diff options
Diffstat (limited to 'sysdeps/ia64/fpu/e_expf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_expf.S | 957 |
1 files changed, 511 insertions, 446 deletions
diff --git a/sysdeps/ia64/fpu/e_expf.S b/sysdeps/ia64/fpu/e_expf.S index 6fe0a833e2..2aad021335 100644 --- a/sysdeps/ia64/fpu/e_expf.S +++ b/sysdeps/ia64/fpu/e_expf.S @@ -1,10 +1,10 @@ .file "expf.s" - -// Copyright (c) 2000 - 2005, Intel Corporation +// Copyright (C) 2000, 2001, Intel Corporation // All rights reserved. // -// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, +// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are @@ -20,7 +20,7 @@ // * 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 @@ -35,503 +35,589 @@ // // 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. +// http://developer.intel.com/opensource. // History -//********************************************************************* -// 02/02/00 Original version -// 04/04/00 Unwind support added -// 08/15/00 Bundle added after call to __libm_error_support to properly +//============================================================== +// 4/04/00 Unwind update +// 4/04/00 Unwind support added +// 8/15/00 Bundle added after call to __libm_error_support to properly // set [the previously overwritten] GR_Parameter_RESULT. -// 08/21/00 Improvements to save 2 cycles on main path, and shorten x=0 case +// 8/21/00 Improvements to save 2 cycles on main path, and shorten x=0 case // 12/07/00 Widen main path, shorten x=inf, nan paths -// 03/15/01 Fix monotonicity problem around x=0 for round to +inf -// 02/05/02 Corrected uninitialize predicate in POSSIBLE_UNDERFLOW path -// 05/20/02 Cleaned up namespace and sf0 syntax -// 07/26/02 Algorithm changed, accuracy improved -// 09/26/02 support of higher precision inputs added, underflow threshold -// corrected -// 11/15/02 Improved performance on Itanium 2, added possible over/under paths -// 05/30/03 Set inexact flag on unmasked overflow/underflow -// 03/31/05 Reformatted delimiters between data tables -// -// -// API -//********************************************************************* -// float expf(float) -// -// Overview of operation -//********************************************************************* -// Take the input x. w is "how many log2/128 in x?" -// w = x * 64/log2 -// NJ = int(w) -// x = NJ*log2/64 + R - -// NJ = 64*n + j -// x = n*log2 + (log2/64)*j + R -// -// So, exp(x) = 2^n * 2^(j/64)* exp(R) -// -// T = 2^n * 2^(j/64) -// Construct 2^n -// Get 2^(j/64) table -// actually all the entries of 2^(j/64) table are stored in DP and -// with exponent bits set to 0 -> multiplication on 2^n can be -// performed by doing logical "or" operation with bits presenting 2^n - -// exp(R) = 1 + (exp(R) - 1) -// P = exp(R) - 1 approximated by Taylor series of 3rd degree -// P = A3*R^3 + A2*R^2 + R, A3 = 1/6, A2 = 1/2 // -// The final result is reconstructed as follows -// exp(x) = T + T*P +#include "libm_support.h" -// Special values -//********************************************************************* -// expf(+0) = 1.0 -// expf(-0) = 1.0 +// Assembly macros +//============================================================== +// integer registers used -// expf(+qnan) = +qnan -// expf(-qnan) = -qnan -// expf(+snan) = +qnan -// expf(-snan) = -qnan + exp_GR_0x0f = r33 + exp_GR_0xf0 = r34 -// expf(-inf) = +0 -// expf(+inf) = +inf + EXP_AD_P_1 = r36 + EXP_AD_P_2 = r37 + EXP_AD_T1 = r38 + EXP_AD_T2 = r39 + exp_GR_Mint = r40 -// Overflow and Underflow -//********************************************************************* -// expf(x) = largest single normal when -// x = 88.72283 = 0x42b17217 + exp_GR_Mint_p_128 = r41 + exp_GR_Ind1 = r42 + EXP_AD_M1 = r43 + exp_GR_Ind2 = r44 + EXP_AD_M2 = r45 -// expf(x) = smallest single normal