1/* 2 * Copyright (c) 1985 Regents of the University of California. 3 * 4 * Use and reproduction of this software are granted in accordance with 5 * the terms and conditions specified in the Berkeley Software License 6 * Agreement (in particular, this entails acknowledgement of the programs' 7 * source, and inclusion of this notice) with the additional understanding 8 * that all recipients should regard themselves as participants in an 9 * ongoing research project and hence should feel obligated to report 10 * their experiences (good or bad) with these elementary function codes, 11 * using "sendbug 4bsd-bugs@BERKELEY", to the authors. 12 * 13 * 14 * @(#)sqrt.s 1.1 (Berkeley) 08/21/85 15 * 16 * double sqrt(arg) revised August 15,1982 17 * double arg; 18 * if(arg<0.0) { _errno = EDOM; return(<a reserved operand>); } 19 * if arg is a reserved operand it is returned as it is 20 * W. Kahan's magic square root 21 * coded by Heidi Stettner and revised by Emile LeBlanc 8/18/82 22 * 23 * entry points:_d_sqrt address of double arg is on the stack 24 * _sqrt double arg is on the stack 25 */ 26 .text 27 .align 1 28 .globl _sqrt 29 .globl _d_sqrt 30 .globl libm$dsqrt_r5 31 .set EDOM,33 32 33_d_sqrt: 34 .word 0x003c # save r5,r4,r3,r2 35 movq *4(ap),r0 36 jmp dsqrt2 37_sqrt: 38 .word 0x003c # save r5,r4,r3,r2 39 movq 4(ap),r0 40dsqrt2: bicw3 $0x807f,r0,r2 # check exponent of input 41 jeql noexp # biased exponent is zero -> 0.0 or reserved 42 bsbb libm$dsqrt_r5 43noexp: ret 44 45/* **************************** internal procedure */ 46 47libm$dsqrt_r5: # ENTRY POINT FOR cdabs and cdsqrt 48 # returns double square root scaled by 49 # 2^r6 50 51 movd r0,r4 52 jleq nonpos # argument is not positive 53 movzwl r4,r2 54 ashl $-1,r2,r0 55 addw2 $0x203c,r0 # r0 has magic initial approximation 56/* 57 * Do two steps of Heron's rule 58 * ((arg/guess) + guess) / 2 = better guess 59 */ 60 divf3 r0,r4,r2 61 addf2 r2,r0 62 subw2 $0x80,r0 # divide by two 63 64 divf3 r0,r4,r2 65 addf2 r2,r0 66 subw2 $0x80,r0 # divide by two 67 68/* Scale argument and approximation to prevent over/underflow */ 69 70 bicw3 $0x807f,r4,r1 71 subw2 $0x4080,r1 # r1 contains scaling factor 72 subw2 r1,r4 73 movl r0,r2 74 subw2 r1,r2 75 76/* Cubic step 77 * 78 * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation, 79 * a is approximation, and n is the original argument. 80 * (let s be scale factor in the following comments) 81 */ 82 clrl r1 83 clrl r3 84 muld2 r0,r2 # r2:r3 = a*a/s 85 subd2 r2,r4 # r4:r5 = n/s - a*a/s 86 addw2 $0x100,r2 # r2:r3 = 4*a*a/s 87 addd2 r4,r2 # r2:r3 = n/s + 3*a*a/s 88 muld2 r0,r4 # r4:r5 = a*n/s - a*a*a/s 89 divd2 r2,r4 # r4:r5 = a*(n-a*a)/(n+3*a*a) 90 addw2 $0x80,r4 # r4:r5 = 2*a*(n-a*a)/(n+3*a*a) 91 addd2 r4,r0 # r0:r1 = a + 2*a*(n-a*a)/(n+3*a*a) 92 rsb # DONE! 93nonpos: 94 jneq negarg 95 ret # argument and root are zero 96negarg: 97 pushl $EDOM 98 calls $1,_infnan # generate the reserved op fault 99 ret 100