| /* Copyright (c) 2018, Oracle and/or its affiliates. All rights reserved. |
| * Copyright (c) 2018, Cavium. All rights reserved. (By BELLSOFT) |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| * |
| */ |
| |
| #include "precompiled.hpp" |
| #include "asm/assembler.hpp" |
| #include "asm/assembler.inline.hpp" |
| #include "runtime/stubRoutines.hpp" |
| #include "macroAssembler_aarch64.hpp" |
| |
| // The following code is a optimized version of fdlibm sin/cos implementation |
| // (C code is in share/runtime/sharedRuntimeTrig.cpp) adapted for AARCH64. |
| |
| // Please refer to sin/cos approximation via polynomial and |
| // trigonometric argument reduction techniques to the following literature: |
| // |
| // [1] Muller, Jean-Michel, Nicolas Brisebarre, Florent De Dinechin, |
| // Claude-Pierre Jeannerod, Vincent Lefevre, Guillaume Melquiond, |
| // Nathalie Revol, Damien Stehlé, and Serge Torres: |
| // Handbook of floating-point arithmetic. |
| // Springer Science & Business Media, 2009. |
| // [2] K. C. Ng |
| // Argument Reduction for Huge Arguments: Good to the Last Bit |
| // July 13, 1992, SunPro |
| // |
| // HOW TO READ THIS CODE: |
| // This code consists of several functions. Each function has following header: |
| // 1) Description |
| // 2) C-pseudo code with differences from fdlibm marked by comments starting |
| // with "NOTE". Check unmodified fdlibm code in |
| // share/runtime/SharedRuntimeTrig.cpp |
| // 3) Brief textual description of changes between fdlibm and current |
| // implementation along with optimization notes (if applicable) |
| // 4) Assumptions, input and output |
| // 5) (Optional) additional notes about intrinsic implementation |
| // Each function is separated in blocks which follow the pseudo-code structure |
| // |
| // HIGH-LEVEL ALGORITHM DESCRIPTION: |
| // - entry point: generate_dsin_dcos(...); |
| // - check corner cases: NaN, INF, tiny argument. |
| // - check if |x| < Pi/4. Then approximate sin/cos via polynomial (kernel_sin/kernel_cos) |
| // -- else proceed to argument reduction routine (__ieee754_rem_pio2) and |
| // use reduced argument to get result via kernel_sin/kernel_cos |
| // |
| // HIGH-LEVEL CHANGES BETWEEN INTRINSICS AND FDLIBM: |
| // 1) two_over_pi table fdlibm representation is int[], while intrinsic version |
| // has these int values converted to double representation to load converted |
| // double values directly (see stubRoutines_aarch4::_two_over_pi) |
| // 2) Several loops are unrolled and vectorized: see comments in code after |
| // labels: SKIP_F_LOAD, RECOMP_FOR1_CHECK, RECOMP_FOR2 |
| // 3) fdlibm npio2_hw table now has "prefix" with constants used in |
| // calculation. These constants are loaded from npio2_hw table instead of |
| // constructing it in code (see stubRoutines_aarch64.cpp) |
| // 4) Polynomial coefficients for sin and cos are moved to table sin_coef |
| // and cos_coef to use the same optimization as in 3). It allows to load most of |
| // required constants via single instruction |
| // |
| // |
| // |
| ///* __ieee754_rem_pio2(x,y) |
| // * |
| // * returns the remainder of x rem pi/2 in y[0]+y[1] (i.e. like x div pi/2) |
| // * x is input argument, y[] is hi and low parts of reduced argument (x) |
| // * uses __kernel_rem_pio2() |
| // */ |
| // // use tables(see stubRoutines_aarch64.cpp): two_over_pi and modified npio2_hw |
| // |
| // BEGIN __ieee754_rem_pio2 PSEUDO CODE |
| // |
| //static int __ieee754_rem_pio2(double x, double *y) { |
| // double z,w,t,r,fn; |
| // double tx[3]; |
| // int e0,i,j,nx,n,ix,hx,i0; |
| // |
| // i0 = ((*(int*)&two24A)>>30)^1; /* high word index */ |
| // hx = *(i0+(int*)&x); /* high word of x */ |
| // ix = hx&0x7fffffff; |
| // if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ |
| // if(hx>0) { |
| // z = x - pio2_1; |
| // if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
| // y[0] = z - pio2_1t; |
| // y[1] = (z-y[0])-pio2_1t; |
| // } else { /* near pi/2, use 33+33+53 bit pi */ |
| // z -= pio2_2; |
| // y[0] = z - pio2_2t; |
| // y[1] = (z-y[0])-pio2_2t; |
| // } |
| // return 1; |
| // } else { /* negative x */ |
| // z = x + pio2_1; |
| // if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
| // y[0] = z + pio2_1t; |
| // y[1] = (z-y[0])+pio2_1t; |
| // } else { /* near pi/2, use 33+33+53 bit pi */ |
| // z += pio2_2; |
| // y[0] = z + pio2_2t; |
| // y[1] = (z-y[0])+pio2_2t; |
| // } |
| // return -1; |
| // } |
| // } |
| // if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ |
| // t = fabsd(x); |
| // n = (int) (t*invpio2+half); |
| // fn = (double)n; |
| // r = t-fn*pio2_1; |
| // w = fn*pio2_1t; /* 1st round good to 85 bit */ |
| // // NOTE: y[0] = r-w; is moved from if/else below to be before "if" |
| // y[0] = r-w; |
| // if(n<32&&ix!=npio2_hw[n-1]) { |
| // // y[0] = r-w; /* quick check no cancellation */ // NOTE: moved earlier |
| // } else { |
| // j = ix>>20; |
| // // y[0] = r-w; // NOTE: moved earlier |
| // i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff); |
| // if(i>16) { /* 2nd iteration needed, good to 118 */ |
| // t = r; |
| // w = fn*pio2_2; |
| // r = t-w; |
| // w = fn*pio2_2t-((t-r)-w); |
| // y[0] = r-w; |
| // i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff); |
| // if(i>49) { /* 3rd iteration need, 151 bits acc */ |
| // t = r; /* will cover all possible cases */ |
| // w = fn*pio2_3; |
| // r = t-w; |
| // w = fn*pio2_3t-((t-r)-w); |
| // y[0] = r-w; |
| // } |
| // } |
| // } |
| // y[1] = (r-y[0])-w; |
| // if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
| // else return n; |
| // } |
| // /* |
| // * all other (large) arguments |
| // */ |
| // // NOTE: this check is removed, because it was checked in dsin/dcos |
| // // if(ix>=0x7ff00000) { /* x is inf or NaN */ |
| // // y[0]=y[1]=x-x; return 0; |
| // // } |
| // /* set z = scalbn(|x|,ilogb(x)-23) */ |
| // *(1-i0+(int*)&z) = *(1-i0+(int*)&x); |
| // e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ |
| // *(i0+(int*)&z) = ix - (e0<<20); |
| // |
| // // NOTE: "for" loop below in unrolled. See comments in asm code |
| // for(i=0;i<2;i++) { |
| // tx[i] = (double)((int)(z)); |
| // z = (z-tx[i])*two24A; |
| // } |
| // |
| // tx[2] = z; |
| // nx = 3; |
| // |
| // // NOTE: while(tx[nx-1]==zeroA) nx--; is unrolled. See comments in asm code |
| // while(tx[nx-1]==zeroA) nx--; /* skip zero term */ |
| // |
| // n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); |
| // if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
| // return n; |
