,3,4,0 - fsetc.s2 0x7F,0x41 // Set FTZ and disable traps - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s2 FR_ftz = FR_Y_hi, FR_scale, FR_result_lo // Result with FTZ - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fsetc.s2 0x7F,0x40 // Disable traps (set s2 default) - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p6) fclass.m.unc p11, p0 = FR_ftz, 0x00F // If exp, FTZ result denorm or zero? - nop.i 999 -} -;; - -{ .mfb -(p11) mov GR_Parameter_TAG = 13 // exp underflow - fmerge.s FR_X = f8,f8 // Save x for error call -(p11) br.cond.spnt __libm_error_region // Branch on exp underflow -} -;; - -{ .mfb - nop.m 999 - mov f8 = FR_RESULT // Was safe after all - br.ret.sptk b0 -} -;; - - -EXP_64_SPECIAL: -// Here if x natval, nan, inf, zero -// If x natval, +inf, or if expm1 and x zero, just return x. -// The other cases must be tested for, and results set. -// These cases do not generate exceptions. -{ .mfi - nop.m 999 - fclass.m p8, p0 = f8, 0x0c3 // Is x nan? - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p6) fclass.m.unc p13, p0 = f8, 0x007 // If exp, is x zero? - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p6) fclass.m.unc p11, p0 = f8, 0x022 // If exp, is x -inf? - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fadd.s0 f8 = f8, f1 // If x nan, result quietized x - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p7) fclass.m.unc p10, p0 = f8, 0x022 // If expm1, is x -inf? - nop.i 999 -} -{ .mfi - nop.m 999 -(p13) fadd.s0 f8 = f0, f1 // If exp and x zero, result 1.0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p11) mov f8 = f0 // If exp and x -inf, result 0 - nop.i 999 -} -;; - -{ .mfb - nop.m 999 -(p10) fsub.s1 f8 = f0, f1 // If expm1, x -inf, result -1.0 - br.ret.sptk b0 // Exit special cases -} -;; - - -EXP_64_UNSUPPORTED: -// Here if x unsupported type -{ .mfb - nop.m 999 - fmpy.s0 f8 = f8, f0 // Return nan - br.ret.sptk b0 -} -;; - -GLOBAL_IEEE754_END(expl) - -LOCAL_LIBM_ENTRY(__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 - add GR_Parameter_RESULT = 48,sp - nop.m 0 - nop.i 0 -};; -{ .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 -};; -LOCAL_LIBM_END(__libm_error_region#) - -.type __libm_error_support#,@function -.global __libm_error_support# |