Update Files

Kha/Kinc/Sources/kinc/libs/.clang-format

@@ -0,0 +1,2 @@
+DisableFormat: true
+SortIncludes: false

Kha/Kinc/Sources/kinc/libs/lz4x.h

@@ -0,0 +1,706 @@
+/*
+
+LZ4X - An optimized LZ4 compressor
+
+Written and placed in the public domain by Ilya Muravyov
+
+*/
+
+#ifndef _CRT_SECURE_NO_WARNINGS
+#define _CRT_SECURE_NO_WARNINGS
+#endif
+#define _CRT_DISABLE_PERFCRIT_LOCKS
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <time.h>
+
+#define NO_UTIME
+
+#ifndef NO_UTIME
+#  include <sys/types.h>
+#  include <sys/stat.h>
+
+#  ifdef _MSC_VER
+#    include <sys/utime.h>
+#  else
+#    include <utime.h>
+#  endif
+#endif
+
+#ifndef _MSC_VER
+#  define _ftelli64 ftello64
+#endif
+
+typedef unsigned char U8;
+typedef unsigned short U16;
+typedef unsigned int U32;
+
+//FILE* g_in;
+//FILE* g_out;
+
+#define LZ4_MAGIC 0x184C2102
+#define BLOCK_SIZE (8<<20) // 8 MB
+#define PADDING_LITERALS 5
+
+#define WINDOW_BITS 16
+#define WINDOW_SIZE (1<<WINDOW_BITS)
+#define WINDOW_MASK (WINDOW_SIZE-1)
+
+#define MIN_MATCH 4
+
+#define EXCESS (16+(BLOCK_SIZE/255))
+
+static U8 g_buf[BLOCK_SIZE+BLOCK_SIZE+EXCESS];
+
+#define MIN(a, b) (((a)<(b))?(a):(b))
+#define MAX(a, b) (((a)>(b))?(a):(b))
+
+#define LOAD_16(p) (*(const U16*)(&g_buf[p]))
+#define LOAD_32(p) (*(const U32*)(&g_buf[p]))
+#define STORE_16(p, x) (*(U16*)(&g_buf[p])=(x))
+#define COPY_32(d, s) (*(U32*)(&g_buf[d])=LOAD_32(s))
+
+#define HASH_BITS 18
+#define HASH_SIZE (1<<HASH_BITS)
+#define NIL (-1)
+
+#define HASH_32(p) ((LOAD_32(p)*0x9E3779B9)>>(32-HASH_BITS))
+
+static inline void wild_copy(int d, int s, int n)
+{
+  COPY_32(d, s);
+  COPY_32(d+4, s+4);
+
+  for (int i=8; i<n; i+=8)
+  {
+    COPY_32(d+i, s+i);
+    COPY_32(d+4+i, s+4+i);
+  }
+}
+
+#if 0
+void compress(const int max_chain)
+{
+  static int head[HASH_SIZE];
+  static int tail[WINDOW_SIZE];
+
+  int n;
+  while ((n=fread(g_buf, 1, BLOCK_SIZE, g_in))>0)
+  {
+    for (int i=0; i<HASH_SIZE; ++i)
+      head[i]=NIL;
+
+    int op=BLOCK_SIZE;
+    int pp=0;
+
+    int p=0;
+    while (p<n)
+    {
+      int best_len=0;
+      int dist=0;
+
+      const int max_match=(n-PADDING_LITERALS)-p;
+      if (max_match>=MAX(12-PADDING_LITERALS, MIN_MATCH))
+      {
+        const int limit=MAX(p-WINDOW_SIZE, NIL);
+        int chain_len=max_chain;
+
+        int s=head[HASH_32(p)];
+        while (s>limit)
+        {
+          if (g_buf[s+best_len]==g_buf[p+best_len] && LOAD_32(s)==LOAD_32(p))
+          {
+            int len=MIN_MATCH;
+            while (len<max_match && g_buf[s+len]==g_buf[p+len])
+              ++len;
+
+            if (len>best_len)
+            {
+              best_len=len;
+              dist=p-s;
+
+              if (len==max_match)
+                break;
+            }
+          }
+
+          if (--chain_len==0)
+            break;
+
+          s=tail[s&WINDOW_MASK];
+        }
+      }
+
+      if (best_len>=MIN_MATCH)
+      {
+        int len=best_len-MIN_MATCH;
+        const int nib=MIN(len, 15);
+
+        if (pp!=p)
+        {
+          const int run=p-pp;
+          if (run>=15)
+          {
+            g_buf[op++]=(15<<4)+nib;
+
+            int j=run-15;
+            for (; j>=255; j-=255)
+              g_buf[op++]=255;
+            g_buf[op++]=j;
+          }
+          else
+            g_buf[op++]=(run<<4)+nib;
+
+          wild_copy(op, pp, run);
+          op+=run;
+        }
+        else
+          g_buf[op++]=nib;
+
+        STORE_16(op, dist);
+        op+=2;
+
+        if (len>=15)
+        {
+          len-=15;
+          for (; len>=255; len-=255)
+            g_buf[op++]=255;
+          g_buf[op++]=len;
+        }
+
+        pp=p+best_len;
+
+        while (p<pp)
+        {
+          const U32 h=HASH_32(p);
+          tail[p&WINDOW_MASK]=head[h];
+          head[h]=p++;
+        }
+      }
+      else
+      {
+        const U32 h=HASH_32(p);
+        tail[p&WINDOW_MASK]=head[h];
+        head[h]=p++;
+      }
+    }
+
+    if (pp!=p)
+    {
+      const int run=p-pp;
+      if (run>=15)
+      {
+        g_buf[op++]=15<<4;
+
+        int j=run-15;
+        for (; j>=255; j-=255)
+          g_buf[op++]=255;
+        g_buf[op++]=j;
+      }
+      else
+        g_buf[op++]=run<<4;
+
+      wild_copy(op, pp, run);
+      op+=run;
+    }
+
+    const int comp_len=op-BLOCK_SIZE;
+    fwrite(&comp_len, 1, sizeof(comp_len), g_out);
+    fwrite(&g_buf[BLOCK_SIZE], 1, comp_len, g_out);
+
+    fprintf(stderr, "%lld -> %lld\r", _ftelli64(g_in), _ftelli64(g_out));
+  }
+}
+
+void compress_optimal()
+{
+  static int head[HASH_SIZE];
+  static int nodes[WINDOW_SIZE][2];
+  static struct
+  {
+    int cum;
+
+    int len;
+    int dist;
+  } path[BLOCK_SIZE+1];
+
+  int n;
+  while ((n=fread(g_buf, 1, BLOCK_SIZE, g_in))>0)
+  {
+    // Pass 1: Find all matches
+
+    for (int i=0; i<HASH_SIZE; ++i)
+      head[i]=NIL;
+
+    for (int p=0; p<n; ++p)
+    {
+      int best_len=0;
+      int dist=0;
+
+      const int max_match=(n-PADDING_LITERALS)-p;
+      if (max_match>=MAX(12-PADDING_LITERALS, MIN_MATCH))
+      {
+        const int limit=MAX(p-WINDOW_SIZE, NIL);
+
+        int* left=&nodes[p&WINDOW_MASK][1];
+        int* right=&nodes[p&WINDOW_MASK][0];
+
+        int left_len=0;
+        int right_len=0;
+
+        const U32 h=HASH_32(p);
+        int s=head[h];
+        head[h]=p;
+
+        while (s>limit)
+        {
+          int len=MIN(left_len, right_len);
+
+          if (g_buf[s+len]==g_buf[p+len])
+          {
+            while (++len<max_match && g_buf[s+len]==g_buf[p+len]);