| //} |
| // |
| // END __ieee754_rem_pio2 PSEUDO CODE |
| // |
| // Changes between fdlibm and intrinsic for __ieee754_rem_pio2: |
| // 1. INF/NaN check for huge argument is removed in comparison with fdlibm |
| // code, because this check is already done in dcos/dsin code |
| // 2. Most constants are now loaded from table instead of direct initialization |
| // 3. Two loops are unrolled |
| // Assumptions: |
| // 1. Assume |X| >= PI/4 |
| // 2. Assume rscratch1 = 0x3fe921fb00000000 (~ PI/4) |
| // 3. Assume ix = r3 |
| // Input and output: |
| // 1. Input: X = r0 |
| // 2. Return n in r2, y[0] == y0 == v4, y[1] == y1 == v5 |
| // NOTE: general purpose register names match local variable names in C code |
| // NOTE: fpu registers are actively reused. See comments in code about their usage |
| void MacroAssembler::generate__ieee754_rem_pio2(address npio2_hw, |
| address two_over_pi, address pio2) { |
| const int64_t PIO2_1t = 0x3DD0B4611A626331ULL; |
| const int64_t PIO2_2 = 0x3DD0B4611A600000ULL; |
| const int64_t PIO2_2t = 0x3BA3198A2E037073ULL; |
| Label X_IS_NEGATIVE, X_IS_MEDIUM_OR_LARGE, X_IS_POSITIVE_LONG_PI, LARGE_ELSE, |
| REDUCTION_DONE, X_IS_MEDIUM_BRANCH_DONE, X_IS_LARGE, NX_SET, |
| X_IS_NEGATIVE_LONG_PI; |
| Register X = r0, n = r2, ix = r3, jv = r4, tmp5 = r5, jx = r6, |
| tmp3 = r7, iqBase = r10, ih = r11, i = r17; |
| // initializing constants first |
| // rscratch1 = 0x3fe921fb00000000 (see assumptions) |
| movk(rscratch1, 0x3ff9, 48); // was 0x3fe921fb0..0 now it's 0x3ff921fb0..0 |
| mov(rscratch2, 0x4002d97c); // 3*PI/4 high word |
| movk(rscratch1, 0x5440, 16); // now rscratch1 == PIO2_1 |
| fmovd(v1, rscratch1); // v1 = PIO2_1 |
| cmp(rscratch2, ix); |
| br(LE, X_IS_MEDIUM_OR_LARGE); |
| |
| block_comment("if(ix<0x4002d97c) {... /* |x| ~< 3pi/4 */ "); { |
| cmp(X, zr); |
| br(LT, X_IS_NEGATIVE); |
| |
| block_comment("if(hx>0) {"); { |
| fsubd(v2, v0, v1); // v2 = z = x - pio2_1 |
| cmp(ix, rscratch1, LSR, 32); |
| mov(n, 1); |
| br(EQ, X_IS_POSITIVE_LONG_PI); |
| |
| block_comment("case: hx > 0 && ix!=0x3ff921fb {"); { /* 33+53 bit pi is good enough */ |
| mov(rscratch2, PIO2_1t); |
| fmovd(v27, rscratch2); |
| fsubd(v4, v2, v27); // v4 = y[0] = z - pio2_1t; |
| fsubd(v5, v2, v4); |
| fsubd(v5, v5, v27); // v5 = y[1] = (z-y[0])-pio2_1t |
| b(REDUCTION_DONE); |
| } |
| |
| block_comment("case: hx > 0 &*& ix==0x3ff921fb {"); { /* near pi/2, use 33+33+53 bit pi */ |
| bind(X_IS_POSITIVE_LONG_PI); |
| mov(rscratch1, PIO2_2); |
| mov(rscratch2, PIO2_2t); |
| fmovd(v27, rscratch1); |
| fmovd(v6, rscratch2); |
| fsubd(v2, v2, v27); // z-= pio2_2 |
| fsubd(v4, v2, v6); // y[0] = z - pio2_2t |
| fsubd(v5, v2, v4); |
| fsubd(v5, v5, v6); // v5 = (z - y[0]) - pio2_2t |
| b(REDUCTION_DONE); |
| } |
| } |
| |
| block_comment("case: hx <= 0)"); { |
| bind(X_IS_NEGATIVE); |
| faddd(v2, v0, v1); // v2 = z = x + pio2_1 |
| cmp(ix, rscratch1, LSR, 32); |
| mov(n, -1); |
| br(EQ, X_IS_NEGATIVE_LONG_PI); |
| |
| block_comment("case: hx <= 0 && ix!=0x3ff921fb) {"); { /* 33+53 bit pi is good enough */ |
| mov(rscratch2, PIO2_1t); |
| fmovd(v27, rscratch2); |
| faddd(v4, v2, v27); // v4 = y[0] = z + pio2_1t; |
| fsubd(v5, v2, v4); |
| faddd(v5, v5, v27); // v5 = y[1] = (z-y[0]) + pio2_1t |
| b(REDUCTION_DONE); |
| } |
| |
| block_comment("case: hx <= 0 && ix==0x3ff921fb"); { /* near pi/2, use 33+33+53 bit pi */ |
| bind(X_IS_NEGATIVE_LONG_PI); |
| mov(rscratch1, PIO2_2); |
| mov(rscratch2, PIO2_2t); |
| fmovd(v27, rscratch1); |
| fmovd(v6, rscratch2); |
| faddd(v2, v2, v27); // z += pio2_2 |
| faddd(v4, v2, v6); // y[0] = z + pio2_2t |
| fsubd(v5, v2, v4); |
| faddd(v5, v5, v6); // v5 = (z - y[0]) + pio2_2t |
| b(REDUCTION_DONE); |
| } |
| } |
| } |
| bind(X_IS_MEDIUM_OR_LARGE); |
| mov(rscratch1, 0x413921fb); |
| cmp(ix, rscratch1); // ix < = 0x413921fb ? |
| br(GT, X_IS_LARGE); |
| |
| block_comment("|x| ~<= 2^19*(pi/2), medium size"); { |
| lea(ih, ExternalAddress(npio2_hw)); |
| ld1(v4, v5, v6, v7, T1D, ih); |
| fabsd(v31, v0); // v31 = t = |x| |
| add(ih, ih, 64); |
| fmaddd(v2, v31, v5, v4); // v2 = t * invpio2 + half (invpio2 = 53 bits of 2/pi, half = 0.5) |
| fcvtzdw(n, v2); // n = (int) v2 |
| frintzd(v2, v2); |
| fmsubd(v3, v2, v6, v31); // v3 = r = t - fn * pio2_1 |
| fmuld(v26, v2, v7); // v26 = w = fn * pio2_1t |
| fsubd(v4, v3, v26); // y[0] = r - w. Calculated before branch |
| cmp(n, 32); |
| br(GT, LARGE_ELSE); |
| subw(tmp5, n, 1); // tmp5 = n - 1 |
| ldrw(jv, Address(ih, tmp5, Address::lsl(2))); |
| cmp(ix, jv); |
| br(NE, X_IS_MEDIUM_BRANCH_DONE); |
| |
| block_comment("else block for if(n<32&&ix!=npio2_hw[n-1])"); { |
| bind(LARGE_ELSE); |
| fmovd(jx, v4); |
| lsr(tmp5, ix, 20); // j = ix >> 20 |
| lsl(jx, jx, 1); |
| sub(tmp3, tmp5, jx, LSR, 32 + 20 + 1); // r7 = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff); |
| |
| block_comment("if(i>16)"); { |
| cmp(tmp3, 16); |
| br(LE, X_IS_MEDIUM_BRANCH_DONE); |
| // i > 16. 2nd iteration needed |
| ldpd(v6, v7, Address(ih, -32)); |
| fmovd(v28, v3); // t = r |
| fmuld(v29, v2, v6); // w = v29 = fn * pio2_2 |
| fsubd(v3, v28, v29); // r = t - w |
| fsubd(v31, v28, v3); // v31 = (t - r) |
| fsubd(v31, v29, v31); // v31 = w - (t - r) = - ((t - r) - w) |
| fmaddd(v26, v2, v7, v31); // v26 = w = fn*pio2_2t - ((t - r) - w) |
| fsubd(v4, v3, v26); // y[0] = r - w |
| fmovd(jx, v4); |
| lsl(jx, jx, 1); |
| sub(tmp3, tmp5, jx, LSR, 32 + 20 + 1); // r7 = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff); |
| |
| block_comment("if(i>49)"); { |
| cmp(tmp3, 49); |
| br(LE, X_IS_MEDIUM_BRANCH_DONE); |
| // 3rd iteration need, 151 bits acc |
| ldpd(v6, v7, Address(ih, -16)); |
| fmovd(v28, v3); // save "r" |
| fmuld(v29, v2, v6); // v29 = fn * pio2_3 |
| fsubd(v3, v28, v29); // r = r - w |
| fsubd(v31, v28, v3); // v31 = (t - r) |
| fsubd(v31, v29, v31); // v31 = w - (t - r) = - ((t - r) - w) |
| fmaddd(v26, v2, v7, v31); // v26 = w = fn*pio2_3t - ((t - r) - w) |
| fsubd(v4, v3, v26); // y[0] = r - w |
| } |
| } |
| } |
| block_comment("medium x tail"); { |
| bind(X_IS_MEDIUM_BRANCH_DONE); |
| fsubd(v5, v3, v4); // v5 = y[1] = (r - y[0]) |
| fsubd(v5, v5, v26); // v5 = y[1] = (r - y[0]) - w |
| cmp(X, zr); |
| br(GT, REDUCTION_DONE); |
| fnegd(v4, v4); |
| negw(n, n); |
| fnegd(v5, v5); |
| b(REDUCTION_DONE); |
| } |
| } |
| |
| block_comment("all other (large) arguments"); { |
| bind(X_IS_LARGE); |
| lsr(rscratch1, ix, 20); // ix >> 20 |
| movz(tmp5, 0x4170, 48); |
| subw(rscratch1, rscratch1, 1046); // e0 |
| fmovd(v24, tmp5); // init two24A value |
