diff options
Diffstat (limited to 'lib/libm/common/trig.h')
| -rw-r--r-- | lib/libm/common/trig.h | 42 |
1 files changed, 21 insertions, 21 deletions
diff --git a/lib/libm/common/trig.h b/lib/libm/common/trig.h index 9e05b0e..e31fb4c 100644 --- a/lib/libm/common/trig.h +++ b/lib/libm/common/trig.h @@ -67,7 +67,7 @@ static const double zero = 0, one = 1, negone = -1, - half = 1.0/2.0, + half = 1.0/2.0, small = 1E-10, /* 1+small**2 == 1; better values for small: * small = 1.5E-9 for VAX D * = 1.2E-8 for IEEE Double @@ -77,27 +77,27 @@ static const double /* sin__S(x*x) ... re-implemented as a macro * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) - * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) - * CODED IN C BY K.C. NG, 1/21/85; + * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) + * CODED IN C BY K.C. NG, 1/21/85; * REVISED BY K.C. NG on 8/13/85. * * sin(x*k) - x * RETURN --------------- on [-PI/4,PI/4] , where k=pi/PI, PI is the rounded - * x + * x * value of pi in machine precision: * * Decimal: - * pi = 3.141592653589793 23846264338327 ..... + * pi = 3.141592653589793 23846264338327 ..... * 53 bits PI = 3.141592653589793 115997963 ..... , - * 56 bits PI = 3.141592653589793 227020265 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , * * Hexadecimal: * pi = 3.243F6A8885A308D313198A2E.... * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 - * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 * * Method: - * 1. Let z=x*x. Create a polynomial approximation to + * 1. Let z=x*x. Create a polynomial approximation to * (sin(k*x)-x)/x = z*(S0 + S1*z^1 + ... + S5*z^5). * Then * sin__S(x*x) = z*(S0 + S1*z^1 + ... + S5*z^5) @@ -105,8 +105,8 @@ static const double * The coefficient S's are obtained by a special Remez algorithm. * * Accuracy: - * In the absence of rounding error, the approximation has absolute error - * less than 2**(-61.11) for VAX D FORMAT, 2**(-57.45) for IEEE DOUBLE. + * In the absence of rounding error, the approximation has absolute error + * less than 2**(-61.11) for VAX D FORMAT, 2**(-57.45) for IEEE DOUBLE. * * Constants: * The hexadecimal values are the intended ones for the following constants. @@ -149,28 +149,28 @@ ic(S5, 1.5868926979889205164E-10 , -33, 1.5CF61DF672B13) /* cos__C(x*x) ... re-implemented as a macro * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) - * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) - * CODED IN C BY K.C. NG, 1/21/85; + * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) + * CODED IN C BY K.C. NG, 1/21/85; * REVISED BY K.C. NG on 8/13/85. * - * x*x + * x*x * RETURN cos(k*x) - 1 + ----- on [-PI/4,PI/4], where k = pi/PI, - * 2 + * 2 * PI is the rounded value of pi in machine precision : * * Decimal: - * pi = 3.141592653589793 23846264338327 ..... + * pi = 3.141592653589793 23846264338327 ..... * 53 bits PI = 3.141592653589793 115997963 ..... , - * 56 bits PI = 3.141592653589793 227020265 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , * * Hexadecimal: * pi = 3.243F6A8885A308D313198A2E.... * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 - * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 * * * Method: - * 1. Let z=x*x. Create a polynomial approximation to + * 1. Let z=x*x. Create a polynomial approximation to * cos(k*x)-1+z/2 = z*z*(C0 + C1*z^1 + ... + C5*z^5) * then * cos__C(z) = z*z*(C0 + C1*z^1 + ... + C5*z^5) @@ -178,9 +178,9 @@ ic(S5, 1.5868926979889205164E-10 , -33, 1.5CF61DF672B13) * The coefficient C's are obtained by a special Remez algorithm. * * Accuracy: - * In the absence of rounding error, the approximation has absolute error - * less than 2**(-64) for VAX D FORMAT, 2**(-58.3) for IEEE DOUBLE. - * + * In the absence of rounding error, the approximation has absolute error + * less than 2**(-64) for VAX D FORMAT, 2**(-58.3) for IEEE DOUBLE. + * * * Constants: * The hexadecimal values are the intended ones for the following constants. |
