isaac.c

/*Written by Timothy B. Terriberry (tterribe@xiph.org) 1999-2009.
  CC0 (Public domain) - see LICENSE file for details
  Based on the public domain implementation by Robert J. Jenkins Jr.*/
#include <float.h>
#include <math.h>
#include <string.h>
#include <ccan/ilog/ilog.h>
#include "isaac.h"


#define ISAAC_MASK        (0xFFFFFFFFU)

/* Extract ISAAC_SZ_LOG bits (starting at bit 2). */
static inline uint32_t lower_bits(uint32_t x)
{
	return (x & ((ISAAC_SZ-1) << 2)) >> 2;
}

/* Extract next ISAAC_SZ_LOG bits (starting at bit ISAAC_SZ_LOG+2). */
static inline uint32_t upper_bits(uint32_t y)
{
	return (y >> (ISAAC_SZ_LOG+2)) & (ISAAC_SZ-1);
}

static void isaac_update(isaac_ctx *_ctx){
  uint32_t *m;
  uint32_t *r;
  uint32_t  a;
  uint32_t  b;
  uint32_t  x;
  uint32_t  y;
  int       i;
  m=_ctx->m;
  r=_ctx->r;
  a=_ctx->a;
  b=_ctx->b+(++_ctx->c);
  for(i=0;i<ISAAC_SZ/2;i++){
    x=m[i];
    a=(a^a<<13)+m[i+ISAAC_SZ/2];
    m[i]=y=m[lower_bits(x)]+a+b;
    r[i]=b=m[upper_bits(y)]+x;
    x=m[++i];
    a=(a^a>>6)+m[i+ISAAC_SZ/2];
    m[i]=y=m[lower_bits(x)]+a+b;
    r[i]=b=m[upper_bits(y)]+x;
    x=m[++i];
    a=(a^a<<2)+m[i+ISAAC_SZ/2];
    m[i]=y=m[lower_bits(x)]+a+b;
    r[i]=b=m[upper_bits(y)]+x;
    x=m[++i];
    a=(a^a>>16)+m[i+ISAAC_SZ/2];
    m[i]=y=m[lower_bits(x)]+a+b;
    r[i]=b=m[upper_bits(y)]+x;
  }
  for(i=ISAAC_SZ/2;i<ISAAC_SZ;i++){
    x=m[i];
    a=(a^a<<13)+m[i-ISAAC_SZ/2];
    m[i]=y=m[lower_bits(x)]+a+b;
    r[i]=b=m[upper_bits(y)]+x;
    x=m[++i];
    a=(a^a>>6)+m[i-ISAAC_SZ/2];
    m[i]=y=m[lower_bits(x)]+a+b;
    r[i]=b=m[upper_bits(y)]+x;
    x=m[++i];
    a=(a^a<<2)+m[i-ISAAC_SZ/2];
    m[i]=y=m[lower_bits(x)]+a+b;
    r[i]=b=m[upper_bits(y)]+x;
    x=m[++i];
    a=(a^a>>16)+m[i-ISAAC_SZ/2];
    m[i]=y=m[lower_bits(x)]+a+b;
    r[i]=b=m[upper_bits(y)]+x;
  }
  _ctx->b=b;
  _ctx->a=a;
  _ctx->n=ISAAC_SZ;
}

static void isaac_mix(uint32_t _x[8]){
  static const unsigned char SHIFT[8]={11,2,8,16,10,4,8,9};
  int i;
  for(i=0;i<8;i++){
    _x[i]^=_x[(i+1)&7]<<SHIFT[i];
    _x[(i+3)&7]+=_x[i];
    _x[(i+1)&7]+=_x[(i+2)&7];
    i++;
    _x[i]^=_x[(i+1)&7]>>SHIFT[i];
    _x[(i+3)&7]+=_x[i];
    _x[(i+1)&7]+=_x[(i+2)&7];
  }
}


void isaac_init(isaac_ctx *_ctx,const unsigned char *_seed,int _nseed){
  _ctx->a=_ctx->b=_ctx->c=0;
  memset(_ctx->r,0,sizeof(_ctx->r));
  isaac_reseed(_ctx,_seed,_nseed);
}

void isaac_reseed(isaac_ctx *_ctx,const unsigned char *_seed,int _nseed){
  uint32_t *m;
  uint32_t *r;
  uint32_t  x[8];
  int       i;
  int       j;
  m=_ctx->m;
  r=_ctx->r;
  if(_nseed>ISAAC_SEED_SZ_MAX)_nseed=ISAAC_SEED_SZ_MAX;
  for(i=0;i<_nseed>>2;i++){
    r[i]^=(uint32_t)_seed[i<<2|3]<<24|(uint32_t)_seed[i<<2|2]<<16|
     (uint32_t)_seed[i<<2|1]<<8|_seed[i<<2];
  }
  _nseed-=i<<2;
  if(_nseed>0){
    uint32_t ri;
    ri=_seed[i<<2];
    for(j=1;j<_nseed;j++)ri|=(uint32_t)_seed[i<<2|j]<<(j<<3);
    r[i++]^=ri;
  }
  x[0]=x[1]=x[2]=x[3]=x[4]=x[5]=x[6]=x[7]=0x9E3779B9U;
  for(i=0;i<4;i++)isaac_mix(x);
  for(i=0;i<ISAAC_SZ;i+=8){
    for(j=0;j<8;j++)x[j]+=r[i+j];
    isaac_mix(x);
    memcpy(m+i,x,sizeof(x));
  }
  for(i=0;i<ISAAC_SZ;i+=8){
    for(j=0;j<8;j++)x[j]+=m[i+j];
    isaac_mix(x);
    memcpy(m+i,x,sizeof(x));
  }
  isaac_update(_ctx);
}