| subw(jv, ix, rscratch1, LSL, 20); // ix - (e0<<20) |
| lsl(jv, jv, 32); |
| subw(rscratch2, rscratch1, 3); |
| bfm(jv, X, 0, 31); // jv = z |
| movw(i, 24); |
| fmovd(v26, jv); // v26 = z |
| |
| block_comment("unrolled for(i=0;i<2;i++) {tx[i] = (double)((int)(z));z = (z-tx[i])*two24A;}"); { |
| // tx[0,1,2] = v6,v7,v26 |
| frintzd(v6, v26); // v6 = (double)((int)v26) |
| sdivw(jv, rscratch2, i); // jv = (e0 - 3)/24 |
| fsubd(v26, v26, v6); |
| sub(sp, sp, 560); |
| fmuld(v26, v26, v24); |
| frintzd(v7, v26); // v7 = (double)((int)v26) |
| movw(jx, 2); // calculate jx as nx - 1, which is initially 2. Not a part of unrolled loop |
| fsubd(v26, v26, v7); |
| } |
| |
| block_comment("nx calculation with unrolled while(tx[nx-1]==zeroA) nx--;"); { |
| fcmpd(v26, 0.0); // if NE then jx == 2. else it's 1 or 0 |
| add(iqBase, sp, 480); // base of iq[] |
| fmuld(v3, v26, v24); |
| br(NE, NX_SET); |
| fcmpd(v7, 0.0); // v7 == 0 => jx = 0. Else jx = 1 |
| csetw(jx, NE); |
| } |
| bind(NX_SET); |
| generate__kernel_rem_pio2(two_over_pi, pio2); |
| // now we have y[0] = v4, y[1] = v5 and n = r2 |
| cmp(X, zr); |
| br(GE, REDUCTION_DONE); |
| fnegd(v4, v4); |
| fnegd(v5, v5); |
| negw(n, n); |
| } |
| bind(REDUCTION_DONE); |
| } |
| |
| ///* |
| // * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) |
| // * double x[],y[]; int e0,nx,prec; int ipio2[]; |
| // * |
| // * __kernel_rem_pio2 return the last three digits of N with |
| // * y = x - N*pi/2 |
| // * so that |y| < pi/2. |
| // * |
| // * The method is to compute the integer (mod 8) and fraction parts of |
| // * (2/pi)*x without doing the full multiplication. In general we |
| // * skip the part of the product that are known to be a huge integer ( |
| // * more accurately, = 0 mod 8 ). Thus the number of operations are |
| // * independent of the exponent of the input. |
| // * |
| // * NOTE: 2/pi int representation is converted to double |
| // * // (2/pi) is represented by an array of 24-bit integers in ipio2[]. |
| // * |
| // * Input parameters: |
| // * x[] The input value (must be positive) is broken into nx |
| // * pieces of 24-bit integers in double precision format. |
| // * x[i] will be the i-th 24 bit of x. The scaled exponent |
| // * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 |
| // * match x's up to 24 bits. |
| // * |
| // * Example of breaking a double positive z into x[0]+x[1]+x[2]: |
| // * e0 = ilogb(z)-23 |
| // * z = scalbn(z,-e0) |
| // * for i = 0,1,2 |
| // * x[i] = floor(z) |
| // * z = (z-x[i])*2**24 |
| // * |
| // * |
| // * y[] ouput result in an array of double precision numbers. |
| // * The dimension of y[] is: |
| // * 24-bit precision 1 |
| // * 53-bit precision 2 |
| // * 64-bit precision 2 |
| // * 113-bit precision 3 |
| // * The actual value is the sum of them. Thus for 113-bit |
| // * precsion, one may have to do something like: |
| // * |
| // * long double t,w,r_head, r_tail; |
| // * t = (long double)y[2] + (long double)y[1]; |
| // * w = (long double)y[0]; |
| // * r_head = t+w; |
| // * r_tail = w - (r_head - t); |
| // * |
| // * e0 The exponent of x[0] |
| // * |
| // * nx dimension of x[] |
| // * |
| // * prec an interger indicating the precision: |
| // * 0 24 bits (single) |
| // * 1 53 bits (double) |
| // * 2 64 bits (extended) |
| // * 3 113 bits (quad) |
| // * |
| // * NOTE: ipio2[] array below is converted to double representation |
| // * //ipio2[] |
| // * // integer array, contains the (24*i)-th to (24*i+23)-th |
| // * // bit of 2/pi after binary point. The corresponding |
| // * // floating value is |
| // * |
| // * ipio2[i] * 2^(-24(i+1)). |
| // * |
| // * Here is the description of some local variables: |
| // * |
| // * jk jk+1 is the initial number of terms of ipio2[] needed |
| // * in the computation. The recommended value is 2,3,4, |
| // * 6 for single, double, extended,and quad. |
| // * |
| // * jz local integer variable indicating the number of |
| // * terms of ipio2[] used. |
| // * |
| // * jx nx - 1 |
| // * |
| // * jv index for pointing to the suitable ipio2[] for the |
| // * computation. In general, we want |
| // * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 |
| // * is an integer. Thus |
| // * e0-3-24*jv >= 0 or (e0-3)/24 >= jv |
| // * Hence jv = max(0,(e0-3)/24). |
| // * |
| // * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. |
| // * |
| // * q[] double array with integral value, representing the |
| // * 24-bits chunk of the product of x and 2/pi. |
| // * |
| // * q0 the corresponding exponent of q[0]. Note that the |
| // * exponent for q[i] would be q0-24*i. |
| // * |
| // * PIo2[] double precision array, obtained by cutting pi/2 |
| // * into 24 bits chunks. |
| // * |
| // * f[] ipio2[] in floating point |
| // * |
| // * iq[] integer array by breaking up q[] in 24-bits chunk. |
| // * |
| // * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] |
| // * |
| // * ih integer. If >0 it indicates q[] is >= 0.5, hence |
| // * it also indicates the *sign* of the result. |
| // * |
| // */ |
| // |
| // Use PIo2 table(see stubRoutines_aarch64.cpp) |
| // |
| // BEGIN __kernel_rem_pio2 PSEUDO CODE |
| // |
| //static int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, /* NOTE: converted to double */ const double *ipio2 // const int *ipio2) { |
| // int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; |
| // double z,fw,f[20],fq[20],q[20]; |
| // |
| // /* initialize jk*/ |
| // // jk = init_jk[prec]; // NOTE: prec==2 for double. jk is always 4. |
| // jp = jk; // NOTE: always 4 |
| // |
| // /* determine jx,jv,q0, note that 3>q0 */ |
| // jx = nx-1; |
| // jv = (e0-3)/24; if(jv<0) jv=0; |
| // q0 = e0-24*(jv+1); |
| // |
| // /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ |
| // j = jv-jx; m = jx+jk; |
| // |
| // // NOTE: split into two for-loops: one with zeroB and one with ipio2[j]. It |
| // // allows the use of wider loads/stores |
| // for(i=0;i<=m;i++,j++) f[i] = (j<0)? zeroB : /* NOTE: converted to double */ ipio2[j]; //(double) ipio2[j]; |
| // |
| // // NOTE: unrolled and vectorized "for". See comments in asm code |
| // /* compute q[0],q[1],...q[jk] */ |
| // for (i=0;i<=jk;i++) { |
| // for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; |
| // } |
| // |
| // jz = jk; |
| //recompute: |
| // /* distill q[] into iq[] reversingly */ |
| // for(i=0,j=jz,z=q[jz];j>0;i++,j--) { |
| // fw = (double)((int)(twon24* z)); |
| // iq[i] = (int)(z-two24B*fw); |
| // z = q[j-1]+fw; |
| // } |
| // |
| // /* compute n */ |
