i386: move math-emu

Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Signed-off-by: Ingo Molnar <mingo@elte.hu>

1 files changed, 1845 insertions, 0 deletions

diff --git a/arch/x86/math-emu/fpu_trig.c b/arch/x86/math-emu/fpu_trig.c
new file mode 100644
index 000000000000..403cbde1d425
--- /dev/null
+++ b/arch/x86/math-emu/fpu_trig.c
@@ -0,0 +1,1845 @@
+/*---------------------------------------------------------------------------+
+ |  fpu_trig.c                                                               |
+ |                                                                           |
+ | Implementation of the FPU "transcendental" functions.                     |
+ |                                                                           |
+ | Copyright (C) 1992,1993,1994,1997,1999                                    |
+ |                       W. Metzenthen, 22 Parker St, Ormond, Vic 3163,      |
+ |                       Australia.  E-mail   billm@melbpc.org.au            |
+ |                                                                           |
+ |                                                                           |
+ +---------------------------------------------------------------------------*/
+
+#include "fpu_system.h"
+#include "exception.h"
+#include "fpu_emu.h"
+#include "status_w.h"
+#include "control_w.h"
+#include "reg_constant.h"       
+
+static void rem_kernel(unsigned long long st0, unsigned long long *y,
+                       unsigned long long st1,
+                       unsigned long long q, int n);
+
+#define BETTER_THAN_486
+
+#define FCOS  4
+
+/* Used only by fptan, fsin, fcos, and fsincos. */
+/* This routine produces very accurate results, similar to
+   using a value of pi with more than 128 bits precision. */
+/* Limited measurements show no results worse than 64 bit precision
+   except for the results for arguments close to 2^63, where the
+   precision of the result sometimes degrades to about 63.9 bits */
+static int trig_arg(FPU_REG *st0_ptr, int even)
+{
+  FPU_REG tmp;
+  u_char tmptag;
+  unsigned long long q;
+  int old_cw = control_word, saved_status = partial_status;
+  int tag, st0_tag = TAG_Valid;
+
+  if ( exponent(st0_ptr) >= 63 )
+    {
+      partial_status |= SW_C2;     /* Reduction incomplete. */
+      return -1;
+    }
+
+  control_word &= ~CW_RC;
+  control_word |= RC_CHOP;
+
+  setpositive(st0_ptr);
+  tag = FPU_u_div(st0_ptr, &CONST_PI2, &tmp, PR_64_BITS | RC_CHOP | 0x3f,
+                  SIGN_POS);
+
+  FPU_round_to_int(&tmp, tag);  /* Fortunately, this can't overflow
+                                   to 2^64 */
+  q = significand(&tmp);
+  if ( q )
+    {
+      rem_kernel(significand(st0_ptr),
+                 &significand(&tmp),
+                 significand(&CONST_PI2),
+                 q, exponent(st0_ptr) - exponent(&CONST_PI2));
+      setexponent16(&tmp, exponent(&CONST_PI2));
+      st0_tag = FPU_normalize(&tmp);
+      FPU_copy_to_reg0(&tmp, st0_tag);
+    }
+
+  if ( (even && !(q & 1)) || (!even && (q & 1)) )
+    {
+      st0_tag = FPU_sub(REV|LOADED|TAG_Valid, (int)&CONST_PI2, FULL_PRECISION);
+
+#ifdef BETTER_THAN_486
+      /* So far, the results are exact but based upon a 64 bit
+         precision approximation to pi/2. The technique used
+         now is equivalent to using an approximation to pi/2 which
+         is accurate to about 128 bits. */
+      if ( (exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64) || (q > 1) )
+        {
+          /* This code gives the effect of having pi/2 to better than
+             128 bits precision. */
+
+          significand(&tmp) = q + 1;
+          setexponent16(&tmp, 63);
+          FPU_normalize(&tmp);
+          tmptag =
+            FPU_u_mul(&CONST_PI2extra, &tmp, &tmp, FULL_PRECISION, SIGN_POS,
+                      exponent(&CONST_PI2extra) + exponent(&tmp));
+          setsign(&tmp, getsign(&CONST_PI2extra));
+          st0_tag = FPU_add(&tmp, tmptag, 0, FULL_PRECISION);
+          if ( signnegative(st0_ptr) )
+            {
+              /* CONST_PI2extra is negative, so the result of the addition
+                 can be negative. This means that the argument is actually
+                 in a different quadrant. The correction is always < pi/2,
+                 so it can't overflow into yet another quadrant. */
+              setpositive(st0_ptr);
+              q++;
+            }
+        }
+#endif /* BETTER_THAN_486 */
+    }
+#ifdef BETTER_THAN_486
+  else
+    {
+      /* So far, the results are exact but based upon a 64 bit
+         precision approximation to pi/2. The technique used
+         now is equivalent to using an approximation to pi/2 which
+         is accurate to about 128 bits. */
+      if ( ((q > 0) && (exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64))
+           || (q > 1) )
+        {
+          /* This code gives the effect of having p/2 to better than
+             128 bits precision. */
+
+          significand(&tmp) = q;
+          setexponent16(&tmp, 63);
+          FPU_normalize(&tmp);         /* This must return TAG_Valid */
+          tmptag = FPU_u_mul(&CONST_PI2extra, &tmp, &tmp, FULL_PRECISION,
+                             SIGN_POS,
+                             exponent(&CONST_PI2extra) + exponent(&tmp));
+          setsign(&tmp, getsign(&CONST_PI2extra));
+          st0_tag = FPU_sub(LOADED|(tmptag & 0x0f), (int)&tmp,
+                            FULL_PRECISION);
+          if ( (exponent(st0_ptr) == exponent(&CONST_PI2)) &&
+              ((st0_ptr->sigh > CONST_PI2.sigh)
+               || ((st0_ptr->sigh == CONST_PI2.sigh)
+                   && (st0_ptr->sigl > CONST_PI2.sigl))) )
+            {
+              /* CONST_PI2extra is negative, so the result of the
+                 subtraction can be larger than pi/2. This means
+                 that the argument is actually in a different quadrant.
