diff options
Diffstat (limited to 'sysdeps/ia64/fpu/e_powl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_powl.S | 4080 |
1 files changed, 2360 insertions, 1720 deletions
diff --git a/sysdeps/ia64/fpu/e_powl.S b/sysdeps/ia64/fpu/e_powl.S index 3f93f6090e..d286e9abad 100644 --- a/sysdeps/ia64/fpu/e_powl.S +++ b/sysdeps/ia64/fpu/e_powl.S @@ -1,10 +1,10 @@ .file "powl.s" - -// Copyright (c) 2000 - 2003, 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 @@ -20,70 +20,61 @@ // * The name of Intel Corporation may not be used to endorse or promote // products derived from this software without specific prior written // permission. - -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR -// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING -// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS -// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -// +// 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. +// problem reports or change requests be submitted to it directly at +// http://developer.intel.com/opensource. // -//********************************************************************* +// ********************************************************************* // // Function: powl(x,y), where -// y +// y // powl(x,y) = x , for double extended precision x and y values // -//********************************************************************* +// ********************************************************************* // -// History: -// 02/02/00 (Hand Optimized) -// 04/04/00 Unwind support added -// 08/15/00 Bundle added after call to __libm_error_support to properly +// History: +// 2/02/00 (Hand Optimized) +// 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. -// 01/22/01 Corrected results for powl(1,inf), powl(1,nan), and +// 1/22/01 Corrected results for powl(1,inf), powl(1,nan), and // powl(snan,0) to be 1 per C99, not nan. Fixed many flag settings. -// 02/06/01 Call __libm_error support if over/underflow when y=2. -// 04/17/01 Support added for y close to 1 and x a non-special value. -// Shared software under/overflow detection for all paths -// 02/07/02 Corrected sf3 setting to disable traps -// 05/13/02 Improved performance of all paths -// 02/10/03 Reordered header: .section, .global, .proc, .align; -// used data8 for long double table values -// 04/17/03 Added missing mutex directive -// 10/13/03 Corrected .endp names to match .proc names -// -//********************************************************************* +// 2/06/01 Call __libm_error support if over/underflow when y=2. +// +// ********************************************************************* // // Resources Used: // -// Floating-Point Registers: -// f8 (Input x and Return Value) -// f9 (Input y) -// f10-f15,f32-f79 +// Floating-Point Registers: +// f8 (Input and Return Value) +// f9-f15,f32-f63,f99 // // General Purpose Registers: -// Locals r14-24,r32-r65 +// Locals r32 - r61 // Parameters to __libm_error_support r62,r63,r64,r65 // // Predicate Registers: p6-p15 // -//********************************************************************* +// ********************************************************************* // // Special Cases and IEEE special conditions: // // Denormal fault raised on denormal inputs -// Overflow exceptions raised when appropriate for pow -// Underflow exceptions raised when appropriate for pow +// Overflow exceptions raised when appropriate for pow +// Underflow exceptions raised when appropriate for pow // (Error Handling Routine called for overflow and Underflow) // Inexact raised when appropriate by algorithm // @@ -111,8 +102,8 @@ // 22. X or Y denorm/unorm and denorm/unorm operand trap is enabled, // generate denorm/unorm fault except if invalid or div_0 raised. // -//********************************************************************* -// +// ********************************************************************* +// // Algorithm // ========= // @@ -122,23 +113,23 @@ // If Y = 0.5, return sqrt(X). // // Compute log(X) to extra precision. -// +// // ker_log_80( X, logX_hi, logX_lo, Safe ); // -// ...logX_hi + logX_lo approximates log(X) to roughly 80 +// ...logX_hi + logX_lo approximates log(X) to roughly 80 // ...significant bits of accuracy. // // Compute Y*log(X) to extra precision. // // P_hi := Y * logX_hi -// P_lo := Y * logX_hi - P_hi ...using FMA -// P_lo := Y * logX_lo + P_lo ...using FMA +// P_lo := Y * logX_hi - P_hi ...using FMA +// P_lo := Y * logX_lo + P_lo ...using FMA // // Compute exp(P_hi + P_lo) // -// Flag := 2; +// Flag := 2; // Expo_Range := 2; (assuming double-extended power function) -// ker_exp_64( P_hi, P_lo, Flag, Expo_Range, +// ker_exp_64( P_hi, P_lo, Flag, Expo_Range, // Z_hi, Z_lo, scale, Safe ) // // scale := sgn * scale @@ -147,7 +138,7 @@ // return scale*Z_hi + (scale*Z_lo) // quickly // Else -// take necessary precaution in computing +// take necessary precaution in computing // scale*Z_hi + (scale*Z_lo) // to set possible exceptions correctly. // End If @@ -161,8 +152,8 @@ // If Y is qNaN, return Y without exception. // If X is qNaN, return X without exception. // -// At this point, X is real and Y is +-inf. -// Thus |X| can only be 1, strictly bigger than 1, or +// At this point, X is real and Y is +-inf. +// Thus |X| can only be 1, strictly bigger than 1, or // strictly less than 1. // // If |X| < 1, then @@ -178,8 +169,8 @@ // ...Note that Y is real, finite, non-zero, and not +1. // // If X is qNaN, return X without exception. -// -// If X is +-0, +// +// If X is +-0, // return ( Y > 0 ? +0 : +inf ) // // If X is +inf @@ -189,11 +180,11 @@ // return -0 ** -Y // return ( Y > 0 ? +inf : +0 ) // -// Case_Invalid +// Case_Invalid // // Return 0 * inf to generate a quiet NaN together // with an invalid exception. -// +// // Implementation // ============== // @@ -202,15 +193,15 @@ // // STAGE 1 // ------- -// This stage contains two threads. +// This stage contains two threads. // // Stage1.Thread1 // // fclass.m X_excep, X_ok = X, (NatVal or s/qNaN) or -// +-0, +-infinity +// +-0, +-infinity // // fclass.nm X_unsupp, X_supp = X, (NatVal or s/qNaN) or -// +-(0, unnorm, norm, infinity) +// +-(0, unnorm, norm, infinity) // // X_norm := fnorm( X ) with traps disabled // @@ -218,26 +209,26 @@ // If (X_unsupp) goto Filtering (Step 2) // // Stage1.Thread2 -// .............. +// .............. // // fclass.m Y_excep, Y_ok = Y, (NatVal or s/qNaN) or -// +-0, +-infinity +// +-0, +-infinity // // fclass.nm Y_unsupp, Y_supp = Y, (NatVal or s/qNaN) or -// +-(0, unnorm, norm, infinity) +// +-(0, unnorm, norm, infinity) // // Y_norm := fnorm( Y ) with traps disabled // // If (Y_excep) goto Filtering (Step 2) // If (Y_unsupp) goto Filtering (Step 2) // -// +// // STAGE 2 // ------- // This stage contains two threads. // -// Stage2.Thread1 -// .............. +// Stage2.Thread1 +// .............. // // Set X_lt_0 if X < 0 (using fcmp) // sgn := +1.0 @@ -254,14 +245,14 @@ // This stage contains two threads. // // -// Stage3.Thread1 -// .............. +// Stage3.Thread1 +// .............. // // X := fnorm(X) in prevailing traps // // -// Stage3.Thread2 -// .............. +// Stage3.Thread2 +// .............. // // Y := fnorm(Y) in prevailing traps // @@ -271,56 +262,60 @@ // Go to Case_Normal. // - -// ************* 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 16 -// L_hi, L_lo -LOCAL_OBJECT_START(Constants_exp_64_Arg) -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_A) -// Reversed -data8 0xAAAAAAABB1B736A0,0x00003FFA -data8 0xAAAAAAAB90CD6327,0x00003FFC -data8 0xFFFFFFFFFFFFFFFF,0x00003FFD -LOCAL_OBJECT_END(Constants_exp_64_A) - -LOCAL_OBJECT_START(Constants_exp_64_P) -// Reversed -data8 0xD00D6C8143914A8A,0x00003FF2 -data8 0xB60BC4AC30304B30,0x00003FF5 -data8 0x888888887474C518,0x00003FF8 -data8 0xAAAAAAAA8DAE729D,0x00003FFA -data8 0xAAAAAAAAAAAAAF61,0x00003FFC -data8 0x80000000000004C7,0x00003FFE -LOCAL_OBJECT_END(Constants_exp_64_P) - -LOCAL_OBJECT_START(Constants_exp_64_T1) -data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29 -data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5 +#include "libm_support.h" + +#ifdef _LIBC +.rodata +#else +.data +#endif + +// Inv_L, L_hi, L_lo +.align 64 +Constants_exp_64_Arg: +ASM_TYPE_DIRECTIVE(Constants_exp_64_Arg,@object) +data4 0x5C17F0BC,0xB8AA3B29,0x0000400B,0x00000000 +data4 0x00000000,0xB17217F4,0x00003FF2,0x00000000 +data4 0xF278ECE6,0xF473DE6A,0x00003FD4,0x00000000 +ASM_SIZE_DIRECTIVE(Constants_exp_64_Arg) + +.align 64 +Constants_exp_64_Exponents: +ASM_TYPE_DIRECTIVE(Constants_exp_64_Exponents,@object) +data4 0x0000007E,0x00000000,0xFFFFFF83,0xFFFFFFFF +data4 0x000003FE,0x00000000,0xFFFFFC03,0xFFFFFFFF +data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF +data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF +data4 0xFFFFFFE2,0xFFFFFFFF,0xFFFFFFC4,0xFFFFFFFF +data4 0xFFFFFFBA,0xFFFFFFFF,0xFFFFFFBA,0xFFFFFFFF +ASM_SIZE_DIRECTIVE(Constants_exp_64_Exponents) + +.align 64 +Constants_exp_64_A: +ASM_TYPE_DIRECTIVE(Constants_exp_64_A,@object) +// Reversed +data4 0xB1B736A0,0xAAAAAAAB,0x00003FFA,0x00000000 +data4 0x90CD6327,0xAAAAAAAB,0x00003FFC,0x00000000 +data4 0xFFFFFFFF,0xFFFFFFFF,0x00003FFD,0x00000000 +ASM_SIZE_DIRECTIVE(Constants_exp_64_A) + +.align 64 +Constants_exp_64_P: +ASM_TYPE_DIRECTIVE(Constants_exp_64_P,@object) +// Reversed +data4 0x43914A8A,0xD00D6C81,0x00003FF2,0x00000000 +data4 0x30304B30,0xB60BC4AC,0x00003FF5,0x00000000 +data4 0x7474C518,0x88888888,0x00003FF8,0x00000000 +data4 0x8DAE729D,0xAAAAAAAA,0x00003FFA,0x00000000 +data4 0xAAAAAF61,0xAAAAAAAA,0x00003FFC,0x00000000 +data4 0x000004C7,0x80000000,0x00003FFE,0x00000000 +ASM_SIZE_DIRECTIVE(Constants_exp_64_P) + +.align 64 +Constants_exp_64_T1: +ASM_TYPE_DIRECTIVE(Constants_exp_64_T1,@object) +data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29 +data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5 data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA @@ -335,263 +330,274 @@ 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 +ASM_SIZE_DIRECTIVE(Constants_exp_64_T1) + +.align 64 +Constants_exp_64_T2: +ASM_TYPE_DIRECTIVE(Constants_exp_64_T2,@object) +data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4 +data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7 +data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E +data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349 +data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987 +data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA +data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610 +data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A +data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8 +data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA +data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50 +data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA +data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07 +data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269 +data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37 -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) - -LOCAL_OBJECT_START(Constants_log_80_P) -// P_8, P_7, ..., P_1 -data8 0xCCCE8B883B1042BC, 0x0000BFFB // P_8 -data8 0xE38997B7CADC2149, 0x00003FFB // P_7 -data8 0xFFFFFFFEB1ACB090, 0x0000BFFB // P_6 -data8 0x9249249806481C81, 0x00003FFC // P_5 -data8 0x0000000000000000, 0x00000000 // Pad for bank conflicts -data8 0xAAAAAAAAAAAAB0EF, 0x0000BFFC // P_4 -data8 0xCCCCCCCCCCC91416, 0x00003FFC // P_3 -data8 0x8000000000000000, 0x0000BFFD // P_2 -data8 0xAAAAAAAAAAAAAAAB, 0x00003FFD // P_1 -LOCAL_OBJECT_END(Constants_log_80_P) - -LOCAL_OBJECT_START(Constants_log_80_Q) -// log2_hi, log2_lo, Q_6, Q_5, Q_4, Q_3, Q_2, Q_1 -data8 0xB172180000000000,0x00003FFE -data8 0x82E308654361C4C6,0x0000BFE2 -data8 0x92492453A51BE0AF,0x00003FFC -data8 0xAAAAAB73A0CFD29F,0x0000BFFC -data8 0xCCCCCCCCCCCE3872,0x00003FFC -data8 0xFFFFFFFFFFFFB4FB,0x0000BFFC -data8 0xAAAAAAAAAAAAAAAB,0x00003FFD -data8 0x8000000000000000,0x0000BFFE -LOCAL_OBJECT_END(Constants_log_80_Q) - -LOCAL_OBJECT_START(Constants_log_80_Z_G_H_h1) -// Z1 - 16 bit fixed, G1 and H1 IEEE single, h1 IEEE double +ASM_SIZE_DIRECTIVE(Constants_exp_64_T2) + +.align 64 +Constants_exp_64_W1: +ASM_TYPE_DIRECTIVE(Constants_exp_64_W1,@object) +data4 0x00000000,0x00000000,0x171EC4B4,0xBE384454 +data4 0x4AA72766,0xBE694741,0xD42518F8,0xBE5D32B6 +data4 0x3A319149,0x3E68D96D,0x62415F36,0xBE68F4DA +data4 0xC9C86A3B,0xBE6DDA2F,0xF49228FE,0x3E6B2E50 +data4 0x1188B886,0xBE49C0C2,0x1A4C2F1F,0x3E64BFC2 +data4 0x2CB98B54,0xBE6A2FBB,0x9A55D329,0x3E5DC5DE +data4 0x39A7AACE,0x3E696490,0x5C66DBA5,0x3E54728B +data4 0xBA1C7D7D,0xBE62B0DB,0x09F1AF5F,0x3E576E04 +data4 0x1A0DD6A1,0x3E612500,0x795FBDEF,0xBE66A419 +data4 0xE1BD41FC,0xBE5CDE8C,0xEA54964F,0xBE621376 +data4 0x476E76EE,0x3E6370BE,0x3427EB92,0x3E390D1A +data4 0x2BF82BF8,0x3E1336DE,0xD0F7BD9E,0xBE5FF1CB +data4 0x0CEB09DD,0xBE60A355,0x0980F30D,0xBE5CA37E +data4 0x4C082D25,0xBE5C541B,0x3B467D29,0xBE5BBECA +data4 0xB9D946C5,0xBE400D8A,0x07ED374A,0xBE5E2A08 +data4 0x365C8B0A,0xBE66CB28,0xD3403BCA,0x3E3AAD5B +data4 0xC7EA21E0,0x3E526055,0xE72880D6,0xBE442C75 +data4 0x85222A43,0x3E58B2BB,0x522C42BF,0xBE5AAB79 +data4 0x469DC2BC,0xBE605CB4,0xA48C40DC,0xBE589FA7 +data4 0x1AA42614,0xBE51C214,0xC37293F4,0xBE48D087 +data4 0xA2D673E0,0x3E367A1C,0x114F7A38,0xBE51BEBB +data4 0x661A4B48,0xBE6348E5,0x1D3B9962,0xBDF52643 +data4 0x35A78A53,0x3E3A3B5E,0x1CECD788,0xBE46C46C +data4 0x7857D689,0xBE60B7EC,0xD14F1AD7,0xBE594D3D +data4 0x4C9A8F60,0xBE4F9C30,0x02DFF9D2,0xBE521873 +data4 0x55E6D68F,0xBE5E4C88,0x667F3DC4,0xBE62140F +data4 0x3BF88747,0xBE36961B,0xC96EC6AA,0x3E602861 +data4 0xD57FD718,0xBE3B5151,0xFC4A627B,0x3E561CD0 +data4 