| // z = scalbnA(z,q0); /* actual value of z */ |
| // z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ |
| // n = (int) z; |
| // z -= (double)n; |
| // ih = 0; |
| // if(q0>0) { /* need iq[jz-1] to determine n */ |
| // i = (iq[jz-1]>>(24-q0)); n += i; |
| // iq[jz-1] -= i<<(24-q0); |
| // ih = iq[jz-1]>>(23-q0); |
| // } |
| // else if(q0==0) ih = iq[jz-1]>>23; |
| // else if(z>=0.5) ih=2; |
| // |
| // if(ih>0) { /* q > 0.5 */ |
| // n += 1; carry = 0; |
| // for(i=0;i<jz ;i++) { /* compute 1-q */ |
| // j = iq[i]; |
| // if(carry==0) { |
| // if(j!=0) { |
| // carry = 1; iq[i] = 0x1000000- j; |
| // } |
| // } else iq[i] = 0xffffff - j; |
| // } |
| // if(q0>0) { /* rare case: chance is 1 in 12 */ |
| // switch(q0) { |
| // case 1: |
| // iq[jz-1] &= 0x7fffff; break; |
| // case 2: |
| // iq[jz-1] &= 0x3fffff; break; |
| // } |
| // } |
| // if(ih==2) { |
| // z = one - z; |
| // if(carry!=0) z -= scalbnA(one,q0); |
| // } |
| // } |
| // |
| // /* check if recomputation is needed */ |
| // if(z==zeroB) { |
| // j = 0; |
| // for (i=jz-1;i>=jk;i--) j |= iq[i]; |
| // if(j==0) { /* need recomputation */ |
| // for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ |
| // |
| // for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ |
| // f[jx+i] = /* NOTE: converted to double */ ipio2[jv+i]; //(double) ipio2[jv+i]; |
| // for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; |
| // q[i] = fw; |
| // } |
| // jz += k; |
| // goto recompute; |
| // } |
| // } |
| // |
| // /* chop off zero terms */ |
| // if(z==0.0) { |
| // jz -= 1; q0 -= 24; |
| // while(iq[jz]==0) { jz--; q0-=24;} |
| // } else { /* break z into 24-bit if necessary */ |
| // z = scalbnA(z,-q0); |
| // if(z>=two24B) { |
| // fw = (double)((int)(twon24*z)); |
| // iq[jz] = (int)(z-two24B*fw); |
| // jz += 1; q0 += 24; |
| // iq[jz] = (int) fw; |
| // } else iq[jz] = (int) z ; |
| // } |
| // |
| // /* convert integer "bit" chunk to floating-point value */ |
| // fw = scalbnA(one,q0); |
| // for(i=jz;i>=0;i--) { |
| // q[i] = fw*(double)iq[i]; fw*=twon24; |
| // } |
| // |
| // /* compute PIo2[0,...,jp]*q[jz,...,0] */ |
| // for(i=jz;i>=0;i--) { |
| // for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; |
| // fq[jz-i] = fw; |
| // } |
| // |
| // // NOTE: switch below is eliminated, because prec is always 2 for doubles |
| // /* compress fq[] into y[] */ |
| // //switch(prec) { |
| // //case 0: |
| // // fw = 0.0; |
| // // for (i=jz;i>=0;i--) fw += fq[i]; |
| // // y[0] = (ih==0)? fw: -fw; |
| // // break; |
| // //case 1: |
| // //case 2: |
| // fw = 0.0; |
| // for (i=jz;i>=0;i--) fw += fq[i]; |
| // y[0] = (ih==0)? fw: -fw; |
| // fw = fq[0]-fw; |
| // for (i=1;i<=jz;i++) fw += fq[i]; |
| // y[1] = (ih==0)? fw: -fw; |
| // // break; |
| // //case 3: /* painful */ |
| // // for (i=jz;i>0;i--) { |
| // // fw = fq[i-1]+fq[i]; |
| // // fq[i] += fq[i-1]-fw; |
| // // fq[i-1] = fw; |
| // // } |
| // // for (i=jz;i>1;i--) { |
| // // fw = fq[i-1]+fq[i]; |
| // // fq[i] += fq[i-1]-fw; |
| // // fq[i-1] = fw; |
| // // } |
| // // for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; |
| // // if(ih==0) { |
| // // y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; |
| // // } else { |
| // // y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; |
| // // } |
| // //} |
| // return n&7; |
| //} |
| // |
| // END __kernel_rem_pio2 PSEUDO CODE |
| // |
| // Changes between fdlibm and intrinsic: |
| // 1. One loop is unrolled and vectorized (see comments in code) |
| // 2. One loop is split into 2 loops (see comments in code) |
| // 3. Non-double code is removed(last switch). Sevaral variables became |
| // constants because of that (see comments in code) |
| // 4. Use of jx, which is nx-1 instead of nx |
| // Assumptions: |
| // 1. Assume |X| >= PI/4 |
| // Input and output: |
| // 1. Input: X = r0, jx == nx - 1 == r6, e0 == rscratch1 |
| // 2. Return n in r2, y[0] == y0 == v4, y[1] == y1 == v5 |
| // NOTE: general purpose register names match local variable names in C code |
| // NOTE: fpu registers are actively reused. See comments in code about their usage |
| void MacroAssembler::generate__kernel_rem_pio2(address two_over_pi, address pio2) { |
| Label Q_DONE, JX_IS_0, JX_IS_2, COMP_INNER_LOOP, RECOMP_FOR2, Q0_ZERO_CMP_LT, |
| RECOMP_CHECK_DONE_NOT_ZERO, Q0_ZERO_CMP_DONE, COMP_FOR, Q0_ZERO_CMP_EQ, |
| INIT_F_ZERO, RECOMPUTE, IH_FOR_INCREMENT, IH_FOR_STORE, RECOMP_CHECK_DONE, |
| Z_IS_LESS_THAN_TWO24B, Z_IS_ZERO, FW_Y1_NO_NEGATION, |
| RECOMP_FW_UPDATED, Z_ZERO_CHECK_DONE, FW_FOR1, IH_AFTER_SWITCH, IH_HANDLED, |
| CONVERTION_FOR, FW_Y0_NO_NEGATION, FW_FOR1_DONE, FW_FOR2, FW_FOR2_DONE, |
| IH_FOR, SKIP_F_LOAD, RECOMP_FOR1, RECOMP_FIRST_FOR, INIT_F_COPY, |
| RECOMP_FOR1_CHECK; |
| Register tmp2 = r1, n = r2, jv = r4, tmp5 = r5, jx = r6, |
| tmp3 = r7, iqBase = r10, ih = r11, tmp4 = r12, tmp1 = r13, |
| jz = r14, j = r15, twoOverPiBase = r16, i = r17, qBase = r18; |
| // jp = jk == init_jk[prec] = init_jk[2] == {2,3,4,6}[2] == 4 |
| // jx = nx - 1 |
| lea(twoOverPiBase, ExternalAddress(two_over_pi)); |
| cmpw(jv, zr); |
| addw(tmp4, jx, 4); // tmp4 = m = jx + jk = jx + 4. jx is in {0,1,2} so m is in [4,5,6] |
| cselw(jv, jv, zr, GE); |
| fmovd(v26, 0.0); |
| addw(tmp5, jv, 1); // jv+1 |
| subsw(j, jv, jx); |
| add(qBase, sp, 320); // base of q[] |
| msubw(rscratch1, i, tmp5, rscratch1); // q0 = e0-24*(jv+1) |
| // use double f[20], fq[20], q[20], iq[20] on stack, which is |
| // (20 + 20 + 20) x 8 + 20 x 4 = 560 bytes. From lower to upper addresses it |
| // will contain f[20], fq[20], q[20], iq[20] |
| // now initialize f[20] indexes 0..m (inclusive) |
| // for(i=0;i<=m;i++,j++) f[i] = (j<0)? zeroB : /* NOTE: converted to double */ ipio2[j]; // (double) ipio2[j]; |
| mov(tmp5, sp); |
| |
| block_comment("for(i=0;i<=m;i++,j++) f[i] = (j<0)? zeroB : /* NOTE: converted to double */ ipio2[j]; // (double) ipio2[j];"); { |
| eorw(i, i, i); |
| br(GE, INIT_F_COPY); |
| bind(INIT_F_ZERO); |
| stpq(v26, v26, Address(post(tmp5, 32))); |
| addw(i, i, 4); |
| addsw(j, j, 4); |
| br(LT, INIT_F_ZERO); |
| subw(i, i, j); |
| movw(j, zr); |
| bind(INIT_F_COPY); |
| add(tmp1, twoOverPiBase, j, LSL, 3); // ipio2[j] start address |
| ld1(v18, v19, v20, v21, T16B, tmp1); |
| add(tmp5, sp, i, ext::uxtx, 3); |
| st1(v18, v19, v20, v21, T16B, tmp5); |
| } |
| // v18..v21 can actually contain f[0..7] |
| cbz(i, SKIP_F_LOAD); // i == 0 => f[i] == f[0] => already loaded |
| ld1(v18, v19, v20, v21, T2D, Address(sp)); // load f[0..7] |
| bind(SKIP_F_LOAD); |