when -// x = -87.33654 = 0xc2aeac4f + exp_GR_min_oflow = r46 + exp_GR_max_zero = r47 + exp_GR_max_norm = r48 + exp_GR_max_uflow = r49 + exp_GR_min_norm = r50 -// expf(x) = largest round-to-nearest single zero when -// x = -103.97208 = 0xc2cff1b5 + exp_GR_17ones = r51 + exp_GR_gt_ln = r52 + exp_GR_T2_size = r53 + exp_GR_17ones_m1 = r56 + exp_GR_one = r57 -// Registers used -//********************************************************************* -// Floating Point registers used: -// f8, input -// f6,f7, f9 -> f15, f32 -> f40 -// General registers used: -// r3, r23 -> r38 -// Predicate registers used: -// p10 -> p15 +GR_SAVE_B0 = r53 +GR_SAVE_PFS = r55 +GR_SAVE_GP = r54 + +GR_Parameter_X = r59 +GR_Parameter_Y = r60 +GR_Parameter_RESULT = r61 +GR_Parameter_TAG = r62 + +FR_X = f10 +FR_Y = f1 +FR_RESULT = f8 -// Assembly macros -//********************************************************************* -// integer registers used -// scratch -rNJ = r3 - -rTmp = r23 -rJ = r23 -rN = r24 -rTblAddr = r25 -rA3 = r26 -rExpHalf = r27 -rLn2Div64 = r28 -r17ones_m1 = r29 -rGt_ln = r29 -rRightShifter = r30 -r64DivLn2 = r31 -// stacked -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 used -FR_X = f10 -FR_Y = f1 -FR_RESULT = f8 -// scratch -fRightShifter = f6 -f64DivLn2 = f7 -fNormX = f9 -fNint = f10 -fN = f11 -fR = f12 -fLn2Div64 = f13 -fA2 = f14 -fA3 = f15 -// stacked -fP = f32 -fT = f33 -fMIN_SGL_OFLOW_ARG = f34 -fMAX_SGL_ZERO_ARG = f35 -fMAX_SGL_NORM_ARG = f36 -fMIN_SGL_NORM_ARG = f37 -fRSqr = f38 -fTmp = f39 -fGt_pln = f39 -fWre_urm_f8 = f40 -fFtz_urm_f8 = f40 - - -RODATA + + EXP_MIN_SGL_OFLOW_ARG = f11 + EXP_MAX_SGL_ZERO_ARG = f12 + EXP_MAX_SGL_NORM_ARG = f13 + EXP_MAX_SGL_UFLOW_ARG = f14 + EXP_MIN_SGL_NORM_ARG = f15 + + exp_coeff_P5 = f32 + exp_coeff_P6 = f33 + exp_coeff_P3 = f34 + exp_coeff_P4 = f35 + + exp_coeff_P1 = f36 + exp_coeff_P2 = f37 + exp_Mx = f38 + exp_Mfloat = f39 + exp_R = f40 + + exp_P1 = f41 + exp_P2 = f42 + exp_P3 = f43 + exp_Rsq = f44 + exp_R4 = f45 + + exp_P4 = f46 + exp_P5 = f47 + exp_P6 = f48 + exp_P7 = f49 + exp_T1 = f50 + + exp_T2 = f51 + exp_T = f52 + exp_A = f53 + exp_norm_f8 = f54 + exp_wre_urm_f8 = f55 + + exp_ftz_urm_f8 = f56 + exp_gt_pln = f57 + + +#ifdef _LIBC +.rodata +#else +.data +#endif + .align 16 -LOCAL_OBJECT_START(_expf_table) -data4 0x42b17218 // Smallest sgl arg to overflow sgl result, +88.7228 -data4 0xc2cff1b5 // Largest sgl for rnd-to-nearest 0 result, -103.9720 -data4 0x42b17217 // Largest sgl arg to give normal sgl result, +88.7228 -data4 0xc2aeac4f // Smallest sgl arg to give normal sgl result, -87.3365 +exp_coeff_1_table: +ASM_TYPE_DIRECTIVE(exp_coeff_1_table,@object) +data8 0x3F56F35FDE4F8563 // p5 +data8 0x3F2A378BEFECCFDD // p6 +data8 0x3FE00000258C581D // p1 +data8 0x3FC555557AE7B3D4 // p2 +ASM_SIZE_DIRECTIVE(exp_coeff_1_table) + + +exp_coeff_2_table: +ASM_TYPE_DIRECTIVE(exp_coeff_2_table,@object) +data8 0x3FA5551BB6592FAE // p3 +data8 0x3F8110E8EBFFD485 // p4 +ASM_SIZE_DIRECTIVE(exp_coeff_2_table) + + +exp_T2_table: +ASM_TYPE_DIRECTIVE(exp_T2_table,@object) +data8 0xa175cf9cd7d85844 , 0x00003f46 // exp(-128) +data8 0xdb7279415a1f9eed , 0x00003f47 // exp(-127) +data8 0x95213b242bd8ca5f , 0x00003f49 // exp(-126) +data8 0xcab03c968c989f83 , 0x00003f4a // exp(-125) +data8 0x89bdb674702961ad , 0x00003f4c // exp(-124) +data8 0xbb35a2eec278be35 , 0x00003f4d // exp(-123) +data8 0xfe71b17f373e7e7a , 0x00003f4e // exp(-122) +data8 0xace9a6ec52a39b63 , 0x00003f50 // exp(-121) +data8 0xeb03423fe393cf1c , 0x00003f51 // exp(-120) +data8 0x9fb52c5bcaef1693 , 0x00003f53 // exp(-119) +data8 0xd910b6377ed60bf1 , 0x00003f54 // exp(-118) +data8 0x9382dad8a9fdbfe4 , 0x00003f56 // exp(-117) +data8 0xc87d0a84dea869a3 , 0x00003f57 // exp(-116) +data8 0x883efb4c6d1087b0 , 0x00003f59 // exp(-115) +data8 