0xCA913FEA,0xBE3A5217,0x9A5D193A,0x3E40A3CC +data4 0x10A9C312,0xBE5AB713,0xC5F57719,0x3E4FDADB +data4 0xDBDF59D5,0x3E361428,0x61B4180D,0x3E5DB5DB +data4 0x7408D856,0xBE42AD5F,0x31B2B707,0x3E2A3148 +ASM_SIZE_DIRECTIVE(Constants_exp_64_W1) + +.align 64 +Constants_exp_64_W2: +ASM_TYPE_DIRECTIVE(Constants_exp_64_W2,@object) +data4 0x00000000,0x00000000,0x37A3D7A2,0xBE641F25 +data4 0xAD028C40,0xBE68DD57,0xF212B1B6,0xBE5C77D8 +data4 0x1BA5B070,0x3E57878F,0x2ECAE6FE,0xBE55A36A +data4 0x569DFA3B,0xBE620608,0xA6D300A3,0xBE53B50E +data4 0x223F8F2C,0x3E5B5EF2,0xD6DE0DF4,0xBE56A0D9 +data4 0xEAE28F51,0xBE64EEF3,0x367EA80B,0xBE5E5AE2 +data4 0x5FCBC02D,0x3E47CB1A,0x9BDAFEB7,0xBE656BA0 +data4 0x805AFEE7,0x3E6E70C6,0xA3415EBA,0xBE6E0509 +data4 0x49BFF529,0xBE56856B,0x00508651,0x3E66DD33 +data4 0xC114BC13,0x3E51165F,0xC453290F,0x3E53333D +data4 0x05539FDA,0x3E6A072B,0x7C0A7696,0xBE47CD87 +data4 0xEB05C6D9,0xBE668BF4,0x6AE86C93,0xBE67C3E3 +data4 0xD0B3E84B,0xBE533904,0x556B53CE,0x3E63E8D9 +data4 0x63A98DC8,0x3E212C89,0x032A7A22,0xBE33138F +data4 0xBC584008,0x3E530FA9,0xCCB93C97,0xBE6ADF82 +data4 0x8370EA39,0x3E5F9113,0xFB6A05D8,0x3E5443A4 +data4 0x181FEE7A,0x3E63DACD,0xF0F67DEC,0xBE62B29D +data4 0x3DDE6307,0x3E65C483,0xD40A24C1,0x3E5BF030 +data4 0x14E437BE,0x3E658B8F,0xED98B6C7,0xBE631C29 +data4 0x04CF7C71,0x3E6335D2,0xE954A79D,0x3E529EED +data4 0xF64A2FB8,0x3E5D9257,0x854ED06C,0xBE6BED1B +data4 0xD71405CB,0x3E5096F6,0xACB9FDF5,0xBE3D4893 +data4 0x01B68349,0xBDFEB158,0xC6A463B9,0x3E628D35 +data4 0xADE45917,0xBE559725,0x042FC476,0xBE68C29C +data4 0x01E511FA,0xBE67593B,0x398801ED,0xBE4A4313 +data4 0xDA7C3300,0x3E699571,0x08062A9E,0x3E5349BE +data4 0x755BB28E,0x3E5229C4,0x77A1F80D,0x3E67E426 +data4 0x6B69C352,0xBE52B33F,0x084DA57F,0xBE6B3550 +data4 0xD1D09A20,0xBE6DB03F,0x2161B2C1,0xBE60CBC4 +data4 0x78A2B771,0x3E56ED9C,0x9D0FA795,0xBE508E31 +data4 0xFD1A54E9,0xBE59482A,0xB07FD23E,0xBE2A17CE +data4 0x17365712,0x3E68BF5C,0xB3785569,0x3E3956F9 +ASM_SIZE_DIRECTIVE(Constants_exp_64_W2) + +.align 64 +Constants_log_80_P: +ASM_TYPE_DIRECTIVE(Constants_log_80_P,@object) +// 1/2, P_8, P_7, ..., P_1 +data4 0x00000000, 0x80000000, 0x00003FFE, 0x00000000 +data4 0x3B1042BC, 0xCCCE8B88, 0x0000BFFB, 0x00000000 +data4 0xCADC2149, 0xE38997B7, 0x00003FFB, 0x00000000 +data4 0xB1ACB090, 0xFFFFFFFE, 0x0000BFFB, 0x00000000 +data4 0x06481C81, 0x92492498, 0x00003FFC, 0x00000000 +data4 0xAAAAB0EF, 0xAAAAAAAA, 0x0000BFFC, 0x00000000 +data4 0xCCC91416, 0xCCCCCCCC, 0x00003FFC, 0x00000000 +data4 0x00000000, 0x80000000, 0x0000BFFD, 0x00000000 +data4 0xAAAAAAAB, 0xAAAAAAAA, 0x00003FFD +ASM_SIZE_DIRECTIVE(Constants_log_80_P) + +.align 64 +Constants_log_80_Q: +ASM_TYPE_DIRECTIVE(Constants_log_80_Q,@object) +// log2_hi, log2_lo, Q_6, Q_5, Q_4, Q_3, Q_2, Q_1 +data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 +data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 +data4 0xA51BE0AF,0x92492453,0x00003FFC,0x00000000 +data4 0xA0CFD29F,0xAAAAAB73,0x0000BFFC,0x00000000 +data4 0xCCCE3872,0xCCCCCCCC,0x00003FFC,0x00000000 +data4 0xFFFFB4FB,0xFFFFFFFF,0x0000BFFC,0x00000000 +data4 0xAAAAAAAB,0xAAAAAAAA,0x00003FFD,0x00000000 +data4 0x00000000,0x80000000,0x0000BFFE,0x00000000 +ASM_SIZE_DIRECTIVE(Constants_log_80_Q) + +.align 64 +Constants_log_80_Z_G_H_h1: +ASM_TYPE_DIRECTIVE(Constants_log_80_Z_G_H_h1,@object) +// Z1 - 16 bit fixed, G1 and H1 IEEE single, h1 IEEE double data4 0x00008000,0x3F800000,0x00000000,0x00000000 -data4 0x00000000,0x00000000,0x00000000,0x00000000 +data4 0x00000000,0x00000000,0x00000000,0x00000000 data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000 data4 0xEBA0E0D1,0x8B1D330B,0x00003FDA,0x00000000 data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000 data4 0x9EADD553,0xE2AF365E,0x00003FE2,0x00000000 data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000 -data4 0x752F34A2,0xF585FEC3,0x0000BFE3,0x00000000 +data4 0x752F34A2,0xF585FEC3,0x0000BFE3,0x00000000 data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000 -data4 0x893B03F3,0xF3546435,0x00003FE2,0x00000000 -data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000 -data4 0x39CDD2AC,0xBABA62E0,0x00003FE4,0x00000000 -data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000 +data4 0x893B03F3,0xF3546435,0x00003FE2,0x00000000 +data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000 +data4 0x39CDD2AC,0xBABA62E0,0x00003FE4,0x00000000 +data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000 data4 0x457978A1,0x8718789F,0x00003FE2,0x00000000 -data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000 -data4 0x3185E56A,0x9442DF96,0x0000BFE4,0x00000000 -data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000 -data4 0x2BBE2CBD,0xCBF9A4BF,0x00003FE4,0x00000000 -data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000 -data4 0x852D5935,0xF3537535,0x00003FE3,0x00000000 -data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000 -data4 0x46CDF32F,0xA1F1E699,0x0000BFDF,0x00000000 -data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000 -data4 0xD8484CE3,0x84A61856,0x00003FE4,0x00000000 +data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000 +data4 0x3185E56A,0x9442DF96,0x0000BFE4,0x00000000 +data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000 +data4 0x2BBE2CBD,0xCBF9A4BF,0x00003FE4,0x00000000 +data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000 +data4 0x852D5935,0xF3537535,0x00003FE3,0x00000000 +data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000 +data4 0x46CDF32F,0xA1F1E699,0x0000BFDF,0x00000000 +data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000 +data4 0xD8484CE3,0x84A61856,0x00003FE4,0x00000000 data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000 -data4 0xFF28821B,0xC7DD97E0,0x0000BFE2,0x00000000 -data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000 -data4 0xEF1FD32F,0xD3C4A887,0x00003FE3,0x00000000 -data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000 -data4 0x464C76DA,0x84672BE6,0x00003FE5,0x00000000 +data4 0xFF28821B,0xC7DD97E0,0x0000BFE2,0x00000000 +data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000 +data4 0xEF1FD32F,0xD3C4A887,0x00003FE3,0x00000000 +data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000 +data4 0x464C76DA,0x84672BE6,0x00003FE5,0x00000000 data4 0x00004211,0x3F042108,0x3F29516A,0x00000000 -data4 0x18835FB9,0x9A43A511,0x0000BFE5,0x00000000 -LOCAL_OBJECT_END(Constants_log_80_Z_G_H_h1) - -LOCAL_OBJECT_START(Constants_log_80_Z_G_H_h2) -// Z2 - 16 bit fixed, G2 and H2 IEEE single, h2 IEEE double -data4 0x00008000,0x3F800000,0x00000000,0x00000000 -data4 0x00000000,0x00000000,0x00000000,0x00000000 -data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000 +data4 0x18835FB9,0x9A43A511,0x0000BFE5,0x00000000 +ASM_SIZE_DIRECTIVE(Constants_log_80_Z_G_H_h1) + +.align 64 +Constants_log_80_Z_G_H_h2: +ASM_TYPE_DIRECTIVE(Constants_log_80_Z_G_H_h2,@object) +// Z2 - 16 bit fixed, G2 and H2 IEEE single, h2 IEEE double +data4 0x00008000,0x3F800000,0x00000000,0x00000000 +data4 0x00000000,0x00000000,0x00000000,0x00000000 +data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000 data4 0x211398BF,0xAD08B116,0x00003FDB,0x00000000 -data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000 -data4 0xC376958E,0xB106790F,0x00003FDE,0x00000000 -data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000 -data4 0x79A7679A,0xFD03F242,0x0000BFDA,0x00000000 -data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000 -data4 0x05E7AE08,0xF03F81C3,0x0000BFDF,0x00000000 -data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000 +data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000 +data4 0xC376958E,0xB106790F,0x00003FDE,0x00000000 +data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000 +data4 0x79A7679A,0xFD03F242,0x0000BFDA,0x00000000 +data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000 +data4 0x05E7AE08,0xF03F81C3,0x0000BFDF,0x00000000 +data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000 data4 0x049EB22F,0xD1B87D3C,0x00003FDE,0x00000000 -data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000 -data4 0x3A9E81E0,0xFABC8B95,0x00003FDF,0x00000000 +data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000 +data4 0x3A9E81E0,0xFABC8B95,0x00003FDF,0x00000000 data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000 -data4 0x7C4B5443,0xF5F3653F,0x00003FDF,0x00000000 -data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000 -data4 0xF65A1773,0xE78AB204,0x00003FE0,0x00000000 -data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000 -data4 0x7B8EF695,0xDB7CBFFF,0x0000BFE0,0x00000000 -data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000 -data4 0xCF773FB3,0xC0241AEA,0x0000BFE0,0x00000000 -data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000 -data4 0xC9539FDF,0xFC8F4D48,0x00003FE1,0x00000000 -data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000 -data4 0x954665C2,0x9CD035FB,0x0000BFE1,0x00000000 -data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000 -data4 0xDD367A30,0xEC9017C7,0x00003FE1,0x00000000 -data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000 -data4 0xCB11189C,0xEE6625D3,0x0000BFE1,0x00000000 -data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000 +data4 0x7C4B5443,0xF5F3653F,0x00003FDF,0x00000000 +data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000 +data4 0xF65A1773,0xE78AB204,0x00003FE0,0x00000000 +data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000 +data4 0x7B8EF695,0xDB7CBFFF,0x0000BFE0,0x00000000 +data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000 +data4 0xCF773FB3,0xC0241AEA,0x0000BFE0,0x00000000 +data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000 +data4 0xC9539FDF,0xFC8F4D48,0x00003FE1,0x00000000 +data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000 +data4 0x954665C2,0x9CD035FB,0x0000BFE1,0x00000000 +data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000 +data4 0xDD367A30,0xEC9017C7,0x00003FE1,0x00000000 +data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000 +data4 0xCB11189C,0xEE6625D3,0x0000BFE1,0x00000000 +data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000 data4 0xBE11C424,0xA49C8DB5,0x0000BFE0,0x00000000 -LOCAL_OBJECT_END(Constants_log_80_Z_G_H_h2) - -LOCAL_OBJECT_START(Constants_log_80_h3_G_H) -// h3 IEEE double extended, H3 and G3 IEEE single -data4 0x112666B0,0xAAACAAB1,0x00003FD3,0x3F7FFC00 +ASM_SIZE_DIRECTIVE(Constants_log_80_Z_G_H_h2) + +.align 64 +Constants_log_80_h3_G_H: +ASM_TYPE_DIRECTIVE(Constants_log_80_h3_G_H,@object) +// h3 IEEE double extended, H3 and G3 IEEE single +data4 0x112666B0,0xAAACAAB1,0x00003FD3,0x3F7FFC00 data4 0x9B7FAD21,0x90051030,0x00003FD8,0x3F7FF400 -data4 0xF4D783C4,0xA6B46F46,0x00003FDA,0x3F7FEC00 -data4 0x11C6DDCA,0xDA148D88,0x0000BFD8,0x3F7FE400 +data4 0xF4D783C4,0xA6B46F46,0x00003FDA,0x3F7FEC00 +data4 0x11C6DDCA,0xDA148D88,0x0000BFD8,0x3F7FE400 data4 0xCA964D95,0xCE65C1D8,0x0000BFD8,0x3F7FDC00 -data4 0x23412D13,0x883838EE,0x0000BFDB,0x3F7FD400 -data4 0x983ED687,0xB7E5CFA1,0x00003FDB,0x3F7FCC08 -data4 0xE3C3930B,0xDBE23B16,0x0000BFD9,0x3F7FC408 -data4 0x48AA4DFC,0x9B92F1FC,0x0000BFDC,0x3F7FBC10 -data4 0xCE9C8F7E,0x9A8CEB15,0x0000BFD9,0x3F7FB410 -data4 0x0DECE74A,0x8C220879,0x00003FDC,0x3F7FAC18 +data4 0x23412D13,0x883838EE,0x0000BFDB,0x3F7FD400 +data4 0x983ED687,0xB7E5CFA1,0x00003FDB,0x3F7FCC08 +data4 0xE3C3930B,0xDBE23B16,0x0000BFD9,0x3F7FC408 +data4 0x48AA4DFC,0x9B92F1FC,0x0000BFDC,0x3F7FBC10 +data4 0xCE9C8F7E,0x9A8CEB15,0x0000BFD9,0x3F7FB410 +data4 0x0DECE74A,0x8C220879,0x00003FDC,0x3F7FAC18 data4 0x2F053150,0xB25CA912,0x0000BFDA,0x3F7FA420 -data4 0xD9A5BE20,0xA5876555,0x00003FDB,0x3F7F9C20 -data4 0x2053F087,0xC919BB6E,0x00003FD9,0x3F7F9428 -data4 0x041E9A77,0xB70BDA79,0x00003FDC,0x3F7F8C30 -data4 0xEA1C9C30,0xF18A5C08,0x00003FDA,0x3F7F8438 -data4 0x796D89E5,0xA3790D84,0x0000BFDD,0x3F7F7C40 -data4 0xA2915A3A,0xE1852369,0x0000BFDD,0x3F7F7448 -data4 0xA39ED868,0xD803858F,0x00003FDC,0x3F7F6C50 -data4 0x9417EBB7,0xB2EEE356,0x0000BFDD,0x3F7F6458 -data4 0x9BB0D07F,0xED5C1F8A,0x0000BFDC,0x3F7F5C68 -data4 0xE87C740A,0xD6D201A0,0x0000BFDD,0x3F7F5470 -data4 0x1CA74025,0xE8DEBF5E,0x00003FDC,0x3F7F4C78 +data4 0xD9A5BE20,0xA5876555,0x00003FDB,0x3F7F9C20 +data4 0x2053F087,0xC919BB6E,0x00003FD9,0x3F7F9428 +data4 0x041E9A77,0xB70BDA79,0x00003FDC,0x3F7F8C30 +data4 0xEA1C9C30,0xF18A5C08,0x00003FDA,0x3F7F8438 +data4 0x796D89E5,0xA3790D84,0x0000BFDD,0x3F7F7C40 +data4 0xA2915A3A,0xE1852369,0x0000BFDD,0x3F7F7448 +data4 0xA39ED868,0xD803858F,0x00003FDC,0x3F7F6C50 +data4 0x9417EBB7,0xB2EEE356,0x0000BFDD,0x3F7F6458 +data4 0x9BB0D07F,0xED5C1F8A,0x0000BFDC,0x3F7F5C68 +data4 0xE87C740A,0xD6D201A0,0x0000BFDD,0x3F7F5470 +data4 0x1CA74025,0xE8DEBF5E,0x00003FDC,0x3F7F4C78 data4 0x1F34A7EB,0x9A995A97,0x0000BFDC,0x3F7F4488 -data4 0x359EED97,0x9CB0F742,0x0000BFDA,0x3F7F3C90 -data4 0xBBC6A1C8,0xD6F833C2,0x0000BFDD,0x3F7F34A0 -data4 0xE71090EC,0xE1F68F2A,0x00003FDC,0x3F7F2CA8 -data4 0xC160A74F,0xD1881CF1,0x0000BFDB,0x3F7F24B8 -data4 0xD78CB5A4,0x9AD05AE2,0x00003FD6,0x3F7F1CC8 -data4 0x9A77DC4B,0xE658CB8E,0x0000BFDD,0x3F7F14D8 -data4 0x6BD6D312,0xBA281296,0x00003FDC,0x3F7F0CE0 -data4 0xF95210D0,0xB478BBEB,0x0000BFDB,0x3F7F04F0 -data4 0x38800100,0x39400480,0x39A00640,0x39E00C41 // H's start here -data4 0x3A100A21,0x3A300F22,0x3A4FF51C,0x3A6FFC1D +data4 0x359EED97,0x9CB0F742,0x0000BFDA,0x3F7F3C90 +data4 0xBBC6A1C8,0xD6F833C2,0x0000BFDD,0x3F7F34A0 +data4 0xE71090EC,0xE1F68F2A,0x00003FDC,0x3F7F2CA8 +data4 0xC160A74F,0xD1881CF1,0x0000BFDB,0x3F7F24B8 +data4 0xD78CB5A4,0x9AD05AE2,0x00003FD6,0x3F7F1CC8 +data4 0x9A77DC4B,0xE658CB8E,0x0000BFDD,0x3F7F14D8 +data4 0x6BD6D312,0xBA281296,0x00003FDC,0x3F7F0CE0 +data4 0xF95210D0,0xB478BBEB,0x0000BFDB,0x3F7F04F0 +data4 0x38800100,0x39400480,0x39A00640,0x39E00C41 // H's start here +data4 0x3A100A21,0x3A300F22,0x3A4FF51C,0x3A6FFC1D data4 