| // calculate 2^q0 and 2^-q0, which we'll need further. |
| // q0 is exponent. So, calculate biased exponent(q0+1023) |
| negw(tmp4, rscratch1); |
| addw(tmp5, rscratch1, 1023); |
| addw(tmp4, tmp4, 1023); |
| // Unroll following for(s) depending on jx in [0,1,2] |
| // for (i=0;i<=jk;i++) { |
| // for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; |
| // } |
| // Unrolling for jx == 0 case: |
| // q[0] = x[0] * f[0] |
| // q[1] = x[0] * f[1] |
| // q[2] = x[0] * f[2] |
| // q[3] = x[0] * f[3] |
| // q[4] = x[0] * f[4] |
| // |
| // Vectorization for unrolled jx == 0 case: |
| // {q[0], q[1]} = {f[0], f[1]} * x[0] |
| // {q[2], q[3]} = {f[2], f[3]} * x[0] |
| // q[4] = f[4] * x[0] |
| // |
| // Unrolling for jx == 1 case: |
| // q[0] = x[0] * f[1] + x[1] * f[0] |
| // q[1] = x[0] * f[2] + x[1] * f[1] |
| // q[2] = x[0] * f[3] + x[1] * f[2] |
| // q[3] = x[0] * f[4] + x[1] * f[3] |
| // q[4] = x[0] * f[5] + x[1] * f[4] |
| // |
| // Vectorization for unrolled jx == 1 case: |
| // {q[0], q[1]} = {f[0], f[1]} * x[1] |
| // {q[2], q[3]} = {f[2], f[3]} * x[1] |
| // q[4] = f[4] * x[1] |
| // {q[0], q[1]} += {f[1], f[2]} * x[0] |
| // {q[2], q[3]} += {f[3], f[4]} * x[0] |
| // q[4] += f[5] * x[0] |
| // |
| // Unrolling for jx == 2 case: |
| // q[0] = x[0] * f[2] + x[1] * f[1] + x[2] * f[0] |
| // q[1] = x[0] * f[3] + x[1] * f[2] + x[2] * f[1] |
| // q[2] = x[0] * f[4] + x[1] * f[3] + x[2] * f[2] |
| // q[3] = x[0] * f[5] + x[1] * f[4] + x[2] * f[3] |
| // q[4] = x[0] * f[6] + x[1] * f[5] + x[2] * f[4] |
| // |
| // Vectorization for unrolled jx == 2 case: |
| // {q[0], q[1]} = {f[0], f[1]} * x[2] |
| // {q[2], q[3]} = {f[2], f[3]} * x[2] |
| // q[4] = f[4] * x[2] |
| // {q[0], q[1]} += {f[1], f[2]} * x[1] |
| // {q[2], q[3]} += {f[3], f[4]} * x[1] |
| // q[4] += f[5] * x[1] |
| // {q[0], q[1]} += {f[2], f[3]} * x[0] |
| // {q[2], q[3]} += {f[4], f[5]} * x[0] |
| // q[4] += f[6] * x[0] |
| block_comment("unrolled and vectorized computation of q[0]..q[jk]"); { |
| cmpw(jx, 1); |
| lsl(tmp5, tmp5, 52); // now it's 2^q0 double value |
| lsl(tmp4, tmp4, 52); // now it's 2^-q0 double value |
| br(LT, JX_IS_0); |
| add(i, sp, 8); |
| ldpq(v26, v27, i); // load f[1..4] |
| br(GT, JX_IS_2); |
| // jx == 1 |
| fmulxvs(v28, T2D, v18, v7); // f[0,1] * x[1] |
| fmulxvs(v29, T2D, v19, v7); // f[2,3] * x[1] |
| fmuld(v30, v20, v7); // f[4] * x[1] |
| fmlavs(v28, T2D, v26, v6, 0); |
| fmlavs(v29, T2D, v27, v6, 0); |
| fmlavs(v30, T2D, v6, v20, 1); // v30 += f[5] * x[0] |
| b(Q_DONE); |
| bind(JX_IS_2); |
| fmulxvs(v28, T2D, v18, v3); // f[0,1] * x[2] |
| fmulxvs(v29, T2D, v19, v3); // f[2,3] * x[2] |
| fmuld(v30, v20, v3); // f[4] * x[2] |
| fmlavs(v28, T2D, v26, v7, 0); |
| fmlavs(v29, T2D, v27, v7, 0); |
| fmlavs(v30, T2D, v7, v20, 1); // v30 += f[5] * x[1] |
| fmlavs(v28, T2D, v19, v6, 0); |
| fmlavs(v29, T2D, v20, v6, 0); |
| fmlavs(v30, T2D, v6, v21, 0); // v30 += f[6] * x[0] |
| b(Q_DONE); |
| bind(JX_IS_0); |
| fmulxvs(v28, T2D, v18, v6); // f[0,1] * x[0] |
| fmulxvs(v29, T2D, v19, v6); // f[2,3] * x[0] |
| fmuld(v30, v20, v6); // f[4] * x[0] |
| bind(Q_DONE); |
| st1(v28, v29, v30, T2D, Address(qBase)); // save calculated q[0]...q[jk] |
| } |
| movz(i, 0x3E70, 48); |
| movw(jz, 4); |
| fmovd(v17, i); // v17 = twon24 |
| fmovd(v30, tmp5); // 2^q0 |
| fmovd(v21, 0.125); |
| fmovd(v20, 8.0); |
| fmovd(v22, tmp4); // 2^-q0 |
| |
| block_comment("recompute loop"); { |
| bind(RECOMPUTE); |
| // for(i=0,j=jz,z=q[jz];j>0;i++,j--) { |
| // fw = (double)((int)(twon24* z)); |
| // iq[i] = (int)(z-two24A*fw); |
| // z = q[j-1]+fw; |
| // } |
| block_comment("distill q[] into iq[] reversingly"); { |
| eorw(i, i, i); |
| movw(j, jz); |
| add(tmp2, qBase, jz, LSL, 3); // q[jz] address |
| ldrd(v18, post(tmp2, -8)); // z = q[j] and moving address to q[j-1] |
| bind(RECOMP_FIRST_FOR); |
| ldrd(v27, post(tmp2, -8)); |
| fmuld(v29, v17, v18); // twon24*z |
| frintzd(v29, v29); // (double)(int) |
| fmsubd(v28, v24, v29, v18); // v28 = z-two24A*fw |
| fcvtzdw(tmp1, v28); // (int)(z-two24A*fw) |
| strw(tmp1, Address(iqBase, i, Address::lsl(2))); |
| faddd(v18, v27, v29); |
| add(i, i, 1); |
| subs(j, j, 1); |
| br(GT, RECOMP_FIRST_FOR); |
| } |
| // compute n |
| fmuld(v18, v18, v30); |
| fmuld(v2, v18, v21); |
| frintmd(v2, v2); // v2 = floor(v2) == rounding towards -inf |
| fmsubd(v18, v2, v20, v18); // z -= 8.0*floor(z*0.125); |
| movw(ih, 2); |
| frintzd(v2, v18); // v2 = (double)((int)z) |
| fcvtzdw(n, v18); // n = (int) z; |
| fsubd(v18, v18, v2); // z -= (double)n; |
| |
| block_comment("q0-dependent initialization"); { |
| cmpw(rscratch1, 0); // if (q0 > 0) |
| br(LT, Q0_ZERO_CMP_LT); |
| subw(j, jz, 1); // j = jz - 1 |
| ldrw(tmp2, Address(iqBase, j, Address::lsl(2))); // tmp2 = iq[jz-1] |
| br(EQ, Q0_ZERO_CMP_EQ); |
| movw(tmp4, 24); |
| subw(tmp4, tmp4, rscratch1); // == 24 - q0 |
| lsrvw(i, tmp2, tmp4); // i = iq[jz-1] >> (24-q0) |
| lslvw(tmp5, i, tmp4); |
| subw(tmp2, tmp2, tmp5); // iq[jz-1] -= i<<(24-q0); |
| strw(tmp2, Address(iqBase, j, Address::lsl(2))); // store iq[jz-1] |
| subw(rscratch2, tmp4, 1); // == 23 - q0 |
| addw(n, n, i); // n+=i |
| lsrvw(ih, tmp2, rscratch2); // ih = iq[jz-1] >> (23-q0) |
| b(Q0_ZERO_CMP_DONE); |
| bind(Q0_ZERO_CMP_EQ); |
| lsr(ih, tmp2, 23); // ih = iq[z-1] >> 23 |
| b(Q0_ZERO_CMP_DONE); |
| bind(Q0_ZERO_CMP_LT); |
| fmovd(v4, 0.5); |
| fcmpd(v18, v4); |
| cselw(ih, zr, ih, LT); // if (z<0.5) ih = 0 |
| } |
| bind(Q0_ZERO_CMP_DONE); |
| cmpw(ih, zr); |
| br(LE, IH_HANDLED); |
| |
| block_comment("if(ih>) {"); { |
| // use rscratch2 as carry |
| |
| block_comment("for(i=0;i<jz ;i++) {...}"); { |
| addw(n, n, 1); |
| eorw(i, i, i); |
| eorw(rscratch2, rscratch2, rscratch2); |
| bind(IH_FOR); |
| ldrw(j, Address(iqBase, i, Address::lsl(2))); // j = iq[i] |
| movw(tmp3, 0x1000000); |
| subw(tmp3, tmp3, rscratch2); |
| cbnzw(rscratch2, IH_FOR_STORE); |
| cbzw(j, IH_FOR_INCREMENT); |
| movw(rscratch2, 1); |
| bind(IH_FOR_STORE); |
| subw(tmp3, tmp3, j); |
| strw(tmp3, Address(iqBase, i, Address::lsl(2))); // iq[i] = 0xffffff - j |
| bind(IH_FOR_INCREMENT); |
| addw(i, i, 1); |
| cmpw(i, jz); |
| br(LT, IH_FOR); |
| } |
| |
| block_comment("if(q0>0) {"); { |
| cmpw(rscratch1, zr); |
| br(LE, IH_AFTER_SWITCH); |
| // tmp3 still has iq[jz-1] value. no need to reload |
| // now, zero high tmp3 bits (rscratch1 number of bits) |
| movw(j, -1); |
| subw(i, jz, 1); // set i to jz-1 |
| lsrv(j, j, rscratch1); |
| andw(tmp3, tmp3, j, LSR, 8); // we have 24-bit-based constants |