+
+            if (len>best_len)
+            {
+              best_len=len;
+              dist=p-s;
+
+              if (len==max_match || len>=(1<<16))
+                break;
+            }
+          }
+
+          if (g_buf[s+len]<g_buf[p+len])
+          {
+            *right=s;
+            right=&nodes[s&WINDOW_MASK][1];
+            s=*right;
+            right_len=len;
+          }
+          else
+          {
+            *left=s;
+            left=&nodes[s&WINDOW_MASK][0];
+            s=*left;
+            left_len=len;
+          }
+        }
+
+        *left=NIL;
+        *right=NIL;
+      }
+
+      path[p].len=best_len;
+      path[p].dist=dist;
+    }
+
+    // Pass 2: Build the shortest path
+
+    path[n].cum=0;
+
+    int count=15;
+
+    for (int p=n-1; p>0; --p)
+    {
+      int c0=path[p+1].cum+1;
+
+      if (--count==0)
+      {
+        count=255;
+        ++c0;
+      }
+
+      int len=path[p].len;
+      if (len>=MIN_MATCH)
+      {
+        int c1=1<<30;
+
+        const int j=MAX(len-255, MIN_MATCH);
+        for (int i=len; i>=j; --i)
+        {
+          int tmp=path[p+i].cum+3;
+
+          if (i>=(15+MIN_MATCH))
+            tmp+=1+((i-(15+MIN_MATCH))/255);
+
+          if (tmp<c1)
+          {
+            c1=tmp;
+            len=i;
+          }
+        }
+
+        if (c1<=c0)
+        {
+          path[p].cum=c1;
+          path[p].len=len;
+
+          count=15;
+        }
+        else
+        {
+          path[p].cum=c0;
+          path[p].len=0;
+        }
+      }
+      else
+        path[p].cum=c0;
+    }
+
+    // Pass 3: Output the codes
+
+    int op=BLOCK_SIZE;
+    int pp=0;
+
+    int p=0;
+    while (p<n)
+    {
+      if (path[p].len>=MIN_MATCH)
+      {
+        int len=path[p].len-MIN_MATCH;
+        const int nib=MIN(len, 15);
+
+        if (pp!=p)
+        {
+          const int run=p-pp;
+          if (run>=15)
+          {
+            g_buf[op++]=(15<<4)+nib;
+
+            int j=run-15;
+            for (; j>=255; j-=255)
+              g_buf[op++]=255;
+            g_buf[op++]=j;
+          }
+          else
+            g_buf[op++]=(run<<4)+nib;
+
+          wild_copy(op, pp, run);
+          op+=run;
+        }
+        else
+          g_buf[op++]=nib;
+
+        STORE_16(op, path[p].dist);
+        op+=2;
+
+        if (len>=15)
+        {
+          len-=15;
+          for (; len>=255; len-=255)
+            g_buf[op++]=255;
+          g_buf[op++]=len;
+        }
+
+        p+=path[p].len;
+
+        pp=p;
+      }
+      else
+        ++p;
+    }
+
+    if (pp!=p)
+    {
+      const int run=p-pp;
+      if (run>=15)
+      {
+        g_buf[op++]=15<<4;
+
+        int j=run-15;
+        for (; j>=255; j-=255)
+          g_buf[op++]=255;
+        g_buf[op++]=j;
+      }
+      else
+        g_buf[op++]=run<<4;
+
+      wild_copy(op, pp, run);
+      op+=run;
+    }
+
+    const int comp_len=op-BLOCK_SIZE;
+    fwrite(&comp_len, 1, sizeof(comp_len), g_out);
+    fwrite(&g_buf[BLOCK_SIZE], 1, comp_len, g_out);
+
+    fprintf(stderr, "%lld -> %lld\r", _ftelli64(g_in), _ftelli64(g_out));
+  }
+}
+#endif
+
+static size_t kread(void* dst, size_t size, const char* src, size_t* offset, size_t compressedSize) {
+  size_t realSize = MIN(size, compressedSize - *offset);
+  memcpy(dst, &src[*offset], realSize);
+  *offset += realSize;
+  return realSize;
+}
+
+static size_t kwrite(void* src, size_t size, char* dst, size_t* offset, int maxOutputSize) {
+  size_t realSize = MIN(size, maxOutputSize - *offset);
+  memcpy(&dst[*offset], src, size);
+  *offset += realSize;
+  return realSize;
+}
+
+//int decompress()
+#ifdef KINC_LZ4X
+#include <kinc/error.h>
+
+int LZ4_decompress_safe(const char *source, char *buf, int compressedSize, int maxOutputSize)
+{
+  size_t read_offset = 0;
+  size_t write_offset = 0;
+  int comp_len;
+  while (kread(&comp_len, sizeof(comp_len), source, &read_offset, compressedSize)>0)
+  {
+    if (comp_len<2 || comp_len>(BLOCK_SIZE+EXCESS)
+        || kread(&g_buf[BLOCK_SIZE], comp_len, source, &read_offset, compressedSize)!=comp_len)
+      return -1;
+
+    int p=0;
+
+    int ip=BLOCK_SIZE;
+    const int ip_end=ip+comp_len;
+
+    for (;;)
+    {
+      const int token=g_buf[ip++];
+      if (token>=16)
+      {
+        int run=token>>4;
+        if (run==15)
+        {
+          for (;;)
+          {
+            const int c=g_buf[ip++];
+            run+=c;
+            if (c!=255)
+              break;
+          }
+        }
+        if ((p+run)>BLOCK_SIZE)
+          return -1;
+
+        wild_copy(p, ip, run);
+        p+=run;
+        ip+=run;
+        if (ip>=ip_end)
+          break;
+      }
+
+      int s=p-LOAD_16(ip);
+      ip+=2;
+      if (s<0)
+        return -1;
+
+      int len=(token&15)+MIN_MATCH;
+      if (len==(15+MIN_MATCH))
+      {
+        for (;;)
+        {
+          const int c=g_buf[ip++];
+          len+=c;
+          if (c!=255)
+            break;
+        }
+      }
+      if ((p+len)>BLOCK_SIZE)
+        return -1;
+
+      if ((p-s)>=4)
+      {
+        wild_copy(p, s, len);
+        p+=len;
+      }
+      else
+      {
+        while (len--!=0)
+          g_buf[p++]=g_buf[s++];
+      }
+    }
+
+    if (kwrite(g_buf, p, buf, &write_offset, maxOutputSize)!=p)
+    {
+      kinc_error_message("Fwrite() failed");
+      return -1;
+    }
+  }
+
+  return 0;
+}
+#endif
+
+#if 0
+int main(int argc, char** argv)
+{
+  const clock_t start=clock();
+
+  int level=4;
+  bool do_decomp=false;
+  bool overwrite=false;
+