0xb92d7373dce9a502 , 0x00003f5a // exp(-114) +data8 0xfbaeb020577fb0cb , 0x00003f5b // exp(-113) +ASM_SIZE_DIRECTIVE(exp_T2_table) + + +exp_T1_table: +ASM_TYPE_DIRECTIVE(exp_T1_table,@object) +data8 0x8000000000000000 , 0x00003fff // exp(16 * 0) +data8 0x87975e8540010249 , 0x00004016 // exp(16 * 1) +data8 0x8fa1fe625b3163ec , 0x0000402d // exp(16 * 2) +data8 0x9826b576512a59d7 , 0x00004044 // exp(16 * 3) +data8 0xa12cc167acbe6902 , 0x0000405b // exp(16 * 4) +data8 0xaabbcdcc279f59e4 , 0x00004072 // exp(16 * 5) +data8 0xb4dbfaadc045d16f , 0x00004089 // exp(16 * 6) +data8 0xbf95e372ccdbf146 , 0x000040a0 // exp(16 * 7) +data8 0xcaf2a62eea10bbfb , 0x000040b7 // exp(16 * 8) +data8 0xd6fbeb62fddbd340 , 0x000040ce // exp(16 * 9) +data8 0xe3bbee32e4a440ea , 0x000040e5 // exp(16 * 10) +data8 0xf13d8517c34199a8 , 0x000040fc // exp(16 * 11) +data8 0xff8c2b166241eedd , 0x00004113 // exp(16 * 12) +data8 0x875a04c0b38d6129 , 0x0000412b // exp(16 * 13) +data8 0x8f610127db6774d7 , 0x00004142 // exp(16 * 14) +data8 0x97e1dd87e5c20bb6 , 0x00004159 // exp(16 * 15) +ASM_SIZE_DIRECTIVE(exp_T1_table) + +// Argument Reduction +// exp_Mx = (int)f8 ==> The value of f8 rounded to int is placed into the +// significand of exp_Mx as a two's +// complement number. + +// Later we want to have exp_Mx in a general register. Do this with a getf.sig +// and call the general register exp_GR_Mint + +// exp_Mfloat = (float)(int)f8 ==> the two's complement number in +// significand of exp_Mx is turned +// into a floating point number. +// R = 1 - exp_Mfloat ==> reduced argument + +// Core Approximation +// Calculate a series in R +// R * p6 + p5 +// R * p4 + p3 +// R * p2 + p1 +// R^2 +// R^4 +// R^2(R * p6 + p5) + (R * p4 + p3) +// R^2(R * p2 + p1) +// R^4(R^2(R * p6 + p5) + (R * p4 + p3)) + (R^2(R * p2 + p1)) +// R + 1 +// exp(R) = (1 + R) + R^4(R^2(R * p6 + p5) + (R * p4 + p3)) + (R^2(R * p2 + p1)) +// exp(R) = 1 + R + R^2 * p1 + R^3 * p2 + R^4 * p3 + R^5 * p4 + R^6 * p5 + R^7 * p6 + +// Reconstruction +// signficand of exp_Mx is two's complement, +// -103 < x < 89 +// The smallest single denormal is 2^-149 = ssdn +// For e^x = ssdn +// x = log(ssdn) = -103.279 +// But with rounding result goes to ssdn until -103.972079 +// The largest single normal is 1.<23 1's> 2^126 ~ 2^127 = lsn +// For e^x = lsn +// x = log(lsn) = 88.7228 // -// 2^(j/64) table, j goes from 0 to 63 -data8 0x0000000000000000 // 2^(0/64) -data8 0x00002C9A3E778061 // 2^(1/64) -data8 0x000059B0D3158574 // 2^(2/64) -data8 0x0000874518759BC8 // 2^(3/64) -data8 0x0000B5586CF9890F // 2^(4/64) -data8 0x0000E3EC32D3D1A2 // 2^(5/64) -data8 0x00011301D0125B51 // 2^(6/64) -data8 0x0001429AAEA92DE0 // 2^(7/64) -data8 0x000172B83C7D517B // 2^(8/64) -data8 0x0001A35BEB6FCB75 // 2^(9/64) -data8 0x0001D4873168B9AA // 2^(10/64) -data8 0x0002063B88628CD6 // 2^(11/64) -data8 0x0002387A6E756238 // 2^(12/64) -data8 0x00026B4565E27CDD // 2^(13/64) -data8 0x00029E9DF51FDEE1 // 2^(14/64) -data8 0x0002D285A6E4030B // 2^(15/64) -data8 0x000306FE0A31B715 // 2^(16/64) -data8 0x00033C08B26416FF // 2^(17/64) -data8 0x000371A7373AA9CB // 2^(18/64) -data8 0x0003A7DB34E59FF7 // 2^(19/64) -data8 0x0003DEA64C123422 // 2^(20/64) -data8 0x0004160A21F72E2A // 2^(21/64) -data8 0x00044E086061892D // 2^(22/64) -data8 0x000486A2B5C13CD0 // 2^(23/64) -data8 0x0004BFDAD5362A27 // 2^(24/64) -data8 0x0004F9B2769D2CA7 // 2^(25/64) -data8 0x0005342B569D4F82 // 2^(26/64) -data8 0x00056F4736B527DA // 2^(27/64) -data8 0x0005AB07DD485429 // 2^(28/64) -data8 0x0005E76F15AD2148 // 2^(29/64) -data8 0x0006247EB03A5585 // 2^(30/64) -data8 0x0006623882552225 // 2^(31/64) -data8 0x0006A09E667F3BCD // 2^(32/64) -data8 0x0006DFB23C651A2F // 2^(33/64) -data8 0x00071F75E8EC5F74 // 2^(34/64) -data8 0x00075FEB564267C9 // 2^(35/64) -data8 