| strw(tmp3, Address(iqBase, i, Address::lsl(2))); // save iq[jz-1] |
| } |
| bind(IH_AFTER_SWITCH); |
| cmpw(ih, 2); |
| br(NE, IH_HANDLED); |
| |
| block_comment("if(ih==2) {"); { |
| fmovd(v25, 1.0); |
| fsubd(v18, v25, v18); // z = one - z; |
| cbzw(rscratch2, IH_HANDLED); |
| fsubd(v18, v18, v30); // z -= scalbnA(one,q0); |
| } |
| } |
| bind(IH_HANDLED); |
| // check if recomputation is needed |
| fcmpd(v18, 0.0); |
| br(NE, RECOMP_CHECK_DONE_NOT_ZERO); |
| |
| block_comment("if(z==zeroB) {"); { |
| |
| block_comment("for (i=jz-1;i>=jk;i--) j |= iq[i];"); { |
| subw(i, jz, 1); |
| eorw(j, j, j); |
| b(RECOMP_FOR1_CHECK); |
| bind(RECOMP_FOR1); |
| ldrw(tmp1, Address(iqBase, i, Address::lsl(2))); |
| orrw(j, j, tmp1); |
| subw(i, i, 1); |
| bind(RECOMP_FOR1_CHECK); |
| cmpw(i, 4); |
| br(GE, RECOMP_FOR1); |
| } |
| cbnzw(j, RECOMP_CHECK_DONE); |
| |
| block_comment("if(j==0) {"); { |
| // for(k=1;iq[jk-k]==0;k++); // let's unroll it. jk == 4. So, read |
| // iq[3], iq[2], iq[1], iq[0] until non-zero value |
| ldp(tmp1, tmp3, iqBase); // iq[0..3] |
| movw(j, 2); |
| cmp(tmp3, zr); |
| csel(tmp1, tmp1, tmp3, EQ); // set register for further consideration |
| cselw(j, j, zr, EQ); // set initial k. Use j as k |
| cmp(zr, tmp1, LSR, 32); |
| addw(i, jz, 1); |
| csincw(j, j, j, NE); |
| |
| block_comment("for(i=jz+1;i<=jz+k;i++) {...}"); { |
| addw(jz, i, j); // i = jz+1, j = k-1. j+i = jz+k (which is a new jz) |
| bind(RECOMP_FOR2); |
| addw(tmp1, jv, i); |
| ldrd(v29, Address(twoOverPiBase, tmp1, Address::lsl(3))); |
| addw(tmp2, jx, i); |
| strd(v29, Address(sp, tmp2, Address::lsl(3))); |
| // f[jx+i] = /* NOTE: converted to double */ ipio2[jv+i]; //(double) ipio2[jv+i]; |
| // since jx = 0, 1 or 2 we can unroll it: |
| // for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; |
| // f[jx+i-j] == (for first iteration) f[jx+i], which is already v29 |
| add(tmp2, sp, tmp2, ext::uxtx, 3); // address of f[jx+i] |
| ldpd(v4, v5, Address(tmp2, -16)); // load f[jx+i-2] and f[jx+i-1] |
| fmuld(v26, v6, v29); // initial fw |
| cbzw(jx, RECOMP_FW_UPDATED); |
| fmaddd(v26, v7, v5, v26); |
| cmpw(jx, 1); |
| br(EQ, RECOMP_FW_UPDATED); |
| fmaddd(v26, v3, v4, v26); |
| bind(RECOMP_FW_UPDATED); |
| strd(v26, Address(qBase, i, Address::lsl(3))); // q[i] = fw; |
| addw(i, i, 1); |
| cmpw(i, jz); // jz here is "old jz" + k |
| br(LE, RECOMP_FOR2); |
| } |
| b(RECOMPUTE); |
| } |
| } |
| } |
| bind(RECOMP_CHECK_DONE); |
| // chop off zero terms |
| fcmpd(v18, 0.0); |
| br(EQ, Z_IS_ZERO); |
| |
| block_comment("else block of if(z==0.0) {"); { |
| bind(RECOMP_CHECK_DONE_NOT_ZERO); |
| fmuld(v18, v18, v22); |
| fcmpd(v18, v24); // v24 is stil two24A |
| br(LT, Z_IS_LESS_THAN_TWO24B); |
| fmuld(v1, v18, v17); // twon24*z |
| frintzd(v1, v1); // v1 = (double)(int)(v1) |
| fmaddd(v2, v24, v1, v18); |
| fcvtzdw(tmp3, v1); // (int)fw |
| fcvtzdw(tmp2, v2); // double to int |
| strw(tmp2, Address(iqBase, jz, Address::lsl(2))); |
| addw(rscratch1, rscratch1, 24); |
| addw(jz, jz, 1); |
| strw(tmp3, Address(iqBase, jz, Address::lsl(2))); // iq[jz] = (int) fw |
| b(Z_ZERO_CHECK_DONE); |
| bind(Z_IS_LESS_THAN_TWO24B); |
| fcvtzdw(tmp3, v18); // (int)z |
| strw(tmp3, Address(iqBase, jz, Address::lsl(2))); // iq[jz] = (int) z |
| b(Z_ZERO_CHECK_DONE); |
| } |
| |
| block_comment("if(z==0.0) {"); { |
| bind(Z_IS_ZERO); |
| subw(jz, jz, 1); |
| ldrw(tmp1, Address(iqBase, jz, Address::lsl(2))); |
| subw(rscratch1, rscratch1, 24); |
| cbz(tmp1, Z_IS_ZERO); |
| } |
| bind(Z_ZERO_CHECK_DONE); |
| // convert integer "bit" chunk to floating-point value |
| // v17 = twon24 |
| // update v30, which was scalbnA(1.0, <old q0>); |
| addw(tmp2, rscratch1, 1023); // biased exponent |
| lsl(tmp2, tmp2, 52); // put at correct position |
| mov(i, jz); |
| fmovd(v30, tmp2); |
| |
| block_comment("for(i=jz;i>=0;i--) {q[i] = fw*(double)iq[i]; fw*=twon24;}"); { |
| bind(CONVERTION_FOR); |
| ldrw(tmp1, Address(iqBase, i, Address::lsl(2))); |
| scvtfwd(v31, tmp1); |
| fmuld(v31, v31, v30); |
| strd(v31, Address(qBase, i, Address::lsl(3))); |
| fmuld(v30, v30, v17); |
| subsw(i, i, 1); |
| br(GE, CONVERTION_FOR); |
| } |
| add(rscratch2, sp, 160); // base for fq |
| // reusing twoOverPiBase |
| lea(twoOverPiBase, ExternalAddress(pio2)); |
| |
| block_comment("compute PIo2[0,...,jp]*q[jz,...,0]. for(i=jz;i>=0;i--) {...}"); { |
| movw(i, jz); |
| movw(tmp2, zr); // tmp2 will keep jz - i == 0 at start |
| bind(COMP_FOR); |
| // for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; |
| fmovd(v30, 0.0); |
| add(tmp5, qBase, i, LSL, 3); // address of q[i+k] for k==0 |
| movw(tmp3, 4); |
| movw(tmp4, zr); // used as k |
| cmpw(tmp2, 4); |
| add(tmp1, qBase, i, LSL, 3); // used as q[i] address |
| cselw(tmp3, tmp2, tmp3, LE); // min(jz - i, jp) |
| |
| block_comment("for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];"); { |
| bind(COMP_INNER_LOOP); |
| ldrd(v18, Address(tmp1, tmp4, Address::lsl(3))); // q[i+k] |
| ldrd(v19, Address(twoOverPiBase, tmp4, Address::lsl(3))); // PIo2[k] |
| fmaddd(v30, v18, v19, v30); // fw += PIo2[k]*q[i+k]; |
| addw(tmp4, tmp4, 1); // k++ |
| cmpw(tmp4, tmp3); |
| br(LE, COMP_INNER_LOOP); |
| } |
| strd(v30, Address(rscratch2, tmp2, Address::lsl(3))); // fq[jz-i] |
| add(tmp2, tmp2, 1); |
| subsw(i, i, 1); |
| br(GE, COMP_FOR); |
| } |
| |
| block_comment("switch(prec) {...}. case 2:"); { |
| // compress fq into y[] |
| // remember prec == 2 |
| |
| block_comment("for (i=jz;i>=0;i--) fw += fq[i];"); { |
| fmovd(v4, 0.0); |
| mov(i, jz); |
| bind(FW_FOR1); |
| ldrd(v1, Address(rscratch2, i, Address::lsl(3))); |
| subsw(i, i, 1); |
| faddd(v4, v4, v1); |
| br(GE, FW_FOR1); |
| } |
| bind(FW_FOR1_DONE); |
| // v1 contains fq[0]. so, keep it so far |
| fsubd(v5, v1, v4); // fw = fq[0] - fw |
| cbzw(ih, FW_Y0_NO_NEGATION); |
| fnegd(v4, v4); |
| bind(FW_Y0_NO_NEGATION); |
| |
| block_comment("for (i=1;i<=jz;i++) fw += fq[i];"); { |
| movw(i, 1); |
| cmpw(jz, 1); |
| br(LT, FW_FOR2_DONE); |
| bind(FW_FOR2); |
| ldrd(v1, Address(rscratch2, i, Address::lsl(3))); |
| addw(i, i, 1); |
| cmp(i, jz); |
| faddd(v5, v5, v1); |
| br(LE, FW_FOR2); |
| } |
| bind(FW_FOR2_DONE); |
| cbz(ih, FW_Y1_NO_NEGATION); |
| fnegd(v5, v5); |
| bind(FW_Y1_NO_NEGATION); |
| add(sp, sp, 560); |
| } |
| } |
| |
| ///* __kernel_sin( x, y, iy) |
| // * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 |
| // * Input x is assumed to be bounded by ~pi/4 in magnitude. |
| // * Input y is the tail of x. |
| // * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). |
| // * |
| // * Algorithm |
