diff options
Diffstat (limited to 'sysdeps/ia64/fpu/e_expf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_expf.S | 957 |
1 files changed, 446 insertions, 511 deletions
diff --git a/sysdeps/ia64/fpu/e_expf.S b/sysdeps/ia64/fpu/e_expf.S index 2aad021..6fe0a83 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, 2001, Intel Corporation + +// Copyright (c) 2000 - 2005, Intel Corporation // All rights reserved. // -// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, -// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. +// Contributed 2000 by the Intel Numerics Group, Intel Corporation // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are @@ -20,7 +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 @@ -35,589 +35,503 @@ // // Intel Corporation is the author of this code, and requests that all // problem reports or change requests be submitted to it directly at -// http://developer.intel.com/opensource. +// http://www.intel.com/software/products/opensource/libraries/num.htm. // History -//============================================================== -// 4/04/00 Unwind update -// 4/04/00 Unwind support added -// 8/15/00 Bundle added after call to __libm_error_support to properly +//********************************************************************* +// 02/02/00 Original 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. -// 8/21/00 Improvements to save 2 cycles on main path, and shorten x=0 case +// 08/21/00 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 // -#include "libm_support.h" - -// Assembly macros -//============================================================== -// integer registers used - - exp_GR_0x0f = r33 - exp_GR_0xf0 = r34 +// The final result is reconstructed as follows +// exp(x) = T + T*P - EXP_AD_P_1 = r36 - EXP_AD_P_2 = r37 - EXP_AD_T1 = r38 - EXP_AD_T2 = r39 - exp_GR_Mint = r40 +// Special values +//********************************************************************* +// expf(+0) = 1.0 +// expf(-0) = 1.0 - exp_GR_Mint_p_128 = r41 - exp_GR_Ind1 = r42 - EXP_AD_M1 = r43 - exp_GR_Ind2 = r44 - EXP_AD_M2 = r45 +// expf(+qnan) = +qnan +// expf(-qnan) = -qnan +// expf(+snan) = +qnan +// expf(-snan) = -qnan - 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(-inf) = +0 +// expf(+inf) = +inf - exp_GR_17ones = r51 - exp_GR_gt_ln = r52 - exp_GR_T2_size = r53 +// Overflow and Underflow +//********************************************************************* +// expf(x) = largest single normal when +// x = 88.72283 = 0x42b17217 - exp_GR_17ones_m1 = r56 - exp_GR_one = r57 +// expf(x) = smallest single normal when +// x = -87.33654 = 0xc2aeac4f +// expf(x) = largest round-to-nearest single zero when +// x = -103.97208 = 0xc2cff1b5 -GR_SAVE_B0 = r53 -GR_SAVE_PFS = r55 -GR_SAVE_GP = r54 +// Registers used +//********************************************************************* +// Floating Point registers used: +// f8, input +// f6,f7, f9 -> f15, f32 -> f40 -GR_Parameter_X = r59 -GR_Parameter_Y = r60 -GR_Parameter_RESULT = r61 -GR_Parameter_TAG = r62 +// General registers used: +// r3, r23 -> r38 -FR_X = f10 -FR_Y = f1 -FR_RESULT = f8 +// Predicate registers used: +// p10 -> p15 +// 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 - - 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 - +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 .align 16 -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 +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 // -// 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. +// 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) -// 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 -.