0x0007A11473EB0187 // 2^(36/64) -data8 0x0007E2F336CF4E62 // 2^(37/64) -data8 0x00082589994CCE13 // 2^(38/64) -data8 0x000868D99B4492ED // 2^(39/64) -data8 0x0008ACE5422AA0DB // 2^(40/64) -data8 0x0008F1AE99157736 // 2^(41/64) -data8 0x00093737B0CDC5E5 // 2^(42/64) -data8 0x00097D829FDE4E50 // 2^(43/64) -data8 0x0009C49182A3F090 // 2^(44/64) -data8 0x000A0C667B5DE565 // 2^(45/64) -data8 0x000A5503B23E255D // 2^(46/64) -data8 0x000A9E6B5579FDBF // 2^(47/64) -data8 0x000AE89F995AD3AD // 2^(48/64) -data8 0x000B33A2B84F15FB // 2^(49/64) -data8 0x000B7F76F2FB5E47 // 2^(50/64) -data8 0x000BCC1E904BC1D2 // 2^(51/64) -data8 0x000C199BDD85529C // 2^(52/64) -data8 0x000C67F12E57D14B // 2^(53/64) -data8 0x000CB720DCEF9069 // 2^(54/64) -data8 0x000D072D4A07897C // 2^(55/64) -data8 0x000D5818DCFBA487 // 2^(56/64) -data8 0x000DA9E603DB3285 // 2^(57/64) -data8 0x000DFC97337B9B5F // 2^(58/64) -data8 0x000E502EE78B3FF6 // 2^(59/64) -data8 0x000EA4AFA2A490DA // 2^(60/64) -data8 0x000EFA1BEE615A27 // 2^(61/64) -data8 0x000F50765B6E4540 // 2^(62/64) -data8 0x000FA7C1819E90D8 // 2^(63/64) -LOCAL_OBJECT_END(_expf_table) +// expf overflows when x > 42b17218 = 88.7228 +// expf returns largest single denormal when x = c2aeac50 +// expf goes to zero when x < c2cff1b5 + +// Consider range of 8-bit two's complement, -128 ---> 127 +// Add 128; range becomes 0 ---> 255 + +// The number (=i) in 0 ---> 255 is used as offset into two tables. +// i = abcd efgh = abcd * 16 + efgh = i1 * 16 + i2 + +// i1 = (exp_GR_Mint + 128) & 0xf0 (show 0xf0 as -0x10 to avoid assembler error) +// (The immediate in the AND is an 8-bit two's complement) +// i1 = i1 + start of T1 table (EXP_AD_T1) +// Note that the entries in T1 are double-extended numbers on 16-byte boundaries +// and that i1 is already shifted left by 16 after the AND. + +// i2 must be shifted left by 4 before adding to the start of the table. +// i2 = ((exp_GR_Mint + 128) & 0x0f) << 4 +// i2 = i2 + start of T2 table (EXP_AD_T2) + +// T = T1 * T2 +// A = T * (1 + R) +// answer = T * (R^2 * p1 + R^3 * p2 + R^4 * p3 + R^5 * p4 + R^6 * p5 + R^7 * p6) + +// T * (1 + R) +// = T * exp(R) + + +.global expf# .section .text -GLOBAL_IEEE754_ENTRY(expf) - -{ .mlx - addl rTblAddr = @ltoff(_expf_table),gp - movl r64DivLn2 = 0x40571547652B82FE // 64/ln(2) +.proc expf# +.align 32 +expf: +#ifdef _LIBC +.global __ieee754_expf# +__ieee754_expf: +#endif + +{ .mfi + alloc r32 = ar.pfs,1,26,4,0 + fcvt.fx.s1 exp_Mx = f8 + mov exp_GR_17ones = 0x1FFFF } { .mlx - addl rA3 = 0x3E2AA, r0 // high bits of 1.0/6.0 rounded to SP - movl rRightShifter = 0x43E8000000000000 // DP Right Shifter + addl EXP_AD_P_1 = @ltoff(exp_coeff_1_table),gp + movl exp_GR_min_oflow = 0x42b17218 } ;; +// Fnorm done to take any enabled faults { .mfi - // point to the beginning of the table - ld8 rTblAddr = [rTblAddr] - fclass.m p14, p0 = f8, 0x22 // test for -INF - shl rA3 = rA3, 12 // 0x3E2AA000, approx to 1.0/6.0 in SP + ld8 EXP_AD_P_1 = [EXP_AD_P_1] + fclass.m p6,p0 = f8, 0x07 //@zero + nop.i 999 } { .mfi - nop.m 0 - fnorm.s1 fNormX = f8 // normalized x - addl rExpHalf = 0xFFFE, r0 // exponent of 1/2 + add exp_GR_max_norm = -1, exp_GR_min_oflow // 0x42b17217 + fnorm exp_norm_f8 = f8 + nop.i 999 } ;; { .mfi - setf.d f64DivLn2 = r64DivLn2 // load 64/ln(2) to FP reg - fclass.m p15, p0 = f8, 0x1e1 // test for NaT,NaN,+Inf - nop.i 0 + setf.s EXP_MIN_SGL_OFLOW_ARG = exp_GR_min_oflow // 0x42b17218 + fclass.m p7,p0 = f8, 0x22 // Test for x=-inf + mov exp_GR_0xf0 = 0x0f0 } { .mlx - // load Right Shifter to FP reg - setf.d fRightShifter = rRightShifter - movl rLn2Div64 = 0x3F862E42FEFA39EF // DP ln(2)/64 in GR + setf.s EXP_MAX_SGL_NORM_ARG = exp_GR_max_norm + movl exp_GR_max_zero = 0xc2cff1b5 } ;; -{ .mfi - nop.m 0 - fcmp.eq.s1 p13, p0 = f0, f8 // test for x = 0.0 - nop.i 