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Unified Diff: src/base/ieee754.cc

Issue 2116753002: [builtins] Unify most of the remaining Math builtins. (Closed) Base URL: https://chromium.googlesource.com/v8/v8.git@2102223005
Patch Set: Created 4 years, 6 months ago
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Index: src/base/ieee754.cc
diff --git a/src/base/ieee754.cc b/src/base/ieee754.cc
index 9a9090de2b3c3d6628a88dc570049694ce26d8a2..94bc7d350fe8cf8dffedd23b8fac70065b497913 100644
--- a/src/base/ieee754.cc
+++ b/src/base/ieee754.cc
@@ -891,6 +891,263 @@ double __kernel_tan(double x, double y, int iy) {
} // namespace
+/* acos(x)
+ * Method :
+ * acos(x) = pi/2 - asin(x)
+ * acos(-x) = pi/2 + asin(x)
+ * For |x|<=0.5
+ * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
+ * For x>0.5
+ * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
+ * = 2asin(sqrt((1-x)/2))
+ * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
+ * = 2f + (2c + 2s*z*R(z))
+ * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
+ * for f so that f+c ~ sqrt(z).
+ * For x<-0.5
+ * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
+ * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ * Function needed: sqrt
+ */
+double acos(double x) {
+ static const double
+ one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+ pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+ pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+ pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+ pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+ pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+ pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+ pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+ pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+ pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+ qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+ qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+ qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+ double z, p, q, r, w, s, c, df;
+ int32_t hx, ix;
+ GET_HIGH_WORD(hx, x);
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x3ff00000) { /* |x| >= 1 */
+ uint32_t lx;
+ GET_LOW_WORD(lx, x);
+ if (((ix - 0x3ff00000) | lx) == 0) { /* |x|==1 */
+ if (hx > 0)
+ return 0.0; /* acos(1) = 0 */
+ else
+ return pi + 2.0 * pio2_lo; /* acos(-1)= pi */
+ }
+ return (x - x) / (x - x); /* acos(|x|>1) is NaN */
+ }
+ if (ix < 0x3fe00000) { /* |x| < 0.5 */
+ if (ix <= 0x3c600000) return pio2_hi + pio2_lo; /*if|x|<2**-57*/
+ z = x * x;
+ p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
+ q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
+ r = p / q;
+ return pio2_hi - (x - (pio2_lo - x * r));
+ } else if (hx < 0) { /* x < -0.5 */
+ z = (one + x) * 0.5;
+ p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
+ q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
+ s = sqrt(z);
+ r = p / q;
+ w = r * s - pio2_lo;
+ return pi - 2.0 * (s + w);
+ } else { /* x > 0.5 */
+ z = (one - x) * 0.5;
+ s = sqrt(z);
+ df = s;
+ SET_LOW_WORD(df, 0);
+ c = (z - df * df) / (s + df);
+ p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
+ q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
+ r = p / q;
+ w = r * s + c;
+ return 2.0 * (df + w);
+ }
+}
+
+/* acosh(x)
+ * Method :
+ * Based on
+ * acosh(x) = log [ x + sqrt(x*x-1) ]
+ * we have
+ * acosh(x) := log(x)+ln2, if x is large; else
+ * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
+ * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
+ *
+ * Special cases:
+ * acosh(x) is NaN with signal if x<1.
+ * acosh(NaN) is NaN without signal.