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 +GLOBAL_IEEE754_ENTRY(expf) + +{ .mlx + addl rTblAddr = @ltoff(_expf_table),gp + movl r64DivLn2 = 0x40571547652B82FE // 64/ln(2) } { .mlx - addl EXP_AD_P_1 = @ltoff(exp_coeff_1_table),gp - movl exp_GR_min_oflow = 0x42b17218 + addl rA3 = 0x3E2AA, r0 // high bits of 1.0/6.0 rounded to SP + movl rRightShifter = 0x43E8000000000000 // DP Right Shifter } ;; -// Fnorm done to take any enabled faults { .mfi - ld8 EXP_AD_P_1 = [EXP_AD_P_1] - fclass.m p6,p0 = f8, 0x07 //@zero - nop.i 999 + // 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 } { .mfi - add exp_GR_max_norm = -1, exp_GR_min_oflow // 0x42b17217 - fnorm exp_norm_f8 = f8 - nop.i 999 + nop.m 0 + fnorm.s1 fNormX = f8 // normalized x + addl rExpHalf = 0xFFFE, r0 // exponent of 1/2 } ;; { .mfi - 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 + 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 } { .mlx - setf.s EXP_MAX_SGL_NORM_ARG = exp_GR_max_norm - movl exp_GR_max_zero = 0xc2cff1b5 + // load Right Shifter to FP reg + setf.d fRightShifter = rRightShifter + movl rLn2Div64 = 0x3F862E42FEFA39EF // DP ln(2)/64 in GR } ;; - -{ .mlx - mov exp_GR_0x0f = 0x00f - movl exp_GR_max_uflow = 0xc2aeac50 +{ .mfi + nop.m 0 + fcmp.eq.s1 p13, p0 = f0, f8 // test for x = 0.0 + nop.i 0 } { .mfb - nop.m 999 -(p6) fma.s f8 = f1,f1,f0 -(p6) br.ret.spnt b0 // quick exit for x=0 + 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 } ;; { .mfi - 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 + setf.exp fA2 = rExpHalf // load A2 to FP reg + fcmp.eq.s0 p6, p0 = f8, f0 // Dummy to flag denorm + nop.i 0 } { .mfb - 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 -} -;; - -{ .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 + 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 } ;; -{ .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 +{ .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 } ;; -// EXP_AD_P_1 now points to exp_T2_table + // max normal and underflow_denorm threshold { .mfi - mov exp_GR_T2_size = 0x100 - fcvt.xf exp_Mfloat = exp_Mx - nop.i 999 + ldfps fMAX_SGL_NORM_ARG, fMIN_SGL_NORM_ARG = [rTblAddr], 8 + nop.f 0 + nop.i 0 } ;; -{ .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 +{ .mfi + nop.m 0 + // x*(64/ln(2)) + Right Shifter + fma.s1 fNint = fNormX, f64DivLn2, fRightShifter + nop.i 0 } ;; -{ .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/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 Underflow p11 - -inf < x <= MAX_SGL_ZERO_ARG +// Possible Underflow p13 - MAX_SGL_ZERO_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 -// Underflow" or "Possible Overflow" arguments. +// If the input is really a single arg, then there will never be +// "Possible Overflow" arguments. // { .mfi - 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 ;; + nop.m 0 + // check for overflow + fcmp.ge.s1 p15, p0 = fNormX, fMIN_SGL_OFLOW_ARG + nop.i 0 } +;; { .mfi - ldfe exp_T1 = [EXP_AD_M1] - fcmp.le.s1 p11,p12 = exp_norm_f8,EXP_MAX_SGL_ZERO_ARG - nop.i 999 ;; + nop.m 0 + // check for underflow and tiny (+0) result + fcmp.le.s1 p11, p0 = fNormX, fMAX_SGL_ZERO_ARG + nop.i 0 } - { .mfb - 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 - 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) + nop.m 0 + fms.s1 fN = fNint, f1, fRightShifter // n in FP register + // branch out if overflow +(p15) br.cond.spnt EXP_CERTAIN_OVERFLOW } ;; -{ .mfi - nop.m 999 -(p13) fcmp.lt.s1 p13,p0 = exp_norm_f8,EXP_MIN_SGL_NORM_ARG - nop.i 999 +{ .