/* Copyright (c) 2002 Michael Stumpf Copyright (c) 2006 Dmitry Xmelkov All rights reserved. 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. * Neither the name of the copyright holders nor the names of contributors may 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 THE COPYRIGHT OWNER OR 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. */ /* $Id: pow.S,v 1.9 2007/01/14 15:12:25 dmix Exp $ */ #include "fp32def.h" #include "asmdef.h" /* float pow (float x, float y); The pow() function returns the value of x raised to the power of y. Args combinations: x y pow(x,y) -------------------------------- +0 NaN NaN exp(log(x)*y) +0 +0,-0 +1 +0 +Inf +0 exp(log(x)*y) +0 -Inf +Inf exp(log(x)*y) +0 y > 0 +0 exp(log(x)*y) +0 y < 0 +Inf exp(log(x)*y) -0 NaN NaN exp(log(x)*y) -0 +0,-0 +1 -0 1,3,5... -0 -exp(log(x)*y) -0 y > 0 +0 exp(log(x)*y) -0 -1,-3,-5... -Inf -exp(log(x)*y) -0 y < 0 +Inf exp(log(x)*y) +1 NaN +1 +1 +Inf,-Inf +1 +1 else +1 exp(log(x)*y) -1 +0,-0 +1 -1 1,3,5... -1 -1 -1,-3,-5... -1 -1 2,4,6... +1 -1 -2,-4,-6... +1 -1 else NaN exp(log(x)*y) +Inf NaN NaN exp(log(x)*y) +Inf +0,-0 +1 +Inf y > 0 +Inf exp(log(x)*y) +Inf y < 0 +0 exp(log(x)*y) -Inf NaN NaN exp(log(x)*y) -Inf +0,-0 +1 -Inf 1,3,5... -Inf -Inf y > 0 +Inf -Inf -1,-3,-5... -0 -Inf y < 0 +0 NaN +0,-0 +1 NaN else NaN exp(log(x)*y) (0,1) NaN NaN exp(log(x)*y) (0,1) +0,-0 +1 exp(log(x)*y) (0,1) +Inf +0 exp(log(x)*y) (0,1) -Inf +Inf exp(log(x)*y) (-1,0) NaN NaN (-1,0) +0,-0 +1 (-1,0) +Inf +0 (-1,0) -Inf +Inf (-1,0) nonintegral NaN x > 1 NaN NaN x > 1 +0,-0 +1 x > 1 +Inf +Inf x > 1 -Inf +0 x < -1 NaN NaN x < -1 +0,-0 +1 x < -1 +Inf +Inf x < -1 -Inf +0 x < -1 nonintegral NaN */ #define FL_1 0x3f800000 /* +1.0 */ ENTRY pow ; ZH := exponent of y X_movw ZL, rB2 lsl ZL rol ZH ; y == 0 ? adiw ZL, 0 cpc rB0, r1 cpc rB1, r1 breq .L_one ; preliminary check cp rA0, r1 cpc rA1, r1 brne 0f ; skip a bit of comparisons ; x == 1.0 ? cpi rA2, hlo8(FL_1) ldi rAE, hhi8(FL_1) cpc rA3, rAE breq .L_ret ; x == -0.0 ? set ; flag: nonintegral y is a legal value cpi rA3, 0x80 cpc rA2, r1 breq .L_int ; x == -Inf ? cpi rA2, 0x80 ldi rAE, 0xff cpc rA3, rAE breq .L_int ; x >= 0 ? 0: tst rA3 brpl .L_pow ; isinf(y) ? cpi ZH, 0xff cpc ZL, r1 cpc rB1, r1 cpc rB0, r1 breq .L_big ; isintegral(y) ? clt ; nonintegral y is not a legal value .L_int: /* Now we have: y is nonzero value ZL == (rB2 << 1) ZH == exponenta, ZH <= 254 */ sec ; hidden bit ror ZL ; This is incorrect for subnormals, no sense: ; result would NaN. ; ffs(). Next two loops are finite due to above 'sec'. X_movw XL, rB0 ; Byte search loop. 1: tst XL brne 2f mov XL, XH mov XH, ZL subi ZH, -8 brcs 1b rjmp .L_noint ; mantisa too big ; Bit search loop. 2: subi ZH, -1 brcc .L_noint ; mantisa too big lsr XL brcc 2b ; Check exponent, is y an integral value? /* Example: 1.0 == 0x3f800000: exponent: ZH := 0x7f byte search: ZH += 2*8 --> 0x8f bit search: ZH += 8 --> 0x97 */ cpi ZH, 0x97 brlo .L_noint breq 3f ; y % 2 == 1 cpi ZH, 0x97 + 24 brsh .L_noint andi rA3, 0x7f ; y is integral, y % 2 == 0 3: push rA3 rcall .L_pow pop r0 sbrc r0, 7 subi rA3, 0x80 .L_ret: ret ; y is not an integral number .L_noint: brts .L_pow .L_nan: rjmp _U(__fp_nan) .L_one: ldi rA0, lo8(FL_1) ldi rA1, hi8(FL_1) ldi rA2, hlo8(FL_1) ldi rA3, hhi8(FL_1) ret ; replace Inf --> big finite (to exclude '0 * Inf' for legal x == -1) .L_big: ldi rB2, 0x7f .L_pow: andi rA3, 0x7f push rB3 push rB2 push rB1 push rB0 rcall _U(log) pop rB0 pop rB1 pop rB2 pop rB3 rcall _U(__mulsf3) rjmp _U(exp) ENDFUNC