| // * 1. Since sin(-x) = -sin(x), we need only to consider positive x. |
| // * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. |
| // * 3. sin(x) is approximated by a polynomial of degree 13 on |
| // * [0,pi/4] |
| // * 3 13 |
| // * sin(x) ~ x + S1*x + ... + S6*x |
| // * where |
| // * |
| // * |sin(x) 2 4 6 8 10 12 | -58 |
| // * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 |
| // * | x | |
| // * |
| // * 4. sin(x+y) = sin(x) + sin'(x')*y |
| // * ~ sin(x) + (1-x*x/2)*y |
| // * For better accuracy, let |
| // * 3 2 2 2 2 |
| // * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) |
| // * then 3 2 |
| // * sin(x) = x + (S1*x + (x *(r-y/2)+y)) |
| // */ |
| //static const double |
| //S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ |
| //S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ |
| //S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ |
| //S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ |
| //S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ |
| //S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ |
| // |
| // NOTE: S1..S6 were moved into a table: StubRoutines::aarch64::_dsin_coef |
| // |
| // BEGIN __kernel_sin PSEUDO CODE |
| // |
| //static double __kernel_sin(double x, double y, bool iy) |
| //{ |
| // double z,r,v; |
| // |
| // // NOTE: not needed. moved to dsin/dcos |
| // //int ix; |
| // //ix = high(x)&0x7fffffff; /* high word of x */ |
| // |
| // // NOTE: moved to dsin/dcos |
| // //if(ix<0x3e400000) /* |x| < 2**-27 */ |
| // // {if((int)x==0) return x;} /* generate inexact */ |
| // |
| // z = x*x; |
| // v = z*x; |
| // r = S2+z*(S3+z*(S4+z*(S5+z*S6))); |
| // if(iy==0) return x+v*(S1+z*r); |
| // else return x-((z*(half*y-v*r)-y)-v*S1); |
| //} |
| // |
| // END __kernel_sin PSEUDO CODE |
| // |
| // Changes between fdlibm and intrinsic: |
| // 1. Removed |x| < 2**-27 check, because if was done earlier in dsin/dcos |
| // 2. Constants are now loaded from table dsin_coef |
| // 3. C code parameter "int iy" was modified to "bool iyIsOne", because |
| // iy is always 0 or 1. Also, iyIsOne branch was moved into |
| // generation phase instead of taking it during code execution |
| // Input ans output: |
| // 1. Input for generated function: X argument = x |
| // 2. Input for generator: x = register to read argument from, iyIsOne |
| // = flag to use low argument low part or not, dsin_coef = coefficients |
| // table address |
| // 3. Return sin(x) value in v0 |
| void MacroAssembler::generate_kernel_sin(FloatRegister x, bool iyIsOne, |
| address dsin_coef) { |
| FloatRegister y = v5, z = v6, v = v7, r = v16, S1 = v17, S2 = v18, |
| S3 = v19, S4 = v20, S5 = v21, S6 = v22, half = v23; |
| lea(rscratch2, ExternalAddress(dsin_coef)); |
| ldpd(S5, S6, Address(rscratch2, 32)); |
| fmuld(z, x, x); // z = x*x; |
| ld1(S1, S2, S3, S4, T1D, Address(rscratch2)); |
| fmuld(v, z, x); // v = z*x; |
| |
| block_comment("calculate r = S2+z*(S3+z*(S4+z*(S5+z*S6)))"); { |
| fmaddd(r, z, S6, S5); |
| // initialize "half" in current block to utilize 2nd FPU. However, it's |
| // not a part of this block |
| fmovd(half, 0.5); |
| fmaddd(r, z, r, S4); |
| fmaddd(r, z, r, S3); |
| fmaddd(r, z, r, S2); |
| } |
| |
| if (!iyIsOne) { |
| // return x+v*(S1+z*r); |
| fmaddd(S1, z, r, S1); |
| fmaddd(v0, v, S1, x); |
| } else { |
| // return x-((z*(half*y-v*r)-y)-v*S1); |
| fmuld(S6, half, y); // half*y |
| fmsubd(S6, v, r, S6); // half*y-v*r |
| fmsubd(S6, z, S6, y); // y - z*(half*y-v*r) = - (z*(half*y-v*r)-y) |
| fmaddd(S6, v, S1, S6); // - (z*(half*y-v*r)-y) + v*S1 == -((z*(half*y-v*r)-y)-v*S1) |
| faddd(v0, x, S6); |
| } |
| } |
| |
| ///* |
| // * __kernel_cos( x, y ) |
| // * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 |
| // * Input x is assumed to be bounded by ~pi/4 in magnitude. |
| // * Input y is the tail of x. |
| // * |
| // * Algorithm |
| // * 1. Since cos(-x) = cos(x), we need only to consider positive x. |
| // * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. |
| // * 3. cos(x) is approximated by a polynomial of degree 14 on |
| // * [0,pi/4] |
| // * 4 14 |
| // * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x |
| // * where the remez error is |
| // * |
| // * | 2 4 6 8 10 12 14 | -58 |
| // * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 |
| // * | | |
| // * |
| // * 4 6 8 10 12 14 |
| // * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then |
| // * cos(x) = 1 - x*x/2 + r |
| // * since cos(x+y) ~ cos(x) - sin(x)*y |
| // * ~ cos(x) - x*y, |
| // * a correction term is necessary in cos(x) and hence |
| // * cos(x+y) = 1 - (x*x/2 - (r - x*y)) |
| // * For better accuracy when x > 0.3, let qx = |x|/4 with |
| // * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. |
| // * Then |
| // * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). |
| // * Note that 1-qx and (x*x/2-qx) is EXACT here, and the |
| // * magnitude of the latter is at least a quarter of x*x/2, |
| // * thus, reducing the rounding error in the subtraction. |
| // */ |
| // |
| //static const double |
| //C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ |
| //C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ |
| //C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ |
| //C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ |
| //C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ |
| //C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ |
| // |
| // NOTE: C1..C6 were moved into a table: StubRoutines::aarch64::_dcos_coef |
| // |
| // BEGIN __kernel_cos PSEUDO CODE |
| // |
| //static double __kernel_cos(double x, double y) |
| //{ |
| // double a,h,z,r,qx=0; |
| // |
| // // NOTE: ix is already initialized in dsin/dcos. Reuse value from register |
| // //int ix; |
| // //ix = high(x)&0x7fffffff; /* ix = |x|'s high word*/ |
| // |
| // // NOTE: moved to dsin/dcos |
| // //if(ix<0x3e400000) { /* if x < 2**27 */ |
| // // if(((int)x)==0) return one; /* generate inexact */ |
| // //} |
| // |
| // z = x*x; |
| // r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); |
| // if(ix < 0x3FD33333) /* if |x| < 0.3 */ |
| // return one - (0.5*z - (z*r - x*y)); |
| // else { |
| // if(ix > 0x3fe90000) { /* x > 0.78125 */ |
| // qx = 0.28125; |
| // } else { |
| // set_high(&qx, ix-0x00200000); /* x/4 */ |
| // set_low(&qx, 0); |
| // } |
| // h = 0.5*z-qx; |
| // a = one-qx; |
| // return a - (h - (z*r-x*y)); |
| // } |
| //} |
| // |
| // END __kernel_cos PSEUDO CODE |
| // |
| // Changes between fdlibm and intrinsic: |