+  while (argc>1 && *argv[1]=='-')
+  {
+    for (int i=1; argv[1][i]!='\0'; ++i)
+    {
+      switch (argv[1][i])
+      {
+      case '1':
+      case '2':
+      case '3':
+      case '4':
+      case '5':
+      case '6':
+      case '7':
+      case '8':
+      case '9':
+        level=argv[1][i]-'0';
+        break;
+      case 'd':
+        do_decomp=true;
+        break;
+      case 'f':
+        overwrite=true;
+        break;
+      default:
+        fprintf(stderr, "Unknown option: -%c\n", argv[1][i]);
+        exit(1);
+      }
+    }
+
+    --argc;
+    ++argv;
+  }
+
+  if (argc<2)
+  {
+    fprintf(stderr,
+        "LZ4X - An optimized LZ4 compressor, v1.60\n"
+        "Written and placed in the public domain by Ilya Muravyov\n"
+        "\n"
+        "Usage: LZ4X [options] infile [outfile]\n"
+        "\n"
+        "Options:\n"
+        "  -1  Compress faster\n"
+        "  -9  Compress better\n"
+        "  -d  Decompress\n"
+        "  -f  Force overwrite of output file\n");
+    exit(1);
+  }
+
+  g_in=fopen(argv[1], "rb");
+  if (!g_in)
+  {
+    perror(argv[1]);
+    exit(1);
+  }
+
+  char out_name[FILENAME_MAX];
+  if (argc<3)
+  {
+    strcpy(out_name, argv[1]);
+    if (do_decomp)
+    {
+      const int p=strlen(out_name)-4;
+      if (p>0 && strcmp(&out_name[p], ".lz4")==0)
+        out_name[p]='\0';
+      else
+        strcat(out_name, ".out");
+    }
+    else
+      strcat(out_name, ".lz4");
+  }
+  else
+    strcpy(out_name, argv[2]);
+
+  if (!overwrite)
+  {
+    FILE* f=fopen(out_name, "rb");
+    if (f)
+    {
+      fclose(f);
+
+      fprintf(stderr, "%s already exists. Overwrite (y/n)? ", out_name);
+      fflush(stderr);
+
+      if (getchar()!='y')
+      {
+        fprintf(stderr, "Not overwritten\n");
+        exit(1);
+      }
+    }
+  }
+
+  if (do_decomp)
+  {
+    int magic;
+    fread(&magic, 1, sizeof(magic), g_in);
+    if (magic!=LZ4_MAGIC)
+    {
+      fprintf(stderr, "%s: Not in Legacy format\n", argv[1]);
+      exit(1);
+    }
+
+    g_out=fopen(out_name, "wb");
+    if (!g_out)
+    {
+      perror(out_name);
+      exit(1);
+    }
+
+    fprintf(stderr, "Decompressing %s:\n", argv[1]);
+
+    if (decompress()!=0)
+    {
+      fprintf(stderr, "%s: Corrupt input\n", argv[1]);
+      exit(1);
+    }
+  }
+  else
+  {
+    g_out=fopen(out_name, "wb");
+    if (!g_out)
+    {
+      perror(out_name);
+      exit(1);
+    }
+
+    const int magic=LZ4_MAGIC;
+    fwrite(&magic, 1, sizeof(magic), g_out);
+
+    fprintf(stderr, "Compressing %s:\n", argv[1]);
+
+    if (level==9)
+      compress_optimal();
+    else
+      compress((level<8)?1<<level:WINDOW_SIZE);
+  }
+
+  fprintf(stderr, "%lld -> %lld in %1.3f sec\n", _ftelli64(g_in),
+      _ftelli64(g_out), double(clock()-start)/CLOCKS_PER_SEC);
+
+  fclose(g_in);
+  fclose(g_out);
+
+#ifndef NO_UTIME
+  struct _stati64 sb;
+  if (_stati64(argv[1], &sb)!=0)
+  {
+    perror("Stat() failed");
+    exit(1);
+  }
+  struct utimbuf ub;
+  ub.actime=sb.st_atime;
+  ub.modtime=sb.st_mtime;
+  if (utime(out_name, &ub)!=0)
+  {
+    perror("Utime() failed");
+    exit(1);
+  }
+#endif
+
+  return 0;
+}
+#endif

Kha/Kinc/Sources/kinc/libs/neon_mathfun.h

@@ -0,0 +1,301 @@
+/* NEON implementation of sin, cos, exp and log
+
+   Inspired by Intel Approximate Math library, and based on the
+   corresponding algorithms of the cephes math library
+*/
+
+/* Copyright (C) 2011  Julien Pommier
+
+  This software is provided 'as-is', without any express or implied
+  warranty.  In no event will the authors be held liable for any damages
+  arising from the use of this software.
+
+  Permission is granted to anyone to use this software for any purpose,
+  including commercial applications, and to alter it and redistribute it
+  freely, subject to the following restrictions:
+
+  1. The origin of this software must not be misrepresented; you must not
+     claim that you wrote the original software. If you use this software
+     in a product, an acknowledgment in the product documentation would be
+     appreciated but is not required.
+  2. Altered source versions must be plainly marked as such, and must not be
+     misrepresented as being the original software.
+  3. This notice may not be removed or altered from any source distribution.
+
+  (this is the zlib license)
+*/
+
+#include <arm_neon.h>
+
+typedef float32x4_t v4sf;  // vector of 4 float
+typedef uint32x4_t v4su;  // vector of 4 uint32
+typedef int32x4_t v4si;  // vector of 4 uint32
+
+#define c_inv_mant_mask ~0x7f800000u
+#define c_cephes_SQRTHF 0.707106781186547524
+#define c_cephes_log_p0 7.0376836292E-2
+#define c_cephes_log_p1 - 1.1514610310E-1
+#define c_cephes_log_p2 1.1676998740E-1
+#define c_cephes_log_p3 - 1.2420140846E-1
+#define c_cephes_log_p4 + 1.4249322787E-1
+#define c_cephes_log_p5 - 1.6668057665E-1
+#define c_cephes_log_p6 + 2.0000714765E-1
+#define c_cephes_log_p7 - 2.4999993993E-1
+#define c_cephes_log_p8 + 3.3333331174E-1
+#define c_cephes_log_q1 -2.12194440e-4
+#define c_cephes_log_q2 0.693359375
+
+/* natural logarithm computed for 4 simultaneous float 
+   return NaN for x <= 0
+*/
+v4sf log_ps(v4sf x) {
+  v4sf one = vdupq_n_f32(1);
+
+  x = vmaxq_f32(x, vdupq_n_f32(0)); /* force flush to zero on denormal values */
+  v4su invalid_mask = vcleq_f32(x, vdupq_n_f32(0));
+
+  v4si ux = vreinterpretq_s32_f32(x);
+  
+  v4si emm0 = vshrq_n_s32(ux, 23);
+
+  /* keep only the fractional part */
+  ux = vandq_s32(ux, vdupq_n_s32(c_inv_mant_mask));
+  ux = vorrq_s32(ux, vreinterpretq_s32_f32(vdupq_n_f32(0.5f)));