+                 The correction is always < pi/2, so it can't overflow
+                 into yet another quadrant. */
+              st0_tag = FPU_sub(REV|LOADED|TAG_Valid, (int)&CONST_PI2,
+                                FULL_PRECISION);
+              q++;
+            }
+        }
+    }
+#endif /* BETTER_THAN_486 */
+
+  FPU_settag0(st0_tag);
+  control_word = old_cw;
+  partial_status = saved_status & ~SW_C2;     /* Reduction complete. */
+
+  return (q & 3) | even;
+}
+
+
+/* Convert a long to register */
+static void convert_l2reg(long const *arg, int deststnr)
+{
+  int tag;
+  long num = *arg;
+  u_char sign;
+  FPU_REG *dest = &st(deststnr);
+
+  if (num == 0)
+    {
+      FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
+      return;
+    }
+
+  if (num > 0)
+    { sign = SIGN_POS; }
+  else
+    { num = -num; sign = SIGN_NEG; }
+
+  dest->sigh = num;
+  dest->sigl = 0;
+  setexponent16(dest, 31);
+  tag = FPU_normalize(dest);
+  FPU_settagi(deststnr, tag);
+  setsign(dest, sign);
+  return;
+}
+
+
+static void single_arg_error(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  if ( st0_tag == TAG_Empty )
+    FPU_stack_underflow();  /* Puts a QNaN in st(0) */
+  else if ( st0_tag == TW_NaN )
+    real_1op_NaN(st0_ptr);       /* return with a NaN in st(0) */
+#ifdef PARANOID
+  else
+    EXCEPTION(EX_INTERNAL|0x0112);
+#endif /* PARANOID */
+}
+
+
+static void single_arg_2_error(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  int isNaN;
+
+  switch ( st0_tag )
+    {
+    case TW_NaN:
+      isNaN = (exponent(st0_ptr) == EXP_OVER) && (st0_ptr->sigh & 0x80000000);
+      if ( isNaN && !(st0_ptr->sigh & 0x40000000) )   /* Signaling ? */
+        {
+          EXCEPTION(EX_Invalid);
+          if ( control_word & CW_Invalid )
+            {
+              /* The masked response */
+              /* Convert to a QNaN */
+              st0_ptr->sigh |= 0x40000000;
+              push();
+              FPU_copy_to_reg0(st0_ptr, TAG_Special);
+            }
+        }
+      else if ( isNaN )
+        {
+          /* A QNaN */
+          push();
+          FPU_copy_to_reg0(st0_ptr, TAG_Special);
+        }
+      else
+        {
+          /* pseudoNaN or other unsupported */
+          EXCEPTION(EX_Invalid);
+          if ( control_word & CW_Invalid )
+            {
+              /* The masked response */
+              FPU_copy_to_reg0(&CONST_QNaN, TAG_Special);
+              push();
+              FPU_copy_to_reg0(&CONST_QNaN, TAG_Special);
+            }
+        }
+      break;              /* return with a NaN in st(0) */
+#ifdef PARANOID
+    default:
+      EXCEPTION(EX_INTERNAL|0x0112);
+#endif /* PARANOID */
+    }
+}
+
+
+/*---------------------------------------------------------------------------*/
+
+static void f2xm1(FPU_REG *st0_ptr, u_char tag)
+{
+  FPU_REG a;
+
+  clear_C1();
+
+  if ( tag == TAG_Valid )
+    {
+      /* For an 80486 FPU, the result is undefined if the arg is >= 1.0 */
+      if ( exponent(st0_ptr) < 0 )
+        {
+        denormal_arg:
+
+          FPU_to_exp16(st0_ptr, &a);
+
+          /* poly_2xm1(x) requires 0 < st(0) < 1. */
+          poly_2xm1(getsign(st0_ptr), &a, st0_ptr);
+        }
+      set_precision_flag_up();   /* 80486 appears to always do this */
+      return;
+    }
+
+  if ( tag == TAG_Zero )
+    return;
+
+  if ( tag == TAG_Special )
+    tag = FPU_Special(st0_ptr);
+
+  switch ( tag )
+    {
+    case TW_Denormal:
+      if ( denormal_operand() < 0 )
+        return;
+      goto denormal_arg;
+    case TW_Infinity:
+      if ( signnegative(st0_ptr) )
+        {
+          /* -infinity gives -1 (p16-10) */
+          FPU_copy_to_reg0(&CONST_1, TAG_Valid);
+          setnegative(st0_ptr);
+        }
+      return;
+    default:
+      single_arg_error(st0_ptr, tag);
+    }
+}
+
+
+static void fptan(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  FPU_REG *st_new_ptr;
+  int q;
+  u_char arg_sign = getsign(st0_ptr);
+
+  /* Stack underflow has higher priority */
+  if ( st0_tag == TAG_Empty )
+    {
+      FPU_stack_underflow();  /* Puts a QNaN in st(0) */
+      if ( control_word & CW_Invalid )
+        {
+          st_new_ptr = &st(-1);
+          push();
+          FPU_stack_underflow();  /* Puts a QNaN in the new st(0) */
+        }
+      return;
+    }
+
+  if ( STACK_OVERFLOW )
+    { FPU_stack_overflow(); return; }
+
+  if ( st0_tag == TAG_Valid )
+    {
+      if ( exponent(st0_ptr) > -40 )
+        {
+          if ( (q = trig_arg(st0_ptr, 0)) == -1 )
+            {
+              /* Operand is out of range */
+              return;
+            }
+
+          poly_tan(st0_ptr);
+          setsign(st0_ptr, (q & 1) ^ (arg_sign != 0));
+          set_precision_flag_up();  /* We do not really know if up or down */
+        }
+      else
+        {
+          /* For a small arg, the result == the argument */
+          /* Underflow may happen */
+
+        denormal_arg:
+
+          FPU_to_exp16(st0_ptr, st0_ptr);
+      
+          st0_tag = FPU_round(st0_ptr, 1, 0, FULL_PRECISION, arg_sign);
+          FPU_settag0(st0_tag);
+        }
+      push();
+      FPU_copy_to_reg0(&CONST_1, TAG_Valid);
+      return;
+    }
+
+  if ( st0_tag == TAG_Zero )
+    {
+      push();
+      FPU_copy_to_reg0(&CONST_1, TAG_Valid);
+      setcc(0);
+      return;
+    }
+
+  if ( st0_tag == TAG_Special )
+    st0_tag = FPU_Special(st0_ptr);
+
+  if ( st0_tag == TW_Denormal )
+    {
+      if ( denormal_operand() < 0 )
+        return;
+
+      goto denormal_arg;
+    }
+
+  if ( st0_tag == TW_Infinity )
+    {
+      /* The 80486 treats infinity as an invalid operand */
+      if ( arith_invalid(0) >= 0 )
+        {
+          st_new_ptr = &st(-1);
+          push();
+          arith_invalid(0);
+        }
+      return;
+    }
+
+  single_arg_2_error(st0_ptr, st0_tag);
+}
+
+
+static void fxtract(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  FPU_REG *st_new_ptr;
+  u_char sign;
+  register FPU_REG *st1_ptr = st0_ptr;  /* anticipate */
+
+  if ( STACK_OVERFLOW )
+    {  FPU_stack_overflow(); return; }
+
+  clear_C1();
+
+  if ( st0_tag == TAG_Valid )
+    {
+      long e;
+
+      push();
+      sign = getsign(st1_ptr);
+      reg_copy(st1_ptr, st_new_ptr);
+      setexponent16(st_new_ptr, exponent(st_new_ptr));
+
+    denormal_arg:
+