| // 1. Removed |x| < 2**-27 check, because if was done earlier in dsin/dcos |
| // 2. Constants are now loaded from table dcos_coef |
| // Input and output: |
| // 1. Input for generated function: X argument = x |
| // 2. Input for generator: x = register to read argument from, dcos_coef |
| // = coefficients table address |
| // 2. Return cos(x) value in v0 |
| void MacroAssembler::generate_kernel_cos(FloatRegister x, address dcos_coef) { |
| Register ix = r3; |
| FloatRegister qx = v1, h = v2, a = v3, y = v5, z = v6, r = v7, C1 = v18, |
| C2 = v19, C3 = v20, C4 = v21, C5 = v22, C6 = v23, one = v25, half = v26; |
| Label IX_IS_LARGE, SET_QX_CONST, DONE, QX_SET; |
| lea(rscratch2, ExternalAddress(dcos_coef)); |
| ldpd(C5, C6, Address(rscratch2, 32)); // load C5, C6 |
| fmuld(z, x, x); // z=x^2 |
| ld1(C1, C2, C3, C4, T1D, Address(rscratch2)); // load C1..C3\4 |
| block_comment("calculate r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))))"); { |
| fmaddd(r, z, C6, C5); |
| fmovd(half, 0.5); |
| fmaddd(r, z, r, C4); |
| fmuld(y, x, y); |
| fmaddd(r, z, r, C3); |
| mov(rscratch1, 0x3FD33333); |
| fmaddd(r, z, r, C2); |
| fmuld(x, z, z); // x = z^2 |
| fmaddd(r, z, r, C1); // r = C1+z(C2+z(C4+z(C5+z*C6))) |
| } |
| // need to multiply r by z to have "final" r value |
| fmovd(one, 1.0); |
| cmp(ix, rscratch1); |
| br(GT, IX_IS_LARGE); |
| block_comment("if(ix < 0x3FD33333) return one - (0.5*z - (z*r - x*y))"); { |
| // return 1.0 - (0.5*z - (z*r - x*y)) = 1.0 - (0.5*z + (x*y - z*r)) |
| fmsubd(v0, x, r, y); |
| fmaddd(v0, half, z, v0); |
| fsubd(v0, one, v0); |
| b(DONE); |
| } |
| block_comment("if(ix >= 0x3FD33333)"); { |
| bind(IX_IS_LARGE); |
| movz(rscratch2, 0x3FE9, 16); |
| cmp(ix, rscratch2); |
| br(GT, SET_QX_CONST); |
| block_comment("set_high(&qx, ix-0x00200000); set_low(&qx, 0);"); { |
| subw(rscratch2, ix, 0x00200000); |
| lsl(rscratch2, rscratch2, 32); |
| fmovd(qx, rscratch2); |
| } |
| b(QX_SET); |
| bind(SET_QX_CONST); |
| block_comment("if(ix > 0x3fe90000) qx = 0.28125;"); { |
| fmovd(qx, 0.28125); |
| } |
| bind(QX_SET); |
| fnmsub(C6, x, r, y); // z*r - xy |
| fnmsub(h, half, z, qx); // h = 0.5*z - qx |
| fsubd(a, one, qx); // a = 1-qx |
| fsubd(C6, h, C6); // = h - (z*r - x*y) |
| fsubd(v0, a, C6); |
| } |
| bind(DONE); |
| } |
| |
| // generate_dsin_dcos creates stub for dsin and dcos |
| // Generation is done via single call because dsin and dcos code is almost the |
| // same(see C code below). These functions work as follows: |
| // 1) handle corner cases: |x| ~< pi/4, x is NaN or INF, |x| < 2**-27 |
| // 2) perform argument reduction if required |
| // 3) call kernel_sin or kernel_cos which approximate sin/cos via polynomial |
| // |
| // BEGIN dsin/dcos PSEUDO CODE |
| // |
| //dsin_dcos(jdouble x, bool isCos) { |
| // double y[2],z=0.0; |
| // int n, ix; |
| // |
| // /* High word of x. */ |
| // ix = high(x); |
| // |
| // /* |x| ~< pi/4 */ |
| // ix &= 0x7fffffff; |
| // if(ix <= 0x3fe921fb) return isCos ? __kernel_cos : __kernel_sin(x,z,0); |
| // |
| // /* sin/cos(Inf or NaN) is NaN */ |
| // else if (ix>=0x7ff00000) return x-x; |
| // else if (ix<0x3e400000) { /* if ix < 2**27 */ |
| // if(((int)x)==0) return isCos ? one : x; /* generate inexact */ |
| // } |
| // /* argument reduction needed */ |
| // else { |
| // n = __ieee754_rem_pio2(x,y); |
| // switch(n&3) { |
| // case 0: return isCos ? __kernel_cos(y[0],y[1]) : __kernel_sin(y[0],y[1], true); |
| // case 1: return isCos ? -__kernel_sin(y[0],y[1],true) : __kernel_cos(y[0],y[1]); |
| // case 2: return isCos ? -__kernel_cos(y[0],y[1]) : -__kernel_sin(y[0],y[1], true); |
| // default: |
| // return isCos ? __kernel_sin(y[0],y[1],1) : -__kernel_cos(y[0],y[1]); |
| // } |
| // } |
| //} |
| // END dsin/dcos PSEUDO CODE |
| // |
| // Changes between fdlibm and intrinsic: |
| // 1. Moved ix < 2**27 from kernel_sin/kernel_cos into dsin/dcos |
| // 2. Final switch use equivalent bit checks(tbz/tbnz) |
| // Input ans output: |
| // 1. Input for generated function: X = r0 |
| // 2. Input for generator: isCos = generate sin or cos, npio2_hw = address |
| // of npio2_hw table, two_over_pi = address of two_over_pi table, |
| // pio2 = address if pio2 table, dsin_coef = address if dsin_coef table, |
| // dcos_coef = address of dcos_coef table |
| // 3. Return result in v0 |
| // NOTE: general purpose register names match local variable names in C code |
| void MacroAssembler::generate_dsin_dcos(bool isCos, address npio2_hw, |
| address two_over_pi, address pio2, address dsin_coef, address dcos_coef) { |
| const int POSITIVE_INFINITY_OR_NAN_PREFIX = 0x7FF0; |
| |
| Label DONE, ARG_REDUCTION, TINY_X, RETURN_SIN, EARLY_CASE; |
| Register X = r0, absX = r1, n = r2, ix = r3; |
| FloatRegister y0 = v4, y1 = v5; |
| block_comment("check |x| ~< pi/4, NaN, Inf and |x| < 2**-27 cases"); { |
| fmovd(X, v0); |
| mov(rscratch2, 0x3e400000); |
| mov(rscratch1, 0x3fe921fb00000000); // pi/4. shifted to reuse later |
| ubfm(absX, X, 0, 62); // absX |
| movz(r10, POSITIVE_INFINITY_OR_NAN_PREFIX, 48); |
| cmp(rscratch2, absX, LSR, 32); |
| lsr(ix, absX, 32); // set ix |
| br(GT, TINY_X); // handle tiny x (|x| < 2^-27) |
| cmp(ix, rscratch1, LSR, 32); |
| br(LE, EARLY_CASE); // if(ix <= 0x3fe921fb) return |
| cmp(absX, r10); |
| br(LT, ARG_REDUCTION); |
| // X is NaN or INF(i.e. 0x7FF* or 0xFFF*). Return NaN (mantissa != 0). |
| // Set last bit unconditionally to make it NaN |
| orr(r10, r10, 1); |
| fmovd(v0, r10); |
| ret(lr); |
| } |
| block_comment("kernel_sin/kernel_cos: if(ix<0x3e400000) {<fast return>}"); { |
| bind(TINY_X); |
| if (isCos) { |
| fmovd(v0, 1.0); |
| } |
| ret(lr); |
| } |
| bind(ARG_REDUCTION); /* argument reduction needed */ |
| block_comment("n = __ieee754_rem_pio2(x,y);"); { |
| generate__ieee754_rem_pio2(npio2_hw, two_over_pi, pio2); |
| } |
| block_comment("switch(n&3) {case ... }"); { |
| if (isCos) { |
| eorw(absX, n, n, LSR, 1); |
| tbnz(n, 0, RETURN_SIN); |
| } else { |
| tbz(n, 0, RETURN_SIN); |
| } |
| generate_kernel_cos(y0, dcos_coef); |
| if (isCos) { |
| tbz(absX, 0, DONE); |
| } else { |
| tbz(n, 1, DONE); |
| } |
| fnegd(v0, v0); |
| ret(lr); |
| bind(RETURN_SIN); |
| generate_kernel_sin(y0, true, dsin_coef); |
| if (isCos) { |
| tbz(absX, 0, DONE); |
| } else { |
| tbz(n, 1, DONE); |
| } |
| fnegd(v0, v0); |
| ret(lr); |
| } |
| bind(EARLY_CASE); |
| eor(y1, T8B, y1, y1); |
| if (isCos) { |
| generate_kernel_cos(v0, dcos_coef); |
| } else { |
| generate_kernel_sin(v0, false, dsin_coef); |
| } |
| bind(DONE); |
| ret(lr); |
| } |
