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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 new file mode 100644 index 0000000000..63bf39a3c1 --- /dev/null +++ b/sysdeps/ia64/fpu/s_expm1l.S @@ -0,0 +1,1431 @@ +.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# |