+      e = exponent16(st_new_ptr);
+      convert_l2reg(&e, 1);
+      setexponentpos(st_new_ptr, 0);
+      setsign(st_new_ptr, sign);
+      FPU_settag0(TAG_Valid);       /* Needed if arg was a denormal */
+      return;
+    }
+  else if ( st0_tag == TAG_Zero )
+    {
+      sign = getsign(st0_ptr);
+
+      if ( FPU_divide_by_zero(0, SIGN_NEG) < 0 )
+        return;
+
+      push();
+      FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
+      setsign(st_new_ptr, sign);
+      return;
+    }
+
+  if ( st0_tag == TAG_Special )
+    st0_tag = FPU_Special(st0_ptr);
+
+  if ( st0_tag == TW_Denormal )
+    {
+      if (denormal_operand() < 0 )
+        return;
+
+      push();
+      sign = getsign(st1_ptr);
+      FPU_to_exp16(st1_ptr, st_new_ptr);
+      goto denormal_arg;
+    }
+  else if ( st0_tag == TW_Infinity )
+    {
+      sign = getsign(st0_ptr);
+      setpositive(st0_ptr);
+      push();
+      FPU_copy_to_reg0(&CONST_INF, TAG_Special);
+      setsign(st_new_ptr, sign);
+      return;
+    }
+  else if ( st0_tag == TW_NaN )
+    {
+      if ( real_1op_NaN(st0_ptr) < 0 )
+        return;
+
+      push();
+      FPU_copy_to_reg0(st0_ptr, TAG_Special);
+      return;
+    }
+  else if ( st0_tag == TAG_Empty )
+    {
+      /* Is this the correct behaviour? */
+      if ( control_word & EX_Invalid )
+        {
+          FPU_stack_underflow();
+          push();
+          FPU_stack_underflow();
+        }
+      else
+        EXCEPTION(EX_StackUnder);
+    }
+#ifdef PARANOID
+  else
+    EXCEPTION(EX_INTERNAL | 0x119);
+#endif /* PARANOID */
+}
+
+
+static void fdecstp(void)
+{
+  clear_C1();
+  top--;
+}
+
+static void fincstp(void)
+{
+  clear_C1();
+  top++;
+}
+
+
+static void fsqrt_(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  int expon;
+
+  clear_C1();
+
+  if ( st0_tag == TAG_Valid )
+    {
+      u_char tag;
+      
+      if (signnegative(st0_ptr))
+        {
+          arith_invalid(0);  /* sqrt(negative) is invalid */
+          return;
+        }
+
+      /* make st(0) in  [1.0 .. 4.0) */
+      expon = exponent(st0_ptr);
+
+    denormal_arg:
+
+      setexponent16(st0_ptr, (expon & 1));
+
+      /* Do the computation, the sign of the result will be positive. */
+      tag = wm_sqrt(st0_ptr, 0, 0, control_word, SIGN_POS);
+      addexponent(st0_ptr, expon >> 1);
+      FPU_settag0(tag);
+      return;
+    }
+
+  if ( st0_tag == TAG_Zero )
+    return;
+
+  if ( st0_tag == TAG_Special )
+    st0_tag = FPU_Special(st0_ptr);
+
+  if ( st0_tag == TW_Infinity )
+    {
+      if ( signnegative(st0_ptr) )
+        arith_invalid(0);  /* sqrt(-Infinity) is invalid */
+      return;
+    }
+  else if ( st0_tag == TW_Denormal )
+    {
+      if (signnegative(st0_ptr))
+        {
+          arith_invalid(0);  /* sqrt(negative) is invalid */
+          return;
+        }
+
+      if ( denormal_operand() < 0 )
+        return;
+
+      FPU_to_exp16(st0_ptr, st0_ptr);
+
+      expon = exponent16(st0_ptr);
+
+      goto denormal_arg;
+    }
+
+  single_arg_error(st0_ptr, st0_tag);
+
+}
+
+
+static void frndint_(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  int flags, tag;
+
+  if ( st0_tag == TAG_Valid )
+    {
+      u_char sign;
+
+    denormal_arg:
+
+      sign = getsign(st0_ptr);
+
+      if (exponent(st0_ptr) > 63)
+        return;
+
+      if ( st0_tag == TW_Denormal )
+        {
+          if (denormal_operand() < 0 )
+            return;
+        }
+
+      /* Fortunately, this can't overflow to 2^64 */
+      if ( (flags = FPU_round_to_int(st0_ptr, st0_tag)) )
+        set_precision_flag(flags);
+
+      setexponent16(st0_ptr, 63);
+      tag = FPU_normalize(st0_ptr);
+      setsign(st0_ptr, sign);
+      FPU_settag0(tag);
+      return;
+    }
+
+  if ( st0_tag == TAG_Zero )
+    return;
+
+  if ( st0_tag == TAG_Special )
+    st0_tag = FPU_Special(st0_ptr);
+
+  if ( st0_tag == TW_Denormal )
+    goto denormal_arg;
+  else if ( st0_tag == TW_Infinity )
+    return;
+  else
+    single_arg_error(st0_ptr, st0_tag);
+}
+
+
+static int fsin(FPU_REG *st0_ptr, u_char tag)
+{
+  u_char arg_sign = getsign(st0_ptr);
+
+  if ( tag == TAG_Valid )
+    {
+      int q;
+
+      if ( exponent(st0_ptr) > -40 )
+        {
+          if ( (q = trig_arg(st0_ptr, 0)) == -1 )
+            {
+              /* Operand is out of range */
+              return 1;
+            }
+
+          poly_sine(st0_ptr);
+          
+          if (q & 2)
+            changesign(st0_ptr);
+
+          setsign(st0_ptr, getsign(st0_ptr) ^ arg_sign);
+
+          /* We do not really know if up or down */
+          set_precision_flag_up();
+          return 0;
+        }
+      else
+        {
+          /* For a small arg, the result == the argument */
+          set_precision_flag_up();  /* Must be up. */
+          return 0;
+        }
+    }
+
+  if ( tag == TAG_Zero )
+    {
+      setcc(0);
+      return 0;
+    }
+
+  if ( tag == TAG_Special )
+    tag = FPU_Special(st0_ptr);
+
+  if ( tag == TW_Denormal )
+    {
+      if ( denormal_operand() < 0 )
+        return 1;
+
+      /* For a small arg, the result == the argument */
+      /* Underflow may happen */
+      FPU_to_exp16(st0_ptr, st0_ptr);
+      
+      tag = FPU_round(st0_ptr, 1, 0, FULL_PRECISION, arg_sign);
+
+      FPU_settag0(tag);
+
+      return 0;
+    }
+  else if ( tag == TW_Infinity )
+    {
+      /* The 80486 treats infinity as an invalid operand */
+      arith_invalid(0);
+      return 1;
+    }
+  else
+    {
+      single_arg_error(st0_ptr, tag);
+      return 1;
+    }
+}
+
+
+static int f_cos(FPU_REG *st0_ptr, u_char tag)
+{
+  u_char st0_sign;
+
+  st0_sign = getsign(st0_ptr);
+
+  if ( tag == TAG_Valid )
+    {
+      int q;
+
+      if ( exponent(st0_ptr) > -40 )
+        {
+          if ( (exponent(st0_ptr) < 0)
+              || ((exponent(st0_ptr) == 0)
+                  && (significand(st0_ptr) <= 0xc90fdaa22168c234LL)) )
+            {
+              poly_cos(st0_ptr);
+
+              /* We do not really know if up or down */
+              set_precision_flag_down();
+          
+              return 0;
+            }
+          else if ( (q = trig_arg(st0_ptr, FCOS)) != -1 )
+            {
+              poly_sine(st0_ptr);
+
+              if ((q+1) & 2)
+                changesign(st0_ptr);
+
+              /* We do not really know if up or down */