0 + +{ .mlx + mov exp_GR_0x0f = 0x00f + movl exp_GR_max_uflow = 0xc2aeac50 } { .mfb - setf.s fA3 = rA3 // load A3 to FP reg -(p14) fma.s.s0 f8 = f0, f1, f0 // result if x = -inf -(p14) br.ret.spnt b0 // exit here if x = -inf + nop.m 999 +(p6) fma.s f8 = f1,f1,f0 +(p6) br.ret.spnt b0 // quick exit for x=0 } ;; { .mfi - setf.exp fA2 = rExpHalf // load A2 to FP reg - fcmp.eq.s0 p6, p0 = f8, f0 // Dummy to flag denorm - nop.i 0 + setf.s EXP_MAX_SGL_ZERO_ARG = exp_GR_max_zero + fclass.m p8,p0 = f8, 0x21 // Test for x=+inf + adds exp_GR_min_norm = 1, exp_GR_max_uflow // 0xc2aeac51 } { .mfb - setf.d fLn2Div64 = rLn2Div64 // load ln(2)/64 to FP reg -(p15) fma.s.s0 f8 = f8, f1, f0 // result if x = NaT,NaN,+Inf -(p15) br.ret.spnt b0 // exit here if x = NaT,NaN,+Inf + ldfpd exp_coeff_P5,exp_coeff_P6 = [EXP_AD_P_1],16 +(p7) fma.s f8 = f0,f0,f0 +(p7) br.ret.spnt b0 // quick exit for x=-inf } ;; -{ .mfb - // overflow and underflow_zero threshold - ldfps fMIN_SGL_OFLOW_ARG, fMAX_SGL_ZERO_ARG = [rTblAddr], 8 -(p13) fma.s.s0 f8 = f1, f1, f0 // result if x = 0.0 -(p13) br.ret.spnt b0 // exit here if x =0.0 +{ .mmf + ldfpd exp_coeff_P1,exp_coeff_P2 = [EXP_AD_P_1],16 + setf.s EXP_MAX_SGL_UFLOW_ARG = exp_GR_max_uflow + fclass.m p9,p0 = f8, 0xc3 // Test for x=nan } ;; - // max normal and underflow_denorm threshold -{ .mfi - ldfps fMAX_SGL_NORM_ARG, fMIN_SGL_NORM_ARG = [rTblAddr], 8 - nop.f 0 - nop.i 0 +{ .mmb + ldfpd exp_coeff_P3,exp_coeff_P4 = [EXP_AD_P_1],16 + setf.s EXP_MIN_SGL_NORM_ARG = exp_GR_min_norm +(p8) br.ret.spnt b0 // quick exit for x=+inf } ;; +// EXP_AD_P_1 now points to exp_T2_table { .mfi - nop.m 0 - // x*(64/ln(2)) + Right Shifter - fma.s1 fNint = fNormX, f64DivLn2, fRightShifter - nop.i 0 + mov exp_GR_T2_size = 0x100 + fcvt.xf exp_Mfloat = exp_Mx + nop.i 999 +} +;; + +{ .mfb + getf.sig exp_GR_Mint = exp_Mx +(p9) fmerge.s f8 = exp_norm_f8, exp_norm_f8 +(p9) br.ret.spnt b0 // quick exit for x=nan } ;; +{ .mmi + nop.m 999 + mov EXP_AD_T2 = EXP_AD_P_1 + add EXP_AD_T1 = exp_GR_T2_size,EXP_AD_P_1 ;; +} + + +{ .mmi + adds exp_GR_Mint_p_128 = 0x80,exp_GR_Mint ;; + and exp_GR_Ind1 = exp_GR_Mint_p_128, exp_GR_0xf0 + and exp_GR_Ind2 = exp_GR_Mint_p_128, exp_GR_0x0f ;; +} + // Divide arguments into the following categories: -// Certain Underflow p11 - -inf < x <= MAX_SGL_ZERO_ARG -// Possible Underflow p13 - MAX_SGL_ZERO_ARG < x < MIN_SGL_NORM_ARG +// Certain Underflow/zero p11 - -inf < x <= MAX_SGL_ZERO_ARG +// Certain Underflow p12 - MAX_SGL_ZERO_ARG < x <= MAX_SGL_UFLOW_ARG +// Possible Underflow p13 - MAX_SGL_UFLOW_ARG < x < MIN_SGL_NORM_ARG // Certain Safe - MIN_SGL_NORM_ARG <= x <= MAX_SGL_NORM_ARG // Possible Overflow p14 - MAX_SGL_NORM_ARG < x < MIN_SGL_OFLOW_ARG // Certain Overflow p15 - MIN_SGL_OFLOW_ARG <= x < +inf // -// If the input is really a single arg, then there will never be -// "Possible Overflow" arguments. +// If the input is really a single arg, then there will never be "Possible +// Underflow" or "Possible Overflow" arguments. // { .mfi - nop.m 0 - // check for overflow - fcmp.ge.s1 p15, p0 = fNormX, fMIN_SGL_OFLOW_ARG - nop.i 0 + add EXP_AD_M1 = exp_GR_Ind1,EXP_AD_T1 + fcmp.ge.s1 p15,p14 = exp_norm_f8,EXP_MIN_SGL_OFLOW_ARG + nop.i 999 +} +{ .mfi + shladd EXP_AD_M2 = exp_GR_Ind2,4,EXP_AD_T2 + fms.s1 exp_R = f1,f8,exp_Mfloat + nop.i 999 ;; } -;; { .mfi - nop.m 0 - // check for underflow and tiny (+0) result - fcmp.le.s1 p11, p0 = fNormX, fMAX_SGL_ZERO_ARG - nop.i 0 + ldfe exp_T1 = [EXP_AD_M1] + fcmp.le.s1 p11,p12 = exp_norm_f8,EXP_MAX_SGL_ZERO_ARG + nop.i 999 ;; } + { .mfb - nop.m 0 - fms.s1 fN = fNint, f1, fRightShifter // n in FP register - // branch out if overflow -(p15) br.cond.spnt EXP_CERTAIN_OVERFLOW + ldfe exp_T2 = [EXP_AD_M2] +(p14) fcmp.gt.s1 p14,p0 = exp_norm_f8,EXP_MAX_SGL_NORM_ARG +(p15) br.cond.spnt