+  x = vreinterpretq_f32_s32(ux);
+
+  emm0 = vsubq_s32(emm0, vdupq_n_s32(0x7f));
+  v4sf e = vcvtq_f32_s32(emm0);
+
+  e = vaddq_f32(e, one);
+
+  /* part2: 
+     if( x < SQRTHF ) {
+       e -= 1;
+       x = x + x - 1.0;
+     } else { x = x - 1.0; }
+  */
+  v4su mask = vcltq_f32(x, vdupq_n_f32(c_cephes_SQRTHF));
+  v4sf tmp = vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(x), mask));
+  x = vsubq_f32(x, one);
+  e = vsubq_f32(e, vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(one), mask)));
+  x = vaddq_f32(x, tmp);
+
+  v4sf z = vmulq_f32(x,x);
+
+  v4sf y = vdupq_n_f32(c_cephes_log_p0);
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p1));
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p2));
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p3));
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p4));
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p5));
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p6));
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p7));
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, vdupq_n_f32(c_cephes_log_p8));
+  y = vmulq_f32(y, x);
+
+  y = vmulq_f32(y, z);
+  
+
+  tmp = vmulq_f32(e, vdupq_n_f32(c_cephes_log_q1));
+  y = vaddq_f32(y, tmp);
+
+
+  tmp = vmulq_f32(z, vdupq_n_f32(0.5f));
+  y = vsubq_f32(y, tmp);
+
+  tmp = vmulq_f32(e, vdupq_n_f32(c_cephes_log_q2));
+  x = vaddq_f32(x, y);
+  x = vaddq_f32(x, tmp);
+  x = vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(x), invalid_mask)); // negative arg will be NAN
+  return x;
+}
+
+#define c_exp_hi 88.3762626647949f
+#define c_exp_lo -88.3762626647949f
+
+#define c_cephes_LOG2EF 1.44269504088896341
+#define c_cephes_exp_C1 0.693359375
+#define c_cephes_exp_C2 -2.12194440e-4
+
+#define c_cephes_exp_p0 1.9875691500E-4
+#define c_cephes_exp_p1 1.3981999507E-3
+#define c_cephes_exp_p2 8.3334519073E-3
+#define c_cephes_exp_p3 4.1665795894E-2
+#define c_cephes_exp_p4 1.6666665459E-1
+#define c_cephes_exp_p5 5.0000001201E-1
+
+/* exp() computed for 4 float at once */
+v4sf exp_ps(v4sf x) {
+  v4sf tmp, fx;
+
+  v4sf one = vdupq_n_f32(1);
+  x = vminq_f32(x, vdupq_n_f32(c_exp_hi));
+  x = vmaxq_f32(x, vdupq_n_f32(c_exp_lo));
+
+  /* express exp(x) as exp(g + n*log(2)) */
+  fx = vmlaq_f32(vdupq_n_f32(0.5f), x, vdupq_n_f32(c_cephes_LOG2EF));
+
+  /* perform a floorf */
+  tmp = vcvtq_f32_s32(vcvtq_s32_f32(fx));
+
+  /* if greater, substract 1 */
+  v4su mask = vcgtq_f32(tmp, fx);    
+  mask = vandq_u32(mask, vreinterpretq_u32_f32(one));
+
+
+  fx = vsubq_f32(tmp, vreinterpretq_f32_u32(mask));
+
+  tmp = vmulq_f32(fx, vdupq_n_f32(c_cephes_exp_C1));
+  v4sf z = vmulq_f32(fx, vdupq_n_f32(c_cephes_exp_C2));
+  x = vsubq_f32(x, tmp);
+  x = vsubq_f32(x, z);
+
+  static const float cephes_exp_p[6] = { c_cephes_exp_p0, c_cephes_exp_p1, c_cephes_exp_p2, c_cephes_exp_p3, c_cephes_exp_p4, c_cephes_exp_p5 };
+  v4sf y = vld1q_dup_f32(cephes_exp_p+0);
+  v4sf c1 = vld1q_dup_f32(cephes_exp_p+1); 
+  v4sf c2 = vld1q_dup_f32(cephes_exp_p+2); 
+  v4sf c3 = vld1q_dup_f32(cephes_exp_p+3); 
+  v4sf c4 = vld1q_dup_f32(cephes_exp_p+4); 
+  v4sf c5 = vld1q_dup_f32(cephes_exp_p+5);
+
+  y = vmulq_f32(y, x);
+  z = vmulq_f32(x,x);
+  y = vaddq_f32(y, c1);
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, c2);
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, c3);
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, c4);
+  y = vmulq_f32(y, x);
+  y = vaddq_f32(y, c5);
+  
+  y = vmulq_f32(y, z);
+  y = vaddq_f32(y, x);
+  y = vaddq_f32(y, one);
+
+  /* build 2^n */
+  int32x4_t mm;
+  mm = vcvtq_s32_f32(fx);
+  mm = vaddq_s32(mm, vdupq_n_s32(0x7f));
+  mm = vshlq_n_s32(mm, 23);
+  v4sf pow2n = vreinterpretq_f32_s32(mm);
+
+  y = vmulq_f32(y, pow2n);
+  return y;
+}
+
+#define c_minus_cephes_DP1 -0.78515625
+#define c_minus_cephes_DP2 -2.4187564849853515625e-4
+#define c_minus_cephes_DP3 -3.77489497744594108e-8
+#define c_sincof_p0 -1.9515295891E-4
+#define c_sincof_p1  8.3321608736E-3
+#define c_sincof_p2 -1.6666654611E-1
+#define c_coscof_p0  2.443315711809948E-005
+#define c_coscof_p1 -1.388731625493765E-003
+#define c_coscof_p2  4.166664568298827E-002
+#define c_cephes_FOPI 1.27323954473516 // 4 / M_PI
+
+/* evaluation of 4 sines & cosines at once.
+
+   The code is the exact rewriting of the cephes sinf function.
+   Precision is excellent as long as x < 8192 (I did not bother to
+   take into account the special handling they have for greater values
+   -- it does not return garbage for arguments over 8192, though, but
+   the extra precision is missing).
+
+   Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
+   surprising but correct result.
+
+   Note also that when you compute sin(x), cos(x) is available at
+   almost no extra price so both sin_ps and cos_ps make use of
+   sincos_ps..
+  */
+void sincos_ps(v4sf x, v4sf *ysin, v4sf *ycos) { // any x
+  v4sf xmm1, xmm2, xmm3, y;
+
+  v4su emm2;
+  
+  v4su sign_mask_sin, sign_mask_cos;
+  sign_mask_sin = vcltq_f32(x, vdupq_n_f32(0));
+  x = vabsq_f32(x);
+
+  /* scale by 4/Pi */
+  y = vmulq_f32(x, vdupq_n_f32(c_cephes_FOPI));
+
+  /* store the integer part of y in mm0 */
+  emm2 = vcvtq_u32_f32(y);
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  emm2 = vaddq_u32(emm2, vdupq_n_u32(1));
+  emm2 = vandq_u32(emm2, vdupq_n_u32(~1));
+  y = vcvtq_f32_u32(emm2);
+
+  /* get the polynom selection mask 
+     there is one polynom for 0 <= x <= Pi/4
+     and another one for Pi/4<x<=Pi/2
+
+     Both branches will be computed.
