| .file "scalbf.s" |
| |
| |
| // Copyright (c) 2000 - 2003, Intel Corporation |
| // All rights reserved. |
| // |
| // Contributed 2000 by the Intel Numerics Group, Intel Corporation |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // met: |
| // |
| // * Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // |
| // * Redistributions in binary form must reproduce the above copyright |
| // notice, this list of conditions and the following disclaimer in the |
| // documentation and/or other materials provided with the distribution. |
| // |
| // * The name of Intel Corporation may not be used to endorse or promote |
| // products derived from this software without specific prior written |
| // permission. |
| |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS |
| // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
| // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
| // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY |
| // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING |
| // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Intel Corporation is the author of this code, and requests that all |
| // problem reports or change requests be submitted to it directly at |
| // http://www.intel.com/software/products/opensource/libraries/num.htm. |
| // |
| // History |
| //============================================================== |
| // 02/02/00 Initial version |
| // 01/26/01 Scalb completely reworked and now standalone version |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 02/10/03 Reordered header: .section, .global, .proc, .align |
| // 08/06/03 Improved performance |
| // |
| // API |
| //============================================================== |
| // float = scalbf (float x, float n) |
| // input floating point f8 and floating point f9 |
| // output floating point f8 |
| // |
| // int_type = 0 if int is 32 bits |
| // int_type = 1 if int is 64 bits |
| // |
| // Returns x* 2**n using an fma and detects overflow |
| // and underflow. |
| // |
| // |
| // Strategy: |
| // Compute biased exponent of result exp_Result = N + exp_X |
| // Break into ranges: |
| // exp_Result > 0x1007e -> Certain overflow |
| // exp_Result = 0x1007e -> Possible overflow |
| // 0x0ff81 <= exp_Result < 0x1007e -> No over/underflow (main path) |
| // 0x0ff81 - 23 <= exp_Result < 0x0ff81 -> Possible underflow |
| // exp_Result < 0x0ff81 - 23 -> Certain underflow |
| |
| FR_Big = f6 |
| FR_NBig = f7 |
| FR_Floating_X = f8 |
| FR_Result = f8 |
| FR_Floating_N = f9 |
| FR_Result2 = f9 |
| FR_Result3 = f10 |
| FR_Norm_X = f11 |
| FR_Two_N = f12 |
| FR_N_float_int = f13 |
| FR_Norm_N = f14 |
| |
| GR_neg_ov_limit= r14 |
| GR_big_exp = r14 |
| GR_N_Biased = r15 |
| GR_Big = r16 |
| GR_exp_Result = r18 |
| GR_pos_ov_limit= r19 |
| GR_exp_sure_ou = r19 |
| GR_Bias = r20 |
| GR_N_as_int = r21 |
| GR_signexp_X = r22 |
| GR_exp_X = r23 |
| GR_exp_mask = r24 |
| GR_max_exp = r25 |
| GR_min_exp = r26 |
| GR_min_den_exp = r27 |
| GR_Scratch = r28 |
| GR_signexp_N = r29 |
| GR_exp_N = r30 |
| |
| GR_SAVE_B0 = r32 |
| GR_SAVE_GP = r33 |
| GR_SAVE_PFS = r34 |
| GR_Parameter_X = r35 |
| GR_Parameter_Y = r36 |
| GR_Parameter_RESULT = r37 |
| GR_Tag = r38 |
| |
| .section .text |
| GLOBAL_IEEE754_ENTRY(scalbf) |
| |
| // |
| // Is x NAN, INF, ZERO, +-? |
| // Build the exponent Bias |
| // |
| { .mfi |
| getf.exp GR_signexp_N = FR_Floating_N // Get signexp of n |
| fclass.m p6,p0 = FR_Floating_X, 0xe7 // @snan | @qnan | @inf | @zero |
| mov GR_Bias = 0x0ffff |
| } |