uint32_t isaac_next_uint32(isaac_ctx *_ctx){
  if(!_ctx->n)isaac_update(_ctx);
  return _ctx->r[--_ctx->n];
}

uint32_t isaac_next_uint(isaac_ctx *_ctx,uint32_t _n){
  uint32_t r;
  uint32_t v;
  uint32_t d;
  do{
    r=isaac_next_uint32(_ctx);
    v=r%_n;
    d=r-v;
  }
  while(((d+_n-1)&ISAAC_MASK)<d);
  return v;
}

/*Returns a uniform random float.
  The expected value is within FLT_MIN (e.g., 1E-37) of 0.5.
  _bits: An initial set of random bits.
  _base: This should be -(the number of bits in _bits), up to -32.
  Return: A float uniformly distributed between 0 (inclusive) and 1
           (exclusive).
          The average value was measured over 2**32 samples to be
           0.50000037448772916.*/
static float isaac_float_bits(isaac_ctx *_ctx,uint32_t _bits,int _base){
  float ret;
  int   nbits_needed;
  while(!_bits){
    if(_base+FLT_MANT_DIG<FLT_MIN_EXP)return 0;
    _base-=32;
    _bits=isaac_next_uint32(_ctx);
  }
  /*Note: This could also be determined with frexp(), for a slightly more
     portable solution, but that takes twice as long, and one has to worry
     about rounding effects, which can over-estimate the exponent when given
     FLT_MANT_DIG+1 consecutive one bits.
    Even the fallback C implementation of ILOGNZ_32() yields an implementation
     25% faster than the frexp() method.*/
  nbits_needed=FLT_MANT_DIG-ilog32_nz(_bits);
#if FLT_MANT_DIG>32
  ret=ldexpf((float)_bits,_base);
# if FLT_MANT_DIG>65
  while(32-nbits_needed<0){
# else
  if(32-nbits_needed<0){
# endif
    _base-=32;
    nbits_needed-=32;
    ret+=ldexpf((float)isaac_next_uint32(_ctx),_base);
  }
  _bits=isaac_next_uint32(_ctx)>>32-nbits_needed;
  ret+=ldexpf((float)_bits,_base-nbits_needed);
#else
  if(nbits_needed>0){
    _bits=_bits<<nbits_needed|isaac_next_uint32(_ctx)>>(32-nbits_needed);
  }
# if FLT_MANT_DIG<32
  else _bits>>=-nbits_needed;
# endif
  ret=ldexpf((float)_bits,_base-nbits_needed);
#endif
  return ret;
}

float isaac_next_float(isaac_ctx *_ctx){
  return isaac_float_bits(_ctx,0,0);
}

float isaac_next_signed_float(isaac_ctx *_ctx){
  uint32_t bits;
  bits=isaac_next_uint32(_ctx);
  return (1|-((int)bits&1))*isaac_float_bits(_ctx,bits>>1,-31);
}

/*Returns a uniform random double.
  _bits: An initial set of random bits.
  _base: This should be -(the number of bits in _bits), up to -32.
  Return: A double uniformly distributed between 0 (inclusive) and 1
           (exclusive).
          The average value was measured over 2**32 samples to be
           0.500006289408060911*/
static double isaac_double_bits(isaac_ctx *_ctx,uint32_t _bits,int _base){
  double ret;
  int    nbits_needed;
  while(!_bits){
    if(_base+DBL_MANT_DIG<DBL_MIN_EXP)return 0;
    _base-=32;
    _bits=isaac_next_uint32(_ctx);
  }
  nbits_needed=DBL_MANT_DIG-ilog32_nz(_bits);
#if DBL_MANT_DIG>32
  ret=ldexp((double)_bits,_base);
# if DBL_MANT_DIG>65
  while(32-nbits_needed<0){
# else
  if(32-nbits_needed<0){
# endif
    _base-=32;
    nbits_needed-=32;
    ret+=ldexp((double)isaac_next_uint32(_ctx),_base);
  }
  _bits=isaac_next_uint32(_ctx)>>(32-nbits_needed);
  ret+=ldexp((double)_bits,_base-nbits_needed);
#else
  if(nbits_needed>0){
    _bits=_bits<<nbits_needed|isaac_next_uint32(_ctx)>>32-nbits_needed;
  }
# if DBL_MANT_DIG<32
  else _bits>>=-nbits_needed;
# endif
  ret=ldexp((double)_bits,exp-DBL_MANT_DIG);
#endif
  return ret;
}

double isaac_next_double(isaac_ctx *_ctx){
  return isaac_double_bits(_ctx,0,0);
}

double isaac_next_signed_double(isaac_ctx *_ctx){
  uint32_t bits;
  bits=isaac_next_uint32(_ctx);
  return (1|-((int)bits&1))*isaac_double_bits(_ctx,bits>>1,-31);
}