+              set_precision_flag_down();
+          
+              return 0;
+            }
+          else
+            {
+              /* Operand is out of range */
+              return 1;
+            }
+        }
+      else
+        {
+        denormal_arg:
+
+          setcc(0);
+          FPU_copy_to_reg0(&CONST_1, TAG_Valid);
+#ifdef PECULIAR_486
+          set_precision_flag_down();  /* 80486 appears to do this. */
+#else
+          set_precision_flag_up();  /* Must be up. */
+#endif /* PECULIAR_486 */
+          return 0;
+        }
+    }
+  else if ( tag == TAG_Zero )
+    {
+      FPU_copy_to_reg0(&CONST_1, TAG_Valid);
+      setcc(0);
+      return 0;
+    }
+
+  if ( tag == TAG_Special )
+    tag = FPU_Special(st0_ptr);
+
+  if ( tag == TW_Denormal )
+    {
+      if ( denormal_operand() < 0 )
+        return 1;
+
+      goto denormal_arg;
+    }
+  else if ( tag == TW_Infinity )
+    {
+      /* The 80486 treats infinity as an invalid operand */
+      arith_invalid(0);
+      return 1;
+    }
+  else
+    {
+      single_arg_error(st0_ptr, tag);  /* requires st0_ptr == &st(0) */
+      return 1;
+    }
+}
+
+
+static void fcos(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  f_cos(st0_ptr, st0_tag);
+}
+
+
+static void fsincos(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  FPU_REG *st_new_ptr;
+  FPU_REG arg;
+  u_char tag;
+
+  /* Stack underflow has higher priority */
+  if ( st0_tag == TAG_Empty )
+    {
+      FPU_stack_underflow();  /* Puts a QNaN in st(0) */
+      if ( control_word & CW_Invalid )
+        {
+          st_new_ptr = &st(-1);
+          push();
+          FPU_stack_underflow();  /* Puts a QNaN in the new st(0) */
+        }
+      return;
+    }
+
+  if ( STACK_OVERFLOW )
+    { FPU_stack_overflow(); return; }
+
+  if ( st0_tag == TAG_Special )
+    tag = FPU_Special(st0_ptr);
+  else
+    tag = st0_tag;
+
+  if ( tag == TW_NaN )
+    {
+      single_arg_2_error(st0_ptr, TW_NaN);
+      return;
+    }
+  else if ( tag == TW_Infinity )
+    {
+      /* The 80486 treats infinity as an invalid operand */
+      if ( arith_invalid(0) >= 0 )
+        {
+          /* Masked response */
+          push();
+          arith_invalid(0);
+        }
+      return;
+    }
+
+  reg_copy(st0_ptr, &arg);
+  if ( !fsin(st0_ptr, st0_tag) )
+    {
+      push();
+      FPU_copy_to_reg0(&arg, st0_tag);
+      f_cos(&st(0), st0_tag);
+    }
+  else
+    {
+      /* An error, so restore st(0) */
+      FPU_copy_to_reg0(&arg, st0_tag);
+    }
+}
+
+
+/*---------------------------------------------------------------------------*/
+/* The following all require two arguments: st(0) and st(1) */
+
+/* A lean, mean kernel for the fprem instructions. This relies upon
+   the division and rounding to an integer in do_fprem giving an
+   exact result. Because of this, rem_kernel() needs to deal only with
+   the least significant 64 bits, the more significant bits of the
+   result must be zero.
+ */
+static void rem_kernel(unsigned long long st0, unsigned long long *y,
+                       unsigned long long st1,
+                       unsigned long long q, int n)
+{
+  int dummy;
+  unsigned long long x;
+
+  x = st0 << n;
+
+  /* Do the required multiplication and subtraction in the one operation */
+
+  /* lsw x -= lsw st1 * lsw q */
+  asm volatile ("mull %4; subl %%eax,%0; sbbl %%edx,%1"
+                :"=m" (((unsigned *)&x)[0]), "=m" (((unsigned *)&x)[1]),
+                "=a" (dummy)
+                :"2" (((unsigned *)&st1)[0]), "m" (((unsigned *)&q)[0])
+                :"%dx");
+  /* msw x -= msw st1 * lsw q */
+  asm volatile ("mull %3; subl %%eax,%0"
+                :"=m" (((unsigned *)&x)[1]), "=a" (dummy)
+                :"1" (((unsigned *)&st1)[1]), "m" (((unsigned *)&q)[0])
+                :"%dx");
+  /* msw x -= lsw st1 * msw q */
+  asm volatile ("mull %3; subl %%eax,%0"
+                :"=m" (((unsigned *)&x)[1]), "=a" (dummy)
+                :"1" (((unsigned *)&st1)[0]), "m" (((unsigned *)&q)[1])
+                :"%dx");
+
+  *y = x;
+}
+
+
+/* Remainder of st(0) / st(1) */
+/* This routine produces exact results, i.e. there is never any
+   rounding or truncation, etc of the result. */
+static void do_fprem(FPU_REG *st0_ptr, u_char st0_tag, int round)
+{
+  FPU_REG *st1_ptr = &st(1);
+  u_char st1_tag = FPU_gettagi(1);
+
+  if ( !((st0_tag ^ TAG_Valid) | (st1_tag ^ TAG_Valid)) )
+    {
+      FPU_REG tmp, st0, st1;
+      u_char st0_sign, st1_sign;
+      u_char tmptag;
+      int tag;
+      int old_cw;
+      int expdif;
+      long long q;
+      unsigned short saved_status;
+      int cc;
+
+    fprem_valid:
+      /* Convert registers for internal use. */
+      st0_sign = FPU_to_exp16(st0_ptr, &st0);
+      st1_sign = FPU_to_exp16(st1_ptr, &st1);
+      expdif = exponent16(&st0) - exponent16(&st1);
+
+      old_cw = control_word;
+      cc = 0;
+
+      /* We want the status following the denorm tests, but don't want
+         the status changed by the arithmetic operations. */
+      saved_status = partial_status;
+      control_word &= ~CW_RC;
+      control_word |= RC_CHOP;
+
+      if ( expdif < 64 )
+        {
+          /* This should be the most common case */
+
+          if ( expdif > -2 )
+            {
+              u_char sign = st0_sign ^ st1_sign;
+              tag = FPU_u_div(&st0, &st1, &tmp,
+                              PR_64_BITS | RC_CHOP | 0x3f,
+                              sign);
+              setsign(&tmp, sign);
+
+              if ( exponent(&tmp) >= 0 )
+                {
+                  FPU_round_to_int(&tmp, tag);  /* Fortunately, this can't
+                                                   overflow to 2^64 */
+                  q = significand(&tmp);
+
+                  rem_kernel(significand(&st0),
+                             &significand(&tmp),
+                             significand(&st1),
+                             q, expdif);
+
+                  setexponent16(&tmp, exponent16(&st1));
+                }
+              else
+                {
+                  reg_copy(&st0, &tmp);
+                  q = 0;
+                }
+
+              if ( (round == RC_RND) && (tmp.sigh & 0xc0000000) )
+                {
+                  /* We may need to subtract st(1) once more,