+  */
+  v4su poly_mask = vtstq_u32(emm2, vdupq_n_u32(2));
+  
+  /* The magic pass: "Extended precision modular arithmetic" 
+     x = ((x - y * DP1) - y * DP2) - y * DP3; */
+  xmm1 = vmulq_n_f32(y, c_minus_cephes_DP1);
+  xmm2 = vmulq_n_f32(y, c_minus_cephes_DP2);
+  xmm3 = vmulq_n_f32(y, c_minus_cephes_DP3);
+  x = vaddq_f32(x, xmm1);
+  x = vaddq_f32(x, xmm2);
+  x = vaddq_f32(x, xmm3);
+
+  sign_mask_sin = veorq_u32(sign_mask_sin, vtstq_u32(emm2, vdupq_n_u32(4)));
+  sign_mask_cos = vtstq_u32(vsubq_u32(emm2, vdupq_n_u32(2)), vdupq_n_u32(4));
+
+  /* Evaluate the first polynom  (0 <= x <= Pi/4) in y1, 
+     and the second polynom      (Pi/4 <= x <= 0) in y2 */
+  v4sf z = vmulq_f32(x,x);
+  v4sf y1, y2;
+
+  y1 = vmulq_n_f32(z, c_coscof_p0);
+  y2 = vmulq_n_f32(z, c_sincof_p0);
+  y1 = vaddq_f32(y1, vdupq_n_f32(c_coscof_p1));
+  y2 = vaddq_f32(y2, vdupq_n_f32(c_sincof_p1));
+  y1 = vmulq_f32(y1, z);
+  y2 = vmulq_f32(y2, z);
+  y1 = vaddq_f32(y1, vdupq_n_f32(c_coscof_p2));
+  y2 = vaddq_f32(y2, vdupq_n_f32(c_sincof_p2));
+  y1 = vmulq_f32(y1, z);
+  y2 = vmulq_f32(y2, z);
+  y1 = vmulq_f32(y1, z);
+  y2 = vmulq_f32(y2, x);
+  y1 = vsubq_f32(y1, vmulq_f32(z, vdupq_n_f32(0.5f)));
+  y2 = vaddq_f32(y2, x);
+  y1 = vaddq_f32(y1, vdupq_n_f32(1));
+
+  /* select the correct result from the two polynoms */  
+  v4sf ys = vbslq_f32(poly_mask, y1, y2);
+  v4sf yc = vbslq_f32(poly_mask, y2, y1);
+  *ysin = vbslq_f32(sign_mask_sin, vnegq_f32(ys), ys);
+  *ycos = vbslq_f32(sign_mask_cos, yc, vnegq_f32(yc));
+}
+
+v4sf sin_ps(v4sf x) {
+  v4sf ysin, ycos; 
+  sincos_ps(x, &ysin, &ycos); 
+  return ysin;
+}
+
+v4sf cos_ps(v4sf x) {
+  v4sf ysin, ycos; 
+  sincos_ps(x, &ysin, &ycos); 
+  return ycos;
+}
+
+

Kha/Kinc/Sources/kinc/libs/sse_mathfun.h

@@ -0,0 +1,711 @@
+/* SIMD (SSE1+MMX or SSE2) implementation of sin, cos, exp and log
+
+   Inspired by Intel Approximate Math library, and based on the
+   corresponding algorithms of the cephes math library
+
+   The default is to use the SSE1 version. If you define USE_SSE2 the
+   the SSE2 intrinsics will be used in place of the MMX intrinsics. Do
+   not expect any significant performance improvement with SSE2.
+*/
+
+/* Copyright (C) 2007  Julien Pommier
+
+  This software is provided 'as-is', without any express or implied
+  warranty.  In no event will the authors be held liable for any damages
+  arising from the use of this software.
+
+  Permission is granted to anyone to use this software for any purpose,
+  including commercial applications, and to alter it and redistribute it
+  freely, subject to the following restrictions:
+
+  1. The origin of this software must not be misrepresented; you must not
+     claim that you wrote the original software. If you use this software
+     in a product, an acknowledgment in the product documentation would be
+     appreciated but is not required.
+  2. Altered source versions must be plainly marked as such, and must not be
+     misrepresented as being the original software.
+  3. This notice may not be removed or altered from any source distribution.
+
+  (this is the zlib license)
+*/
+
+#include <xmmintrin.h>
+
+/* yes I know, the top of this file is quite ugly */
+
+#ifdef _MSC_VER /* visual c++ */
+# define ALIGN16_BEG __declspec(align(16))
+# define ALIGN16_END 
+#else /* gcc or icc */
+# define ALIGN16_BEG
+# define ALIGN16_END __attribute__((aligned(16)))
+#endif
+
+/* __m128 is ugly to write */
+typedef __m128 v4sf;  // vector of 4 float (sse1)
+
+#ifdef USE_SSE2
+# include <emmintrin.h>
+typedef __m128i v4si; // vector of 4 int (sse2)
+#else
+typedef __m64 v2si;   // vector of 2 int (mmx)
+#endif
+
+/* declare some SSE constants -- why can't I figure a better way to do that? */
+#define _PS_CONST(Name, Val)                                            \
+  static const ALIGN16_BEG float _ps_##Name[4] ALIGN16_END = { Val, Val, Val, Val }
+#define _PI32_CONST(Name, Val)                                            \
+  static const ALIGN16_BEG int _pi32_##Name[4] ALIGN16_END = { Val, Val, Val, Val }
+#define _PS_CONST_TYPE(Name, Type, Val)                                 \
+  static const ALIGN16_BEG Type _ps_##Name[4] ALIGN16_END = { Val, Val, Val, Val }
+
+_PS_CONST(1  , 1.0f);
+_PS_CONST(0p5, 0.5f);
+/* the smallest non denormalized float number */
+_PS_CONST_TYPE(min_norm_pos, int, 0x00800000);
+_PS_CONST_TYPE(mant_mask, int, 0x7f800000);
+_PS_CONST_TYPE(inv_mant_mask, int, ~0x7f800000);
+
+_PS_CONST_TYPE(sign_mask, int, (int)0x80000000);
+_PS_CONST_TYPE(inv_sign_mask, int, ~0x80000000);
+
+_PI32_CONST(1, 1);
+_PI32_CONST(inv1, ~1);
+_PI32_CONST(2, 2);
+_PI32_CONST(4, 4);
+_PI32_CONST(0x7f, 0x7f);
+
+_PS_CONST(cephes_SQRTHF, 0.707106781186547524);
+_PS_CONST(cephes_log_p0, 7.0376836292E-2);
+_PS_CONST(cephes_log_p1, - 1.1514610310E-1);
+_PS_CONST(cephes_log_p2, 1.1676998740E-1);
+_PS_CONST(cephes_log_p3, - 1.2420140846E-1);
+_PS_CONST(cephes_log_p4, + 1.4249322787E-1);
+_PS_CONST(cephes_log_p5, - 1.6668057665E-1);
+_PS_CONST(cephes_log_p6, + 2.0000714765E-1);
+_PS_CONST(cephes_log_p7, - 2.4999993993E-1);
+_PS_CONST(cephes_log_p8, + 3.3333331174E-1);
+_PS_CONST(cephes_log_q1, -2.12194440e-4);
+_PS_CONST(cephes_log_q2, 0.693359375);
+
+#ifndef USE_SSE2
+typedef union xmm_mm_union {
+  __m128 xmm;
+  __m64 mm[2];
+} xmm_mm_union;
+
+#define COPY_XMM_TO_MM(xmm_, mm0_, mm1_) {          \
+    xmm_mm_union u; u.xmm = xmm_;                   \
+    mm0_ = u.mm[0];                                 \
+    mm1_ = u.mm[1];                                 \
+}
+
+#define COPY_MM_TO_XMM(mm0_, mm1_, xmm_) {                         \
+    xmm_mm_union u; u.mm[0]=mm0_; u.mm[1]=mm1_; xmm_ = u.xmm;      \
+  }
+
+#endif // USE_SSE2
+
+/* natural logarithm computed for 4 simultaneous float 
+   return NaN for x <= 0
+*/
+v4sf log_ps(v4sf x) {
+#ifdef USE_SSE2
+  v4si emm0;
+#else
+  v2si mm0, mm1;
+#endif
+  v4sf one = *(v4sf*)_ps_1;
+
+  v4sf invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps());
+
+  x = _mm_max_ps(x, *(v4sf*)_ps_min_norm_pos);  /* cut off denormalized stuff */