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 } ;; - { .mfi - nop.m 999 - fma.s1 exp_Rsq = exp_R,exp_R,f0 - nop.i 999 + 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 } { .mfi - nop.m 999 - fma.s1 exp_P3 = exp_R,exp_coeff_P2,exp_coeff_P1 - nop.i 999 + addl rN = 0xFFFF - 63, rNJ // biased and shifted n + fnma.s1 fR = fLn2Div64, fN, fNormX // R = x - N*ln(2)/64 + nop.i 0 } ;; { .mfi - 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 + shladd rJ = rJ, 3, rTblAddr // address in the 2^(j/64) table + nop.f 0 + shr rN = rN, 6 // biased n } ;; - { .mfi - nop.m 999 - fma.s1 exp_P7 = f1,exp_R,f1 - nop.i 999 + ld8 rJ = [rJ] + nop.f 0 + shl rN = rN, 52 // 2^n bits in DP format } ;; - { .mfi - 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 + or rN = rN, rJ // bits of 2^n * 2^(j/64) in DP format + nop.f 0 + nop.i 0 } ;; { .mfi - nop.m 999 - fma.s1 exp_T = exp_T1,exp_T2,f0 - nop.i 999 + setf.d fT = rN // 2^n * 2^(j/64) + fma.s1 fP = fA3, fR, fA2 // A3*R + A2 + nop.i 0 } { .mfi - nop.m 999 - fma.s1 exp_P4 = exp_Rsq,exp_P1,exp_P2 - nop.i 999 + nop.m 0 + fma.s1 fRSqr = fR, fR, f0 // R^2 + nop.i 0 } ;; { .mfi - 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 + nop.m 0 + fma.s1 fP = fP, fRSqr, fR // P = (A3*R + A2)*R^2 + R + nop.i 0 } ;; -{ .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) +{ .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 } ;; { .mfb - nop.m 999 - fma.s f8 = exp_T,exp_P6,exp_A - br.ret.sptk b0 + 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 } ;; -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 +EXP_POSSIBLE_OVERFLOW: -// Calculate answer with WRE set. +// 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. -// 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. +// 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 { .mfi - mov exp_GR_gt_ln = 0x1007F - fsetc.s2 0x7F,0x42 - nop.i 999 + mov rGt_ln = 0x1007f // Exponent for largest single + 1 ulp + fsetc.s2 0x7F,0x42 // Get user's round mode, set wre + nop.i 0 } ;; { .mfi - 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 + 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 } ;; { .mfi - nop.m 999 - fsetc.s2 0x7F,0x40 - nop.i 999 + nop.m 0 + fsetc.s2 0x7F,0x40 // Turn off wre in sf2 + nop.i 0 } ;; { .mfi - nop.m 999 - fcmp.ge.unc.s1 p6, p0 = exp_wre_urm_f8, exp_gt_pln - nop.i 999 + nop.m 0 + fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow + nop.i 0 } ;; { .mfb - nop.m 999 - nop.f 999 -(p6) br.cond.spnt L(EXP_CERTAIN_OVERFLOW) // Branch if really overflow + nop.m 0 + nop.f 0 +(p6) br.cond.spnt EXP_CERTAIN_OVERFLOW // Branch if overflow } ;; { .mfb - nop.m 999 - fma.s f8 = exp_T, exp_P6, exp_A - br.ret.sptk b0 // Exit if really no overflow + nop.m 0 + fma.s.s0 f8 = fP, fT, fT + br.ret.sptk b0 // Exit if really no overflow } ;; -L(EXP_CERTAIN_OVERFLOW): +// here if overflow +EXP_CERTAIN_OVERFLOW: { .mmi - sub exp_GR_17ones_m1 = exp_GR_17ones, r0, 1 ;; - setf.exp f9 = exp_GR_17ones_m1 - nop.i 999 ;; + addl r17ones_m1 = 0x1FFFE, r0 +;; + setf.exp fTmp = r17ones_m1 + nop.i 0 } +;; { .mfi - nop.m 999 - fmerge.s FR_X = f8,f8 - nop.i 999 + alloc r32=ar.pfs,0,3,4,0 + fmerge.s FR_X = f8,f8 + nop.i 0 } { .mfb - mov GR_Parameter_TAG = 16 - fma.s FR_RESULT = f9, f9, f0 // Set I,O and +INF result - br.cond.sptk __libm_error_region ;; + 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 } +;; -L(EXP_POSSIBLE_UNDERFLOW): +EXP_POSSIBLE_UNDERFLOW: -// We got an answer. EXP_MAX_SGL_UFLOW_ARG < x < EXP_MIN_SGL_NORM_ARG -// underflow is a possibility, not a certainty +// Here if fMAX_SGL_ZERO_ARG < x < fMIN_SGL_NORM_ARG +// Underflow is a possibility, not a certainty // We define an underflow when the answer with // ftz set @@ -637,144 +551,165 @@ L(EXP_POSSIBLE_UNDERFLOW): // E // -----+--------------------+--------------------+----- // | | | -// 1.1...10 2^-7f 1.1...11 2^-7f 1.0...00 2^-7e -// 0.1...11 2^-7e (biased, 1) +// 1.1...10 2^-3fff 1.1...11 2^-3fff 1.0...00 2^-3ffe +// 0.1...11 2^-3ffe (biased, 1) // largest dn smallest normal -// 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 999 - fsetc.s2 0x7F,0x41 - nop.i 999 + nop.m 0 + fsetc.s2 0x7F,0x41 // Get user's round mode, set ftz + nop.i 0 } ;; { .mfi - nop.m 999 - fma.s.s2 exp_ftz_urm_f8 = exp_T, exp_P6, exp_A - nop.i 999 + nop.m 0 + fma.s.s2 fFtz_urm_f8 = fP, fT, fT // Result with ftz set + nop.i 0 } ;; - { .mfi - nop.m 999 - fsetc.s2 0x7F,0x40 - nop.i 999 + nop.m 0 + fsetc.s2 0x7F,0x40 // Turn off ftz in sf2 + nop.i 0 } ;; { .mfi - nop.m 999 - fcmp.eq.unc.s1 p6, p0 = exp_ftz_urm_f8, f0 - nop.i 999 + 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 } ;; -{ .mfb - nop.m 999 - nop.f 999 -(p6) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW) // Branch if really underflow +{ .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 } ;; -{ .mfb - nop.m 999 - fma.s f8 = exp_T, exp_P6, exp_A - br.ret.sptk b0 // Exit if really no underflow +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 } ;; -L(EXP_CERTAIN_UNDERFLOW): { .mfi - nop.m 999 - fmerge.s FR_X = f8,f8 - nop.i 999 + nop.m 0 + fmerge.se fTmp = fTmp, f64DivLn2 // Small with non-trial signif + nop.i 0 } +;; + { .mfb - 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 ;; + nop.m 0 + fma.s.s0 f8 = fTmp, fTmp, f0 // Set I,U, tiny (+0.0) result + br.cond.sptk EXP_UNDERFLOW_COMMON } +;; -L(EXP_CERTAIN_UNDERFLOW_ZERO): -{ .mmi - mov exp_GR_one = 1 ;; - setf.exp f9 = exp_GR_one - nop.i 999 ;; +EXP_UNDERFLOW_COMMON: +// Determine if underflow result is zero or nonzero +{ .mfi + alloc r32=ar.pfs,0,3,4,0 + fcmp.eq.s1 p6, p0 = f8, f0 + nop.i 0 } +;; -{ .mfi - 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 } +;; + +EXP_UNDERFLOW_NONZERO: +// Here if x < fMIN_SGL_NORM_ARG and result nonzero; +// I, U are set { .mfb - 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 ;; + mov GR_Parameter_TAG = 17 + nop.f 0 // FR_RESULT already set + br.cond.sptk __libm_error_region } +;; -.endp expf -ASM_SIZE_DIRECTIVE(expf) +EXP_UNDERFLOW_ZERO: +// Here if x < fMIN_SGL_NORM_ARG and result zero; +// I, U are set +{ .mfb + mov GR_Parameter_TAG = 17 + nop.f 0 // FR_RESULT already set + br.cond.sptk __libm_error_region +} +;; +GLOBAL_IEEE754_END(expf) -.proc __libm_error_region -__libm_error_region: + +LOCAL_LIBM_ENTRY(__libm_error_region) .prologue { .mfi - add GR_Parameter_Y=-32,sp // Parameter 2 value - nop.f 999 + 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 + 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 - nop.m 0 - nop.m 0 - add GR_Parameter_RESULT = 48,sp + add GR_Parameter_RESULT = 48,sp + nop.m 0 + nop.i 0 };; { .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 +};; -.endp __libm_error_region -ASM_SIZE_DIRECTIVE(__libm_error_region) +LOCAL_LIBM_END(__libm_error_region) .type __libm_error_support#,@function |