+                     to get a result <= 1/2 of st(1). */
+                  unsigned long long x;
+                  expdif = exponent16(&st1) - exponent16(&tmp);
+                  if ( expdif <= 1 )
+                    {
+                      if ( expdif == 0 )
+                        x = significand(&st1) - significand(&tmp);
+                      else /* expdif is 1 */
+                        x = (significand(&st1) << 1) - significand(&tmp);
+                      if ( (x < significand(&tmp)) ||
+                          /* or equi-distant (from 0 & st(1)) and q is odd */
+                          ((x == significand(&tmp)) && (q & 1) ) )
+                        {
+                          st0_sign = ! st0_sign;
+                          significand(&tmp) = x;
+                          q++;
+                        }
+                    }
+                }
+
+              if (q & 4) cc |= SW_C0;
+              if (q & 2) cc |= SW_C3;
+              if (q & 1) cc |= SW_C1;
+            }
+          else
+            {
+              control_word = old_cw;
+              setcc(0);
+              return;
+            }
+        }
+      else
+        {
+          /* There is a large exponent difference ( >= 64 ) */
+          /* To make much sense, the code in this section should
+             be done at high precision. */
+          int exp_1, N;
+          u_char sign;
+
+          /* prevent overflow here */
+          /* N is 'a number between 32 and 63' (p26-113) */
+          reg_copy(&st0, &tmp);
+          tmptag = st0_tag;
+          N = (expdif & 0x0000001f) + 32;  /* This choice gives results
+                                              identical to an AMD 486 */
+          setexponent16(&tmp, N);
+          exp_1 = exponent16(&st1);
+          setexponent16(&st1, 0);
+          expdif -= N;
+
+          sign = getsign(&tmp) ^ st1_sign;
+          tag = FPU_u_div(&tmp, &st1, &tmp, PR_64_BITS | RC_CHOP | 0x3f,
+                          sign);
+          setsign(&tmp, sign);
+
+          FPU_round_to_int(&tmp, tag);  /* Fortunately, this can't
+                                           overflow to 2^64 */
+
+          rem_kernel(significand(&st0),
+                     &significand(&tmp),
+                     significand(&st1),
+                     significand(&tmp),
+                     exponent(&tmp)
+                     ); 
+          setexponent16(&tmp, exp_1 + expdif);
+
+          /* It is possible for the operation to be complete here.
+             What does the IEEE standard say? The Intel 80486 manual
+             implies that the operation will never be completed at this
+             point, and the behaviour of a real 80486 confirms this.
+           */
+          if ( !(tmp.sigh | tmp.sigl) )
+            {
+              /* The result is zero */
+              control_word = old_cw;
+              partial_status = saved_status;
+              FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
+              setsign(&st0, st0_sign);
+#ifdef PECULIAR_486
+              setcc(SW_C2);
+#else
+              setcc(0);
+#endif /* PECULIAR_486 */
+              return;
+            }
+          cc = SW_C2;
+        }
+
+      control_word = old_cw;
+      partial_status = saved_status;
+      tag = FPU_normalize_nuo(&tmp);
+      reg_copy(&tmp, st0_ptr);
+
+      /* The only condition to be looked for is underflow,
+         and it can occur here only if underflow is unmasked. */
+      if ( (exponent16(&tmp) <= EXP_UNDER) && (tag != TAG_Zero)
+          && !(control_word & CW_Underflow) )
+        {
+          setcc(cc);
+          tag = arith_underflow(st0_ptr);
+          setsign(st0_ptr, st0_sign);
+          FPU_settag0(tag);
+          return;
+        }
+      else if ( (exponent16(&tmp) > EXP_UNDER) || (tag == TAG_Zero) )
+        {
+          stdexp(st0_ptr);
+          setsign(st0_ptr, st0_sign);
+        }
+      else
+        {
+          tag = FPU_round(st0_ptr, 0, 0, FULL_PRECISION, st0_sign);
+        }
+      FPU_settag0(tag);
+      setcc(cc);
+
+      return;
+    }
+
+  if ( st0_tag == TAG_Special )
+    st0_tag = FPU_Special(st0_ptr);
+  if ( st1_tag == TAG_Special )
+    st1_tag = FPU_Special(st1_ptr);
+
+  if ( ((st0_tag == TAG_Valid) && (st1_tag == TW_Denormal))
+            || ((st0_tag == TW_Denormal) && (st1_tag == TAG_Valid))
+            || ((st0_tag == TW_Denormal) && (st1_tag == TW_Denormal)) )
+    {
+      if ( denormal_operand() < 0 )
+        return;
+      goto fprem_valid;
+    }
+  else if ( (st0_tag == TAG_Empty) || (st1_tag == TAG_Empty) )
+    {
+      FPU_stack_underflow();
+      return;
+    }
+  else if ( st0_tag == TAG_Zero )
+    {
+      if ( st1_tag == TAG_Valid )
+        {
+          setcc(0); return;
+        }
+      else if ( st1_tag == TW_Denormal )
+        {
+          if ( denormal_operand() < 0 )
+            return;
+          setcc(0); return;
+        }
+      else if ( st1_tag == TAG_Zero )
+        { arith_invalid(0); return; } /* fprem(?,0) always invalid */
+      else if ( st1_tag == TW_Infinity )
+        { setcc(0); return; }
+    }
+  else if ( (st0_tag == TAG_Valid) || (st0_tag == TW_Denormal) )
+    {
+      if ( st1_tag == TAG_Zero )
+        {
+          arith_invalid(0); /* fprem(Valid,Zero) is invalid */
+          return;
+        }
+      else if ( st1_tag != TW_NaN )
+        {
+          if ( ((st0_tag == TW_Denormal) || (st1_tag == TW_Denormal))
+               && (denormal_operand() < 0) )
+            return;
+
+          if ( st1_tag == TW_Infinity )
+            {
+              /* fprem(Valid,Infinity) is o.k. */
+              setcc(0); return;
+            }
+        }
+    }
+  else if ( st0_tag == TW_Infinity )
+    {
+      if ( st1_tag != TW_NaN )
+        {
+          arith_invalid(0); /* fprem(Infinity,?) is invalid */
+          return;
+        }
+    }
+
+  /* One of the registers must contain a NaN if we got here. */
+
+#ifdef PARANOID
+  if ( (st0_tag != TW_NaN) && (st1_tag != TW_NaN) )
+      EXCEPTION(EX_INTERNAL | 0x118);
+#endif /* PARANOID */
+
+  real_2op_NaN(st1_ptr, st1_tag, 0, st1_ptr);
+
+}
+
+
+/* ST(1) <- ST(1) * log ST;  pop ST */
+static void fyl2x(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  FPU_REG *st1_ptr = &st(1), exponent;
+  u_char st1_tag = FPU_gettagi(1);
+  u_char sign;