+
+#ifndef USE_SSE2
+  /* part 1: x = frexpf(x, &e); */
+  COPY_XMM_TO_MM(x, mm0, mm1);
+  mm0 = _mm_srli_pi32(mm0, 23);
+  mm1 = _mm_srli_pi32(mm1, 23);
+#else
+  emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
+#endif
+  /* keep only the fractional part */
+  x = _mm_and_ps(x, *(v4sf*)_ps_inv_mant_mask);
+  x = _mm_or_ps(x, *(v4sf*)_ps_0p5);
+
+#ifndef USE_SSE2
+  /* now e=mm0:mm1 contain the really base-2 exponent */
+  mm0 = _mm_sub_pi32(mm0, *(v2si*)_pi32_0x7f);
+  mm1 = _mm_sub_pi32(mm1, *(v2si*)_pi32_0x7f);
+  v4sf e = _mm_cvtpi32x2_ps(mm0, mm1);
+  _mm_empty(); /* bye bye mmx */
+#else
+  emm0 = _mm_sub_epi32(emm0, *(v4si*)_pi32_0x7f);
+  v4sf e = _mm_cvtepi32_ps(emm0);
+#endif
+
+  e = _mm_add_ps(e, one);
+
+  /* part2: 
+     if( x < SQRTHF ) {
+       e -= 1;
+       x = x + x - 1.0;
+     } else { x = x - 1.0; }
+  */
+  v4sf mask = _mm_cmplt_ps(x, *(v4sf*)_ps_cephes_SQRTHF);
+  v4sf tmp = _mm_and_ps(x, mask);
+  x = _mm_sub_ps(x, one);
+  e = _mm_sub_ps(e, _mm_and_ps(one, mask));
+  x = _mm_add_ps(x, tmp);
+
+
+  v4sf z = _mm_mul_ps(x,x);
+
+  v4sf y = *(v4sf*)_ps_cephes_log_p0;
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p1);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p2);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p3);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p4);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p5);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p6);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p7);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p8);
+  y = _mm_mul_ps(y, x);
+
+  y = _mm_mul_ps(y, z);
+  
+
+  tmp = _mm_mul_ps(e, *(v4sf*)_ps_cephes_log_q1);
+  y = _mm_add_ps(y, tmp);
+
+
+  tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
+  y = _mm_sub_ps(y, tmp);
+
+  tmp = _mm_mul_ps(e, *(v4sf*)_ps_cephes_log_q2);
+  x = _mm_add_ps(x, y);
+  x = _mm_add_ps(x, tmp);
+  x = _mm_or_ps(x, invalid_mask); // negative arg will be NAN
+  return x;
+}
+
+_PS_CONST(exp_hi,	88.3762626647949f);
+_PS_CONST(exp_lo,	-88.3762626647949f);
+
+_PS_CONST(cephes_LOG2EF, 1.44269504088896341);
+_PS_CONST(cephes_exp_C1, 0.693359375);
+_PS_CONST(cephes_exp_C2, -2.12194440e-4);
+
+_PS_CONST(cephes_exp_p0, 1.9875691500E-4);
+_PS_CONST(cephes_exp_p1, 1.3981999507E-3);
+_PS_CONST(cephes_exp_p2, 8.3334519073E-3);
+_PS_CONST(cephes_exp_p3, 4.1665795894E-2);
+_PS_CONST(cephes_exp_p4, 1.6666665459E-1);
+_PS_CONST(cephes_exp_p5, 5.0000001201E-1);
+
+v4sf exp_ps(v4sf x) {
+  v4sf tmp = _mm_setzero_ps(), fx;
+#ifdef USE_SSE2
+  v4si emm0;
+#else
+  v2si mm0, mm1;
+#endif
+  v4sf one = *(v4sf*)_ps_1;
+
+  x = _mm_min_ps(x, *(v4sf*)_ps_exp_hi);
+  x = _mm_max_ps(x, *(v4sf*)_ps_exp_lo);
+
+  /* express exp(x) as exp(g + n*log(2)) */
+  fx = _mm_mul_ps(x, *(v4sf*)_ps_cephes_LOG2EF);
+  fx = _mm_add_ps(fx, *(v4sf*)_ps_0p5);
+
+  /* how to perform a floorf with SSE: just below */
+#ifndef USE_SSE2
+  /* step 1 : cast to int */
+  tmp = _mm_movehl_ps(tmp, fx);
+  mm0 = _mm_cvttps_pi32(fx);
+  mm1 = _mm_cvttps_pi32(tmp);
+  /* step 2 : cast back to float */
+  tmp = _mm_cvtpi32x2_ps(mm0, mm1);
+#else
+  emm0 = _mm_cvttps_epi32(fx);
+  tmp  = _mm_cvtepi32_ps(emm0);
+#endif
+  /* if greater, substract 1 */
+  v4sf mask = _mm_cmpgt_ps(tmp, fx);    
+  mask = _mm_and_ps(mask, one);
+  fx = _mm_sub_ps(tmp, mask);
+
+  tmp = _mm_mul_ps(fx, *(v4sf*)_ps_cephes_exp_C1);
+  v4sf z = _mm_mul_ps(fx, *(v4sf*)_ps_cephes_exp_C2);
+  x = _mm_sub_ps(x, tmp);
+  x = _mm_sub_ps(x, z);
+
+  z = _mm_mul_ps(x,x);
+  
+  v4sf y = *(v4sf*)_ps_cephes_exp_p0;
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p1);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p2);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p3);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p4);
+  y = _mm_mul_ps(y, x);
+  y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p5);
+  y = _mm_mul_ps(y, z);
+  y = _mm_add_ps(y, x);
+  y = _mm_add_ps(y, one);
+
+  /* build 2^n */
+#ifndef USE_SSE2
+  z = _mm_movehl_ps(z, fx);
+  mm0 = _mm_cvttps_pi32(fx);
+  mm1 = _mm_cvttps_pi32(z);
+  mm0 = _mm_add_pi32(mm0, *(v2si*)_pi32_0x7f);
+  mm1 = _mm_add_pi32(mm1, *(v2si*)_pi32_0x7f);
+  mm0 = _mm_slli_pi32(mm0, 23); 
+  mm1 = _mm_slli_pi32(mm1, 23);
+  
+  v4sf pow2n; 
+  COPY_MM_TO_XMM(mm0, mm1, pow2n);
+  _mm_empty();
+#else
+  emm0 = _mm_cvttps_epi32(fx);
+  emm0 = _mm_add_epi32(emm0, *(v4si*)_pi32_0x7f);
+  emm0 = _mm_slli_epi32(emm0, 23);
+  v4sf pow2n = _mm_castsi128_ps(emm0);
+#endif
+  y = _mm_mul_ps(y, pow2n);
+  return y;
+}
+
+_PS_CONST(minus_cephes_DP1, -0.78515625);
+_PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
+_PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
+_PS_CONST(sincof_p0, -1.9515295891E-4);
+_PS_CONST(sincof_p1,  8.3321608736E-3);
+_PS_CONST(sincof_p2, -1.6666654611E-1);
+_PS_CONST(coscof_p0,  2.443315711809948E-005);
+_PS_CONST(coscof_p1, -1.388731625493765E-003);
+_PS_CONST(coscof_p2,  4.166664568298827E-002);
+_PS_CONST(cephes_FOPI, 1.27323954473516); // 4 / M_PI
+
+
+/* evaluation of 4 sines at onces, using only SSE1+MMX intrinsics so
+   it runs also on old athlons XPs and the pentium III of your grand
+   mother.
+
+   The code is the exact rewriting of the cephes sinf function.
+   Precision is excellent as long as x < 8192 (I did not bother to
+   take into account the special handling they have for greater values
+   -- it does not return garbage for arguments over 8192, though, but
+   the extra precision is missing).
+
+   Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
+   surprising but correct result.
+
+   Performance is also surprisingly good, 1.33 times faster than the
+   macos vsinf SSE2 function, and 1.5 times faster than the
+   __vrs4_sinf of amd's ACML (which is only available in 64 bits). Not
+   too bad for an SSE1 function (with no special tuning) !
+   However the latter libraries probably have a much better handling of NaN,
+   Inf, denormalized and other special arguments..
+
+   On my core 1 duo, the execution of this function takes approximately 95 cycles.