| { .mfi |
| mov GR_Big = 35000 // If N this big then certain overflow |
| fcvt.fx.trunc.s1 FR_N_float_int = FR_Floating_N // Get N in significand |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| getf.exp GR_signexp_X = FR_Floating_X // Get signexp of x |
| fclass.m p7,p0 = FR_Floating_N, 0x0b // Test for n=unorm |
| nop.i 0 |
| } |
| // |
| // Normalize n |
| // |
| { .mfi |
| mov GR_exp_mask = 0x1ffff // Exponent mask |
| fnorm.s1 FR_Norm_N = FR_Floating_N |
| nop.i 0 |
| } |
| ;; |
| |
| // |
| // Is n NAN, INF, ZERO, +-? |
| // |
| { .mfi |
| mov GR_big_exp = 0x1003e // Exponent at which n is integer |
| fclass.m p9,p0 = FR_Floating_N, 0xe7 // @snan | @qnan | @inf | @zero |
| mov GR_max_exp = 0x1007e // Exponent of maximum float |
| } |
| // |
| // Normalize x |
| // |
| { .mfb |
| nop.m 0 |
| fnorm.s1 FR_Norm_X = FR_Floating_X |
| (p7) br.cond.spnt SCALBF_N_UNORM // Branch if n=unorm |
| } |
| ;; |
| |
| SCALBF_COMMON1: |
| // Main path continues. Also return here from u=unorm path. |
| // Handle special cases if x = Nan, Inf, Zero |
| { .mfb |
| nop.m 0 |
| fcmp.lt.s1 p7,p0 = FR_Floating_N, f0 // Test N negative |
| (p6) br.cond.spnt SCALBF_NAN_INF_ZERO |
| } |
| ;; |
| |
| // Handle special cases if n = Nan, Inf, Zero |
| { .mfi |
| getf.sig GR_N_as_int = FR_N_float_int // Get n from significand |
| fclass.m p8,p0 = FR_Floating_X, 0x0b // Test for x=unorm |
| mov GR_exp_sure_ou = 0x1000e // Exp_N where x*2^N sure over/under |
| } |
| { .mfb |
| mov GR_min_exp = 0x0ff81 // Exponent of minimum float |
| fcvt.xf FR_N_float_int = FR_N_float_int // Convert N to FP integer |
| (p9) br.cond.spnt SCALBF_NAN_INF_ZERO |
| } |
| ;; |
| |
| { .mmi |
| and GR_exp_N = GR_exp_mask, GR_signexp_N // Get exponent of N |
| (p7) sub GR_Big = r0, GR_Big // Limit for N |
| nop.i 0 |
| } |
| ;; |
| |
| { .mib |
| cmp.lt p9,p0 = GR_exp_N, GR_big_exp // N possible non-integer? |
| cmp.ge p6,p0 = GR_exp_N, GR_exp_sure_ou // N certain over/under? |
| (p8) br.cond.spnt SCALBF_X_UNORM // Branch if x=unorm |
| } |
| ;; |
| |
| SCALBF_COMMON2: |
| // Main path continues. Also return here from x=unorm path. |
| // Create biased exponent for 2**N |
| { .mmi |
| (p6) mov GR_N_as_int = GR_Big // Limit N |
| ;; |
| add GR_N_Biased = GR_Bias,GR_N_as_int |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| setf.exp FR_Two_N = GR_N_Biased // Form 2**N |
| (p9) fcmp.neq.unc.s1 p9,p0 = FR_Norm_N, FR_N_float_int // Test if N an integer |
| and GR_exp_X = GR_exp_mask, GR_signexp_X // Get exponent of X |
| } |
| ;; |
| |
| // |
| // Compute biased result exponent |
| // Branch if N is not an integer |
| // |
| { .mib |
| add GR_exp_Result = GR_exp_X, GR_N_as_int |
| mov GR_min_den_exp = 0x0ff81 - 23 // Exponent of min denorm float |
| (p9) br.cond.spnt SCALBF_N_NOT_INT |
| } |
| ;; |
| |
| // |
| // Raise Denormal operand flag with compare |
| // Do final operation |
| // |
| { .mfi |
| cmp.lt p7,p6 = GR_exp_Result, GR_max_exp // Test no overflow |
| fcmp.ge.s0 p0,p11 = FR_Floating_X,FR_Floating_N // Dummy to set denorm |
| cmp.lt p9,p0 = GR_exp_Result, GR_min_den_exp // Test sure underflow |
| } |
| { .mfb |
| nop.m 0 |
| fma.s.s0 FR_Result = FR_Two_N,FR_Norm_X,f0 |
| (p9) br.cond.spnt SCALBF_UNDERFLOW // Branch if certain underflow |
| } |
| ;; |
| |
| { .mib |
| (p6) cmp.gt.unc p6,p8 = GR_exp_Result, GR_max_exp // Test sure overflow |
| (p7) cmp.ge.unc p7,p9 = GR_exp_Result, GR_min_exp // Test no over/underflow |
| (p7) br.ret.sptk b0 // Return from main path |
| } |
| ;; |
| |
| { .bbb |