0x3A87F20B,0x3A97F68B,0x3AA7EB86,0x3AB7E101 -data4 0x3AC7E701,0x3AD7DD7B,0x3AE7D474,0x3AF7CBED -data4 0x3B03E1F3,0x3B0BDE2F,0x3B13DAAA,0x3B1BD766 -data4 0x3B23CC5C,0x3B2BC997,0x3B33C711,0x3B3BBCC6 -data4 0x3B43BAC0,0x3B4BB0F4,0x3B53AF6D,0x3B5BA620 -data4 0x3B639D12,0x3B6B9444,0x3B7393BC,0x3B7B8B6D -LOCAL_OBJECT_END(Constants_log_80_h3_G_H) - -GR_sig_inv_ln2 = r14 -GR_rshf_2to51 = r15 -GR_exp_2tom51 = r16 -GR_rshf = r17 -GR_exp_half = r18 -GR_sign_mask = r19 -GR_exp_square_oflow = r20 -GR_exp_square_uflow = r21 -GR_exp_ynear1_oflow = r22 -GR_exp_ynear1_uflow = r23 -GR_signif_Z = r24 - -GR_signexp_x = r32 - -GR_exp_x = r33 - +data4 0x3AC7E701,0x3AD7DD7B,0x3AE7D474,0x3AF7CBED +data4 0x3B03E1F3,0x3B0BDE2F,0x3B13DAAA,0x3B1BD766 +data4 0x3B23CC5C,0x3B2BC997,0x3B33C711,0x3B3BBCC6 +data4 0x3B43BAC0,0x3B4BB0F4,0x3B53AF6D,0x3B5BA620 +data4 0x3B639D12,0x3B6B9444,0x3B7393BC,0x3B7B8B6D +ASM_SIZE_DIRECTIVE(Constants_log_80_h3_G_H) + +.align 64 +Constant_half: +ASM_TYPE_DIRECTIVE(Constant_half,@object) +data4 0x00000000,0x80000000,0x00003FFE +ASM_SIZE_DIRECTIVE(Constant_half) + +GR_Expo_Range = r32 +GR_Flag = r33 GR_Table_Ptr = r34 GR_Table_Ptr1 = r35 +GR_BIAS = r35 GR_Index1 = r36 +GR_sign_mask = r36 GR_Index2 = r37 GR_Expo_X = r37 +GR_signif_Z = r38 GR_M = r38 GR_X_0 = r39 @@ -614,49 +620,45 @@ GR_k = r44 GR_Big_Pos_Exp = r45 -GR_exp_pos_max = r46 -GR_exp_bias_p_k = r47 +GR_BIAS_p_k = r47 +GR_BIASed_exp_y = r47 +GR_Big_Neg_Exp = r48 GR_Index3 = r48 GR_temp = r48 GR_vsm_expo = r49 +GR_y_sign = r49 GR_T1_ptr = r50 -GR_P_ptr1 = r50 GR_T2_ptr = r51 -GR_P_ptr2 = r51 GR_N_fix = r52 GR_exp_y = r53 GR_signif_y = r54 -GR_signexp_y = r55 -GR_fraction_y = r55 +GR_exp_and_sign_y = r55 GR_low_order_bit = r56 -GR_exp_mask = r57 -GR_exp_bias = r58 -GR_y_sign = r59 -GR_table_base = r60 -GR_ptr_exp_Arg = r61 -GR_Delta_Exp = r62 -GR_Special_Exp = r63 -GR_exp_neg_max = r64 -GR_Big_Neg_Exp = r65 - -//** Registers for unwind support +GR_get_exp_mask = r57 +GR_exponent_zero = r58 + +// ** Registers for unwind support GR_SAVE_PFS = r59 GR_SAVE_B0 = r60 GR_SAVE_GP = r61 -GR_Parameter_X = r62 -GR_Parameter_Y = r63 -GR_Parameter_RESULT = r64 -GR_Parameter_TAG = r65 +GR_Parameter_X = r62 +GR_Parameter_Y = r63 +GR_Parameter_RESULT = r64 +GR_Parameter_TAG = r65 -//** +FR_X = f8 +FR_Y = f9 +FR_RESULT = f99 + +// ** FR_Input_X = f8 -FR_Result = f8 +FR_Output = f8 FR_Input_Y = f9 FR_Neg = f10 @@ -669,6 +671,7 @@ FR_poly_hi = f11 FR_Sgn = f12 +FR_Neg_X = f13 FR_half_W = f13 FR_X_cor = f14 @@ -695,11 +698,13 @@ FR_Scale = f36 FR_G_1 = f37 FR_G = f37 FR_Wsq = f37 +FR_L_Inv = f37 FR_temp = f37 FR_H_1 = f38 FR_H = f38 FR_W4 = f38 +FR_float_N = f38 FR_h = f39 FR_h_1 = f39 @@ -715,7 +720,9 @@ FR_L_lo = f41 FR_A_1 = f41 FR_h_2 = f42 +FR_P_6 = f42 +FR_abs_W = f43 FR_W1 = f43 FR_G_3 = f44 @@ -733,6 +740,7 @@ FR_H_3 = f47 FR_float_N = f48 +FR_P_4 = f49 FR_A_2 = f49 FR_Q_4 = f50 @@ -760,6 +768,7 @@ FR_Two = f56 FR_Big = f57 FR_neg_2_mK = f58 +FR_NBig = f58 FR_r = f59 @@ -768,1253 +777,1652 @@ FR_poly_lo = f60 FR_poly = f61 FR_P_5 = f62 -FR_Result_small = f62 FR_rsq = f63 -FR_Delta = f64 - -FR_save_Input_X = f65 -FR_norm_X = f66 -FR_norm_Y = f67 -FR_Y_lo_2 = f68 - -FR_P_6 = f69 -FR_Result_big = f69 - -FR_RSHF_2TO51 = f70 -FR_INV_LN2_2TO63 = f71 -FR_2TOM51 = f72 -FR_RSHF = f73 -FR_TMP1 = f74 -FR_TMP2 = f75 -FR_TMP3 = f76 -FR_Tscale = f77 -FR_P_4 = f78 -FR_NBig = f79 - +FR_Result = f99 +FR_Result_small = f100 +FR_Result_big = f101 .section .text -GLOBAL_LIBM_ENTRY(powl) -// -// Get significand of x. It is the critical path. -// +.proc powl# +.global powl# +.align 64 + +powl: { .mfi - getf.sig GR_signif_Z = FR_Input_X // Get significand of x - fclass.m p11, p12 = FR_Input_X, 0x0b // Test x unorm - nop.i 999 +alloc GR_Expo_Range = ar.pfs,0,30,4,0 +(p0) fclass.m.unc p7, p13 = FR_Input_Y, 0x1E7 +nop.i 0 } { .mfi - nop.m 999 - fnorm.s1 FR_norm_X = FR_Input_X // Normalize x - mov GR_exp_half = 0xffff - 1 // Exponent for 0.5 -} -;; - +(p0) getf.exp GR_exp_and_sign_y = FR_Input_Y +// +// Save State +// +(p0) fclass.m.unc p6, p12 = FR_Input_X, 0x1E7 +nop.i 0 +};; { .mfi - alloc r32 = ar.pfs,0,30,4,0 - fclass.m p7, p0 = FR_Input_Y, 0x1E7 // Test y natval, nan, inf, zero - mov GR_exp_pos_max = 0x13fff // Max exponent for pos oflow test +(p0) getf.sig GR_signif_y = FR_Input_Y +(p0) fcmp.eq.unc.s1 p12, p13 = FR_Input_X, f1 +nop.i 0 } { .mfi - addl GR_table_base = @ltoff(Constants_exp_64_Arg#), gp // Ptr to tables - fnorm.s1 FR_norm_Y = FR_Input_Y // Normalize y - mov GR_exp_neg_max = 0x33fff // Max exponent for neg oflow test + nop.m 999 +// +// Check for y = 1 +// Identify EM unsupporteds. +// Load FR_half = .5 +// +(p0) fadd.s1 FR_Two = f1, f1 +// +// Load 1/2 in GP register +// +nop.i 0 } ;; -{ .mfi - getf.exp GR_signexp_y = FR_Input_Y // Get sign and exp of y -(p12) fclass.m p11, p0 = FR_Input_Y, 0x0b // Test y unorm - mov GR_sign_mask = 0x20000 // Sign mask -} -{ .mfi - ld8 GR_table_base = [GR_table_base] // Get base address for tables - fadd.s1 FR_Two = f1, f1 // Form 2.0 for square test - mov GR_exp_mask = 0x1FFFF // Exponent mask +{ .mmi + nop.m 999 +(p0) addl GR_Table_Ptr = @ltoff(Constant_half#), gp + nop.i 999 } ;; -{ .mfi - getf.sig GR_signif_y = FR_Input_Y // Get significand of y - fclass.m p6, p0 = FR_Input_X, 0x1E7 // Test x natval, nan, inf, zero +{ .mmi + ld8 GR_Table_Ptr = [GR_Table_Ptr] + nop.m 999 nop.i 999 } ;; +{ .mlx +(p0) ldfe FR_Half =[GR_Table_Ptr],0 +(p0) movl GR_get_exp_mask = 0x1FFFF ;; +} + { .mfi - getf.exp GR_signexp_x = FR_Input_X // Get signexp of x - fmerge.s FR_save_Input_X = FR_Input_X, FR_Input_X - extr.u GR_Index1 = GR_signif_Z, 59, 4 // Extract upper 4 signif bits of x + nop.m 999 +(p0) fclass.nm.unc p9, p15 = FR_Input_Y, 0x1FF +// +// Create FR_Two = 2 +// Get exp and significand of Y +// Crate Masks +// sgn = 1 +// +(p0) and GR_exp_y = GR_get_exp_mask,GR_exp_and_sign_y } -{ .mfb - setf.exp FR_Half = GR_exp_half // Load half - nop.f 999 -(p11) br.cond.spnt POWL_DENORM // Branch if x or y denorm/unorm +{ .mlx + nop.m 999 +(p0) movl GR_exponent_zero = 0xFFFF ;; } -;; - -// Return here from POWL_DENORM -POWL_COMMON: { .mfi - setf.exp FR_Big = GR_exp_pos_max // Form big pos value for oflow test - fclass.nm p11, p0 = FR_Input_Y, 0x1FF // Test Y unsupported - shl GR_Index1 = GR_Index1,5 // Adjust index1 pointer x 32 + nop.m 999 +(p0) mov FR_Sgn = f1 + nop.i 999 } { .mfi - add GR_Table_Ptr = 0x7c0, GR_table_base // Constants_log_80_Z_G_H_h1 - fma.s1 FR_Sgn = f1,f1,f0 // Assume result positive - mov GR_exp_bias = 0xFFFF // Form exponent bias + nop.m 999 +(p0) fcmp.eq.unc.s1 p10, p11 = FR_Input_Y, f1 + nop.i 999 ;; } -;; - +{ .mfb + nop.m 999 // // Identify NatVals, NaNs, Infs, and Zeros. +// Load Half // -// +(p0) fclass.nm.unc p8, p14 = FR_Input_X, 0x1FF +// // Remove sign bit from exponent of y. -// Check for x = 1 +// Check for x = 1 +// +(p6) br.cond.spnt L(POWL_64_SPECIAL) ;; +} +{ .mib + nop.m 999 + nop.i 999 +(p7) br.cond.spnt L(POWL_64_SPECIAL) ;; +} +{ .mib + nop.m 999 + nop.i 999 +(p8) br.cond.spnt L(POWL_64_UNSUPPORT) ;; +} +{ .mib + nop.m 999 + nop.i 999 +(p9) br.cond.spnt L(POWL_64_UNSUPPORT) ;; +} +{ .mfi +(p0) cmp.lt.unc p9, p0 = GR_exp_y,GR_exponent_zero +(p0) fcmp.lt.unc.s1 p6, p13 = FR_Input_X, f0 +// // Branch on Infs, Nans, Zeros, and Natvals // Check to see that exponent < 0 // +(p0) sub GR_exp_y = GR_exp_y,GR_exponent_zero +} +// x not zero, is y ==2? { .mfi - setf.exp FR_NBig = GR_exp_neg_max // Form big neg value for oflow test - fclass.nm p8, p0 = FR_Input_X, 0x1FF // Test X unsupported - and GR_exp_y = GR_exp_mask,GR_signexp_y // Get biased exponent of y + nop.m 999 +(p11) fcmp.eq.unc.s1 p7, p14 = FR_Input_Y, FR_Two + nop.i 999 ;; } { .mfb - add GR_Index1 = GR_Index1,GR_Table_Ptr - nop.f 999 -(p6) br.cond.spnt POWL_64_SPECIAL // Branch if x natval, nan, inf, zero + nop.m 999 +(p9) fcmp.lt.unc.s1 p9, p0 = FR_Input_X, f0 +(p7) br.cond.spnt L(POWL_64_SQUARE) ;; // Branch if x not zero and y=2 } -;; - -// load Z_1 from Index1 - -// There is logic starting here to determine if y is an integer when x < 0. -// If 0 < |y| < 1 then clearly y is not an integer. -// If |y| > 1, then the significand of y is shifted left by the size of -// the exponent of y. This preserves the lsb of the integer part + the -// fractional bits. The lsb of the integer can be tested to determine if -// the integer is even or odd. The fractional bits can be tested. If zero, -// then y is an integer. +{ .mfi + nop.m 999 +(p6) fmerge.ns FR_Neg_X = FR_Input_X, FR_Input_X + nop.i 999 ;; +} +{ .mfi + nop.m 999 +(p10) fmpy.s0 FR_Result = FR_Input_X, f1 // +// For y = 1, compute result = x +// For x = 1, compute 1 +// When Y is one return X and possible raise +// denormal operand exception. +// Remove exponent BIAS +// +(p6) shl GR_exp_and_sign_y= GR_signif_y,GR_exp_y ;; +} { .mfi - ld2 GR_Z_1 =[GR_Index1],4 // Load Z_1 - fmerge.s FR_Z = f0, FR_norm_X // Z = |x| - extr.u GR_X_0 = GR_signif_Z, 49, 15 // Extract X_0 from significand +(p9) or GR_exp_and_sign_y = 0xF,GR_signif_y +(p12) fma.s0 FR_Result = FR_Input_Y, f0, f1 + nop.i 999 ;; } -{ .mfb - cmp.lt p9, p0 = GR_exp_y,GR_exp_bias // Test 0 < |y| < 1 - nop.f 999 -(p7) br.cond.spnt POWL_64_SPECIAL // Branch if y natval, nan, inf, zero +{ .mii + nop.m 999 +(p6) extr.u GR_exp_y = GR_exp_and_sign_y,63,1 ;; +(p6) cmp.ne.unc p9, p0 = GR_exp_y, r0 } -;; - -{ .mfb - ldfs FR_G_1 = [GR_Index1],4 // Load G_1 - fcmp.eq.s1 p10, p0 = FR_Input_Y, f1 // Test Y = +1.0 -(p8) br.cond.spnt POWL_64_UNSUPPORT // Branch if x unsupported +{ .mii + nop.m 999 +// +// Both predicates can be set. +// Don't consider y's < 1. +// +(p6) shl GR_signif_y= GR_exp_and_sign_y,1 ;; +// +// Is shift off integer part of y. +// Get y's even or odd bit. +// +(p6) cmp.ne.unc p8, p0 = GR_signif_y, r0 } -;; - +{ .mib + nop.m 999 + nop.i 999 // -// X_0 = High order 15 bit of Z +// Is the fractional part of the y = 0? +// Is the integer even or odd. // -{ .mfb - ldfs FR_H_1 = [GR_Index1],8 // Load H_1 -(p9) fcmp.lt.unc.s1 p9, p0 = FR_Input_X, f0 // Test x<0, 0 <|y|<1 -(p11) br.cond.spnt POWL_64_UNSUPPORT // Branch if y unsupported +(p10) br.cond.spnt L(POWL_64_RETURN) ;; +} +{ .mib + nop.m 999 + nop.i 999 +(p12) br.cond.spnt L(POWL_64_RETURN) ;; +} +{ .mib + nop.m 999 + nop.i 999 +(p8) br.cond.spnt L(POWL_64_XNEG) ;; } -;; - { .mfi - ldfe FR_h_1 = [GR_Index1] // Load h_1 - fcmp.eq.s1 p7, p0 = FR_Input_Y, FR_Two // Test y = 2.0 - pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // X_1 = X_0 * Z_1 (bits 15-30) - // Wait 4 cycles to use result + nop.m 999 +(p9) fmerge.ns FR_Sgn = FR_Sgn, FR_Sgn + nop.i 999 } { .mfi - add GR_Table_Ptr = 0x9c0, GR_table_base // Constants_log_80_Z_G_H_h2 - nop.f 999 - sub GR_exp_y = GR_exp_y,GR_exp_bias // Get true exponent of y + nop.m 999 +(p0) fcmp.eq.unc.s0 p11, p0 = FR_Input_Y, FR_Half + nop.i 999 ;; } -;; - // -// Branch for (x < 0) and Y not an integer. +// Raise possible denormal operand exception for both +// X and Y. // { .mfb - nop.m 999 - fcmp.lt.s1 p6, p0 = FR_Input_X, f0 // Test x < 0 -(p9) br.cond.spnt POWL_64_XNEG // Branch if x < 0, 0 < |y| < 1 + nop.m 999 +// +// Branch for (x < 0) and Y not an integer. +// +(p0) fcmp.eq.unc.s0 p12, p0 = FR_Input_X, f1 +// +// For x < 0 and y integer, make x positive +// For x < 0 and y odd integer,, set sign = -1. +// +(p11) br.cond.spnt L(POWL_64_SQRT) ;; +} +{ .mmf +(p0) cmp.eq.unc p15, p14 = r0, r0 + nop.m 999 +(p13) fnorm.s1 FR_Z = FR_Input_X ;; +} +{ .mfi + nop.m 999 +(p6) fnorm.s1 FR_Z = FR_Neg_X + nop.i 999 } ;; -{ .mfi +// +// Branch to embedded sqrt(x) +// +// +// Computes ln( x ) to extra precision +// Input FR 1: FR_X +// Output FR 2: FR_Y_hi +// Output FR 3: FR_Y_lo +// Output PR 1: PR_Safe +// + +{ .mmi nop.m 999 - fcmp.eq.s1 p12, p0 = FR_Input_X, f1 // Test x=+1.0 +(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_Z_G_H_h1#), gp nop.i 999 } -{ .mfb - nop.m 999 - fsub.s1 FR_W = FR_Z, f1 // W = Z - 1 -(p7) br.cond.spnt POWL_64_SQUARE // Branch if y=2 -} ;; -{ .mfi +{ .mmi + ld8 GR_Table_Ptr = [GR_Table_Ptr] nop.m 999 -(p10) fmpy.s0 FR_Result = FR_Input_X, f1 // If y=+1.0, result=x -(p6) shl GR_fraction_y= GR_signif_y,GR_exp_y // Get lsb of int + fraction - // Wait 4 cycles to use result + nop.i 999 } ;; + +{ .mlx + nop.m 999 +(p0) movl GR_BIAS = 0x000000000000FFFF ;; +} { .mfi - nop.m 999 -(p12) fma.s0 FR_Result = FR_Input_Y, f0, f1 // If x=1.0, result=1, chk denorm - extr.u GR_Index2 = GR_X_1, 6, 4 // Extract index2 + nop.m 999 +(p0) fsub.s1 FR_W = FR_Z, f1 + nop.i 999 ;; } -;; - -// -// N = exponent of Z -// -{ .mib - getf.exp GR_N = FR_Z // Get exponent of Z (also x) - shl GR_Index2=GR_Index2,5 // Index2 x 32 bytes -(p10) br.ret.spnt b0 // Exit if y=+1.0 +// +// Z = Norm(X) - both + and - case +// Set Safe = True +// +{ .mmb +(p0) getf.sig GR_signif_Z = FR_Z +(p0) getf.exp GR_N = FR_Z + nop.b 999 ;; +} +{ .mii + nop.m 999 +// +// Get significand of Z +// W = Z - 1 +// +(p0) extr.u GR_Index1 = GR_signif_Z, 59, 4 ;; +// +// Index1 = High order 4 bits of Z +// X_0 = High order 15 bit of Z +// +(p0) shl GR_Index1 = GR_Index1,5 ;; +} +{ .mfi + nop.m 999 +// +// Add offset to Index1 ptr. +// +(p0) fabs FR_abs_W = FR_W +// +// BIAS = 0x000...FFFF +// Adjust Index1 ptr ( x 32) . +// +(p0) add GR_Index1 = GR_Index1,GR_Table_Ptr +} +{ .mmi + nop.m 999 ;; +(p0) ld2 GR_Z_1 =[GR_Index1],4 +(p0) extr.u GR_X_0 = GR_signif_Z, 49, 15 } ;; -{ .mib - add GR_Index2 = GR_Index2, GR_Table_Ptr // Pointer to table 2 +{ .mmi + nop.m 999 +(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_Z_G_H_h2#), gp nop.i 999 -(p12) br.ret.spnt b0 // Exit if x=+1.0 } ;; { .mmi - ld2 GR_Z_2 =[GR_Index2],4 // Load Z_2 -;; - ldfs FR_G_2 = [GR_Index2],4 // Load G_2 + ld8 GR_Table_Ptr = [GR_Table_Ptr] + nop.m 999 nop.i 999 } ;; -{ .mii - ldfs FR_H_2 = [GR_Index2],8 // Load H_2 -(p6) tbit.nz.unc p9, p0 = GR_fraction_y, 63 // Test x<0 and y odd integer - add GR_Table_Ptr = 0xbcc, GR_table_base // Constants_log_80_h3_G_H, G_3 -} -;; +{ .mmi +(p0) ldfs FR_G_1 = [GR_Index1],4 ;; +(p0) ldfs FR_H_1 = [GR_Index1],8 + nop.i 999 ;; +} // -// For x < 0 and y odd integer,, set sign = -1. +// Adjust Index2 (x 32). // { .mfi - getf.exp GR_M = FR_W // Get signexp of W - nop.f 999 - pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // X_2 = X_1 * Z_2 (bits 15-30) +(p0) ldfe FR_h_1 = [GR_Index1],0 + nop.f 999 +(p0) pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 ;; } -{ .mfi - ldfe FR_h_2 = [GR_Index2] // Load h_2 -(p9) fnma.s1 FR_Sgn = f1, f1, f0 // If x<0, y odd int, result negative - sub GR_N = GR_N, GR_exp_bias // Get true exponent of x = N +{ .mmi + nop.m 999 ;; +// +// load Z_1 from Index1 +// abs_W = |W| +// Point to Table2 +// +(p0) getf.exp GR_M = FR_abs_W +// +// M = M - BIAS +// Load G_1 +// N = exponent of Z +// + nop.i 999;; } -;; - -{ .mfi - add GR_Table_Ptr1 = 0xdc0, GR_table_base // Ptr to H_3 - fcmp.eq.s0 p11, p0 = FR_Input_Y, FR_Half // Test y=0.5, also set denorm -(p6) shl GR_fraction_y= GR_fraction_y, 1 // Shift left 1 to get fraction +{ .mmi + nop.m 999 + nop.m 999 + nop.i 999;; } -;; - -{ .mmb - setf.sig FR_float_N = GR_N -(p6) cmp.ne.unc p8, p0 = GR_fraction_y, r0 // Test x<0 and y not integer -(p8) br.cond.spnt POWL_64_XNEG // Branch if x<0 and y not int +{ .mmi + nop.m 999 + nop.m 999 + nop.i 999;; } -;; - +{ .mmi + nop.m 999 + nop.m 999 +(p0) extr.u GR_Index2 = GR_X_1, 6, 4 ;; +} +{ .mii + nop.m 999 +// +// Extract Index2 +// Load H_1 +// Is -8 > M ? // -// Raise possible denormal operand exception for both X and Y. -// Set pointers in case |x| near 1 -// Branch to embedded sqrt(x) if y=0.5 +(p0) shl GR_Index2=GR_Index2,5 ;; +(p0) add GR_Index2 = GR_Index2, GR_Table_Ptr +} // -{ .mfi - add GR_P_ptr1 = 0x6b0, GR_table_base // Constants_log_80_P, P8, NEAR path - fcmp.eq.s0 p12, p0 = FR_Input_X, FR_Input_Y // Dummy to set denormal - add GR_P_ptr2 = 0x700, GR_table_base // Constants_log_80_P, P4, NEAR path +// M = exponent of abs_W +// X_1 = X_0 * Z_1 +// +{ .mii +(p0) sub GR_M = GR_M, GR_BIAS + nop.i 999 ;; +(p0) cmp.gt.unc p7, p14 = -8, GR_M } -{ .mfb - cmp.eq p15, p14 = r0, r0 // Assume result safe (no over/under) - fsub.s1 FR_Delta = FR_Input_Y,f1 // Delta = y - 1.0 -(p11) br.cond.spnt POWL_64_SQRT // Branch if y=0.5 +{ .mib + nop.m 999 + nop.i 999 +(p7) br.cond.spnt L(LOGL80_NEAR) ;; } -;; - // -// Computes ln( x ) to extra precision -// Input FR 1: FR_X -// Output FR 2: FR_Y_hi -// Output FR 3: FR_Y_lo -// Output PR 1: PR_Safe +// Load h_1 +// Possible branch out. +// Add offset of table to Index2 // { .mfi - and GR_M = GR_exp_mask, GR_M // Mask to get exponent of W - nop.f 999 - extr.u GR_Index3 = GR_X_2, 1, 5 // Get index3 +(p0) ld2 GR_Z_2 =[GR_Index2],4 +(p0) fmerge.se FR_S = f1,FR_Z +(p0) sub GR_N = GR_N, GR_BIAS } ;; { .mmi - shladd GR_Table_Ptr1 = GR_Index3,2,GR_Table_Ptr1 // Ptr to H_3 - shladd GR_Index3 = GR_Index3,4,GR_Table_Ptr // Ptr to G_3 - sub GR_M = GR_M, GR_exp_bias // Get true exponent of W -} -;; - -{ .mib - ldfs FR_G_3 = [GR_Index3],-12 // Load G_3 - cmp.gt p7, p14 = -8, GR_M // Test if |x-1| < 2^-8 -(p7) br.cond.spnt LOGL80_NEAR // Branch if |x-1| < 2^-8 -} -;; - -// Here if |x-1| >= 2^-8 -{ .mmf - ldfs FR_H_3 = [GR_Table_Ptr1] // Load H_3 nop.m 999 - nop.f 999 +(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_h3_G_H#), gp + nop.i 999 } ;; -{ .mfi - ldfe FR_h_3 = [GR_Index3] // Load h_3 - fmerge.se FR_S = f1,FR_Z // S = merge of 1.0 and signif(Z) - nop.i 999 -} -{ .mfi - add GR_Table_Ptr = 0x740, GR_table_base // Constants_log_80_Q - fmpy.s1 FR_G = FR_G_1, FR_G_2 // G = G_1 * G_2 +{ .mmi + ld8 GR_Table_Ptr = [GR_Table_Ptr] + nop.m 999 nop.i 999 } ;; +// +// load Z_2 +// N - BIAS +// Point to Table 3. +// S = merging of Z and 1.0 +// +{ .mmi +(p0) ldfs FR_G_2 = [GR_Index2],4 +(p0) setf.sig FR_float_N = GR_N +(p0) add GR_Table_Ptr1 = 0x200,GR_Table_Ptr ;; +} // -// Begin Loading Q's - load log2_hi part +// load G_2 +// X_2 = X_1 * Z_2 +// Add offset to Table 2 ptr. +// float_N = significand of N // -{ .mfi - ldfe FR_log2_hi = [GR_Table_Ptr],16 // Load log2_hi - fadd.s1 FR_H = FR_H_1, FR_H_2 // H = H_1 + H_2 - nop.i 999 -};; - +{ .mmi +(p0) ldfs FR_H_2 = [GR_Index2],8 ;; // -// h = h_1 + h_2 +// load H_2 +// G = G * G_2 // +(p0) ldfe FR_h_2 = [GR_Index2],0 +(p0) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 ;; +} +{ .mmi + nop.m 999 + nop.m 999 + nop.i 999;; +} +{ .mmi + nop.m 999 + nop.m 999 + nop.i 999;; +} +{ .mmi + nop.m 999 + nop.m 999 + nop.i 999;; +} +{ .mii + nop.m 999 + nop.i 999 ;; +(p0) extr.u GR_Index3 = GR_X_2, 1, 5 ;; +} { .mfi - ldfe FR_log2_lo = [GR_Table_Ptr],16 // Load log2_lo - fadd.s1 FR_h = FR_h_1, FR_h_2 // h = h_1 + h_2 - nop.i 999 +(p0) shladd GR_Table_Ptr1 = GR_Index3,2,GR_Table_Ptr1 + nop.f 999 +// +// h = h_1 + h_2 +// Adjust Index3 +// +(p0) shladd GR_Index3 = GR_Index3,4,GR_Table_Ptr ;; +} +{ .mmb + nop.m 999 +(p0) ldfe FR_h_3 = [GR_Index3],12 + nop.b 999 ;; +} +{ .mmf +(p0) ldfs FR_H_3 = [GR_Table_Ptr1],0 +// +// float_N = Make N a fp number +// Load h_3 +// Get pointer to Q table. +// +(p0) ldfs FR_G_3 = [GR_Index3],0 +(p0) fmpy.s1 FR_G = FR_G_1, FR_G_2 } ;; -{ .mfi - ldfe FR_Q_6 = [GR_Table_Ptr],16 // Load Q_6 - fcvt.xf FR_float_N = FR_float_N +{ .mmi + nop.m 999 +(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_Q#), gp nop.i 999 } ;; -{ .mfi - ldfe FR_Q_5 = [GR_Table_Ptr],16 // Load Q_5 - nop.f 999 +{ .mmi + ld8 GR_Table_Ptr = [GR_Table_Ptr] + nop.m 999 nop.i 999 } ;; + + +{ .mfi +(p0) ldfe FR_log2_hi = [GR_Table_Ptr],16 +(p0) fadd.s1 FR_H = FR_H_1, FR_H_2 + nop.i 999 ;; +} +{ .mmf + nop.m 999 // -// G = G_1 * G_2 * G_3 +// G = G_1 * G_2 * G_3 // -{ .mfi - ldfe FR_Q_4 = [GR_Table_Ptr],16 // Load Q_4 - fmpy.s1 FR_G = FR_G, FR_G_3 - nop.i 999 +(p0) ldfe FR_log2_lo = [GR_Table_Ptr],16 +// +// load h_2 +// H = H_1 + H_2 +// Get Index3 +// +(p0) fadd.s1 FR_h = FR_h_1, FR_h_2 ;; } -;; - // -// H = H_1 + H_2 + H_3 +// Load log2_lo part +// r = G*S -1 // { .mfi - ldfe FR_Q_3 = [GR_Table_Ptr],16 // Load Q_3 - fadd.s1 FR_H = FR_H, FR_H_3 - nop.i 999 +(p0) ldfe FR_Q_6 = [GR_Table_Ptr],16 +// +// Load H_3 +// +(p0) fcvt.xf FR_float_N = FR_float_N + nop.i 999 ;; } -;; - // -// Y_lo = poly + Y_lo +// Load Q_6 // -// h = h_1 + h_2 + h_3 +{ .mmi +(p0) ldfe FR_Q_5 = [GR_Table_Ptr],16 ;; +(p0) ldfe FR_Q_4 = [GR_Table_Ptr],16 + nop.i 999 ;; +} +{ .mmi +(p0) ldfe FR_Q_3 = [GR_Table_Ptr],16 ;; +(p0) ldfe FR_Q_2 = [GR_Table_Ptr],16 + nop.i 999 ;; +} +{ .mmf + nop.m 999 // +// poly_lo = Q_5 + r * Q_6 +// Load Q_2 +// rsq = r * r +// +(p0) ldfe FR_Q_1 = [GR_Table_Ptr],16 +// +// h = h_1 + h_2 + h_3 +// H = H_1 + H_2 + H_3 +// Load G_3. +// Begin Loading Q's - load log2_hi part +// +(p0) fmpy.s1 FR_G = FR_G, FR_G_3 +} { .mfi - ldfe FR_Q_2 = [GR_Table_Ptr],16 // Load Q_2 - fadd.s1 FR_h = FR_h, FR_h_3 - nop.i 999 + nop.m 999 +(p0) fadd.s1 FR_H = FR_H, FR_H_3 + nop.i 999 } ;; // -// GS_hi = G*S -// r = G*S -1 +// Y_lo = poly + Y_lo // -{ .mfi - ldfe FR_Q_1 = [GR_Table_Ptr],16 // Load Q_1 - fmpy.s1 FR_GS_hi = FR_G, FR_S + +{ .mmi + nop.m 999 +(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_Arg#), gp nop.i 999 } -{ .mfi +;; + +{ .mmi + ld8 GR_Table_Ptr = [GR_Table_Ptr] nop.m 999 - fms.s1 FR_r = FR_G, FR_S, f1 nop.i 999 } ;; + +{ .mfi + nop.m 999 +(p0) fadd.s1 FR_h = FR_h, FR_h_3 + nop.i 999 ;; +} +{ .mfi + nop.m 999 // -// poly_lo = Q_5 + r * Q_6 +// Load Q_5 // +(p0) fmpy.s1 FR_GS_hi = FR_G, FR_S + nop.i 999 +} { .mfi - getf.exp GR_Delta_Exp = FR_Delta // Get signexp of y-1 for exp calc - fma.s1 FR_poly_lo = FR_r, FR_Q_6, FR_Q_5 - nop.i 999 + nop.m 999 +(p0) fms.s1 FR_r = FR_G, FR_S, f1 + nop.i 999 ;; } +{ .mfi + nop.m 999 +(p0) fma.s1 FR_poly_lo = FR_r, FR_Q_6, FR_Q_5 + nop.i 999 +} +{ .mfi + nop.m 999 // -// r_cor = GS_hi -1 +// GS_hi = G*S +// Load Q_4 // +(p0) fsub.s1 FR_r_cor = FR_GS_hi, f1 + nop.i 999 ;; +} { .mfi - nop.m 999 - fsub.s1 FR_r_cor = FR_GS_hi, f1 - nop.i 999 + nop.m 999 +(p0) fms.s1 FR_GS_lo = FR_G, FR_S, FR_GS_hi + nop.i 999 } -;; - +{ .mfi + nop.m 999 +(p0) fma.s1 FR_poly = FR_r, FR_Q_2, FR_Q_1 + nop.i 999 ;; +} +{ .mfi + nop.m 999 // +// Load Q_3 +// r_cor = GS_hi -1 // GS_lo = G*S - GS_hi // +(p0) fmpy.s1 FR_rsq = FR_r, FR_r + nop.i 999 +} { .mfi - nop.m 999 - fms.s1 FR_GS_lo = FR_G, FR_S, FR_GS_hi - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_G = FR_float_N, FR_log2_hi, FR_H + nop.i 999 ;; } -;; - +{ .mfi + nop.m 999 // -// rsq = r * r +// poly = poly_hi + rsq * poly_lo +// Tbl = float_N*log2_hi + H // -{ .mfi - nop.m 999 - fmpy.s1 FR_rsq = FR_r, FR_r - nop.i 999 +(p0) fma.s1 FR_Y_lo = FR_float_N, FR_log2_lo, FR_h + nop.i 999 ;; } +{ .mfi + nop.m 999 // -// G = float_N*log2_hi + H +// r_cor = r_cor - r +// poly_hi = r * Q_2 + Q_1 // -{ .mfi - nop.m 999 - fma.s1 FR_G = FR_float_N, FR_log2_hi, FR_H - nop.i 999 +(p0) fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_4 + nop.i 999 } -;; - +{ .mfi + nop.m 999 // -// Y_lo = float_N*log2_lo + h +// Load Q_1 // +(p0) fsub.s1 FR_r_cor = FR_r_cor, FR_r + nop.i 999 ;; +} { .mfi - nop.m 999 - fma.s1 FR_Y_lo = FR_float_N, FR_log2_lo, FR_h - nop.i 999 + nop.m 999 +// +// Y_lo = float_N*log2_lo + h +// +(p0) fadd.s1 FR_Y_hi = FR_G, FR_r + nop.i 999 ;; } -;; - +{ .mfi + nop.m 999 // -// poly_lo = Q_4 + r * poly_lo -// r_cor = r_cor - r +// poly_lo = Q_4 + r * poly_lo;; +// r_cor = r_cor + GS_lo;; // +(p0) fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_3 + nop.i 999 +} { .mfi - nop.m 999 - fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_4 - nop.i 999 + nop.m 999 +(p0) fadd.s1 FR_r_cor = FR_r_cor, FR_GS_lo + nop.i 999 ;; } { .mfi - nop.m 999 - fsub.s1 FR_r_cor = FR_r_cor, FR_r - nop.i 999 + nop.m 999 +(p0) fadd.s1 FR_r_cor = FR_r_cor, FR_Y_lo + nop.i 999 } -;; - +{ .mfi + nop.m 999 // -// poly_hi = r * Q_2 + Q_1 -// Y_hi = G + r +// poly_lo = Q_3 + r * poly_lo;; // +(p0) fma.s1 FR_poly = FR_rsq, FR_poly_lo, FR_poly + nop.i 999 ;; +} { .mfi - nop.m 999 - fma.s1 FR_poly = FR_r, FR_Q_2, FR_Q_1 - nop.i 999 + nop.m 999 +(p0) fsub.s1 FR_Y_lo = FR_G, FR_Y_hi + nop.i 999 +} +{ .mmi +(p0) ldfe FR_L_Inv = [GR_Table_Ptr],16 ;; +(p0) ldfe FR_L_hi = [GR_Table_Ptr],16 + nop.i 999 ;; } { .mfi - nop.m 999 - fadd.s1 FR_Y_hi = FR_G, FR_r - nop.i 999 +(p0) ldfe FR_L_lo = [GR_Table_Ptr],16 + nop.f 999 + nop.i 999 ;; } -;; - +{ .mfi + nop.m 999 // -// poly_lo = Q_3 + r * poly_lo -// r_cor = r_cor + GS_lo +// Y_hi = Tbl + r +// r_cor = r_cor + Y_lo // -{ .mfi - nop.m 999 - fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_3 - nop.i 999 +(p0) fma.s1 FR_poly = FR_rsq, FR_poly, FR_r_cor + nop.i 999 ;; } { .mfi + nop.m 999 +// Y_lo = Tbl - Y_hi +// poly = rsq * poly + r_cor +// +(p0) fadd.s1 FR_Y_lo = FR_Y_lo, FR_r + nop.i 999 ;; +} +{ .mfb + nop.m 999 +// +// Y_lo = Y_lo + r +// +(p0) fadd.s1 FR_Y_lo = FR_Y_lo, FR_poly +// +// Load L_Inv +// Load L_hi +// Load L_lo +// all long before they are needed. +// They are used in LOGL_RETURN PATH +// +br.cond.sptk L(LOGL_RETURN) ;; +} +L(LOGL80_NEAR): +// +// Branch LOGL80_NEAR +// + +{ .mmi nop.m 999 - fadd.s1 FR_r_cor = FR_r_cor, FR_GS_lo +(p0) addl GR_Table_Ptr = @ltoff(Constants_log_80_P#), gp nop.i 999 } ;; -// -// Y_lo = G - Y_hi -// -{ .mfi +{ .mmi + ld8 GR_Table_Ptr = [GR_Table_Ptr] nop.m 999 - fsub.s1 FR_Y_lo_2 = FR_G, FR_Y_hi nop.i 999 } ;; +{ .mfi + nop.m 999 +(p0) fmpy.s1 FR_Wsq = FR_W, FR_W +(p0) add GR_Table_Ptr1 = 0x50,GR_Table_Ptr +} // -// r_cor = r_cor + Y_lo -// poly = poly_hi + rsq * poly_lo +// Adjust ptr to 1/2 +// Adjust Ptr1 to P_4 // -{ .mfi - add GR_Table_Ptr = 0x0, GR_table_base // Constants_exp_64_Arg - fadd.s1 FR_r_cor = FR_r_cor, FR_Y_lo - nop.i 999 +{ .mmi +(p0) ldfe FR_Half = [GR_Table_Ptr],16 ;; +(p0) ldfe FR_P_4 = [GR_Table_Ptr1],16 + nop.i 999 } -{ .mfi - nop.m 999 - fma.s1 FR_poly = FR_rsq, FR_poly_lo, FR_poly - nop.i 999 +// +// Load 1/2 +// +{ .mmi +(p0) ldfe FR_P_8 = [GR_Table_Ptr],16 ;; +(p0) ldfe FR_P_3 = [GR_Table_Ptr1],16 + nop.i 999 +} +{ .mmi +(p0) ldfe FR_P_7 = [GR_Table_Ptr],16 ;; +(p0) ldfe FR_P_2 = [GR_Table_Ptr1],16 + nop.i 999 } -;; - // -// Load L_hi -// Load L_lo -// all long before they are needed. -// They are used in LOGL_RETURN PATH +// Load P_7 +// half_W = .5 * W +// Load P_3 // -// Y_lo = Y_lo + r -// poly = rsq * poly + r_cor +{ .mmi +(p0) ldfe FR_P_6 = [GR_Table_Ptr],16 ;; +(p0) ldfe FR_P_1 = [GR_Table_Ptr1],16 + nop.i 999 ;; +} +// +// Load P_6 +// Wsq = w * w +// poly = w*P_4 + P_3 +// Load P_2 // { .mfi - ldfe FR_L_hi = [GR_Table_Ptr],16 // Load L_hi - fadd.s1 FR_Y_lo = FR_Y_lo_2, FR_r - nop.i 999 +(p0) ldfe FR_P_5 = [GR_Table_Ptr],16 +// +// Load P_5 +// poly_lo = w * P_8 + P_7 +// Y_hi = w - (1/2)w*w +// Load P_1 +// +(p0) fmpy.s1 FR_W4 = FR_Wsq, FR_Wsq + nop.i 999 } { .mfi - nop.m 999 - fma.s1 FR_poly = FR_rsq, FR_poly, FR_r_cor - nop.i 999 + nop.m 999 +(p0) fmpy.s1 FR_W3 = FR_Wsq, FR_W + nop.i 999 } ;; -{ .mfb - ldfe FR_L_lo = [GR_Table_Ptr],16 // Load L_lo - fadd.s1 FR_Y_lo = FR_Y_lo, FR_poly - br.cond.sptk LOGL_RETURN // Branch to common code -} -;; - - -LOGL80_NEAR: -// Here if |x-1| < 2^-8 // -// Branch LOGL80_NEAR +// Y_lo = W3 * poly + Y_lo // -{ .mmf - ldfe FR_P_8 = [GR_P_ptr1],16 // Load P_8 - ldfe FR_P_4 = [GR_P_ptr2],16 // Load P_4 - fmpy.s1 FR_Wsq = FR_W, FR_W -} -;; - { .mmi - ldfe FR_P_7 = [GR_P_ptr1],16 // Load P_7 - ldfe FR_P_3 = [GR_P_ptr2],16 // Load P_3 + nop.m 999 +(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_Arg#), gp nop.i 999 } ;; { .mmi - ldfe FR_P_6 = [GR_P_ptr1],16 // Load P_6 - ldfe FR_P_2 = [GR_P_ptr2],16 // Load P_2 + ld8 GR_Table_Ptr = [GR_Table_Ptr] + nop.m 999 nop.i 999 } ;; + { .mmi - ldfe FR_P_5 = [GR_P_ptr1],16 // Load P_5 - ldfe FR_P_1 = [GR_P_ptr2],16 // Load P_1 - nop.i 999 +(p0) ldfe FR_L_Inv = [GR_Table_Ptr],16 ;; +(p0) ldfe FR_L_hi = [GR_Table_Ptr],16 + nop.i 999 ;; } -;; - { .mfi - getf.exp GR_Delta_Exp = FR_Delta // Get signexp of y-1 for exp calc - fmpy.s1 FR_W4 = FR_Wsq, FR_Wsq - nop.i 999 +(p0) ldfe FR_L_lo = [GR_Table_Ptr],16 +// +// Load P_8 +// Load P_4 +// +(p0) fmpy.s1 FR_half_W = FR_Half, FR_W + nop.i 999 ;; } { .mfi - add GR_Table_Ptr = 0x0, GR_table_base // Constants_exp_64_Arg - fmpy.s1 FR_W3 = FR_Wsq, FR_W - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_poly_lo = FR_W, FR_P_8,FR_P_7 + nop.i 999 } -;; - { .mfi - nop.m 999 - fmpy.s1 FR_half_W = FR_Half, FR_W - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_poly = FR_W, FR_P_4, FR_P_3 + nop.i 999 ;; } -;; - { .mfi - ldfe FR_L_hi = [GR_Table_Ptr],16 - fma.s1 FR_poly_lo = FR_W, FR_P_8,FR_P_7 - nop.i 999 + nop.m 999 +(p0) fnma.s1 FR_Y_hi = FR_W, FR_half_W, FR_W + nop.i 999 ;; } { .mfi - nop.m 999 - fma.s1 FR_poly = FR_W, FR_P_4, FR_P_3 - nop.i 999 + nop.m 999 +// +// W4 = Wsq * Wsq +// poly = w *poly + P_2 +// +(p0) fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_6 + nop.i 999 } -;; - { .mfi - ldfe FR_L_lo = [GR_Table_Ptr],16 - fnma.s1 FR_Y_hi = FR_W, FR_half_W, FR_W - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_poly = FR_W, FR_poly, FR_P_2 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_6 - nop.i 999 + nop.m 999 +(p0) fsub.s1 FR_Y_lo = FR_W, FR_Y_hi + nop.i 999 ;; } { .mfi - nop.m 999 - fma.s1 FR_poly = FR_W, FR_poly, FR_P_2 - nop.i 999 + nop.m 999 +// +// poly = w * poly + P_1 +// w3 = wsq * w +// +(p0) fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_5 + nop.i 999 } -;; - { .mfi - nop.m 999 - fsub.s1 FR_Y_lo = FR_W, FR_Y_hi - nop.i 999 + nop.m 999 +// +// poly_lo = w * poly_lo + P_6 +// Y_lo = W - Y_hi +// +(p0) fma.s1 FR_poly = FR_W, FR_poly, FR_P_1 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_5 - nop.i 999 + nop.m 999 +(p0) fnma.s1 FR_Y_lo = FR_W, FR_half_W, FR_Y_lo + nop.i 999 ;; } { .mfi - nop.m 999 - fma.s1 FR_poly = FR_W, FR_poly, FR_P_1 - nop.i 999 + nop.m 999 +// +// poly_lo = w * poly_lo + +// Y_lo = Y_lo - w * (1/2)w +// +(p0) fma.s1 FR_poly = FR_poly_lo, FR_W4, FR_poly + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fnma.s1 FR_Y_lo = FR_W, FR_half_W, FR_Y_lo - nop.i 999 + nop.m 999 +// +// Y_lo = (W-Y_hi) - w * (1/2)w +// poly = W4* poly_lo + poly +// +(p0) fma.s1 FR_Y_lo = FR_poly, FR_W3, FR_Y_lo + nop.i 999 ;; +} +L(LOGL_RETURN): +{ .mfi +(p0) add GR_Expo_Range = 0x2,r0 +// +// Load L_Inv +// Load L_hi +// Load L_lo +// all long before they are needed. +// +// +// kernel_log_80 computed ln(X) +// and return logX_hi and logX_lo as results. +// PR_pow_Safe set as well. +// +(p0) fmpy.s1 FR_X_lo = FR_Input_Y, FR_logx_lo +// +// Compute Y * (logX_hi + logX_lo) +// P_hi -> X +// P_lo -> X_cor +// (Manipulate names so that inputs are in +// the place kernel_exp expects them) +// Set GR_Flag to 2 +// Set GR_Expo_Range to Double +// +// This function computes exp( x + x_cor) +// Input FR 1: FR_X +// Input FR 2: FR_X_cor +// Input GR 1: GR_Flag +// Input GR 2: GR_Expo_Range +// Output FR 3: FR_Y_hi +// Output FR 4: FR_Y_lo +// Output FR 5: FR_Scale +// Output PR 1: PR_Safe +// +(p0) cmp.eq.unc p15, p0 = r0, r0 } ;; -{ .mfi - nop.m 999 - fma.s1 FR_poly = FR_poly_lo, FR_W4, FR_poly - nop.i 999 +{ .mmi +(p0) addl GR_W1_ptr = @ltoff(Constants_exp_64_W1#), gp +(p0) addl GR_W2_ptr = @ltoff(Constants_exp_64_W2#), gp +(p0) add GR_Flag = 0x2,r0 } ;; -{ .mfi - nop.m 999 - fma.s1 FR_Y_lo = FR_poly, FR_W3, FR_Y_lo - nop.i 999 +{ .mmi + ld8 GR_W1_ptr = [GR_W1_ptr] + ld8 GR_W2_ptr = [GR_W2_ptr] +(p0) cmp.ne.unc p7, p0 = 0x1, GR_Flag } ;; +{ .mlx + nop.m 999 +(p0) movl GR_Mask = 0x1FFFF ;; +} -LOGL_RETURN: -// Common code for completion of both logx paths +{ .mlx + nop.m 999 +(p0) movl GR_BIAS = 0x0FFFF ;; +} +{ .mfi + nop.m 999 // -// L_hi, L_lo already loaded. -// -// -// kernel_log_80 computed ln(X) -// and return logX_hi and logX_lo as results. -// PR_pow_Safe set as well. +// X_lo = Y * logX_lo // +(p0) fma.s1 FR_P_hi = FR_Input_Y, FR_logx_hi,FR_X_lo + nop.i 999 ;; +} +{ .mfi + nop.m 999 // -// Compute Y * (logX_hi + logX_lo) -// P_hi -> X -// P_lo -> X_cor -// (Manipulate names so that inputs are in -// the place kernel_exp expects them) +// Set Safe=True +// Flag is always 2 for this routine // -// This function computes exp( x + x_cor) -// Input FR 1: FR_X -// Input FR 2: FR_X_cor -// Output FR 3: FR_Y_hi -// Output FR 4: FR_Y_lo -// Output FR 5: FR_Scale -// Output PR 1: PR_Safe +(p0) fmpy.s1 FR_float_N = FR_X, FR_L_Inv + nop.i 999 +} +{ .mfi + nop.m 999 // -// P15 is True +// X_hi = Y * logX_hi + X_lo +// Set GR_Flag = 2 for exp(x + xcor) // -// Load constants used in computing N using right-shift technique -{ .mlx - mov GR_exp_2tom51 = 0xffff-51 - movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 +(p0) fms.s1 FR_P_lo= FR_Input_Y, FR_logx_hi, FR_P_hi + nop.i 999 ;; } -{ .mlx - add GR_Special_Exp = -50,GR_exp_bias - movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51) +{ .mmi + nop.m 999 ;; +(p0) getf.exp GR_Expo_X = FR_X + nop.i 999 ;; } -;; - +{ .mfi +(p0) and GR_Expo_X = GR_Expo_X, GR_Mask // +// Calculate unBIASed exponent of X // Point to Table of W1s // Point to Table of W2s // -{ .mmi - add GR_W1_ptr = 0x2b0, GR_table_base // Constants_exp_64_W1 - add GR_W2_ptr = 0x4b0, GR_table_base // Constants_exp_64_W2 - cmp.le p6,p0= GR_Delta_Exp,GR_Special_Exp -};; - -// 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 - +(p0) fcvt.fx.s1 FR_N = FR_float_N + nop.i 999 ;; +} { .mfi - setf.sig FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63 - nop.f 999 - and GR_Delta_Exp=GR_Delta_Exp,GR_exp_mask // Get exponent of y-1 + nop.m 999 +(p0) fadd.s1 FR_P_lo = FR_P_lo, FR_X_lo +// +// Float_N = X * L_Inv +// Create exponent BIAS +// Get BIASed exponent of X +// +(p0) sub GR_Expo_X = GR_Expo_X, GR_BIAS ;; } -{ .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 +{ .mib +(p0) cmp.gt.unc p9, p0 = -6, GR_Expo_X + nop.i 999 +// +// N = fcvt.fx(float_N) +// If -6 > Expo_X, set P9 +// +(p9) br.cond.spnt L(EXPL_SMALL) } ;; -{ .mfi - nop.m 999 - fmpy.s1 FR_X_lo = FR_Input_Y, FR_logx_lo // logx_lo is Y_lo - cmp.eq p15, p0= r0, r0 // Set p15, assume safe -};; - +// +// If expo_X < -6 goto exp_small +// { .mmi - setf.exp FR_2TOM51 = GR_exp_2tom51 // Form 2^-51 for scaling float_N - setf.d FR_RSHF = GR_rshf // Form right shift const 1.1000 * 2^63 - add GR_Table_Ptr1 = 0x50, GR_table_base // Constants_exp_64_P for - // EXPL_SMALL path + nop.m 999 +(p0) addl GR_T1_ptr = @ltoff(Constants_exp_64_T1#), gp +(p0) cmp.lt.unc p10, p0 = 14, GR_Expo_X } ;; { .mmi - ldfe FR_P_6 = [GR_Table_Ptr1],16 // Load P_6 for EXPL_SMALL path -;; - ldfe FR_P_5 = [GR_Table_Ptr1],16 // Load P_5 for EXPL_SMALL path + ld8 GR_T1_ptr = [GR_T1_ptr] + nop.m 999 nop.i 999 } ;; -{ .mfi - ldfe FR_P_4 = [GR_Table_Ptr1],16 // Load P_4 for EXPL_SMALL path - fma.s1 FR_P_hi = FR_Input_Y, FR_logx_hi,FR_X_lo // logx_hi ix Y_hi - nop.i 999 +{ .mib + nop.m 999 + nop.i 999 +// +// If 14 < Expo_X, set P10 +// Create pointer to T1 table +// +(p10) br.cond.spnt L(EXPL_HUGE) ;; } -;; + { .mmi - ldfe FR_P_3 = [GR_Table_Ptr1],16 // Load P_3 for EXPL_SMALL path -;; - ldfe FR_P_2 = [GR_Table_Ptr1],16 // Load P_2 for EXPL_SMALL path +(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_Exponents#), gp +(p0) addl GR_T2_ptr = @ltoff(Constants_exp_64_T2#), gp nop.i 999 } ;; -// N = 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_P_1 = [GR_Table_Ptr1] // Load P_1 for EXPL_SMALL path - fma.s1 FR_N = FR_X, FR_INV_LN2_2TO63, FR_RSHF_2TO51 - nop.i 999 -} -{ .mfb - nop.m 999 - fms.s1 FR_P_lo= FR_Input_Y, FR_logx_hi, FR_P_hi // P_hi is X -(p6) br.cond.spnt POWL_Y_ALMOST_1 // Branch if |y-1| < 2^-50 -} -;; - { .mmi - getf.exp GR_Expo_X = FR_X - add GR_T1_ptr = 0x0b0, GR_table_base // Constants_exp_64_T1 - add GR_T2_ptr = 0x1b0, GR_table_base // Constants_exp_64_T2 + ld8 GR_Table_Ptr = [GR_Table_Ptr] + ld8 GR_T2_ptr = [GR_T2_ptr] + nop.i 999 } ;; -// float_N = round_int(N) -// The signficand of N 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_fix. - -// Since N 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 - add GR_Table_Ptr = 0x20, GR_table_base // Constants_exp_64_A - fms.s1 FR_float_N = FR_N, FR_2TOM51, FR_RSHF // Form float_N - nop.i 999 -} -// Create low part of Y(ln(x)_hi + ln(x)_lo) as P_lo -{ .mfi - mov GR_Big_Pos_Exp = 0x3ffe // 16382, largest safe exponent - fadd.s1 FR_P_lo = FR_P_lo, FR_X_lo - mov GR_Big_Neg_Exp = -0x3ffd // -16381 smallest safe exponent -};; - -{ .mfi - nop.m 999 - fmpy.s1 FR_rsq = FR_X, FR_X // rsq = X*X for EXPL_SMALL path - mov GR_vsm_expo = -70 // Exponent for very small path +{ .mmi +(p0) shladd GR_Table_Ptr = GR_Expo_Range,4,GR_Table_Ptr ;; +// +// Adjust T1_ptr by x 4 for single-precision values +// Adjust T2_ptr by x 4 for single-precision values +// +(p0) ld8 GR_Big_Pos_Exp = [GR_Table_Ptr],8 + nop.i 999 ;; } +// +// Load double W1 +// Load +max exponent +// { .mfi - nop.m 999 - fma.s1 FR_poly_lo = FR_P_6, FR_X, FR_P_5 // poly_lo for EXPL_SMALL path - add GR_temp = 0x1,r0 // For tiny signif if small path +(p0) ld8 GR_Big_Neg_Exp = [GR_Table_Ptr],0 +// +// If 14 < Expo_X, goto exp_huge +// +(p0) fcvt.xf FR_float_N = FR_N + nop.i 999 } ;; // -// If expo_X < -6 goto exp_small +// Load double W2 +// Load -max exponent +// Load ptr to A's // + { .mmi - getf.sig GR_N_fix = FR_N - ldfe FR_A_3 = [GR_Table_Ptr],16 // Load A_3 - and GR_Expo_X = GR_Expo_X, GR_exp_mask // Get exponent of X +(p0) getf.sig GR_N_fix = FR_N +(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_A#), gp + nop.i 999 } ;; -{ .mfi - ldfe FR_A_2 = [GR_Table_Ptr],16 // Load A_2 - nop.f 999 - sub GR_Expo_X = GR_Expo_X, GR_exp_bias // Get true exponent of X +{ .mmi + ld8 GR_Table_Ptr = [GR_Table_Ptr] + nop.m 999 + nop.i 999 } ;; // -// If -6 > Expo_X, set P9 and branch +// Load single T1 +// Load single T2 +// W_1_p1 = W_1 + 1 // -{ .mfb - cmp.gt p9, p0 = -6, GR_Expo_X - fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_X // r = X - L_hi * float_N -(p9) br.cond.spnt EXPL_SMALL // Branch if |X| < 2^-6 +{ .mmi +(p0) ldfe FR_A_3 = [GR_Table_Ptr],16 ;; +// +// Load A_3 +// if k > big_pos_exp, set p14 and Safe=False +// +(p0) ldfe FR_A_2 = [GR_Table_Ptr],16 +(p0) extr.u GR_M1 = GR_N_fix, 6, 6 } -;; - +{ .mmi + nop.m 999 ;; +(p0) shladd GR_W1_ptr = GR_M1,3,GR_W1_ptr // -// If 14 <= Expo_X, set P10 +// float_N = fcvt.xf(N) +// N_fix = significand of N +// Create pointer to T2 table // -{ .mib - cmp.le p10, p0 = 14, GR_Expo_X - nop.i 999 -(p10) br.cond.spnt EXPL_HUGE // Branch if |X| >= 2^14 +(p0) extr.u GR_M2 = GR_N_fix, 0, 6 } -;; - // -// Load single T1 -// Load single T2 -// W_1_p1 = W_1 + 1 +// r = r + X_cor +// Adjust W1_ptr by x 8 for double-precision values +// Adjust W2_ptr by x 8 for double-precision values +// Adjust Table_ptr by Expo_Rangex16 // { .mmi - nop.m 999 - nop.m 999 - extr.u GR_M1 = GR_N_fix, 6, 6 // Extract index M_1 +(p0) shladd GR_T1_ptr = GR_M1,2,GR_T1_ptr ;; +(p0) ldfd FR_W1 = [GR_W1_ptr],0 +(p0) shladd GR_W2_ptr = GR_M2,3,GR_W2_ptr } -;; - // -// k = extr.u(N_fix,0,6) +// Load ptr to A's // -{ .mmi - shladd GR_W1_ptr = GR_M1,3,GR_W1_ptr // Point to W1 - shladd GR_T1_ptr = GR_M1,2,GR_T1_ptr // Point to T1 - extr.u GR_M2 = GR_N_fix, 0, 6 // Extract index M_2 +{ .mfi +(p0) ldfs FR_T1 = [GR_T1_ptr],0 +(p0) fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_X +(p0) shladd GR_T2_ptr = GR_M2,2,GR_T2_ptr ;; } -;; - -// 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. { .mmi - ldfd FR_W1 = [GR_W1_ptr] - shladd GR_W2_ptr = GR_M2,3,GR_W2_ptr // Point to W2 - extr GR_k = GR_N_fix, 12, 32 // Extract k +(p0) ldfd FR_W2 = [GR_W2_ptr],0 +(p0) ldfs FR_T2 = [GR_T2_ptr],0 +// +// r = x - L_hi * float_N +// M2 = extr.u(N_fix,0,6) +// M1 = extr.u(N_fix,6,6) +// +(p0) extr GR_k = GR_N_fix, 12, 52 ;; } -;; - +// +// Load A_1 +// poly = A_3 * r + A_2 +// rsq = r*r +// +{ .mii +(p0) add GR_BIAS_p_k = GR_BIAS, GR_k +(p0) cmp.gt.unc p14,p15 = GR_k,GR_Big_Pos_Exp ;; +(p15) cmp.lt p14,p15 = GR_k,GR_Big_Neg_Exp +} +// +// BIAS_p_K = BIAS + k +// T = T1 * T2 +// { .mfi - ldfs FR_T1 = [GR_T1_ptr] - fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r - shladd GR_T2_ptr = GR_M2,2,GR_T2_ptr // Point to T2 +(p0) setf.exp FR_Scale = GR_BIAS_p_k + nop.f 999 + nop.i 999 ;; } { .mfi - add GR_exp_bias_p_k = GR_exp_bias, GR_k - nop.f 999 - cmp.gt p14,p15 = GR_k,GR_Big_Pos_Exp + nop.m 999 +(p0) fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r + nop.i 999 } -;; - // -// if k < big_neg_exp, set p14 and Safe=False +// W = W_1_p1 * W2 + W1 // -{ .mmi - ldfs FR_T2 = [GR_T2_ptr] -(p15) cmp.lt p14,p15 = GR_k,GR_Big_Neg_Exp - nop.i 999 +{ .mfi +(p0) ldfe FR_A_1 = [GR_Table_Ptr],16 + nop.f 999 + nop.i 999 ;; } -;; - -{ .mmi - setf.exp FR_Scale = GR_exp_bias_p_k - ldfd FR_W2 = [GR_W2_ptr] - nop.i 999 +{ .mfi + nop.m 999 +(p0) fadd.s1 FR_W_1_p1 = FR_W1, f1 + nop.i 999 ;; } -;; - { .mfi - ldfe FR_A_1 = [GR_Table_Ptr],16 - fadd.s1 FR_r = FR_r, FR_X_cor - nop.i 999 + nop.m 999 +// +// k = extr.u(N_fix,0,6) +// r = r - N * L_lo +// Load ptr to Table of exponent thresholds. +// +(p0) fadd.s1 FR_r = FR_r, FR_X_cor + nop.i 999 } -;; - { .mfi - nop.m 999 - fadd.s1 FR_W_1_p1 = FR_W1, f1 - nop.i 999 + nop.m 999 +(p0) fmpy.s1 FR_T = FR_T1, FR_T2 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fma.s1 FR_poly = FR_r, FR_A_3, FR_A_2 - nop.i 999 + nop.m 999 +// +// if k < big_neg_exp, set p14 and Safe=False +// Load A_2 +// +(p0) fma.s1 FR_W = FR_W2, FR_W_1_p1, FR_W1 + nop.i 999 ;; } { .mfi - nop.m 999 - fmpy.s1 FR_rsq = FR_r, FR_r - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_poly = FR_r, FR_A_3, FR_A_2 + nop.i 999 } -;; - { .mfi - nop.m 999 - fmpy.s1 FR_T = FR_T1, FR_T2 - nop.i 999 + nop.m 999 +(p0) fmpy.s1 FR_rsq = FR_r, FR_r + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fma.s1 FR_W = FR_W2, FR_W_1_p1, FR_W1 - nop.i 999 + nop.m 999 +(p0) mov FR_Y_hi = FR_T + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fma.s1 FR_TMP1 = FR_Scale, FR_Sgn, f0 - nop.i 999 + nop.m 999 +// +// Scale = set_exp(BIAS_p_k) +// poly = r * poly + A_1 +// +(p0) fadd.s1 FR_Wp1 = FR_W, f1 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fma.s1 FR_poly = FR_r, FR_poly, FR_A_1 - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_poly = FR_r, FR_poly, FR_A_1 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fma.s1 FR_TMP2 = FR_T, f1, f0 // TMP2 = Y_hi = T - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_poly = FR_rsq, FR_poly,FR_r + nop.i 999 ;; } -;; - { .mfi + nop.m 999 +// +// Wp1 = W + 1 +// poly = rsq * poly + rk +// +(p0) fma.s1 FR_Y_lo = FR_Wp1, FR_poly, FR_W + nop.i 999 ;; +} +{ .mfb + nop.m 999 +// +// Y_lo = poly * Wp1 + W +// Y_hi = T +// +(p0) fmpy.s1 FR_Y_lo = FR_Y_lo, FR_T +// +// Y_lo = T * Y_lo +// +(p0) br.cond.sptk L(EXPL_RETURN) ;; +} + +L(EXPL_SMALL): + +// +// r4 = rsq * rsq +// + +{ .mmi nop.m 999 - fadd.s1 FR_Wp1 = FR_W, f1 +(p0) addl GR_Table_Ptr1 = @ltoff(Constants_exp_64_P), gp nop.i 999 } ;; -{ .mfi +{ .mmi + ld8 GR_Table_Ptr1 = [GR_Table_Ptr1] nop.m 999 - fma.s1 FR_poly = FR_rsq, FR_poly,FR_r nop.i 999 } ;; -{ .mfi - nop.m 999 - fma.s1 FR_Tscale = FR_T, FR_TMP1, f0 // Scale * Sgn * T - nop.i 999 +{ .mmf + nop.m 999 +(p0) ldfe FR_P_6 = [GR_Table_Ptr1],16 +// +// Return +// +(p0) fadd.s1 FR_r = FR_X,f0 ;; } -{ .mfi + +{ .mmi nop.m 999 - fma.s1 FR_Y_lo = FR_Wp1, FR_poly, FR_W +(p0) addl GR_Table_Ptr = @ltoff(Constants_exp_64_Exponents#), gp nop.i 999 } ;; -{ .mfb - nop.m 999 - fmpy.s1 FR_TMP3 = FR_Y_lo, FR_Tscale - br.cond.sptk POWL_64_SHARED +{ .mmi + ld8 GR_Table_Ptr = [GR_Table_Ptr] +(p0) ldfe FR_P_5 = [GR_Table_Ptr1],16 + nop.i 999 } ;; - -EXPL_SMALL: -// Here if |ylogx| < 2^-6 // -// Begin creating lsb to perturb final result +// Is input very small? +// Load P_5 +// +{ .mii +(p0) ldfe FR_P_4 = [GR_Table_Ptr1],16 +(p0) add GR_Table_Ptr = 0x040,GR_Table_Ptr ;; +(p0) shladd GR_Table_Ptr = GR_Expo_Range,3,GR_Table_Ptr ;; +} +{ .mmb +(p0) ldfe FR_P_3 = [GR_Table_Ptr1],16 // +// Adjust ptr. +// +(p0) ld8 GR_vsm_expo = [GR_Table_Ptr],0 + nop.b 999 ;; +} { .mfi - setf.sig FR_temp = GR_temp - fma.s1 FR_poly_lo = FR_poly_lo, FR_X, FR_P_4 - cmp.lt p12, p0 = GR_Expo_X, GR_vsm_expo // Test |ylogx| < 2^-70 + nop.m 999 +// +// r = X (don't seem to need X_Cor) +// Load the threshold exponents +// +(p0) fmpy.s1 FR_rsq = FR_r, FR_r + nop.i 999 ;; } +// +// Load the negative integer +// Load P_5 +// { .mfi - nop.m 999 - fma.s1 FR_poly_hi = FR_P_2, FR_X, FR_P_1 - nop.i 999 +(p0) cmp.lt.unc p12, p0 = GR_Expo_X, GR_vsm_expo + nop.f 999 + nop.i 999 ;; +} +{ .mfb + nop.m 999 +// +// rsq = r * r +// Offset into exponents +// +(p0) fmpy.s1 FR_r4 = FR_rsq, FR_rsq +(p12) br.cond.spnt L(EXPL_VERY_SMALL) ;; } -;; - { .mfi - nop.m 999 - fmpy.s1 FR_TMP2 = f1, f1 - nop.i 999 +(p0) ldfe FR_P_2 = [GR_Table_Ptr1],16 +// +// Load p4,p3,p2,p1 +// +(p0) fma.s1 FR_poly_lo = FR_P_6, FR_r, FR_P_5 +// +// Y_lo = r4 * poly_lo + poly_hi +// Scale = 1.0 +// +(p0) add GR_temp = 0x1,r0 ;; } +{ .mmf + nop.m 999 +(p0) ldfe FR_P_1 = [GR_Table_Ptr1],0 +(p0) mov FR_Scale = f1 +} +// +// Begin creating lsb to perturb final result +// { .mfi - nop.m 999 - fmpy.s1 FR_TMP1 = FR_Sgn, f1 - nop.i 999 +(p0) setf.sig FR_temp = GR_temp +(p0) mov FR_Y_hi = f1 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fmpy.s1 FR_r4 = FR_rsq, FR_rsq -(p12) cmp.eq p15, p0 = r0, r0 // Set safe if |ylogx| < 2^-70 + nop.m 999 +// +// poly_lo = p_5 + p_6 * r +// poly_hi = p_1 + p_2 * r +// +(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_P_4 + nop.i 999 ;; } -{ .mfb - nop.m 999 -(p12) fmpy.s1 FR_TMP3 = FR_Sgn, FR_X -(p12) br.cond.spnt POWL_64_SHARED // Branch if |ylogx| < 2^-70 +{ .mfi + nop.m 999 +// +// poly_lo = p_4 + poly_lo * r +// poly_hi = r + poly_hi * rsq +// +(p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_P_3 + nop.i 999 } -;; - { .mfi - nop.m 999 - fma.s1 FR_poly_lo = FR_poly_lo, FR_X, FR_P_3 - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_poly_hi = FR_P_2, FR_r, FR_P_1 + nop.i 999 ;; } { .mfi - nop.m 999 - fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, FR_X - nop.i 999 + nop.m 999 +(p0) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, FR_r + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fma.s1 FR_Y_lo = FR_poly_lo, FR_r4, FR_poly_hi - nop.i 999 + nop.m 999 +// +// poly_lo = p_3 + poly_lo * r +// Y_hi = 1, always +// +(p0) fma.s1 FR_Y_lo = FR_poly_lo, FR_r4, FR_poly_hi + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fmpy.s1 FR_TMP3 = FR_Y_lo, FR_TMP1 // Add sign info - nop.i 999 + nop.m 999 +// +// Set lsb in fp register +// +(p0) for FR_temp = FR_Y_lo,FR_temp + nop.i 999 ;; } -;; - +{ .mfb + nop.m 999 // // Toggle on last bit of Y_lo +// +(p0) fmerge.se FR_Y_lo = FR_Y_lo,FR_temp +// // Set lsb of Y_lo to 1 // +(p0) br.cond.sptk L(EXPL_RETURN) ;; +} +L(EXPL_VERY_SMALL): { .mfi - nop.m 999 - for FR_temp = FR_Y_lo,FR_temp - nop.i 999 + nop.m 999 +(p0) mov FR_Y_lo = FR_r +(p0) cmp.eq.unc p15, p0 = r0, r0 } -;; - +{ .mfi + nop.m 999 +(p0) mov FR_Scale = f1 + nop.i 999 +};; { .mfb - nop.m 999 - fmerge.se FR_TMP3 = FR_TMP3,FR_temp - br.cond.sptk POWL_64_SHARED + nop.m 999 +(p0) mov FR_Y_hi = f1 +// +// If flag_not_1, +// Y_hi = 1.0 +// Y_lo = X + X_cor +// PR_Safe = true +// +(p0) br.cond.sptk L(EXPL_RETURN) ;; } -;; - - -EXPL_HUGE: -// Here if |ylogx| >= 2^14 +L(EXPL_HUGE): { .mfi - mov GR_temp = 0x0A1DC // If X < 0, exponent -24100 - fcmp.gt.s1 p12, p13 = FR_X, f0 // Test X > 0 - cmp.eq p14, p15 = r0, r0 // Set Safe to false + nop.m 999 +// +// Return for flag=2 +// +(p0) fcmp.gt.unc.s1 p12, p13 = FR_X, f0 +(p0) cmp.eq.unc p14, p15 = r0, r0 ;; } -;; - -{ .mmi -(p12) mov GR_Mask = 0x15DC0 // If X > 0, exponent +24000 -(p13) mov GR_Mask = 0x0A240 // If X < 0, exponent -24000 - nop.i 999 +{ .mlx + nop.m 999 +// +// Set Safe to false +// Is x > 0 +// +(p12) movl GR_Mask = 0x15DC0 ;; } -;; - -{ .mmf - setf.exp FR_TMP2 = GR_Mask // Form Y_hi = TMP2 -(p13) setf.exp FR_Y_lo = GR_temp // If X < 0, Y_lo = 2^-24100 -(p12) mov FR_Y_lo = f1 // IF X > 0, Y_lo = 1.0 +{ .mlx +(p12) setf.exp FR_Y_hi = GR_Mask +(p13) movl GR_Mask = 0xA240 ;; +} +{ .mlx +(p13) setf.exp FR_Y_hi = GR_Mask +// +// x > 0: Create mask for Y_hi = 2**(24,000) +// x <= 0: Create mask for Y_hi = 2**(-24,000) +// +(p13) movl GR_temp = 0xA1DC ;; } -;; - { .mfi - nop.m 999 - fmpy.s1 FR_TMP1 = FR_TMP2, FR_Sgn // TMP1 = Y_hi * Sgn - nop.i 999 +(p13) setf.exp FR_Y_lo = GR_temp +// +// x < =0: Create mask for 2**(-24,100) +// x <= 0: Y_lo = w**(-24,100) +// +(p12) mov FR_Y_lo = f1 + nop.i 999 ;; } -;; - -{ .mfb - nop.m 999 - fmpy.s1 FR_TMP3 = FR_Y_lo,FR_TMP1 // TMP3 = Y_lo * (Y_hi * Sgn) - br.cond.sptk POWL_64_SHARED +{ .mfi + nop.m 999 +(p12) mov FR_Scale = FR_Y_hi + nop.i 999 ;; } -;; - -POWL_Y_ALMOST_1: -// Here if delta = |y-1| < 2^-50 +{ .mfi + nop.m 999 // -// x**(1 + delta) = x * e (ln(x)*delta) = x ( 1 + ln(x) * delta) +// x > 0: Y_lo = 1.0 +// x > 0: Scale = 2**(24,000) // -// Computation will be safe for 2^-16381 <= x < 2^16383 - +(p13) mov FR_Scale = FR_Y_hi + nop.i 999 ;; +} +L(EXPL_RETURN): { .mfi - mov GR_exp_ynear1_oflow = 0xffff + 16383 - fma.s1 FR_TMP1 = FR_Input_X,FR_Delta,f0 - and GR_exp_x = GR_exp_mask, GR_signexp_x + nop.m 999 +// +// Scale = 2**(24,000) +// +// +// exp(y *ln(x)) almost complete +// FR_Scale is Scale +// f34 is Z_hi +// f35 is Z_lo +// +(p0) fmpy.s1 FR_Sgn = FR_Scale, FR_Sgn + nop.i 999 ;; } -;; - { .mfi - cmp.lt p15, p14 = GR_exp_x, GR_exp_ynear1_oflow - fma.s1 FR_TMP2 = FR_logx_hi,f1,FR_X_lo - mov GR_exp_ynear1_uflow = 0xffff - 16381 + nop.m 999 +// +// sgn * scale +// +(p0) fmpy.s1 FR_Y_lo = FR_Y_lo,FR_Sgn + nop.i 999 ;; } -;; - { .mfb -(p15) cmp.ge p15, p14 = GR_exp_x, GR_exp_ynear1_uflow - fma.s1 FR_TMP3 = FR_Input_X,f1,f0 - br.cond.sptk POWL_64_SHARED -};; - -POWL_64_SQUARE: + nop.m 999 +// +// Z_lo * (sgn * scale) // -// Here if x not zero and y=2. +(p0) fma.s0 FR_Result = FR_Y_hi, FR_Sgn, FR_Y_lo // -// Setup for multipath code +// Z_hi * (sgn * scale) + Z_lo // +(p15) br.cond.sptk L(POWL_64_RETURN) ;; +} { .mfi - mov GR_exp_square_oflow = 0xffff + 8192 // Exponent where x*x overflows - fmerge.se FR_TMP1 = FR_Input_X, FR_Input_X - and GR_exp_x = GR_exp_mask, GR_signexp_x // Get exponent of x + nop.m 999 +(p0) fsetc.s3 0x7F,0x01 + nop.i 999 +} +{ .mlx + nop.m 999 +// +// Z_hi * (sgn * scale) + Z_lo with wre & td +// Z_hi * (sgn * scale) + Z_lo with fz & td +// +(p0) movl GR_T1_ptr = 0x00000000013FFF ;; } -;; - { .mfi - cmp.lt p15, p14 = GR_exp_x, GR_exp_square_oflow // Decide safe/unsafe - fmerge.se FR_TMP2 = FR_Input_X, FR_Input_X - mov GR_exp_square_uflow = 0xffff - 8191 // Exponent where x*x underflows + nop.m 999 +(p0) fma.s3 FR_Result_small = FR_Y_hi, FR_Sgn, FR_Y_lo + nop.i 999 } -;; - { .mfi -(p15) cmp.ge p15, p14 = GR_exp_x, GR_exp_square_uflow // Decide safe/unsafe - fma.s1 FR_TMP3 = f0,f0,f0 - nop.i 999 + nop.m 999 +(p0) fsetc.s3 0x7F,0x40 + nop.i 999 ;; } -;; - +{ .mfi + nop.m 999 // -// This is the shared path that will set overflow and underflow. +// Return if no danger of over of underflow. // -POWL_64_SHARED: - +(p0) fsetc.s2 0x7F,0x42 + nop.i 999;; +} +{ .mfi + nop.m 999 // -// Return if no danger of over or underflow. +// S0 user supplied status +// S2 user supplied status + WRE + TD (Overflows) +// S3 user supplied status + FZ + TD (Underflows) // -{ .mfb - nop.m 999 - fma.s0 FR_Result = FR_TMP1, FR_TMP2, FR_TMP3 -(p15) br.ret.sptk b0 // Main path return if certain no over/underflow +(p0) fma.s2 FR_Result_big = FR_Y_hi, FR_Sgn, FR_Y_lo + nop.i 999 ;; } -;; - // -// S0 user supplied status -// S2 user supplied status + WRE + TD (Overflows) -// S2 user supplied status + FZ + TD (Underflows) +// S0 user supplied status +// S2 user supplied status + WRE + TD (Overflows) +// S3 user supplied status + FZ + TD (Underflows) // // // If (Safe) is true, then @@ -2022,742 +2430,973 @@ POWL_64_SHARED: // No overflow or underflow here, but perhaps inexact. // Return // Else -// Determine if overflow or underflow was raised. -// Fetch +/- overflow threshold for IEEE double extended - +// Determine if overflow or underflow was raised. +// Fetch +/- overflow threshold for IEEE single, double, +// double extended +// { .mfi - nop.m 999 - fsetc.s2 0x7F,0x41 // For underflow test, set S2=User+TD+FTZ - nop.i 999 +(p0) setf.exp FR_Big = GR_T1_ptr +(p0) fsetc.s2 0x7F,0x40 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fma.s2 FR_Result_small = FR_TMP1, FR_TMP2, FR_TMP3 - nop.i 999 + nop.m 999 +(p0) fclass.m.unc p11, p0 = FR_Result_small, 0x00F + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fsetc.s2 0x7F,0x42 // For overflow test, set S2=User+TD+WRE - nop.i 999 + nop.m 999 +(p0) fmerge.ns FR_NBig = FR_Big, FR_Big + nop.i 999 } -;; - { .mfi - nop.m 999 - fma.s2 FR_Result_big = FR_TMP1, FR_TMP2,FR_TMP3 - nop.i 999 + nop.m 999 +// +// Create largest double exponent + 1. +// Create smallest double exponent - 1. +// Identify denormals +// +(p0) fcmp.ge.unc.s1 p8, p0 = FR_Result_big , FR_Big + nop.i 999 ;; +} +{ .mii + nop.m 999 + nop.i 999 ;; +// +// fcmp: resultS2 <= - overflow threshold +// fclass: resultS3 is denorm/unorm/0 +// +(p8) mov GR_Parameter_TAG = 18 ;; +} +{ .mfb + nop.m 999 +// +// fcmp: resultS2 >= + overflow threshold +// +(p0) fcmp.le.unc.s1 p9, p0 = FR_Result_big, FR_NBig +(p8) br.cond.spnt __libm_error_region ;; +} +{ .mii + nop.m 999 + nop.i 999 ;; +(p9) mov GR_Parameter_TAG = 18 +} +{ .mib + nop.m 999 + nop.i 999 +(p9) br.cond.spnt __libm_error_region ;; +} +// +// Report that pow overflowed - either +Inf, or -Inf +// +{ .mmb +(p11) mov GR_Parameter_TAG = 19 + nop.m 999 +(p11) br.cond.spnt __libm_error_region ;; +} +{ .mib + nop.m 999 + nop.i 999 +// +// Report that pow underflowed +// +(p0) br.cond.sptk L(POWL_64_RETURN) ;; } -;; + +L(POWL_64_SQUARE): +// Here if x not zero and y=2. +// Must call __libm_error_support for overflow or underflow +// +// S0 user supplied status +// S2 user supplied status + WRE + TD (Overflows) +// S3 user supplied status + FZ + TD (Underflows) +// { .mfi - nop.m 999 - fsetc.s2 0x7F,0x40 // Reset S2=User - nop.i 999 + nop.m 999 +(p0) fma.s0 FR_Result = FR_Input_X, FR_Input_X, f0 + nop.i 999 } -;; - { .mfi - nop.m 999 - fclass.m p11, p0 = FR_Result_small, 0x00F // Test small result unorm/zero - nop.i 999 + nop.m 999 +(p0) fsetc.s3 0x7F,0x01 + nop.i 999 +} +{ .mlx + nop.m 999 +(p0) movl GR_T1_ptr = 0x00000000013FFF ;; } -;; - { .mfi - nop.m 999 - fcmp.ge.s1 p8, p0 = FR_Result_big , FR_Big // Test >= + oflow threshold - nop.i 999 + nop.m 999 +(p0) fma.s3 FR_Result_small = FR_Input_X, FR_Input_X, f0 + nop.i 999 } -;; - -{ .mfb -(p11) mov GR_Parameter_TAG = 19 // Set tag for underflow - fcmp.le.s1 p9, p0 = FR_Result_big, FR_NBig // Test <= - oflow threshold -(p11) br.cond.spnt __libm_error_region // Branch if pow underflowed +{ .mfi + nop.m 999 +(p0) fsetc.s3 0x7F,0x40 + nop.i 999 ;; +} +{ .mfi + nop.m 999 +// +// Return if no danger of over of underflow. +// +(p0) fsetc.s2 0x7F,0x42 + nop.i 999;; +} +{ .mfi + nop.m 999 +(p0) fma.s2 FR_Result_big = FR_Input_X, FR_Input_X, f0 + nop.i 999 ;; +} +// +// S0 user supplied status +// S2 user supplied status + WRE + TD (Overflows) +// S3 user supplied status + FZ + TD (Underflows) +// +// +// If (Safe) is true, then +// Compute result using user supplied status field. +// No overflow or underflow here, but perhaps inexact. +// Return +// Else +// Determine if overflow or underflow was raised. +// Fetch +/- overflow threshold for IEEE single, double, +// double extended +// +{ .mfi +(p0) setf.exp FR_Big = GR_T1_ptr +(p0) fsetc.s2 0x7F,0x40 + nop.i 999 ;; +} +{ .mfi + nop.m 999 +(p0) fclass.m.unc p11, p0 = FR_Result_small, 0x00F + nop.i 999 ;; +} +{ .mfi + nop.m 999 +(p0) fmerge.ns FR_NBig = FR_Big, FR_Big + nop.i 999 +} +{ .mfi + nop.m 999 +// +// Create largest double exponent + 1. +// Create smallest double exponent - 1. +// Identify denormals +// +(p0) fcmp.ge.unc.s1 p8, p0 = FR_Result_big , FR_Big + nop.i 999 ;; +} +{ .mii + nop.m 999 + nop.i 999 ;; +// +// fcmp: resultS2 <= - overflow threshold +// fclass: resultS3 is denorm/unorm/0 +// +(p8) mov GR_Parameter_TAG = 18 ;; } -;; - { .mfb -(p8) mov GR_Parameter_TAG = 18 // Set tag for overflow - nop.f 999 -(p8) br.cond.spnt __libm_error_region // Branch if pow +overflow + nop.m 999 +// +// fcmp: resultS2 >= + overflow threshold +// +(p0) fcmp.le.unc.s1 p9, p0 = FR_Result_big, FR_NBig +(p8) br.cond.spnt __libm_error_region ;; } -;; - -{ .mbb -(p9) mov GR_Parameter_TAG = 18 // Set tag for overflow -(p9) br.cond.spnt __libm_error_region // Branch if pow -overflow - br.ret.sptk b0 // Branch if result really ok +{ .mii + nop.m 999 + nop.i 999 ;; +(p9) mov GR_Parameter_TAG = 18 } -;; +{ .mib + nop.m 999 + nop.i 999 +(p9) br.cond.spnt __libm_error_region ;; +} +// +// Report that pow overflowed - either +Inf, or -Inf +// +{ .mmb +(p11) mov GR_Parameter_TAG = 19 + nop.m 999 +(p11) br.cond.spnt __libm_error_region ;; +} +{ .mib + nop.m 999 + nop.i 999 +// +// Report that pow underflowed +// +(p0) br.cond.sptk L(POWL_64_RETURN) ;; +} + -POWL_64_SPECIAL: -// Here if x or y is NatVal, nan, inf, or zero + +L(POWL_64_SPECIAL): { .mfi - nop.m 999 - fcmp.eq.s1 p15, p0 = FR_Input_X, f1 // Test x=+1 - nop.i 999 + nop.m 999 +(p0) fcmp.eq.s1 p15, p0 = FR_Input_X, f1 // Is x=+1 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fclass.m p8, p0 = FR_Input_X, 0x143 // Test x natval, snan - nop.i 999 + nop.m 999 +(p0) fclass.m.unc p14, p0 = FR_Input_Y, 0x023 + nop.i 999 ;; } -;; { .mfi - nop.m 999 -(p15) fcmp.eq.unc.s0 p6,p0 = FR_Input_Y, f0 // If x=1, flag invalid if y=SNaN - nop.i 999 + nop.m 999 +(p15) fcmp.eq.unc.s0 p6,p0 = FR_Input_Y, f0 // If x=1, flag invalid if y=SNaN + nop.i 999 } { .mfb - nop.m 999 -(p15) fmpy.s0 FR_Result = f1,f1 // If x=1, result=1 -(p15) br.ret.spnt b0 // Exit if x=1 + nop.m 999 +(p15) fmpy.s0 FR_Result = f1,f1 // If x=1, result=1 +(p15) br.cond.spnt L(POWL_64_RETURN) ;; // Exit if x=1 } -;; { .mfi - nop.m 999 - fclass.m p6, p0 = FR_Input_Y, 0x007 // Test y zero - nop.i 999 + nop.m 999 +(p0) fclass.m.unc p13, p0 = FR_Input_X, 0x023 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fclass.m p9, p0 = FR_Input_Y, 0x143 // Test y natval, snan - nop.i 999 + nop.m 999 +(p0) fclass.m.unc p8, p0 = FR_Input_X, 0x143 + nop.i 999 } -;; - { .mfi - nop.m 999 - fclass.m p10, p0 = FR_Input_X, 0x083 // Test x qnan - nop.i 999 + nop.m 999 +(p0) fclass.m.unc p9, p0 = FR_Input_Y, 0x143 + nop.i 999 ;; } { .mfi - nop.m 999 -(p8) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X // If x=snan, result=qnan -(p6) cmp.ne p8,p0 = r0,r0 // Don't exit if x=snan, y=0 ==> result=+1 + nop.m 999 +(p0) fclass.m.unc p10, p0 = FR_Input_X, 0x083 + nop.i 999 } -;; - { .mfi - nop.m 999 -(p6) fclass.m.unc p15, p0 = FR_Input_X,0x007 // Test x=0, y=0 - nop.i 999 + nop.m 999 +(p0) fclass.m.unc p11, p0 = FR_Input_Y, 0x083 + nop.i 999 ;; } -{ .mfb - nop.m 999 -(p9) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X // If y=snan, result=qnan -(p8) br.ret.spnt b0 // Exit if x=snan, y not 0, - // result=qnan +{ .mfi + nop.m 999 +(p0) fclass.m.unc p6, p0 = FR_Input_Y, 0x007 + nop.i 999 } -;; - { .mfi - nop.m 999 - fcmp.eq.s1 p7, p0 = FR_Input_Y, f1 // Test y +1.0 - nop.i 999 + nop.m 999 +(p0) fcmp.eq.unc.s1 p7, p0 = FR_Input_Y, f1 + nop.i 999 ;; +} +{ .mfi + nop.m 999 +// +// set p13 if x +/- Inf +// set p14 if y +/- Inf +// set p8 if x Natval or +/-SNaN +// set p9 if y Natval or +/-SNaN +// set p10 if x QNaN +// set p11 if y QNaNs +// set p6 if y is +/-0 +// set p7 if y is 1 +// +(p8) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X +(p6) cmp.ne p8,p0 = r0,r0 ;; // Don't exit if x=snan, y=0 ==> result=+1 } { .mfb - nop.m 999 -(p10) fmpy.s0 FR_Result = FR_Input_X, f0 // If x=qnan, result=qnan -(p9) br.ret.spnt b0 // Exit if y=snan, result=qnan + nop.m 999 +(p9) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X +(p8) br.cond.spnt L(POWL_64_RETURN) ;; +} +{ .mfb + nop.m 999 +(p10) fmpy.s0 FR_Result = FR_Input_X, f0 +(p9) br.cond.spnt L(POWL_64_RETURN) ;; } -;; - { .mfi - nop.m 999 -(p6) fclass.m.unc p8, p0 = FR_Input_X,0x0C3 // Test x=nan, y=0 - nop.i 999 + nop.m 999 +// +// Produce result for SNaN and NatVals and return +// +(p6) fclass.m.unc p15, p0 = FR_Input_X,0x007 + nop.i 999 +} +{ .mfi + nop.m 999 +// +// If Y +/- 0, set p15 if x +/- 0 +// +(p6) fclass.m.unc p8, p0 = FR_Input_X,0x0C3 + nop.i 999 ;; } -;; { .mfi - nop.m 999 -(p6) fcmp.eq.s0 p9,p0 = FR_Input_X, f0 // If y=0, flag if x denormal - nop.i 999 + nop.m 999 +(p6) fcmp.eq.s0 p9,p0 = FR_Input_X, f0 // If y=0, flag if x denormal + nop.i 999 } { .mfi - nop.m 999 -(p6) fadd.s0 FR_Result = f1, f0 // If y=0, result=1 - nop.i 999 + nop.m 999 +(p6) fadd.s0 FR_Result = f1, f0 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fclass.m p11, p0 = FR_Input_Y, 0x083 // Test y qnan - nop.i 999 + nop.m 999 +// +// Set p8 if y = +/-0 and X is a QNaN/SNaN +// If y = +/-0, let result = 1.0 +// +(p7) fmpy.s0 FR_Result = FR_Input_X,f1 +// +// If y == 1, result = x * 1 +// +(p15) mov GR_Parameter_TAG = 20 } -{ .mfb -(p15) mov GR_Parameter_TAG = 20 // Error tag for x=0, y=0 -(p7) fmpy.s0 FR_Result = FR_Input_X,f1 // If y=1, result=x -(p15) br.cond.spnt __libm_error_region // Branch if x=0, y=0, result=1 +{ .mib + nop.m 999 + nop.i 999 +(p15) br.cond.spnt __libm_error_region ;; } -;; - -{ .mfb -(p8) mov GR_Parameter_TAG = 23 // Error tag for x=nan, y=0 - fclass.m p14, p0 = FR_Input_Y, 0x023 // Test y inf -(p8) br.cond.spnt __libm_error_region // Branch if x=snan, y=0, - // result=1 +{ .mib + nop.m 999 +// +// If x and y are both zero, result = 1.0 and call error +// support. +// +(p8) mov GR_Parameter_TAG = 23 +(p8) br.cond.spnt __libm_error_region ;; } -;; - -{ .mfb - nop.m 999 - fclass.m p13, p0 = FR_Input_X, 0x023 // Test x inf -(p6) br.ret.spnt b0 // Exit y=0, x not nan or 0, - // result=1 +{ .mib + nop.m 999 + nop.i 999 +// +// If y = +/-0 and x is a QNaN, result = 1.0 and call error +// support. +// +(p6) br.cond.spnt L(POWL_64_RETURN) ;; } -;; +// If x=0, y=-inf, go to the X_IS_ZERO path { .mfb - nop.m 999 -(p14) fcmp.eq.unc.s1 p0,p14 = FR_Input_X,f0 // Test x not 0, y=inf -(p7) br.ret.spnt b0 // Exit y=1, x not snan, - // result=x + nop.m 999 +(p14) fcmp.eq.unc.s1 p0,p14 = FR_Input_X,f0 +(p7) br.cond.spnt L(POWL_64_RETURN) ;; } -;; -{ .mfb - nop.m 999 -(p10) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X // If x=qnan, y not snan, - // result=qnan -(p10) br.ret.spnt b0 // Exit x=qnan, y not snan, - // result=qnan +{ .mfi + nop.m 999 +// +// Produce all results for x**0 and x**1 +// Let all the result x ** 0 == 1 and return +// Let all x ** 1 == x and return +// +(p10) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X + nop.i 999 ;; } -;; - { .mfb - nop.m 999 -(p11) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X // If y=qnan, x not nan or 1, - // result=qnan -(p11) br.ret.spnt b0 // Exit y=qnan, x not nan or 1, - // result=qnan + nop.m 999 +(p11) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X +(p10) br.cond.spnt L(POWL_64_RETURN) ;; } -;; - -{ .mbb - nop.m 999 -(p14) br.cond.spnt POWL_64_Y_IS_INF // Branch if y=inf, x not 1 or nan -(p13) br.cond.spnt POWL_64_X_IS_INF // Branch if x=inf, y not 1 or nan +{ .mib + nop.m 999 + nop.i 999 +(p11) br.cond.spnt L(POWL_64_RETURN) ;; } -;; - - -POWL_64_X_IS_ZERO: -// Here if x=0, y not nan or 1 or inf or 0 - -// There is logic starting here to determine if y is an integer when x = 0. -// If 0 < |y| < 1 then clearly y is not an integer. -// If |y| > 1, then the significand of y is shifted left by the size of -// the exponent of y. This preserves the lsb of the integer part + the -// fractional bits. The lsb of the integer can be tested to determine if -// the integer is even or odd. The fractional bits can be tested. If zero, -// then y is an integer. +{ .mib + nop.m 999 + nop.i 999 +// +// Return result for x or y QNaN input with QNaN result +// +(p14) br.cond.spnt L(POWL_64_Y_IS_INF) ;; +} +{ .mib + nop.m 999 + nop.i 999 +(p13) br.cond.spnt L(POWL_64_X_IS_INF) ;; +} +L(POWL_64_X_IS_ZERO): +{ .mmb +(p0) getf.sig GR_signif_y = FR_Input_Y +(p0) getf.exp GR_BIASed_exp_y = FR_Input_Y + nop.b 999 ;; +} +{ .mlx + nop.m 999 +(p0) movl GR_Mask = 0x1FFFF +} +{ .mlx + nop.m 999 +(p0) movl GR_y_sign = 0x20000 ;; +} +// +// Get BIASed exp and significand of y // { .mfi - and GR_exp_y = GR_exp_mask,GR_signexp_y // Get biased exponent of y - nop.f 999 - and GR_y_sign = GR_sign_mask,GR_signexp_y // Get sign of y +(p0) and GR_exp_y = GR_Mask,GR_BIASed_exp_y + nop.f 999 +(p0) and GR_y_sign = GR_y_sign,GR_BIASed_exp_y } -;; - +{ .mlx + nop.m 999 +(p0) movl GR_BIAS = 0xFFFF ;; +} +{ .mfi +(p0) cmp.lt.unc p9, p8 = GR_exp_y,GR_BIAS + nop.f 999 // // Maybe y is < 1 already, so // can never be an integer. +// Remove sign bit from exponent. +// +(p0) sub GR_exp_y = GR_exp_y,GR_BIAS ;; +} +{ .mii + nop.m 999 + nop.i 999 ;; +// +// Remove exponent BIAS // +(p8) shl GR_exp_y= GR_signif_y,GR_exp_y ;; +} { .mfi - cmp.lt p9, p8 = GR_exp_y,GR_exp_bias // Test 0 < |y| < 1 - nop.f 999 - sub GR_exp_y = GR_exp_y,GR_exp_bias // Get true exponent of y +(p9) or GR_exp_y= 0xF,GR_signif_y + nop.f 999 + nop.i 999 ;; } -;; - +{ .mii + nop.m 999 // // Shift significand of y looking for nonzero bits // For y > 1, shift signif_y exp_y bits to the left -// For y < 1, turn on 4 low order bits of significand of y +// For y < 1, turn on 4 low order bits of significand of y // so that the fraction will always be non-zero // -{ .mmi -(p9) or GR_exp_y= 0xF,GR_signif_y // Force nonzero fraction if y<1 -;; - nop.m 999 -(p8) shl GR_exp_y= GR_signif_y,GR_exp_y // Get lsb of int + fraction - // Wait 4 cycles to use result +(p0) shl GR_signif_y= GR_exp_y,1 ;; +(p0) extr.u GR_low_order_bit = GR_exp_y,63,1 } -;; - -{ .mmi - nop.m 999 -;; - nop.m 999 - nop.i 999 -} -;; - -{ .mmi - nop.m 999 -;; - nop.m 999 - shl GR_fraction_y= GR_exp_y,1 // Shift left 1 to get fraction -} -;; - // // Integer part of y shifted off. // Get y's low even or odd bit - y might not be an int. // { .mii - cmp.eq p13,p0 = GR_fraction_y, r0 // Test for y integer - cmp.eq p8,p0 = GR_y_sign, r0 // Test for y > 0 -;; -(p13) tbit.nz.unc p13,p0 = GR_exp_y, 63 // Test if y an odd integer -} -;; - -{ .mfi -(p13) cmp.eq.unc p13,p14 = GR_y_sign, r0 // Test y pos odd integer -(p8) fcmp.eq.s0 p12,p0 = FR_Input_Y, f0 // If x=0 and y>0 flag if y denormal - nop.i 999 +(p0) cmp.eq.unc p13,p0 = GR_signif_y, r0 +(p0) cmp.eq.unc p8,p9 = GR_y_sign, r0 ;; +// +// Is y an int? +// Is y positive +// +(p13) cmp.ne.unc p13,p0 = GR_low_order_bit, r0 ;; } -;; - // -// Return +/-0 when x=+/-0 and y is positive odd integer +// Is y and int and odd? // { .mfb - nop.m 999 -(p13) mov FR_Result = FR_Input_X // If x=0, y pos odd int, result=x -(p13) br.ret.spnt b0 // Exit x=0, y pos odd int, result=x +(p13) cmp.eq.unc p13,p14 = GR_y_sign, r0 +(p8) fcmp.eq.s0 p12,p0 = FR_Input_Y, f0 // If x=0 and y>0 flag if y denormal + nop.b 999 ;; } -;; - +{ .mfb + nop.m 999 // -// Return +/-inf when x=+/-0 and y is negative odd int +// Is y and int and odd and positive? // -{ .mfb -(p14) mov GR_Parameter_TAG = 21 -(p14) frcpa.s0 FR_Result, p0 = f1, FR_Input_X // Result +-inf, set Z flag -(p14) br.cond.spnt __libm_error_region +(p13) mov FR_Result = FR_Input_X +(p13) br.cond.sptk L(POWL_64_RETURN) ;; } -;; - +{ .mfi + nop.m 999 // -// Return +0 when x=+/-0 and y positive and not an odd integer +// Return +/-0 when x=+/-0 and y is and odd pos. int // -{ .mfb - nop.m 999 -(p8) mov FR_Result = f0 // If x=0, y>0 and not odd integer, result=+0 -(p8) br.ret.sptk b0 // Exit x=0, y>0 and not odd integer, result=+0 +(p14) frcpa.s0 FR_Result, p10 = f1, FR_Input_X +(p14) mov GR_Parameter_TAG = 21 +} +{ .mib + nop.m 999 + nop.i 999 +(p14) br.cond.spnt __libm_error_region ;; } -;; +{ .mfb + nop.m 999 // -// Return +inf when x=+/-0 and y is negative and not odd int +// Return +/-0 when x=+/-Inf and y is and odd neg int +// and raise dz exception // -{ .mfb - mov GR_Parameter_TAG = 21 - frcpa.s0 FR_Result, p10 = f1,f0 // Result +inf, raise Z flag - br.cond.sptk __libm_error_region +(p8) mov FR_Result = f0 +(p8) br.cond.sptk L(POWL_64_RETURN) ;; } -;; - - -POWL_64_X_IS_INF: +{ .mfi + nop.m 999 // -// Here if x=inf, y not 1 or nan +// Return +0 when x=+/-0 and y > 0 and not odd. // +(p9) frcpa.s0 FR_Result, p10 = f1,f0 +(p9) mov GR_Parameter_TAG = 21 +} +{ .mib + nop.m 999 + nop.i 999 +(p9) br.cond.sptk __libm_error_region ;; +} +L(POWL_64_X_IS_INF): { .mfi - and GR_exp_y = GR_exp_mask,GR_signexp_y // Get biased exponent y - fclass.m p13, p0 = FR_Input_X,0x022 // Test x=-inf - nop.i 999 +(p0) getf.exp GR_exp_y = FR_Input_Y +(p0) fclass.m.unc p13, p0 = FR_Input_X,0x022 +(p0) mov GR_Mask = 0x1FFFF ;; } -;; { .mfi - and GR_y_sign = GR_sign_mask,GR_signexp_y // Get sign of y - fcmp.eq.s0 p9,p0 = FR_Input_Y, f0 // Dummy to set flag if y denorm - nop.i 999 +(p0) getf.sig GR_signif_y = FR_Input_Y +(p0) fcmp.eq.s0 p9,p0 = FR_Input_Y, f0 // Flag if y denormal + nop.i 999 ;; } -;; // -// Maybe y is < 1 already, so -// isn't an int. +// Get exp and significand of y +// Create exponent mask and sign mask // -{ .mfi -(p13) cmp.lt.unc p9, p8 = GR_exp_y,GR_exp_bias // Test 0 < |y| < 1 if x=-inf - fclass.m p11, p0 = FR_Input_X,0x021 // Test x=+inf - sub GR_exp_y = GR_exp_y,GR_exp_bias // Get true exponent y +{ .mlx +(p0) and GR_low_order_bit = GR_Mask,GR_exp_y +(p0) movl GR_BIAS = 0xFFFF } -;; - +{ .mmi + nop.m 999 ;; // -// Shift significand of y looking for nonzero bits -// For y > 1, shift signif_y exp_y bits to the left -// For y < 1, turn on 4 low order bits of significand of y -// so that the fraction will always be non-zero +// Remove sign bit from exponent. // -{ .mmi -(p9) or GR_exp_y= 0xF,GR_signif_y // Force nonzero fraction if y<1 -;; -(p11) cmp.eq.unc p14,p12 = GR_y_sign, r0 // Test x=+inf, y>0 -(p8) shl GR_exp_y= GR_signif_y,GR_exp_y // Get lsb of int + fraction - // Wait 4 cycles to use result -} -;; - +(p0) cmp.lt.unc p9, p8 = GR_low_order_bit,GR_BIAS // -// Return +inf for x=+inf, y > 0 -// Return +0 for x=+inf, y < 0 +// Maybe y is < 1 already, so +// isn't an int. // -{ .mfi - nop.m 999 -(p12) mov FR_Result = f0 // If x=+inf, y<0, result=+0 - nop.i 999 +(p0) sub GR_low_order_bit = GR_low_order_bit,GR_BIAS } -{ .mfb - nop.m 999 -(p14) fma.s0 FR_Result = FR_Input_X,f1,f0 // If x=+inf, y>0, result=+inf -(p11) br.ret.sptk b0 // Exit x=+inf +{ .mlx + nop.m 999 +(p0) movl GR_sign_mask = 0x20000 ;; } -;; - +{ .mfi +(p0) and GR_sign_mask = GR_sign_mask,GR_exp_y // -// Here only if x=-inf. Wait until can use result of shl... +// Return +Inf when x=+/-0 and y < 0 and not odd and raise +// divide-by-zero exception. // +(p0) fclass.m.unc p11, p0 = FR_Input_X,0x021 + nop.i 999 ;; +} { .mmi - nop.m 999 -;; - nop.m 999 - nop.i 999 + nop.m 999 ;; +// +// Is shift off integer part of y. +// Get y's even or odd bit - y might not be an int. +// +(p11) cmp.eq.unc p11,p12 = GR_sign_mask, r0 +// +// Remove exponent BIAS +// +(p8) shl GR_exp_y = GR_signif_y,GR_low_order_bit ;; } -;; - { .mfi - cmp.eq p8,p9 = GR_y_sign, r0 // Test y pos - nop.f 999 - shl GR_fraction_y = GR_exp_y,1 // Shift left 1 to get fraction +(p9) or GR_exp_y = 0xF,GR_signif_y +// +// Is y positive or negative when x is +Inf? +// Is y and int when x = -Inf +// +(p11) mov FR_Result = FR_Input_X + nop.i 999 ;; } -;; - -{ .mmi - cmp.eq p13,p0 = GR_fraction_y, r0 // Test y integer -;; - nop.m 999 -(p13) tbit.nz.unc p13,p0 = GR_exp_y, 63 // Test y odd integer +{ .mfi + nop.m 999 +(p12) mov FR_Result = f0 + nop.i 999 ;; } -;; - +{ .mii + nop.m 999 // -// Is y even or odd? +// Shift signficand looking for nonzero bits +// For y non-ints, upset the significand. // +(p0) shl GR_signif_y = GR_exp_y,1 ;; +(p13) cmp.eq.unc p13,p0 = GR_signif_y, r0 +} { .mii -(p13) cmp.eq.unc p14,p10 = GR_y_sign, r0 // Test x=-inf, y pos odd int -(p13) cmp.ne.and p8,p9 = r0,r0 // If y odd int, turn off p8,p9 - nop.i 999 + nop.m 999 +(p0) extr.u GR_low_order_bit = GR_exp_y,63,1 ;; +(p13) cmp.ne.unc p13,p0 = GR_low_order_bit, r0 +} +{ .mib + nop.m 999 + nop.i 999 +(p11) br.cond.sptk L(POWL_64_RETURN) ;; +} +{ .mib + nop.m 999 + nop.i 999 +(p12) br.cond.sptk L(POWL_64_RETURN) ;; } -;; - // -// Return -0 for x = -inf and y < 0 and odd int. -// Return -Inf for x = -inf and y > 0 and odd int. +// Return Inf for y > 0 +// Return +0 for y < 0 +// Is y even or odd? // -{ .mfi - nop.m 999 -(p10) fmerge.ns FR_Result = f0, f0 // If x=-inf, y neg odd int, result=-0 - nop.i 999 +{ .mii +(p13) cmp.eq.unc p13,p10 = GR_sign_mask, r0 +(p0) cmp.eq.unc p8,p9 = GR_sign_mask, r0 ;; + nop.i 999 } { .mfi - nop.m 999 -(p14) fmpy.s0 FR_Result = FR_Input_X,f1 // If x=-inf, y pos odd int, result=-inf - nop.i 999 -} -;; - + nop.m 999 // -// Return Inf for x = -inf and y > 0 not an odd int. -// Return +0 for x = -inf and y < 0 not an odd int. +// For x = -inf, y is and int, positive +// and odd +// Is y positive in general? // -.pred.rel "mutex",p8,p9 -{ .mfi - nop.m 999 -(p8) fmerge.ns FR_Result = FR_Input_X, FR_Input_X // If x=-inf, y>0 not odd int - // result=+inf - nop.i 999 +(p13) mov FR_Result = FR_Input_X + nop.i 999 ;; } { .mfb - nop.m 999 -(p9) fmpy.s0 FR_Result = f0,f0 // If x=-inf, y<0 not odd int - // result=+0 - br.ret.sptk b0 // Exit for x=-inf + nop.m 999 +(p10) fmerge.ns FR_Result = f0, f0 +(p13) br.cond.sptk L(POWL_64_RETURN) ;; } -;; - - -POWL_64_Y_IS_INF: -// Here if y=inf, x not 1 or nan +{ .mib + nop.m 999 + nop.i 999 +(p10) br.cond.sptk L(POWL_64_RETURN) ;; +} +{ .mfi + nop.m 999 // -// For y = +Inf and |x| < 1 returns 0 -// For y = +Inf and |x| > 1 returns Inf -// For y = -Inf and |x| < 1 returns Inf -// For y = -Inf and |x| > 1 returns 0 -// For y = Inf and |x| = 1 returns 1 +// Return -Inf for x = -inf and y > 0 and odd int. +// Return -0 for x = -inf and y < 0 and odd int. // -{ .mfi - nop.m 999 - fclass.m p8, p0 = FR_Input_Y, 0x021 // Test y=+inf - nop.i 999 +(p8) fmerge.ns FR_Result = FR_Input_X, FR_Input_X + nop.i 999 ;; } -;; - -{ .mfi - nop.m 999 - fclass.m p9, p0 = FR_Input_Y, 0x022 // Test y=-inf - nop.i 999 +{ .mfb + nop.m 999 +(p9) mov FR_Result = f0 +(p8) br.cond.sptk L(POWL_64_RETURN) ;; } -;; - +{ .mib + nop.m 999 + nop.i 999 +(p9) br.cond.sptk L(POWL_64_RETURN) ;; +} +L(POWL_64_Y_IS_INF): { .mfi - nop.m 999 - fabs FR_X = FR_Input_X // Form |x| - nop.i 999 + nop.m 999 +// +// Return Inf for x = -inf and y > 0 not an odd int. +// Return +0 for x = -inf and y < 0 and not an odd int. +// +(p0) fclass.m.unc p8, p0 = FR_Input_Y, 0x021 + nop.i 999 } -;; - { .mfi - nop.m 999 - fcmp.eq.s0 p10,p0 = FR_Input_X, f0 // flag if x denormal - nop.i 999 + nop.m 999 +(p0) fclass.m.unc p9, p0 = FR_Input_Y, 0x022 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p8) fcmp.lt.unc.s1 p6, p0 = FR_X, f1 // Test y=+inf, |x|<1 - nop.i 999 + nop.m 999 +(p0) fabs FR_X = FR_Input_X + nop.i 999 ;; } -;; { .mfi - nop.m 999 -(p8) fcmp.gt.unc.s1 p7, p0 = FR_X, f1 // Test y=+inf, |x|>1 - nop.i 999 + nop.m 999 +(p0) fcmp.eq.s0 p10,p0 = FR_Input_X, f0 // flag if x denormal + nop.i 999 ;; } -;; { .mfi - nop.m 999 -(p9) fcmp.lt.unc.s1 p12, p0 = FR_X, f1 // Test y=-inf, |x|<1 - nop.i 999 + nop.m 999 +// +// Find y = +/- Inf +// Compute |x| +// +(p8) fcmp.lt.unc.s1 p6, p0 = FR_X, f1 + nop.i 999 } { .mfi - nop.m 999 -(p6) fmpy.s0 FR_Result = f0,f0 // If y=+inf, |x|<1, result=+0 - nop.i 999 + nop.m 999 +(p8) fcmp.gt.unc.s1 p7, p0 = FR_X, f1 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p9) fcmp.gt.unc.s1 p13, p0 = FR_X, f1 // Test y=-inf, |x|>1 - nop.i 999 + nop.m 999 +(p9) fcmp.lt.unc.s1 p12, p0 = FR_X, f1 + nop.i 999 } { .mfi - nop.m 999 -(p7) fmpy.s0 FR_Result = FR_Input_Y, f1 // If y=+inf, |x|>1, result=+inf - nop.i 999 + nop.m 999 +(p9) fcmp.gt.unc.s1 p13, p0 = FR_X, f1 + nop.i 999 ;; } -;; - { .mfi - nop.m 999 - fcmp.eq.s1 p14, p0 = FR_X, f1 // Test y=inf, |x|=1 - nop.i 999 + nop.m 999 +// +// For y = +Inf and |x| < 1 returns 0 +// For y = +Inf and |x| > 1 returns Inf +// For y = -Inf and |x| < 1 returns Inf +// For y = -Inf and |x| > 1 returns 0 +// +(p6) mov FR_Result = f0 + nop.i 999 ;; } { .mfi - nop.m 999 -(p12) fnma.s0 FR_Result = FR_Input_Y, f1, f0 // If y=-inf, |x|<1, result=+inf - nop.i 999 + nop.m 999 +(p7) mov FR_Result = FR_Input_Y + nop.i 999 ;; } -;; - { .mfi - nop.m 999 -(p13) mov FR_Result = f0 // If y=-inf, |x|>1, result=+0 - nop.i 999 + nop.m 999 +(p12) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_Y + nop.i 999 ;; } -;; - { .mfb - nop.m 999 -(p14) fmpy.s0 FR_Result = f1,f1 // If y=inf, |x|=1, result=+1 - br.ret.sptk b0 // Common return for y=inf + nop.m 999 +(p13) mov FR_Result = f0 +// +// Produce x ** +/- Inf results +// +(p6) br.cond.spnt L(POWL_64_RETURN) ;; } -;; - - -// Here if x or y denorm/unorm -POWL_DENORM: -{ .mmi - getf.sig GR_signif_Z = FR_norm_X // Get significand of x -;; - getf.exp GR_signexp_y = FR_norm_Y // Get sign and exp of y - nop.i 999 +{ .mib + nop.m 999 + nop.i 999 +(p7) br.cond.spnt L(POWL_64_RETURN) ;; } -;; - -{ .mfi - getf.sig GR_signif_y = FR_norm_Y // Get significand of y - nop.f 999 - nop.i 999 +{ .mib + nop.m 999 + nop.i 999 +(p12) br.cond.spnt L(POWL_64_RETURN) ;; } -;; - { .mib - getf.exp GR_signexp_x = FR_norm_X // Get sign and exp of x - extr.u GR_Index1 = GR_signif_Z, 59, 4 // Extract upper 4 signif bits of x - br.cond.sptk POWL_COMMON // Branch back to main path + nop.m 999 + nop.i 999 +(p13) br.cond.spnt L(POWL_64_RETURN) ;; } -;; - - -POWL_64_UNSUPPORT: +{ .mfb + nop.m 999 // -// Raise exceptions for specific -// values - pseudo NaN and -// infinities. -// Return NaN and raise invalid +// +/-1 ** +/-Inf, result is +1 // -{ .mfb - nop.m 999 - fmpy.s0 FR_Result = FR_Input_X,f0 - br.ret.sptk b0 +(p0) fmpy.s0 FR_Result = f1,f1 +(p0) br.cond.sptk L(POWL_64_RETURN) ;; } -;; - -POWL_64_XNEG: +L(POWL_64_UNSUPPORT): +{ .mfb + nop.m 999 // -// Raise invalid for x < 0 and -// y not an integer +// Return NaN and raise invalid // +(p0) fmpy.s0 FR_Result = FR_Input_X,f0 +// +// Raise exceptions for specific +// values - pseudo NaN and +// infinities. +// +(p0) br.cond.sptk L(POWL_64_RETURN) ;; +} +L(POWL_64_XNEG): { .mfi - nop.m 999 - frcpa.s0 FR_Result, p8 = f0, f0 - mov GR_Parameter_TAG = 22 + nop.m 999 +(p0) frcpa.s0 FR_Result, p8 = f0, f0 +// +// Raise invalid for x < 0 and +// y not an integer and +// +(p0) mov GR_Parameter_TAG = 22 } { .mib - nop.m 999 - nop.i 999 - br.cond.sptk __libm_error_region + nop.m 999 + nop.i 999 +(p0) br.cond.sptk __libm_error_region ;; } -;; - -POWL_64_SQRT: +L(POWL_64_SQRT): { .mfi - nop.m 999 - frsqrta.s0 FR_Result,p10 = FR_save_Input_X - nop.i 999 ;; + nop.m 999 +(p0) frsqrta.s0 FR_Result,p10 = FR_Input_X + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fma.s1 f62=FR_Half,FR_save_Input_X,f0 - nop.i 999 ;; + nop.m 999 +(p10) fma.s1 f62=FR_Half,FR_Input_X,f0 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fma.s1 f63=FR_Result,FR_Result,f0 - nop.i 999 ;; + nop.m 999 +// +// Step (2) +// h = 1/2 * a in f9 +// +(p10) fma.s1 f63=FR_Result,FR_Result,f0 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fnma.s1 f32=f63,f62,FR_Half - nop.i 999 ;; + nop.m 999 +// +// Step (3) +// t1 = y0 * y0 in f10 +// +(p10) fnma.s1 f32=f63,f62,f11 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fma.s1 f33=f32,FR_Result,FR_Result - nop.i 999 ;; + nop.m 999 +// +// Step (4) +// t2 = 1/2 - t1 * h in f10 +// +(p10) fma.s1 f33=f32,FR_Result,FR_Result + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fma.s1 f34=f33,f62,f0 - nop.i 999 ;; + nop.m 999 +// +// Step (5) +// y1 = y0 + t2 * y0 in f13 +// +(p10) fma.s1 f34=f33,f62,f0 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fnma.s1 f35=f34,f33,FR_Half - nop.i 999 ;; + nop.m 999 +// +// Step (6) +// t3 = y1 * h in f10 +// +(p10) fnma.s1 f35=f34,f33,f11 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fma.s1 f63=f35,f33,f33 - nop.i 999 ;; + nop.m 999 +// +// Step (7) +// t4 = 1/2 - t3 * y1 in f10 +// +(p10) fma.s1 f63=f35,f33,f33 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fma.s1 f32=FR_save_Input_X,f63,f0 - nop.i 999 + nop.m 999 +// +// Step (8) +// y2 = y1 + t4 * y1 in f13 +// +(p10) fma.s1 f32=FR_Input_X,f63,f0 + nop.i 999 } { .mfi - nop.m 999 -(p10) fma.s1 FR_Result=f63,f62,f0 - nop.i 999 ;; + nop.m 999 +// +// Step (9) +// S = a * y2 in f10 +// +(p10) fma.s1 FR_Result=f63,f62,f0 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fma.s1 f33=f11,f63,f0 - nop.i 999 ;; + nop.m 999 +// +// Step (10) +// t5 = y2 * h in f9 +// +(p10) fma.s1 f33=f11,f63,f0 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fnma.s1 f34=f32,f32,FR_save_Input_X - nop.i 999 + nop.m 999 +// +// Step (11) +// H = 1/2 * y2 in f11 +// +(p10) fnma.s1 f34=f32,f32,f8 + nop.i 999 } { .mfi - nop.m 999 -(p10) fnma.s1 f35=FR_Result,f63,FR_Half - nop.i 999 ;; + nop.m 999 +// +// Step (12) +// d = a - S * S in f12 +// +(p10) fnma.s1 f35=FR_Result,f63,f11 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fma.s1 f62=f33,f34,f32 - nop.i 999 + nop.m 999 +// +// Step (13) +// t6 = 1/2 - t5 * y2 in f7 +// +(p10) fma.s1 f62=f33,f34,f32 + nop.i 999 } { .mfi - nop.m 999 -(p10) fma.s1 f63=f33,f35,f33 - nop.i 999 ;; + nop.m 999 +// +// Step (14) +// S1 = S + d * H in f13 +// +(p10) fma.s1 f63=f33,f35,f33 + nop.i 999 ;; } { .mfi - nop.m 999 -(p10) fnma.s1 f32=f62,f62,FR_save_Input_X - nop.i 999 ;; + nop.m 999 +// +// Step (15) +// H1 = H + t6 * h in f7 +// +(p10) fnma.s1 f32=f62,f62,FR_Input_X + nop.i 999 ;; } { .mfb - nop.m 999 -(p10) fma.s0 FR_Result=f32,f63,f62 - br.ret.sptk b0 // Exit for x > 0, y = 0.5 + nop.m 999 +// +// Step (16) +// d1 = a - S1 * S1 +// +(p10) fma.s0 FR_Result=f32,f63,f62 +// +// Step (17) +// R = S1 + d1 * H1 +// +(p10) br.cond.sptk L(POWL_64_RETURN) ;; } -;; - -GLOBAL_LIBM_END(powl) +{ .mib + nop.m 999 + nop.i 999 +// +// Do the Newton-Raphson iteration from the EAS. +// +(p0) br.cond.sptk L(POWL_64_RETURN) ;; +} +// +// Take care of the degenerate cases. +// +L(POWL_64_RETURN): +{ .mfb + nop.m 999 +(p0) mov FR_Output = FR_Result +(p0) br.ret.sptk b0 ;; +} +.endp powl +ASM_SIZE_DIRECTIVE(powl) -LOCAL_LIBM_ENTRY(__libm_error_region) +.proc __libm_error_region +__libm_error_region: .prologue { .mfi add GR_Parameter_Y=-32,sp // Parameter 2 value @@ -2772,32 +3411,32 @@ LOCAL_LIBM_ENTRY(__libm_error_region) mov GR_SAVE_GP=gp // Save gp };; { .mmi - stfe [GR_Parameter_Y] = FR_Input_Y,16 // Save Parameter 2 on stack + 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_save_Input_X // Store Parameter 1 on stack + 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 + 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 + 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 + add GR_Parameter_RESULT = 48,sp };; { .mmi - ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack + 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 + add sp = 64,sp // Restore stack pointer + mov b0 = GR_SAVE_B0 // Restore return address };; { .mib mov gp = GR_SAVE_GP // Restore gp @@ -2805,6 +3444,7 @@ LOCAL_LIBM_ENTRY(__libm_error_region) 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 .global __libm_error_support# |