+
+   From what I have observed on the experiments with Intel AMath lib, switching to an
+   SSE2 version would improve the perf by only 10%.
+
+   Since it is based on SSE intrinsics, it has to be compiled at -O2 to
+   deliver full speed.
+*/
+v4sf sin_ps(v4sf x) { // any x
+  v4sf xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
+
+#ifdef USE_SSE2
+  v4si emm0, emm2;
+#else
+  v2si mm0, mm1, mm2, mm3;
+#endif
+  sign_bit = x;
+  /* take the absolute value */
+  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
+  /* extract the sign bit (upper one) */
+  sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
+  
+  /* scale by 4/Pi */
+  y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
+
+#ifdef USE_SSE2
+  /* store the integer part of y in mm0 */
+  emm2 = _mm_cvttps_epi32(y);
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
+  emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
+  y = _mm_cvtepi32_ps(emm2);
+
+  /* get the swap sign flag */
+  emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
+  emm0 = _mm_slli_epi32(emm0, 29);
+  /* get the polynom selection mask 
+     there is one polynom for 0 <= x <= Pi/4
+     and another one for Pi/4<x<=Pi/2
+
+     Both branches will be computed.
+  */
+  emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
+  emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
+  
+  v4sf swap_sign_bit = _mm_castsi128_ps(emm0);
+  v4sf poly_mask = _mm_castsi128_ps(emm2);
+  sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
+  
+#else
+  /* store the integer part of y in mm0:mm1 */
+  xmm2 = _mm_movehl_ps(xmm2, y);
+  mm2 = _mm_cvttps_pi32(y);
+  mm3 = _mm_cvttps_pi32(xmm2);
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1);
+  mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1);
+  mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1);
+  mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1);
+  y = _mm_cvtpi32x2_ps(mm2, mm3);
+  /* get the swap sign flag */
+  mm0 = _mm_and_si64(mm2, *(v2si*)_pi32_4);
+  mm1 = _mm_and_si64(mm3, *(v2si*)_pi32_4);
+  mm0 = _mm_slli_pi32(mm0, 29);
+  mm1 = _mm_slli_pi32(mm1, 29);
+  /* get the polynom selection mask */
+  mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2);
+  mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2);
+  mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64());
+  mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64());
+  v4sf swap_sign_bit, poly_mask;
+  COPY_MM_TO_XMM(mm0, mm1, swap_sign_bit);
+  COPY_MM_TO_XMM(mm2, mm3, poly_mask);
+  sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
+  _mm_empty(); /* good-bye mmx */
+#endif
+  
+  /* The magic pass: "Extended precision modular arithmetic" 
+     x = ((x - y * DP1) - y * DP2) - y * DP3; */
+  xmm1 = *(v4sf*)_ps_minus_cephes_DP1;
+  xmm2 = *(v4sf*)_ps_minus_cephes_DP2;
+  xmm3 = *(v4sf*)_ps_minus_cephes_DP3;
+  xmm1 = _mm_mul_ps(y, xmm1);
+  xmm2 = _mm_mul_ps(y, xmm2);
+  xmm3 = _mm_mul_ps(y, xmm3);
+  x = _mm_add_ps(x, xmm1);
+  x = _mm_add_ps(x, xmm2);
+  x = _mm_add_ps(x, xmm3);
+
+  /* Evaluate the first polynom  (0 <= x <= Pi/4) */
+  y = *(v4sf*)_ps_coscof_p0;
+  v4sf z = _mm_mul_ps(x,x);
+
+  y = _mm_mul_ps(y, z);
+  y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1);
+  y = _mm_mul_ps(y, z);
+  y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2);
+  y = _mm_mul_ps(y, z);
+  y = _mm_mul_ps(y, z);
+  v4sf tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
+  y = _mm_sub_ps(y, tmp);
+  y = _mm_add_ps(y, *(v4sf*)_ps_1);
+  
+  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */
+
+  v4sf y2 = *(v4sf*)_ps_sincof_p0;
+  y2 = _mm_mul_ps(y2, z);
+  y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
+  y2 = _mm_mul_ps(y2, z);
+  y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
+  y2 = _mm_mul_ps(y2, z);
+  y2 = _mm_mul_ps(y2, x);
+  y2 = _mm_add_ps(y2, x);
+
+  /* select the correct result from the two polynoms */  
+  xmm3 = poly_mask;
+  y2 = _mm_and_ps(xmm3, y2); //, xmm3);
+  y = _mm_andnot_ps(xmm3, y);
+  y = _mm_add_ps(y,y2);
+  /* update the sign */
+  y = _mm_xor_ps(y, sign_bit);
+  return y;
+}
+
+/* almost the same as sin_ps */
+v4sf cos_ps(v4sf x) { // any x
+  v4sf xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
+#ifdef USE_SSE2
+  v4si emm0, emm2;
+#else
+  v2si mm0, mm1, mm2, mm3;
+#endif
+  /* take the absolute value */
+  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
+  
+  /* scale by 4/Pi */
+  y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
+  
+#ifdef USE_SSE2
+  /* store the integer part of y in mm0 */
+  emm2 = _mm_cvttps_epi32(y);
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
+  emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
+  y = _mm_cvtepi32_ps(emm2);
+
+  emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
+  
+  /* get the swap sign flag */
+  emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
+  emm0 = _mm_slli_epi32(emm0, 29);
+  /* get the polynom selection mask */
+  emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
+  emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
+  
+  v4sf sign_bit = _mm_castsi128_ps(emm0);
+  v4sf poly_mask = _mm_castsi128_ps(emm2);
+#else
+  /* store the integer part of y in mm0:mm1 */
+  xmm2 = _mm_movehl_ps(xmm2, y);
+  mm2 = _mm_cvttps_pi32(y);
+  mm3 = _mm_cvttps_pi32(xmm2);
+
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1);
+  mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1);
+  mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1);
+  mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1);
+
+  y = _mm_cvtpi32x2_ps(mm2, mm3);
+
+
+  mm2 = _mm_sub_pi32(mm2, *(v2si*)_pi32_2);
+  mm3 = _mm_sub_pi32(mm3, *(v2si*)_pi32_2);
+
+  /* get the swap sign flag in mm0:mm1 and the 
+     polynom selection mask in mm2:mm3 */
+
+  mm0 = _mm_andnot_si64(mm2, *(v2si*)_pi32_4);
+  mm1 = _mm_andnot_si64(mm3, *(v2si*)_pi32_4);
+  mm0 = _mm_slli_pi32(mm0, 29);
+  mm1 = _mm_slli_pi32(mm1, 29);
+
+  mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2);
+  mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2);
+
+  mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64());
+  mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64());
+
+  v4sf sign_bit, poly_mask;
+  COPY_MM_TO_XMM(mm0, mm1, sign_bit);
+  COPY_MM_TO_XMM(mm2, mm3, poly_mask);
+  _mm_empty(); /* good-bye mmx */
+#endif
+  /* The magic pass: "Extended precision modular arithmetic" 
+     x = ((x - y * DP1) - y * DP2) - y * DP3; */
+  xmm1 = *(v4sf*)_ps_minus_cephes_DP1;
+  xmm2 = *(v4sf*)_ps_minus_cephes_DP2;
+  xmm3 = *(v4sf*)_ps_minus_cephes_DP3;
+  xmm1 = _mm_mul_ps(y, xmm1);
+  xmm2 = _mm_mul_ps(y, xmm2);
+  xmm3 = _mm_mul_ps(y, xmm3);
+  x = _mm_add_ps(x, xmm1);
+  x = _mm_add_ps(x, xmm2);
+  x = _mm_add_ps(x, xmm3);
+  
+  /* Evaluate the first polynom  (0 <= x <= Pi/4) */
+  y = *(v4sf*)_ps_coscof_p0;
+  v4sf z = _mm_mul_ps(x,x);
+
+  y = _mm_mul_ps(y, z);
+  y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1);
+  y = _mm_mul_ps(y, z);
+  y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2);
+  y = _mm_mul_ps(y, z);
+  y = _mm_mul_ps(y, z);
+  v4sf tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
+  y = _mm_sub_ps(y, tmp);
+  y = _mm_add_ps(y, *(v4sf*)_ps_1);
+  
+  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */
+
+  v4sf y2 = *(v4sf*)_ps_sincof_p0;
+  y2 = _mm_mul_ps(y2, z);
+  y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
+  y2 = _mm_mul_ps(y2, z);
+  y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
+  y2 = _mm_mul_ps(y2, z);
+  y2 = _mm_mul_ps(y2, x);
+  y2 = _mm_add_ps(y2, x);
+
+  /* select the correct result from the two polynoms */  
+  xmm3 = poly_mask;
+  y2 = _mm_and_ps(xmm3, y2); //, xmm3);
+  y = _mm_andnot_ps(xmm3, y);
+  y = _mm_add_ps(y,y2);
+  /* update the sign */
+  y = _mm_xor_ps(y, sign_bit);
+
+  return y;
+}
+
+/* since sin_ps and cos_ps are almost identical, sincos_ps could replace both of them..