L(EXP_CERTAIN_OVERFLOW) ;; } -;; { .mfb - getf.sig rNJ = fNint // bits of n, j - // check for underflow and deno result - fcmp.lt.s1 p13, p0 = fNormX, fMIN_SGL_NORM_ARG - // branch out if underflow and tiny (+0) result -(p11) br.cond.spnt EXP_CERTAIN_UNDERFLOW + nop.m 999 +(p12) fcmp.le.s1 p12,p0 = exp_norm_f8,EXP_MAX_SGL_UFLOW_ARG +(p11) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW_ZERO) } ;; { .mfi - nop.m 0 - // check for possible overflow - fcmp.gt.s1 p14, p0 = fNormX, fMAX_SGL_NORM_ARG - extr.u rJ = rNJ, 0, 6 // bits of j + nop.m 999 +(p13) fcmp.lt.s1 p13,p0 = exp_norm_f8,EXP_MIN_SGL_NORM_ARG + nop.i 999 } +;; + + { .mfi - addl rN = 0xFFFF - 63, rNJ // biased and shifted n - fnma.s1 fR = fLn2Div64, fN, fNormX // R = x - N*ln(2)/64 - nop.i 0 + nop.m 999 + fma.s1 exp_Rsq = exp_R,exp_R,f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 exp_P3 = exp_R,exp_coeff_P2,exp_coeff_P1 + nop.i 999 } ;; { .mfi - shladd rJ = rJ, 3, rTblAddr // address in the 2^(j/64) table - nop.f 0 - shr rN = rN, 6 // biased n + nop.m 999 + fma.s1 exp_P1 = exp_R,exp_coeff_P6,exp_coeff_P5 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 exp_P2 = exp_R,exp_coeff_P4,exp_coeff_P3 + nop.i 999 } ;; + { .mfi - ld8 rJ = [rJ] - nop.f 0 - shl rN = rN, 52 // 2^n bits in DP format + nop.m 999 + fma.s1 exp_P7 = f1,exp_R,f1 + nop.i 999 } ;; + { .mfi - or rN = rN, rJ // bits of 2^n * 2^(j/64) in DP format - nop.f 0 - nop.i 0 + nop.m 999 + fma.s1 exp_P5 = exp_Rsq,exp_P3,f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 exp_R4 = exp_Rsq,exp_Rsq,f0 + nop.i 999 } ;; { .mfi - setf.d fT = rN // 2^n * 2^(j/64) - fma.s1 fP = fA3, fR, fA2 // A3*R + A2 - nop.i 0 + nop.m 999 + fma.s1 exp_T = exp_T1,exp_T2,f0 + nop.i 999 } { .mfi - nop.m 0 - fma.s1 fRSqr = fR, fR, f0 // R^2 - nop.i 0 + nop.m 999 + fma.s1 exp_P4 = exp_Rsq,exp_P1,exp_P2 + nop.i 999 } ;; { .mfi - nop.m 0 - fma.s1 fP = fP, fRSqr, fR // P = (A3*R + A2)*R^2 + R - nop.i 0 + nop.m 999 + fma.s1 exp_A = exp_T,exp_P7,f0 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 exp_P6 = exp_R4,exp_P4,exp_P5 + nop.i 999 } ;; -{ .mbb - nop.m 0 - // branch out if possible underflow -(p13) br.cond.spnt EXP_POSSIBLE_UNDERFLOW - // branch out if possible overflow result -(p14) br.cond.spnt EXP_POSSIBLE_OVERFLOW +{ .bbb +(p12) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW) +(p13) br.cond.spnt L(EXP_POSSIBLE_UNDERFLOW) +(p14) br.cond.spnt L(EXP_POSSIBLE_OVERFLOW) } ;; { .mfb - nop.m 0 - // final result in the absence of over- and underflow - fma.s.s0 f8 = fP, fT, fT - // exit here in the absence of over- and underflow - br.ret.sptk b0 + nop.m 999 + fma.s f8 = exp_T,exp_P6,exp_A + br.ret.sptk b0 } ;; -EXP_POSSIBLE_OVERFLOW: +L(EXP_POSSIBLE_OVERFLOW): + +// We got an answer. EXP_MAX_SGL_NORM_ARG < x < EXP_MIN_SGL_OFLOW_ARG +// overflow is a possibility, not a certainty +// Set wre in s2 and perform the last operation with s2 + +// We define an overflow when the answer with +// WRE set +// user-defined rounding mode +// is lsn +1 + +// Is the exponent 1 more than the largest single? +// If so, go to ERROR RETURN, else (no overflow) get the answer and +// leave. + +// Largest single is FE (biased single) +// FE - 7F + FFFF = 1007E + +// Create + largest_single_plus_ulp +// Create - largest_single_plus_ulp -// Here if fMAX_SGL_NORM_ARG < x < fMIN_SGL_OFLOW_ARG -// This cannot happen if input is a single, only if input higher precision. -// Overflow is a possibility, not a certainty. +// Calculate answer with WRE set. -// Recompute result using status field 2 with user's rounding mode, -// and wre set. If result is larger than largest single, then we have -// overflow +// Cases when answer is lsn+1 are as follows: + +// midpoint +// | +// lsn | lsn+1 +// --+----------|----------+------------ +// | +// +inf +inf -inf +// RN RN +// RZ +// exp_gt_pln contains the floating point number lsn+1. +// The setf.exp puts 0x1007f in the exponent and 0x800... in the significand. + +// If the answer is >= lsn+1, we have overflowed. +// Then p6 is TRUE. Set the overflow tag, save input in FR_X, +// do the final calculation for IEEE result, and branch to error return. { .mfi - mov rGt_ln = 0x1007f // Exponent for largest single + 1 ulp - fsetc.s2 0x7F,0x42 // Get user's round mode, set wre - nop.i 0 + mov exp_GR_gt_ln = 0x1007F + fsetc.s2 0x7F,0x42 + nop.i 999 } ;; { .mfi - setf.exp fGt_pln = rGt_ln // Create largest single + 1 ulp - fma.s.s2 fWre_urm_f8 = fP, fT, fT // Result with wre set - nop.i 0 + setf.exp exp_gt_pln = exp_GR_gt_ln + fma.s.s2 exp_wre_urm_f8 = exp_T, exp_P6, exp_A + nop.i 999 } ;; { .mfi - nop.m 0 - fsetc.s2 0x7F,0x40 // Turn off wre in sf2 - nop.i 0 + nop.m 999 + fsetc.s2 0x7F,0x40 + nop.i 999 } ;; { .mfi - nop.m 0 - fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow - nop.i 0 + nop.m 999 + fcmp.ge.unc.s1 p6, p0 = exp_wre_urm_f8, exp_gt_pln + nop.i 999 } ;; { .mfb - nop.m 0 - nop.f 0 -(p6) br.cond.spnt EXP_CERTAIN_OVERFLOW // Branch if overflow + nop.m 999 + nop.f 999 +(p6) br.cond.spnt L(EXP_CERTAIN_OVERFLOW) // Branch if really overflow } ;; { .mfb - nop.m 0 - fma.s.s0 f8 = fP, fT, fT - br.ret.sptk b0 // Exit if really no overflow + nop.m 999 + fma.s f8 = exp_T, exp_P6, exp_A + br.ret.sptk b0 // Exit if really no overflow } ;; -// here if overflow -EXP_CERTAIN_OVERFLOW: +L(EXP_CERTAIN_OVERFLOW): { .mmi - addl r17ones_m1 = 0x1FFFE, r0 -;; - setf.exp fTmp = r17ones_m1 - nop.i 0 + sub exp_GR_17ones_m1 = exp_GR_17ones, r0, 1 ;; + setf.exp f9 = exp_GR_17ones_m1 + nop.i 999 ;; } -;; { .mfi - alloc r32=ar.pfs,0,3,4,0 - fmerge.s FR_X = f8,f8 - nop.i 0 + nop.m 999 + fmerge.s FR_X = f8,f8 + nop.i 999 } { .mfb - mov GR_Parameter_TAG = 16 - fma.s.s0 FR_RESULT = fTmp, fTmp, fTmp // Set I,O and +INF result - br.cond.sptk __libm_error_region + mov GR_Parameter_TAG = 16 + fma.s FR_RESULT = f9, f9, f0 // Set I,O and +INF result + br.cond.sptk __libm_error_region ;; } -;; -EXP_POSSIBLE_UNDERFLOW: +L(EXP_POSSIBLE_UNDERFLOW): -// Here if fMAX_SGL_ZERO_ARG < x < fMIN_SGL_NORM_ARG -// Underflow is a possibility, not a certainty +// We got an answer. EXP_MAX_SGL_UFLOW_ARG < x < EXP_MIN_SGL_NORM_ARG +// underflow is a possibility, not a certainty // We define an underflow when the answer with // ftz set @@ -551,165 +637,144 @@ EXP_POSSIBLE_UNDERFLOW: // E // -----+--------------------+--------------------+----- // | | | -// 1.1...10 2^-3fff 1.1...11 2^-3fff 1.0...00 2^-3ffe -// 0.1...11 2^-3ffe (biased, 1) +// 1.1...10 2^-7f 1.1...11 2^-7f 1.0...00 2^-7e +// 0.1...11 2^-7e (biased, 1) // largest dn smallest normal -{ .mfi - nop.m 0 - fsetc.s2 0x7F,0x41 // Get user's round mode, set ftz - nop.i 0 -} -;; +// If the answer is = 0, we have underflowed. +// Then p6 is TRUE. Set the underflow tag, save input in FR_X, +// do the final calculation for IEEE result, and branch to error return. { .mfi - nop.m 0 - fma.s.s2 fFtz_urm_f8 = fP, fT, fT // Result with ftz set - nop.i 0 + nop.m 999 + fsetc.s2 0x7F,0x41 + nop.i 999 } ;; { .mfi - nop.m 0 - fsetc.s2 0x7F,0x40 // Turn off ftz in sf2 - nop.i 0 + nop.m 999 + fma.s.s2 exp_ftz_urm_f8 = exp_T, exp_P6, exp_A + nop.i 999 } ;; + { .mfi - nop.m 0 - fcmp.eq.s1 p6, p7 = fFtz_urm_f8, f0 // Test for underflow - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s.s0 f8 = fP, fT, fT // Compute result, set I, maybe U - nop.i 0 + nop.m 999 + fsetc.s2 0x7F,0x40 + nop.i 999 } ;; -{ .mbb - nop.m 0 -(p6) br.cond.spnt EXP_UNDERFLOW_COMMON // Branch if really underflow -(p7) br.ret.sptk b0 // Exit if really no underflow +{ .mfi + nop.m 999 + fcmp.eq.unc.s1 p6, p0 = exp_ftz_urm_f8, f0 + nop.i 999 } ;; -EXP_CERTAIN_UNDERFLOW: -// Here if x < fMAX_SGL_ZERO_ARG -// Result will be zero (or smallest denorm if round to +inf) with I, U set -{ .mmi - mov rTmp = 1 -;; - setf.exp fTmp = rTmp // Form small normal - nop.i 0 +{ .mfb + nop.m 999 + nop.f 999 +(p6) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW) // Branch if really underflow } ;; -{ .mfi - nop.m 0 - fmerge.se fTmp = fTmp, f64DivLn2 // Small with non-trial signif - nop.i 0 -} -;; - { .mfb - nop.m 0 - fma.s.s0 f8 = fTmp, fTmp, f0 // Set I,U, tiny (+0.0) result - br.cond.sptk EXP_UNDERFLOW_COMMON + nop.m 999 + fma.s f8 = exp_T, exp_P6, exp_A + br.ret.sptk b0 // Exit if really no underflow } ;; -EXP_UNDERFLOW_COMMON: -// Determine if underflow result is zero or nonzero +L(EXP_CERTAIN_UNDERFLOW): { .mfi - alloc r32=ar.pfs,0,3,4,0 - fcmp.eq.s1 p6, p0 = f8, f0 - nop.i 0 + nop.m 999 + fmerge.s FR_X = f8,f8 + nop.i 999 } -;; - { .mfb - nop.m 0 - fmerge.s FR_X = fNormX,fNormX -(p6) br.cond.spnt EXP_UNDERFLOW_ZERO + mov GR_Parameter_TAG = 17 + fma.s FR_RESULT = exp_T, exp_P6, exp_A // Set I,U and tiny result + br.cond.sptk __libm_error_region ;; } -;; -EXP_UNDERFLOW_NONZERO: -// Here if x < fMIN_SGL_NORM_ARG and result nonzero; -// I, U are set -{ .mfb - mov GR_Parameter_TAG = 17 - nop.f 0 // FR_RESULT already set - br.cond.sptk __libm_error_region +L(EXP_CERTAIN_UNDERFLOW_ZERO): +{ .mmi + mov exp_GR_one = 1 ;; + setf.exp f9 = exp_GR_one + nop.i 999 ;; } -;; -EXP_UNDERFLOW_ZERO: -// Here if x < fMIN_SGL_NORM_ARG and result zero; -// I, U are set +{ .mfi + nop.m 999 + fmerge.s FR_X = f8,f8 + nop.i 999 +} { .mfb - mov GR_Parameter_TAG = 17 - nop.f 0 // FR_RESULT already set - br.cond.sptk __libm_error_region + mov GR_Parameter_TAG = 17 + fma.s FR_RESULT = f9, f9, f0 // Set I,U and tiny (+0.0) result + br.cond.sptk __libm_error_region ;; } -;; -GLOBAL_IEEE754_END(expf) +.endp expf +ASM_SIZE_DIRECTIVE(expf) -LOCAL_LIBM_ENTRY(__libm_error_region) +.proc __libm_error_region +__libm_error_region: .prologue { .mfi - add GR_Parameter_Y=-32,sp // Parameter 2 value - nop.f 0 + add GR_Parameter_Y=-32,sp // Parameter 2 value + nop.f 999 .save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs + mov GR_SAVE_PFS=ar.pfs // Save ar.pfs } { .mfi .fframe 64 - add sp=-64,sp // Create new stack - nop.f 0 - mov GR_SAVE_GP=gp // Save gp + add sp=-64,sp // Create new stack + nop.f 0 + mov GR_SAVE_GP=gp // Save gp };; { .mmi - stfs [GR_Parameter_Y] = FR_Y,16 // Store Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address + stfs [GR_Parameter_Y] = FR_Y,16 // Store Parameter 2 on stack + add GR_Parameter_X = 16,sp // Parameter 1 address .save b0, GR_SAVE_B0 - mov GR_SAVE_B0=b0 // Save b0 + mov GR_SAVE_B0=b0 // Save b0 };; .body { .mfi - stfs [GR_Parameter_X] = FR_X // Store Parameter 1 on stack - nop.f 0 - add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address + stfs [GR_Parameter_X] = FR_X // Store Parameter 1 on stack + nop.f 0 + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address } { .mib - stfs [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 + stfs [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 + nop.m 0 + nop.m 0 + add GR_Parameter_RESULT = 48,sp };; { .mmi - ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack + ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack .restore sp - add sp = 64,sp // Restore stack pointer - mov b0 = GR_SAVE_B0 // Restore return address + add sp = 64,sp // Restore stack pointer + mov b0 = GR_SAVE_B0 // Restore return address };; { .mib - mov gp = GR_SAVE_GP // Restore gp - mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs - br.ret.sptk b0 // Return -};; + 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) +.endp __libm_error_region +ASM_SIZE_DIRECTIVE(__libm_error_region) .type __libm_error_support#,@function |