+  int e, tag;
+
+  clear_C1();
+
+  if ( (st0_tag == TAG_Valid) && (st1_tag == TAG_Valid) )
+    {
+    both_valid:
+      /* Both regs are Valid or Denormal */
+      if ( signpositive(st0_ptr) )
+        {
+          if ( st0_tag == TW_Denormal )
+            FPU_to_exp16(st0_ptr, st0_ptr);
+          else
+            /* Convert st(0) for internal use. */
+            setexponent16(st0_ptr, exponent(st0_ptr));
+
+          if ( (st0_ptr->sigh == 0x80000000) && (st0_ptr->sigl == 0) )
+            {
+              /* Special case. The result can be precise. */
+              u_char esign;
+              e = exponent16(st0_ptr);
+              if ( e >= 0 )
+                {
+                  exponent.sigh = e;
+                  esign = SIGN_POS;
+                }
+              else
+                {
+                  exponent.sigh = -e;
+                  esign = SIGN_NEG;
+                }
+              exponent.sigl = 0;
+              setexponent16(&exponent, 31);
+              tag = FPU_normalize_nuo(&exponent);
+              stdexp(&exponent);
+              setsign(&exponent, esign);
+              tag = FPU_mul(&exponent, tag, 1, FULL_PRECISION);
+              if ( tag >= 0 )
+                FPU_settagi(1, tag);
+            }
+          else
+            {
+              /* The usual case */
+              sign = getsign(st1_ptr);
+              if ( st1_tag == TW_Denormal )
+                FPU_to_exp16(st1_ptr, st1_ptr);
+              else
+                /* Convert st(1) for internal use. */
+                setexponent16(st1_ptr, exponent(st1_ptr));
+              poly_l2(st0_ptr, st1_ptr, sign);
+            }
+        }
+      else
+        {
+          /* negative */
+          if ( arith_invalid(1) < 0 )
+            return;
+        }
+
+      FPU_pop();
+
+      return;
+    }
+
+  if ( st0_tag == TAG_Special )
+    st0_tag = FPU_Special(st0_ptr);
+  if ( st1_tag == TAG_Special )
+    st1_tag = FPU_Special(st1_ptr);
+
+  if ( (st0_tag == TAG_Empty) || (st1_tag == TAG_Empty) )
+    {
+      FPU_stack_underflow_pop(1);
+      return;
+    }
+  else if ( (st0_tag <= TW_Denormal) && (st1_tag <= TW_Denormal) )
+    {
+      if ( st0_tag == TAG_Zero )
+        {
+          if ( st1_tag == TAG_Zero )
+            {
+              /* Both args zero is invalid */
+              if ( arith_invalid(1) < 0 )
+                return;
+            }
+          else
+            {
+              u_char sign;
+              sign = getsign(st1_ptr)^SIGN_NEG;
+              if ( FPU_divide_by_zero(1, sign) < 0 )
+                return;
+
+              setsign(st1_ptr, sign);
+            }
+        }
+      else if ( st1_tag == TAG_Zero )
+        {
+          /* st(1) contains zero, st(0) valid <> 0 */
+          /* Zero is the valid answer */
+          sign = getsign(st1_ptr);
+          
+          if ( signnegative(st0_ptr) )
+            {
+              /* log(negative) */
+              if ( arith_invalid(1) < 0 )
+                return;
+            }
+          else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+            return;
+          else
+            {
+              if ( exponent(st0_ptr) < 0 )
+                sign ^= SIGN_NEG;
+
+              FPU_copy_to_reg1(&CONST_Z, TAG_Zero);
+              setsign(st1_ptr, sign);
+            }
+        }
+      else
+        {
+          /* One or both operands are denormals. */
+          if ( denormal_operand() < 0 )
+            return;
+          goto both_valid;
+        }
+    }
+  else if ( (st0_tag == TW_NaN) || (st1_tag == TW_NaN) )
+    {
+      if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
+        return;
+    }
+  /* One or both arg must be an infinity */
+  else if ( st0_tag == TW_Infinity )
+    {
+      if ( (signnegative(st0_ptr)) || (st1_tag == TAG_Zero) )
+        {
+          /* log(-infinity) or 0*log(infinity) */
+          if ( arith_invalid(1) < 0 )
+            return;
+        }
+      else
+        {
+          u_char sign = getsign(st1_ptr);
+
+          if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
+            return;
+
+          FPU_copy_to_reg1(&CONST_INF, TAG_Special);
+          setsign(st1_ptr, sign);
+        }
+    }
+  /* st(1) must be infinity here */
+  else if ( ((st0_tag == TAG_Valid) || (st0_tag == TW_Denormal))
+            && ( signpositive(st0_ptr) ) )
+    {
+      if ( exponent(st0_ptr) >= 0 )
+        {
+          if ( (exponent(st0_ptr) == 0) &&
+              (st0_ptr->sigh == 0x80000000) &&
+              (st0_ptr->sigl == 0) )
+            {
+              /* st(0) holds 1.0 */
+              /* infinity*log(1) */
+              if ( arith_invalid(1) < 0 )
+                return;
+            }
+          /* else st(0) is positive and > 1.0 */
+        }
+      else
+        {
+          /* st(0) is positive and < 1.0 */
+
+          if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+            return;
+
+          changesign(st1_ptr);
+        }
+    }
+  else
+    {
+      /* st(0) must be zero or negative */
+      if ( st0_tag == TAG_Zero )
+        {
+          /* This should be invalid, but a real 80486 is happy with it. */
+
+#ifndef PECULIAR_486
+          sign = getsign(st1_ptr);
+          if ( FPU_divide_by_zero(1, sign) < 0 )
+            return;
+#endif /* PECULIAR_486 */
+
+          changesign(st1_ptr);
+        }
+      else if ( arith_invalid(1) < 0 )    /* log(negative) */
+        return;
+    }
+
+  FPU_pop();
+}
+
+
+static void fpatan(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  FPU_REG *st1_ptr = &st(1);
+  u_char st1_tag = FPU_gettagi(1);
+  int tag;
+
+  clear_C1();
+  if ( !((st0_tag ^ TAG_Valid) | (st1_tag ^ TAG_Valid)) )
+    {
+    valid_atan:
+
+      poly_atan(st0_ptr, st0_tag, st1_ptr, st1_tag);
+
+      FPU_pop();
+
+      return;
+    }
+
+  if ( st0_tag == TAG_Special )
+    st0_tag = FPU_Special(st0_ptr);
+  if ( st1_tag == TAG_Special )
+    st1_tag = FPU_Special(st1_ptr);
+
+  if ( ((st0_tag == TAG_Valid) && (st1_tag == TW_Denormal))
+            || ((st0_tag == TW_Denormal) && (st1_tag == TAG_Valid))
+            || ((st0_tag == TW_Denormal) && (st1_tag == TW_Denormal)) )
+    {
+      if ( denormal_operand() < 0 )
+        return;
+
+      goto valid_atan;
+    }
+  else if ( (st0_tag == TAG_Empty) || (st1_tag == TAG_Empty) )