| (p6) br.cond.spnt SCALBF_OVERFLOW // Branch if certain overflow |
| (p8) br.cond.spnt SCALBF_POSSIBLE_OVERFLOW // Branch if possible overflow |
| (p9) br.cond.spnt SCALBF_POSSIBLE_UNDERFLOW // Branch if possible underflow |
| } |
| ;; |
| |
| // Here if possible underflow. |
| // Resulting exponent: 0x0ff81-23 <= exp_Result < 0x0ff81 |
| SCALBF_POSSIBLE_UNDERFLOW: |
| // |
| // Here if possible overflow. |
| // Resulting exponent: 0x1007e = exp_Result |
| SCALBF_POSSIBLE_OVERFLOW: |
| |
| // Set up necessary status fields |
| // |
| // S0 user supplied status |
| // S2 user supplied status + WRE + TD (Overflows) |
| // S3 user supplied status + FZ + TD (Underflows) |
| // |
| { .mfi |
| mov GR_pos_ov_limit = 0x1007f // Exponent for positive overflow |
| fsetc.s3 0x7F,0x41 |
| nop.i 0 |
| } |
| { .mfi |
| mov GR_neg_ov_limit = 0x3007f // Exponent for negative overflow |
| fsetc.s2 0x7F,0x42 |
| nop.i 0 |
| } |
| ;; |
| |
| // |
| // Do final operation with s2 and s3 |
| // |
| { .mfi |
| setf.exp FR_NBig = GR_neg_ov_limit |
| fma.s.s3 FR_Result3 = FR_Two_N,FR_Norm_X,f0 |
| nop.i 0 |
| } |
| { .mfi |
| setf.exp FR_Big = GR_pos_ov_limit |
| fma.s.s2 FR_Result2 = FR_Two_N,FR_Norm_X,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| // Check for overflow or underflow. |
| // Restore s3 |
| // Restore s2 |
| // |
| { .mfi |
| nop.m 0 |
| fsetc.s3 0x7F,0x40 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fsetc.s2 0x7F,0x40 |
| nop.i 0 |
| } |
| ;; |
| |
| // |
| // Is the result zero? |
| // |
| { .mfi |
| nop.m 0 |
| fclass.m p6, p0 = FR_Result3, 0x007 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fcmp.ge.s1 p7, p8 = FR_Result2 , FR_Big |
| nop.i 0 |
| } |
| ;; |
| |
| // |
| // Detect masked underflow - Tiny + Inexact Only |
| // |
| { .mfi |
| nop.m 0 |
| (p6) fcmp.neq.unc.s1 p6, p0 = FR_Result , FR_Result2 |
| nop.i 0 |
| } |
| ;; |
| |
| // |
| // Is result bigger the allowed range? |
| // Branch out for underflow |
| // |
| { .mfb |
| nop.m 0 |
| (p8) fcmp.le.unc.s1 p9, p10 = FR_Result2 , FR_NBig |
| (p6) br.cond.spnt SCALBF_UNDERFLOW |
| } |
| ;; |
| |
| // |
| // Branch out for overflow |
| // |
| { .bbb |
| (p7) br.cond.spnt SCALBF_OVERFLOW |
| (p9) br.cond.spnt SCALBF_OVERFLOW |
| br.ret.sptk b0 // Return from main path. |
| } |
| ;; |
| |
| // Here if result overflows |
| SCALBF_OVERFLOW: |
| { .mib |
| alloc r32=ar.pfs,3,0,4,0 |
| addl GR_Tag = 55, r0 // Set error tag for overflow |
| br.cond.sptk __libm_error_region // Call error support for overflow |
| } |
| ;; |
| |
| // Here if result underflows |
| SCALBF_UNDERFLOW: |
| { .mib |
| alloc r32=ar.pfs,3,0,4,0 |
| addl GR_Tag = 56, r0 // Set error tag for underflow |
| br.cond.sptk __libm_error_region // Call error support for underflow |
| } |
| ;; |
| |
| SCALBF_NAN_INF_ZERO: |
| |
| // |
| // Before entry, N has been converted to a fp integer in significand of |
| // FR_N_float_int |
| // |
| // Convert N_float_int to floating point value |
| // |
| { .mfi |
| getf.sig GR_N_as_int = FR_N_float_int |
| fclass.m p6,p0 = FR_Floating_N, 0xc3 //@snan | @qnan |
| nop.i 0 |
| } |
| { .mfi |
| addl GR_Scratch = 1,r0 |
| fcvt.xf FR_N_float_int = FR_N_float_int |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fclass.m p7,p0 = FR_Floating_X, 0xc3 //@snan | @qnan |
| shl GR_Scratch = GR_Scratch,63 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fclass.m p8,p0 = FR_Floating_N, 0x21 // @inf |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fclass.m p9,p0 = FR_Floating_N, 0x22 // @-inf |
| nop.i 0 |