+   it is almost as fast, and gives you a free cosine with your sine */
+void sincos_ps(v4sf x, v4sf *s, v4sf *c) {
+  v4sf xmm1, xmm2, xmm3 = _mm_setzero_ps(), sign_bit_sin, y;
+#ifdef USE_SSE2
+  v4si emm0, emm2, emm4;
+#else
+  v2si mm0, mm1, mm2, mm3, mm4, mm5;
+#endif
+  sign_bit_sin = x;
+  /* take the absolute value */
+  x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
+  /* extract the sign bit (upper one) */
+  sign_bit_sin = _mm_and_ps(sign_bit_sin, *(v4sf*)_ps_sign_mask);
+  
+  /* scale by 4/Pi */
+  y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
+    
+#ifdef USE_SSE2
+  /* store the integer part of y in emm2 */
+  emm2 = _mm_cvttps_epi32(y);
+
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
+  emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
+  y = _mm_cvtepi32_ps(emm2);
+
+  emm4 = emm2;
+
+  /* get the swap sign flag for the sine */
+  emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
+  emm0 = _mm_slli_epi32(emm0, 29);
+  v4sf swap_sign_bit_sin = _mm_castsi128_ps(emm0);
+
+  /* get the polynom selection mask for the sine*/
+  emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
+  emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
+  v4sf poly_mask = _mm_castsi128_ps(emm2);
+#else
+  /* store the integer part of y in mm2:mm3 */
+  xmm3 = _mm_movehl_ps(xmm3, y);
+  mm2 = _mm_cvttps_pi32(y);
+  mm3 = _mm_cvttps_pi32(xmm3);
+
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1);
+  mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1);
+  mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1);
+  mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1);
+
+  y = _mm_cvtpi32x2_ps(mm2, mm3);
+
+  mm4 = mm2;
+  mm5 = mm3;
+
+  /* get the swap sign flag for the sine */
+  mm0 = _mm_and_si64(mm2, *(v2si*)_pi32_4);
+  mm1 = _mm_and_si64(mm3, *(v2si*)_pi32_4);
+  mm0 = _mm_slli_pi32(mm0, 29);
+  mm1 = _mm_slli_pi32(mm1, 29);
+  v4sf swap_sign_bit_sin;
+  COPY_MM_TO_XMM(mm0, mm1, swap_sign_bit_sin);
+
+  /* get the polynom selection mask for the sine */
+
+  mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2);
+  mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2);
+  mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64());
+  mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64());
+  v4sf poly_mask;
+  COPY_MM_TO_XMM(mm2, mm3, poly_mask);
+#endif
+
+  /* The magic pass: "Extended precision modular arithmetic" 
+     x = ((x - y * DP1) - y * DP2) - y * DP3; */
+  xmm1 = *(v4sf*)_ps_minus_cephes_DP1;
+  xmm2 = *(v4sf*)_ps_minus_cephes_DP2;
+  xmm3 = *(v4sf*)_ps_minus_cephes_DP3;
+  xmm1 = _mm_mul_ps(y, xmm1);
+  xmm2 = _mm_mul_ps(y, xmm2);
+  xmm3 = _mm_mul_ps(y, xmm3);
+  x = _mm_add_ps(x, xmm1);
+  x = _mm_add_ps(x, xmm2);
+  x = _mm_add_ps(x, xmm3);
+
+#ifdef USE_SSE2
+  emm4 = _mm_sub_epi32(emm4, *(v4si*)_pi32_2);
+  emm4 = _mm_andnot_si128(emm4, *(v4si*)_pi32_4);
+  emm4 = _mm_slli_epi32(emm4, 29);
+  v4sf sign_bit_cos = _mm_castsi128_ps(emm4);
+#else
+  /* get the sign flag for the cosine */
+  mm4 = _mm_sub_pi32(mm4, *(v2si*)_pi32_2);
+  mm5 = _mm_sub_pi32(mm5, *(v2si*)_pi32_2);
+  mm4 = _mm_andnot_si64(mm4, *(v2si*)_pi32_4);
+  mm5 = _mm_andnot_si64(mm5, *(v2si*)_pi32_4);
+  mm4 = _mm_slli_pi32(mm4, 29);
+  mm5 = _mm_slli_pi32(mm5, 29);
+  v4sf sign_bit_cos;
+  COPY_MM_TO_XMM(mm4, mm5, sign_bit_cos);
+  _mm_empty(); /* good-bye mmx */
+#endif
+
+  sign_bit_sin = _mm_xor_ps(sign_bit_sin, swap_sign_bit_sin);
+
+  
+  /* Evaluate the first polynom  (0 <= x <= Pi/4) */
+  v4sf z = _mm_mul_ps(x,x);
+  y = *(v4sf*)_ps_coscof_p0;
+
+  y = _mm_mul_ps(y, z);
+  y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1);
+  y = _mm_mul_ps(y, z);
+  y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2);
+  y = _mm_mul_ps(y, z);
+  y = _mm_mul_ps(y, z);
+  v4sf tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
+  y = _mm_sub_ps(y, tmp);
+  y = _mm_add_ps(y, *(v4sf*)_ps_1);
+  
+  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */
+
+  v4sf y2 = *(v4sf*)_ps_sincof_p0;
+  y2 = _mm_mul_ps(y2, z);
+  y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
+  y2 = _mm_mul_ps(y2, z);
+  y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
+  y2 = _mm_mul_ps(y2, z);
+  y2 = _mm_mul_ps(y2, x);
+  y2 = _mm_add_ps(y2, x);
+
+  /* select the correct result from the two polynoms */  
+  xmm3 = poly_mask;
+  v4sf ysin2 = _mm_and_ps(xmm3, y2);
+  v4sf ysin1 = _mm_andnot_ps(xmm3, y);
+  y2 = _mm_sub_ps(y2,ysin2);
+  y = _mm_sub_ps(y, ysin1);
+
+  xmm1 = _mm_add_ps(ysin1,ysin2);
+  xmm2 = _mm_add_ps(y,y2);
+ 
+  /* update the sign */
+  *s = _mm_xor_ps(xmm1, sign_bit_sin);
+  *c = _mm_xor_ps(xmm2, sign_bit_cos);
+}
+