+    {
+      FPU_stack_underflow_pop(1);
+      return;
+    }
+  else if ( (st0_tag == TW_NaN) || (st1_tag == TW_NaN) )
+    {
+      if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) >= 0 )
+          FPU_pop();
+      return;
+    }
+  else if ( (st0_tag == TW_Infinity) || (st1_tag == TW_Infinity) )
+    {
+      u_char sign = getsign(st1_ptr);
+      if ( st0_tag == TW_Infinity )
+        {
+          if ( st1_tag == TW_Infinity )
+            {
+              if ( signpositive(st0_ptr) )
+                {
+                  FPU_copy_to_reg1(&CONST_PI4, TAG_Valid);
+                }
+              else
+                {
+                  setpositive(st1_ptr);
+                  tag = FPU_u_add(&CONST_PI4, &CONST_PI2, st1_ptr,
+                                  FULL_PRECISION, SIGN_POS,
+                                  exponent(&CONST_PI4), exponent(&CONST_PI2));
+                  if ( tag >= 0 )
+                    FPU_settagi(1, tag);
+                }
+            }
+          else
+            {
+              if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
+                return;
+
+              if ( signpositive(st0_ptr) )
+                {
+                  FPU_copy_to_reg1(&CONST_Z, TAG_Zero);
+                  setsign(st1_ptr, sign);   /* An 80486 preserves the sign */
+                  FPU_pop();
+                  return;
+                }
+              else
+                {
+                  FPU_copy_to_reg1(&CONST_PI, TAG_Valid);
+                }
+            }
+        }
+      else
+        {
+          /* st(1) is infinity, st(0) not infinity */
+          if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+            return;
+
+          FPU_copy_to_reg1(&CONST_PI2, TAG_Valid);
+        }
+      setsign(st1_ptr, sign);
+    }
+  else if ( st1_tag == TAG_Zero )
+    {
+      /* st(0) must be valid or zero */
+      u_char sign = getsign(st1_ptr);
+
+      if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+        return;
+
+      if ( signpositive(st0_ptr) )
+        {
+          /* An 80486 preserves the sign */
+          FPU_pop();
+          return;
+        }
+
+      FPU_copy_to_reg1(&CONST_PI, TAG_Valid);
+      setsign(st1_ptr, sign);
+    }
+  else if ( st0_tag == TAG_Zero )
+    {
+      /* st(1) must be TAG_Valid here */
+      u_char sign = getsign(st1_ptr);
+
+      if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
+        return;
+
+      FPU_copy_to_reg1(&CONST_PI2, TAG_Valid);
+      setsign(st1_ptr, sign);
+    }
+#ifdef PARANOID
+  else
+    EXCEPTION(EX_INTERNAL | 0x125);
+#endif /* PARANOID */
+
+  FPU_pop();
+  set_precision_flag_up();  /* We do not really know if up or down */
+}
+
+
+static void fprem(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  do_fprem(st0_ptr, st0_tag, RC_CHOP);
+}
+
+
+static void fprem1(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  do_fprem(st0_ptr, st0_tag, RC_RND);
+}
+
+
+static void fyl2xp1(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  u_char sign, sign1;
+  FPU_REG *st1_ptr = &st(1), a, b;
+  u_char st1_tag = FPU_gettagi(1);
+
+  clear_C1();
+  if ( !((st0_tag ^ TAG_Valid) | (st1_tag ^ TAG_Valid)) )
+    {
+    valid_yl2xp1:
+
+      sign = getsign(st0_ptr);
+      sign1 = getsign(st1_ptr);
+
+      FPU_to_exp16(st0_ptr, &a);
+      FPU_to_exp16(st1_ptr, &b);
+
+      if ( poly_l2p1(sign, sign1, &a, &b, st1_ptr) )
+        return;
+
+      FPU_pop();
+      return;
+    }
+
+  if ( st0_tag == TAG_Special )
+    st0_tag = FPU_Special(st0_ptr);
+  if ( st1_tag == TAG_Special )
+    st1_tag = FPU_Special(st1_ptr);
+
+  if ( ((st0_tag == TAG_Valid) && (st1_tag == TW_Denormal))
+            || ((st0_tag == TW_Denormal) && (st1_tag == TAG_Valid))
+            || ((st0_tag == TW_Denormal) && (st1_tag == TW_Denormal)) )
+    {
+      if ( denormal_operand() < 0 )
+        return;
+
+      goto valid_yl2xp1;
+    }
+  else if ( (st0_tag == TAG_Empty) | (st1_tag == TAG_Empty) )
+    {
+      FPU_stack_underflow_pop(1);
+      return;
+    }
+  else if ( st0_tag == TAG_Zero )
+    {
+      switch ( st1_tag )
+        {
+        case TW_Denormal:
+          if ( denormal_operand() < 0 )
+            return;
+
+        case TAG_Zero:
+        case TAG_Valid:
+          setsign(st0_ptr, getsign(st0_ptr) ^ getsign(st1_ptr));
+          FPU_copy_to_reg1(st0_ptr, st0_tag);
+          break;
+
+        case TW_Infinity:
+          /* Infinity*log(1) */
+          if ( arith_invalid(1) < 0 )
+            return;
+          break;
+
+        case TW_NaN:
+          if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
+            return;
+          break;
+
+        default:
+#ifdef PARANOID
+          EXCEPTION(EX_INTERNAL | 0x116);
+          return;
+#endif /* PARANOID */
+          break;
+        }
+    }
+  else if ( (st0_tag == TAG_Valid) || (st0_tag == TW_Denormal) )
+    {
+      switch ( st1_tag )
+        {
+        case TAG_Zero:
+          if ( signnegative(st0_ptr) )
+            {
+              if ( exponent(st0_ptr) >= 0 )
+                {
+                  /* st(0) holds <= -1.0 */
+#ifdef PECULIAR_486   /* Stupid 80486 doesn't worry about log(negative). */
+                  changesign(st1_ptr);
+#else
+                  if ( arith_invalid(1) < 0 )
+                    return;
+#endif /* PECULIAR_486 */
+                }
+              else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+                return;
+              else
+                changesign(st1_ptr);
+            }
+          else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+            return;
+          break;
+
+        case TW_Infinity:
+          if ( signnegative(st0_ptr) )
+            {
+              if ( (exponent(st0_ptr) >= 0) &&
+                  !((st0_ptr->sigh == 0x80000000) &&
+                    (st0_ptr->sigl == 0)) )
+                {
+                  /* st(0) holds < -1.0 */
+#ifdef PECULIAR_486   /* Stupid 80486 doesn't worry about log(negative). */
+                  changesign(st1_ptr);
+#else
+                  if ( arith_invalid(1) < 0 ) return;
+#endif /* PECULIAR_486 */
+                }
+              else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+                return;
+              else
+                changesign(st1_ptr);
+            }