| } |
| ;; |
| |
| // |
| // Either X or N is a Nan, return result and possible raise invalid. |
| // |
| { .mfb |
| nop.m 0 |
| (p6) fma.s.s0 FR_Result = FR_Floating_N,FR_Floating_X,f0 |
| (p6) br.ret.spnt b0 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 0 |
| (p7) fma.s.s0 FR_Result = FR_Floating_N,FR_Floating_X,f0 |
| (p7) br.ret.spnt b0 |
| } |
| ;; |
| |
| // |
| // If N + Inf do something special |
| // For N = -Inf, create Int |
| // |
| { .mfb |
| nop.m 0 |
| (p8) fma.s.s0 FR_Result = FR_Floating_X, FR_Floating_N,f0 |
| (p8) br.ret.spnt b0 |
| } |
| { .mfi |
| nop.m 0 |
| (p9) fnma.s.s0 FR_Floating_N = FR_Floating_N, f1, f0 |
| nop.i 0 |
| } |
| ;; |
| |
| // |
| // If N==-Inf,return x/(-N) |
| // |
| { .mfb |
| cmp.ne p7,p0 = GR_N_as_int,GR_Scratch |
| (p9) frcpa.s0 FR_Result,p0 = FR_Floating_X,FR_Floating_N |
| (p9) br.ret.spnt b0 |
| } |
| ;; |
| |
| // |
| // Is N an integer. |
| // |
| { .mfi |
| nop.m 0 |
| (p7) fcmp.neq.unc.s1 p7,p0 = FR_Norm_N, FR_N_float_int |
| nop.i 0 |
| } |
| ;; |
| |
| // |
| // If N not an int, return NaN and raise invalid. |
| // |
| { .mfb |
| nop.m 0 |
| (p7) frcpa.s0 FR_Result,p0 = f0,f0 |
| (p7) br.ret.spnt b0 |
| } |
| ;; |
| |
| // |
| // Always return x in other path. |
| // |
| { .mfb |
| nop.m 0 |
| fma.s.s0 FR_Result = FR_Floating_X,f1,f0 |
| br.ret.sptk b0 |
| } |
| ;; |
| |
| // Here if n not int |
| // Return NaN and raise invalid. |
| SCALBF_N_NOT_INT: |
| { .mfb |
| nop.m 0 |
| frcpa.s0 FR_Result,p0 = f0,f0 |
| br.ret.sptk b0 |
| } |
| ;; |
| |
| // Here if n=unorm |
| SCALBF_N_UNORM: |
| { .mfb |
| getf.exp GR_signexp_N = FR_Norm_N // Get signexp of normalized n |
| fcvt.fx.trunc.s1 FR_N_float_int = FR_Norm_N // Get N in significand |
| br.cond.sptk SCALBF_COMMON1 // Return to main path |
| } |
| ;; |
| |
| // Here if x=unorm |
| SCALBF_X_UNORM: |
| { .mib |
| getf.exp GR_signexp_X = FR_Norm_X // Get signexp of normalized x |
| nop.i 0 |
| br.cond.sptk SCALBF_COMMON2 // Return to main path |
| } |
| ;; |
| |
| GLOBAL_IEEE754_END(scalbf) |
| LOCAL_LIBM_ENTRY(__libm_error_region) |
| |
| // |
| // Get stack address of N |
| // |
| .prologue |
| { .mfi |
| add GR_Parameter_Y=-32,sp |
| nop.f 0 |
| .save ar.pfs,GR_SAVE_PFS |
| mov GR_SAVE_PFS=ar.pfs |
| } |
| // |
| // Adjust sp |
| // |
| { .mfi |
| .fframe 64 |
| add sp=-64,sp |
| nop.f 0 |
| mov GR_SAVE_GP=gp |
| };; |
| |
| // |
| // Store N on stack in correct position |
| // Locate the address of x on stack |
| // |
| { .mmi |
| stfs [GR_Parameter_Y] = FR_Norm_N,16 |
| add GR_Parameter_X = 16,sp |
| .save b0, GR_SAVE_B0 |
| mov GR_SAVE_B0=b0 |
| };; |
| |
| // |
| // Store x on the stack. |
| // Get address for result on stack. |
| // |
| .body |
| { .mib |
| stfs [GR_Parameter_X] = FR_Norm_X |
| add GR_Parameter_RESULT = 0,GR_Parameter_Y |
| nop.b 0 |
| } |
| { .mib |
| stfs [GR_Parameter_Y] = FR_Result |
| add GR_Parameter_Y = -16,GR_Parameter_Y |
| br.call.sptk b0=__libm_error_support# |
| };; |
| |
| // |
| // Get location of result on stack |
| // |
| { .mmi |
| add GR_Parameter_RESULT = 48,sp |
| nop.m 0 |
| nop.i 0 |
| };; |
| |
| // |
| // Get the new result |
| // |
| { .mmi |
| ldfs FR_Result = [GR_Parameter_RESULT] |
| .restore sp |
| add sp = 64,sp |
| mov b0 = GR_SAVE_B0 |
| };; |
| |
| // |
| // Restore gp, ar.pfs and return |
| // |
| { .mib |
| mov gp = GR_SAVE_GP |
| mov ar.pfs = GR_SAVE_PFS |
| br.ret.sptk b0 |
| };; |
| |
| LOCAL_LIBM_END(__libm_error_region) |
| |
| .type __libm_error_support#,@function |
| .global __libm_error_support# |