+ */
+double acosh(double x) {
+ static const double
+ one = 1.0,
+ ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
+ double t;
+ int32_t hx;
+ uint32_t lx;
+ EXTRACT_WORDS(hx, lx, x);
+ if (hx < 0x3ff00000) { /* x < 1 */
+ return (x - x) / (x - x);
+ } else if (hx >= 0x41b00000) { /* x > 2**28 */
+ if (hx >= 0x7ff00000) { /* x is inf of NaN */
+ return x + x;
+ } else {
+ return log(x) + ln2; /* acosh(huge)=log(2x) */
+ }
+ } else if (((hx - 0x3ff00000) | lx) == 0) {
+ return 0.0; /* acosh(1) = 0 */
+ } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
+ t = x * x;
+ return log(2.0 * x - one / (x + sqrt(t - one)));
+ } else { /* 1<x<2 */
+ t = x - one;
+ return log1p(t + sqrt(2.0 * t + t * t));
+ }
+}
+
+/* asin(x)
+ * Method :
+ * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ * we approximate asin(x) on [0,0.5] by
+ * asin(x) = x + x*x^2*R(x^2)
+ * where
+ * R(x^2) is a rational approximation of (asin(x)-x)/x^3
+ * and its remez error is bounded by
+ * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
+ *
+ * For x in [0.5,1]
+ * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
+ * then for x>0.98
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
+ * For x<=0.98, let pio4_hi = pio2_hi/2, then
+ * f = hi part of s;
+ * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
+ * and
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
+ * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ */
+double asin(double x) {
+ static const double
+ one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+ huge = 1.000e+300,
+ pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+ pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+ pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
+ /* coefficient for R(x^2) */
+ pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+ pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+ pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+ pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+ pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+ pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+ qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+ qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+ qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+ double t, w, p, q, c, r, s;
+ int32_t hx, ix;
+
+ t = 0;
+ GET_HIGH_WORD(hx, x);
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x3ff00000) { /* |x|>= 1 */
+ uint32_t lx;
+ GET_LOW_WORD(lx, x);
+ if (((ix - 0x3ff00000) | lx) == 0) /* asin(1)=+-pi/2 with inexact */
+ return x * pio2_hi + x * pio2_lo;
+ return (x - x) / (x - x); /* asin(|x|>1) is NaN */
+ } else if (ix < 0x3fe00000) { /* |x|<0.5 */
+ if (ix < 0x3e400000) { /* if |x| < 2**-27 */
+ if (huge + x > one) return x; /* return x with inexact if x!=0*/
+ } else {
+ t = x * x;
+ }
+ p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
+ q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
+ w = p / q;
+ return x + x * w;
+ }
+ /* 1> |x|>= 0.5 */
+ w = one - fabs(x);
+ t = w * 0.5;
+ p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
+ q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
+ s = sqrt(t);
+ if (ix >= 0x3FEF3333) { /* if |x| > 0.975 */
+ w = p / q;
+ t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
+ } else {
+ w = s;
+ SET_LOW_WORD(w, 0);
+ c = (t - w * w) / (s + w);
+ r = p / q;
+ p = 2.0 * s * r - (pio2_lo - 2.0 * c);
+ q = pio4_hi - 2.0 * w;
+ t = pio4_hi - (p - q);
+ }
+ if (hx > 0)
+ return t;
+ else
+ return -t;
+}
+/* asinh(x)
+ * Method :
+ * Based on
+ * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
+ * we have
+ * asinh(x) := x if 1+x*x=1,
+ * := sign(x)*(log(x)+ln2)) for large |x|, else
+ * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
+ * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
+ */
+double asinh(double x) {
+ static const double
+ one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+ ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
+ huge = 1.00000000000000000000e+300;
+
+ double t, w;
+ int32_t hx, ix;
+ GET_HIGH_WORD(hx, x);
+ ix = hx & 0x7fffffff;
+ if (ix >= 0x7ff00000) return x + x; /* x is inf or NaN */
+ if (ix < 0x3e300000) { /* |x|<2**-28 */
+ if (huge + x > one) return x; /* return x inexact except 0 */
+ }
+ if (ix > 0x41b00000) { /* |x| > 2**28 */
+ w = log(fabs(x)) + ln2;
+ } else if (ix > 0x40000000) { /* 2**28 > |x| > 2.0 */
+ t = fabs(x);
+ w = log(2.0 * t + one / (sqrt(x * x + one) + t));
+ } else { /* 2.0 > |x| > 2**-28 */
+ t = x * x;
+ w = log1p(fabs(x) + t / (one + sqrt(one + t)));
+ }
+ if (hx > 0) {
+ return w;
+ } else {
+ return -w;
+ }
+}
+
/* atan(x)
* Method
* 1. Reduce x to positive by atan(x) = -atan(-x).
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