+          else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+            return;
+          break;
+
+        case TW_NaN:
+          if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
+            return;
+        }
+
+    }
+  else if ( st0_tag == TW_NaN )
+    {
+      if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
+        return;
+    }
+  else if ( st0_tag == TW_Infinity )
+    {
+      if ( st1_tag == TW_NaN )
+        {
+          if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
+            return;
+        }
+      else if ( signnegative(st0_ptr) )
+        {
+#ifndef PECULIAR_486
+          /* This should have higher priority than denormals, but... */
+          if ( arith_invalid(1) < 0 )  /* log(-infinity) */
+            return;
+#endif /* PECULIAR_486 */
+          if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
+            return;
+#ifdef PECULIAR_486
+          /* Denormal operands actually get higher priority */
+          if ( arith_invalid(1) < 0 )  /* log(-infinity) */
+            return;
+#endif /* PECULIAR_486 */
+        }
+      else if ( st1_tag == TAG_Zero )
+        {
+          /* log(infinity) */
+          if ( arith_invalid(1) < 0 )
+            return;
+        }
+        
+      /* st(1) must be valid here. */
+
+      else if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
+        return;
+
+      /* The Manual says that log(Infinity) is invalid, but a real
+         80486 sensibly says that it is o.k. */
+      else
+        {
+          u_char sign = getsign(st1_ptr);
+          FPU_copy_to_reg1(&CONST_INF, TAG_Special);
+          setsign(st1_ptr, sign);
+        }
+    }
+#ifdef PARANOID
+  else
+    {
+      EXCEPTION(EX_INTERNAL | 0x117);
+      return;
+    }
+#endif /* PARANOID */
+
+  FPU_pop();
+  return;
+
+}
+
+
+static void fscale(FPU_REG *st0_ptr, u_char st0_tag)
+{
+  FPU_REG *st1_ptr = &st(1);
+  u_char st1_tag = FPU_gettagi(1);
+  int old_cw = control_word;
+  u_char sign = getsign(st0_ptr);
+
+  clear_C1();
+  if ( !((st0_tag ^ TAG_Valid) | (st1_tag ^ TAG_Valid)) )
+    {
+      long scale;
+      FPU_REG tmp;
+
+      /* Convert register for internal use. */
+      setexponent16(st0_ptr, exponent(st0_ptr));
+
+    valid_scale:
+
+      if ( exponent(st1_ptr) > 30 )
+        {
+          /* 2^31 is far too large, would require 2^(2^30) or 2^(-2^30) */
+
+          if ( signpositive(st1_ptr) )
+            {
+              EXCEPTION(EX_Overflow);
+              FPU_copy_to_reg0(&CONST_INF, TAG_Special);
+            }
+          else
+            {
+              EXCEPTION(EX_Underflow);
+              FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
+            }
+          setsign(st0_ptr, sign);
+          return;
+        }
+
+      control_word &= ~CW_RC;
+      control_word |= RC_CHOP;
+      reg_copy(st1_ptr, &tmp);
+      FPU_round_to_int(&tmp, st1_tag);      /* This can never overflow here */
+      control_word = old_cw;
+      scale = signnegative(st1_ptr) ? -tmp.sigl : tmp.sigl;
+      scale += exponent16(st0_ptr);
+
+      setexponent16(st0_ptr, scale);
+
+      /* Use FPU_round() to properly detect under/overflow etc */
+      FPU_round(st0_ptr, 0, 0, control_word, sign);
+
+      return;
+    }
+
+  if ( st0_tag == TAG_Special )
+    st0_tag = FPU_Special(st0_ptr);
+  if ( st1_tag == TAG_Special )
+    st1_tag = FPU_Special(st1_ptr);
+
+  if ( (st0_tag == TAG_Valid) || (st0_tag == TW_Denormal) )
+    {
+      switch ( st1_tag )
+        {
+        case TAG_Valid:
+          /* st(0) must be a denormal */
+          if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+            return;
+
+          FPU_to_exp16(st0_ptr, st0_ptr);  /* Will not be left on stack */
+          goto valid_scale;
+
+        case TAG_Zero:
+          if ( st0_tag == TW_Denormal )
+            denormal_operand();
+          return;
+
+        case TW_Denormal:
+          denormal_operand();
+          return;
+
+        case TW_Infinity:
+          if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
+            return;
+
+          if ( signpositive(st1_ptr) )
+            FPU_copy_to_reg0(&CONST_INF, TAG_Special);
+          else
+            FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
+          setsign(st0_ptr, sign);
+          return;
+
+        case TW_NaN:
+          real_2op_NaN(st1_ptr, st1_tag, 0, st0_ptr);
+          return;
+        }
+    }
+  else if ( st0_tag == TAG_Zero )
+    {
+      switch ( st1_tag )
+        {
+        case TAG_Valid:
+        case TAG_Zero:
+          return;
+
+        case TW_Denormal:
+          denormal_operand();
+          return;
+
+        case TW_Infinity:
+          if ( signpositive(st1_ptr) )
+            arith_invalid(0); /* Zero scaled by +Infinity */
+          return;
+
+        case TW_NaN:
+          real_2op_NaN(st1_ptr, st1_tag, 0, st0_ptr);
+          return;
+        }
+    }
+  else if ( st0_tag == TW_Infinity )
+    {
+      switch ( st1_tag )
+        {
+        case TAG_Valid:
+        case TAG_Zero:
+          return;
+
+        case TW_Denormal:
+          denormal_operand();
+          return;
+
+        case TW_Infinity:
+          if ( signnegative(st1_ptr) )
+            arith_invalid(0); /* Infinity scaled by -Infinity */
+          return;
+
+        case TW_NaN:
+          real_2op_NaN(st1_ptr, st1_tag, 0, st0_ptr);
+          return;
+        }
+    }
+  else if ( st0_tag == TW_NaN )
+    {
+      if ( st1_tag != TAG_Empty )
+        { real_2op_NaN(st1_ptr, st1_tag, 0, st0_ptr); return; }
+    }
+
+#ifdef PARANOID
+  if ( !((st0_tag == TAG_Empty) || (st1_tag == TAG_Empty)) )
+    {
+      EXCEPTION(EX_INTERNAL | 0x115);
+      return;
+    }
+#endif
+
+  /* At least one of st(0), st(1) must be empty */
+  FPU_stack_underflow();
+
+}
+
+
+/*---------------------------------------------------------------------------*/
+
+static FUNC_ST0 const trig_table_a[] = {
+  f2xm1, fyl2x, fptan, fpatan,
+  fxtract, fprem1, (FUNC_ST0)fdecstp, (FUNC_ST0)fincstp
+};
+
+void FPU_triga(void)
+{
+  (trig_table_a[FPU_rm])(&st(0), FPU_gettag0());
+}
+
+
+static FUNC_ST0 const trig_table_b[] =
+  {
+    fprem, fyl2xp1, fsqrt_, fsincos, frndint_, fscale, (FUNC_ST0)fsin, fcos
+  };
+
+void FPU_trigb(void)
+{
+  (trig_table_b[FPU_rm])(&st(0), FPU_gettag0());
+}